Intelligent Scatter Radio, RF Harvesting Analysis, and Resource Allocation for Ultra-Low-Power Internet-of-Things

Ubiquitous sensing anywhere and anytime is envisioned under the general umbrella of Internet-of-Things (IoT). The objective of this dissertation is to contribute ultra-lowpower IoT technology, exploiting novel concepts in wireless communications and networking. The first part of this work studies far field radio frequency (RF) energy harvesting, taking into account non-linearity, sensitivity, and saturation effects of existing rectenna circuits. The proposed methodology offers the statistics of the harvested power for any given rectenna model, under mild assumptions. It is also demonstrated that currentlyused linear RF harvesting models in the literature deviate from reality. In the second part, scatter radio technology, i.e., communication via means of reflection, is studied in order to enable ultra-low-power radio communication with single-transistor front-ends. The thesis proposes low-complexity detection schemes as well as decoding techniques for short block-length channel codes, tailored to coherent, as well as noncoherent reception of scatter radio. The goal was to target resource-constrained, i.e., hardware-“thin”, scatter radio tags and simple, low-latency receivers. The developed detection and decoding algorithms are based on composite hypothesis testing framework. Interestingly, it is demonstrated that the bit error rate (BER) performance gap between coherent and noncoherent reception depends on the kind of channel codes employed, the fading conditions, as well as the utilized coding interleaving depth. The third part of this work proposes a multistatic scatter radio network architecture, based on orthogonal signaling, contrasted to existing architectures for dyadic Nakagami fading. Orthogonal signaling allows for collision free multi-user access for low-bitrate tags. It is shown that the proposed scatter radio architecture offers better diversity order, more reliable reception, as well as better field coverage, while demonstrating smaller sensitivity to the topology of the scatter radio tags, compared to existing monostatic architecture. Finally, the last part of the dissertation studies resource allocation in multi-cell backscatter sensor networks (BSNs). The average long-term signal-to interference-plus-noise ratio (SINR) of linear detectors is explored for multi-cell BSNs, and subsequently harnessed to allocate frequency sub-channels at tags. The proposed resource allocation algorithm is based on the Max-Sum inference algorithm and its convergence-complexity trade-off is quantified. Experimental studies in an outdoor scatter radio testbed corroborate the theoretical findings of this work. Hopefully, this thesis will establish the viability of scatter radio for ultra-low-power communications, enabling critical current and future IoT applications.

Precision agriculture: 80-85% of total water is consumed for agriculture purposes, thus, intelligent plant irrigation that could save even a small amount of water, e.g., 30%, would offer significant socioeconomic impact.
• healthcare: patient identification and authentication, patient tracking, and patient data collection, • building management systems: smart homes, smart museums and gyms, • environmental sensing: precision agriculture, smart farming, environmental monitoring, and environmental variables data collection, • personal and social: social networking, thefts, losses, and historical queries. Each application has specific requirements in terms of: latency, throughput, communication range, energy, scalability, and security. Depending on the intended application, designers may have to make a trade-off among these requirements to achieve a good balance in terms of cost versus benefits.
To attain full functionality and deliver high-quality services to IoT customers, IoT integrates six key elements.
• Communication: connectivity establishment between heterogeneous objects to deliver specific services. IoT devices should be low-power and offer resiliency against communication errors.
• Computation: Processing units (e.g., micro-controllers, microprocessors), software and cloud platforms, and software applications constitute the computational resources of IoT.
• Services: IoT services depend on the IoT application.
• Semantics: the ability (a) to discover and use resources and modeling information and (b) to recognize and analyze data for efficient decision making, in order to provide the required services.
To this end, it is worth noting that by the end of 2020, 212 billion IoT smart objects are expected to be deployed globally [4]. Furthermore, the whole annual economic impact caused by the IoT is estimated to be in the range of 2.7 trillion to 6.2 trillion dollars by 2025 [5].

Background and Motivation
It is apparent that RFID systems lie at the heart of IoT-the majority of low-power IoT devices in many applications are RFID tags [1][2][3]. RFID tags emit information wirelessly through the backscatter principle (or simply scatter principle) [6]: A carrier wave (CW) illuminator emits a radio frequency (RF) continuous CW signal, which in turn impinges on the antenna of an RF tag. The tag terminates its antenna load according to the data to be transmitted in order to modulate the information on top of the impinged signal. The incident signal is modulated and scattered back towards a reader (interrogator) for decoding and processing. The principle of scatter radio: CW illuminator may be co-located with the reader or dislocated from the reader. Abbreviations LO, PA, LNA, and ADC, stand for local oscillator, power amplifier, low-noise amplifier, and analog-to-digital converter, respectively.
tenna loads and can be expressed as where Z a is the antenna impedance. The most common choice in scatter radio is M = 2 load values, but extension to more than 2 loads can be found in [8,9]. Since backscatter radios reflect the incident signal without actively radiating, the energy cost for scattering operation needs to be carefully evaluated. The energy cost required for backscattering is due to the termination of the antenna between load values, i.e., backscattering can be realized by the alternation of a simple RF transistor switch.
In addition, a very simple logic unit is embedded at the tags, in order to decide the modulation type and the transmitted bit sequence according to the sensed data. Overall, due to the absence of active signal conditioning components, scatter radio communication demands ultra-low power consumption, in the order of 10 µWatt [10], and at the same time requires low monetary cost.
Depending on the modulation, tags alter their antenna load accordingly. For instance, for amplitude-shift keying (ASK), the tag terminates its antenna at load Z 0 or Z 1 depending on the transmitted bit "0" or "1" over a bit duration T [11]. Whereas, for frequency-shift keying (FSK), the tag alternates the antenna load between Z 0 and Z 1 over a bit duration T with rate f 0 for bit "0" and rate f 1 for bit "1" [12]. More sophisticated continuous-phase modulations at tags, such as minimum shift-keying, are designed in [13].
Reflection coefficients Γ 0 and Γ 1 highly affect the performance of scatter radio systems in terms of both bit error rate (BER) as well as in terms of RF harvested energy, explained subsequently. Particularly, increasing the absolute difference of Γ 0 and Γ 1 , i.e., the quantity |Γ 0 − Γ 1 |, the amplitude of the backscattered signal is magnified and thus, the corresponding received signal-to-noise ratio (SNR) is increased (equivalently the BER Figure 1.3: Passive versus semi-passive tag. The first is powered only through the RF harvested energy scavenged from incident CW signal, while the second is powered through an ambient source or through a storage unit that may be a battery or super-capacitor. while the control logic is the "brain" of the tag, determining the tag's communication operations through software or hardware resources. Note that the storage unit may contain a harvesting circuit responsible for charging a battery or a super-capacitor, or alternatively, the powering can be accomplished by an external ambient source.

• Realistic Signal and Wireless Channel Scatter Radio Model
The vast majority of the works conducting physical layer research on scatter radio assumes Rayleigh fading for CW illuminator-to-tag and tag-to-reader links [24][25][26]. Small-scale fading channel models with line-of-sight LoS component, such as Nakagami or Rician fading [27], are more appropriate for fading modeling in scatter radio. That assumption is made because wireless scatter radio links are usually subject to strong LoS signal, due to the relatively small distance involved. Hence, a major goal of this dissertation is to incorporate realistic small-scale fading channel models in scatter radio wireless model.
In practice, path-loss is a major source of signal attenuation in scatter radio links, e.g., CW illuminator-to-tag-to-reader compound link is in practice extremely powerlimited due to strong power loss. Thus, it becomes imperative to incorporate pathloss-related parameters in scatter radio wireless model, especially for systems operating with multiple tags, because, in practice, the power level of signals backscattered from multiple tags is highly different, e.g., it may differ by several dBs. Existing the mismatch between prior art and industry-level RF harvesting models deserves further investigation.

• Venture of Alternative Scatter Radio Network Architecture
Let us first present the following toy example: consider a scatter radio point-topoint scenario with a CW illuminator or carrier emitter (CE), a tag, and a reader placed co-linearly, i.e., CE and reader are dislocated. CE-to-reader range is 100 meters and the tag is placed somewhere on the line segment formed by the CE and the reader. Suppose that x is the CE-to-tag distance. Then, for free-space propagation loss, the quantity y(x) = 1 x 2 1 100−x 2 is proportional to the path-loss at the reader under backscattering operation, for x ∈ (0, 100). Fig. 1.4 shows that function y is minimized at x = 50, while as x moves either towards 0 or 100, function y tends to increase. This simple example discloses that strong asymmetries in scatter radio link-even for free-space model-can offer 2 orders of magnitude larger path-loss compared to fully symmetric case of x = 50. The fully symmetric case corresponds also to the case where CE and reader are co-located, i.e., they belong to the same device. As a result, in order to realize ultra-low power and massive wireless connectivity in IoT without compromising on communication ranges, the scatter radio architecture needs to be redesigned.
There are two different architectures for scatter radio systems, namely the monostatic and the bistatic architectures. In the monostatic architecture [32], the reader consists of both the CW illuminator and the receiver of signals reflected back from the tags. In the bistatic architecture [33], the CW illuminator and the receiver of the reflected (backscattered) signals are distinct units, located at different positions, offering flexible network topologies with asymmetric scatter radio links. At the network level, the extension of bistatic architecture is the multi-bistatic (or simply multistatic) architecture with several low-cost CEs available, two orders of magnitude cheaper than the reader. Simple intuition as well as the observation from Fig. 1.4 indicate that due to the morphology of the multistatic architecture, each tag can be close to a CE with high probability, offering two desired implications: (a) the tag-to-reader coverage is increased with high probability and (b) using passive tags that harvest RF energy from the illuminating emitters, the probability of energy outage during the energy harvesting phase can be decreased. A detailed comparison among these two scatter radio architectures will be the subject of a chapter in this dissertation.

• Resource Allocation in Backscatter Sensor Networks
Wireless sensor networks (WSNs) have been emerged as a notorious framework to support any environmental sensing application. The key components of lowpower, large-scale WSNs are: (a) the ultra-low-power devices (sensors) that sense and send the data and (b) the fusion centers (cores) that gather the measured Introduction algorithms as well as resource allocation algorithms that both account the idiosyncrasies of multi-cell BSNs would be an interesting research avenue.

Objectives
In order to offer a tangible improvement of IoT technology under the prism of wireless communications and networking, the objectives of this dissertation are: 1. Accurate RF energy harvesting analytical tools for ultra-low-power IoT devices equipped with any rectifier circuit.
2. Enhanced scatter radio receiver designs for extended tag-to-reader communication ranges, which could be harnessed with ultra-low complexity at current and future ultra-low-power IoT devices.
3. New scatter radio network architecture with extended coverage and reliability that could potentially leverage the adoption of scatter radios in network-based, ultralow-power IoT applications. 4. Resource allocation for multi-cell backscatter sensor networks that will reduce installation cost and extend network coverage of future environmental sensing applications.
For each of the above topics a unique chapter is devoted.

Contributions and Organization
The contributions of each chapter can be summarized as follows: • Chapter 2 offers nonlinear far field RF energy harvesting in wireless communications. A linear RF harvesting model is commonly assumed in recent simultaneous wireless information and power transfer (SWIPT) research, i.e., RF harvested power is assumed to be a scaled version of the input (received) power. However, rectifiers typically used in the microwave and RFID industry are nonlinear devices; thus, RF harvesting efficiency is not constant, but depends on the input power. To approximate the real energy harvesting model, a piece-wise linear approximation is proposed, amenable to closed-form and tuning-free modeling. Three example scenarios are considered, including duty-cycled (non-continuous), as well as continuous SWIPT, comparing linear with industry-level non-linear RF harvesting. It is demonstrated that the proposed methodology, even though simple, offers exact performance for all studied metrics. On the other hand, linear RF harvesting models offer results that deviate from reality, and in some cases are off by one order of magnitude.
• Chapter 3 proposes physical layer receiver designs for scatter radio point-to-point systems. We provide a detailed exposition of a scatter radio signal model that accounts for all microwave, tag-related, and wireless channel parameters of FSK modulation at tags. The latter is ideal for the power-limited regime, which in turn is the operating regime of ultra-low-power IoT devices. Coherent and noncoherent detection and decoding algorithms tailored to the scatter radio FSK signal model are designed. For fixed energy budget per packet, noncoherent schemes do not sacrifice energy per information bit as the requirement for training bits of coherent schemes (for channel estimation) at the packet preamble is eliminated. Noncoherent symbol-by-symbol and sequence detectors based on hybrid composite hypothesis test (HCHT) and generalized likelihood-ratio test (GLRT), for the uncoded case and noncoherent decoders based on HCHT, for small block-length channel codes, are derived. Small block-length reduces significantly the processing delay at the reader when multiple tags need to be processed simultaneously. Diversity order analysis under a fully interleaved coherent coded system reveals that the offered diversity order of maximum-likelihood (ML) decoder for scatter radio FSK is the same with ML text-book decoders of Marconi radios. BER performance comparison under Rician, Rayleigh or no fading, taking into account fixed energy budget per packet is presented. It is shown that the performance gap between coherent and noncoherent reception depends on what channel codes are employed, the fading conditions (e.g., Rayleigh vs Rician vs no fading), as well as the utilized coding interleaving depth; the choice of one coding scheme over another depends on the wireless fading parameters and the design choice for extra diversity vs extra power gain. Finally, experimental outdoor results at 13 dBm transmission power corroborate the practicality of the proposed detection and decoding techniques for extended range scatter radios.
• Chapter 4 compares two scatter radio network architectures. Specifically, monostatic and multistatic scatter radio network architectures are evaluated and contrasted in terms of several multi-tag performance metrics. The dyadic Nakagami fading model is employed to model the small-scale fading in scatter radio links and the path-loss is also incorporated in the power of fading random variables, filling a gap in the literature. Maximum-likelihood coherent and noncoherent BER, diversity order, average information and energy outage probability comparison is performed, under the dyadic Nakagami fading. The proposed closed-form expressions for average energy and information outage probability are evaluated over an ensemble of square grid topologies, offering a topology-independent performance assessment.
Judicious simulation study over realistic small-scale fading and path-loss models reveals that not only the BER decay is doubled in a multistatic architecture compared to a monostatic one, but also, energy and information outage events are less frequent in multistatic systems due to the flexible morphology of the multistatic architecture. It is shown that the multistatic architecture can offer very low BER in fully asymmetric scatter radio network topologies where monostatic architecture cannot be defined. As a contribution of [40], a proof-of-concept digital multistatic, scatter radio WSN with a single receiver, four low-cost emitters and multiple ambientlypowered, low-bitrate tags, is experimentally demonstrated (at 13 dBm transmission power), covering an area of 3500 m 2 .
• Chapter 5 focuses on multi-cell backscatter sensor networks (BSNs), consisting of few cores that employ conventional Marconi radio technology and act as fusion centers, as well as scatter radio sensors that are responsible for measuring environmental quantities and transmission of the sensed information towards the cores. A complete multi-cell scatter radio signal and wireless model is offered incorporating pathlosses, tag-and microwave-related parameters over a dyadic Rician fading channel.
A new multi-tag channel estimation closed-form solution is proposed based on a linear minimum mean-squared error (LMMSE) estimator. The average long-term signal-to-interference-plus-noise ratio (SINR) of maximum-ratio combining (MRC) and zero-forcing (ZF) linear detectors is found and subsequently harnessed to allocate frequency sub-channels at tags. The proposed resource allocation algorithm is based on the Max-Sum algorithm, obtained from the inference literature, adhering to simple message-passing update rules. The algorithm is very lightweight and converges to the optimal solution within very few iteration steps. Detailed simulation results reveal that the ZF detector is more suitable for large-scale BSNs when multiple receiver antennas can be exploited at the receiver side, capable to cancel out the intra-cell interference. It is found that the proposed Max-Sum algorithm offers remarkable convergence-complexity trade-off as it is very lightweight and converges to the desired optimal solution very quickly.
Finally, chapter 6 contains the dissertation's concluding remarks and examines future research directions.

Chapter 2 Nonlinear Far Field RF Energy Harvesting Analysis
This chapter focuses on far field RF energy harvesting in contemporary wireless communications systems. In contrast to the vast majority of wireless communications RF harvesting prior art which neglects the nonlinearities imposed by the presence of the diodes in rectifier circuits, we model the RF harvested power as an arbitrary nonlinear, continuous, and non-decreasing function of received power, taking into account sensitivity and saturation effects. To approximate the real energy harvesting model, a piece-wise linear approximation is proposed, amenable to closed-form and tuning-free modeling. Three performance metrics are examined, comparing how close to real industry-level nonlinear RF harvesting is the proposed piece-wise linear approximation versus the linear baseline RF harvesting models from prior art. It is demonstrated that the proposed methodology, even though simple, offers exact performance for all studied metrics. On the other hand, linear RF harvesting modeling results deviate from reality, and in some cases the gap is more than an order of magnitude. The material of this chapter is filling a gap in recent wireless communications RF harvesting literature, opening new research avenues for practical RF harvesting in Internet-of-Things.

Related Work
Simultaneous wireless information and power transfer (SWIPT) literature within the wireless communications theory research community has mainly studied protocol architecture problems as well as fundamental performance metrics. Protocols that split time or power among RF energy harvesting and information transfer modules within a radio terminal are studied in [41], so that specific communication tasks are performed, while the radio ter- minal is solely powered by the receiving RF signal. The aspect of wireless power transfer in wireless communication imposes additional energy harvesting constraints [42]. Multiuser orthogonal frequency-division multiplexing (OFDM) systems with SWIPT-based resource allocation algorithms have been proposed in [43,44]. The objective in [45] is to maximize the total harvested power at the energy harvesting receiver under minimum required signal-to-interference-plus-noise ratio (SINR) constraints, whereas the authors in [46] study the minimization of total transmit power under energy harvesting and minimum required signal-to-interference-plus-noise constraints. Both [45,46] formulated the underlying optimization problems as semidefinite programs and solved them with standard convex optimization algorithms. The above works are a small sample of existing RF harvesting literature in wireless communications, which is vastly evolving. Recent reviews such as in [47][48][49][50][51], offer the current perspective of the wireless communications theory community in RF harvesting.
RF energy harvesting suffers from limited available density issues, typically in the regime of sub-microWatt incident RF power, e.g., work in [52] reports 0.1µWatt/cm 2 from cellular GSM base stations. In sharp contrast, other ambient energy sources like sun, motion or electrochemistry can offer high density power. 1 Such limited RF density in RF energy harvesting can power only ultra low-power devices in continuous (non-duty-cycled) operation or low-power devices, such as low-power wireless sensors in delay-limited, dutycycled operation, since sufficient RF energy must be scavenged before operation. That is due to the fact that far field wireless power decreases very fast with distance, e.g., with the second power of distance in free space, while RF harvesting circuits have limited sensitivity as well as efficiency (explained in more detail subsequently).
The most critical component of far field RF harvesting circuits is the rectenna, i.e., the antenna and the rectifier that converts the input RF signal to DC voltage. The rectifier circuit usually consists of one or multiple diodes, imposing strong nonlinearity on the conversion of power. It has been noticed that the rectifier circuit operates in three input RF power regimes, stemming directly from the presence of diodes. First, for input power below the sensitivity of the harvester (i.e., the minimum power for harvesting operation), the harvested power is zero. Second, for input power between sensitivity and saturation threshold (the power level above which the output harvesting power saturates), the harvested power is a continuous, nonlinear, increasing function of input RF power, with response depending on the operating frequency and the circuit components of the rectifier. Lastly, for input power above saturation, the output power of harvester is saturated, i.e., it is constant. The above three characteristic regimes are depicted in Fig. 2.1, with the black-dashed line curve, which adhere to a variety of circuits in the microwave literature [29][30][31]. The nonlinearity of harvested power as a function of input power is also verified by the fact that conversion efficiency in the microwave circuits literature is always referenced to specific level of input power. Unfortunately, the vast majority of recent communications theory SWIPT papers, for simplification purposes, adopts linear input-output models for harvested power as a function of input RF power, also depicted with red-solid curve in Fig. 2.1.
A diode-based rectifier and broadband rectenna are designed in [54] for energy harvesting from ambient RF signals, while work in [55] designed monopole dual-band antenna for RF energy harvesting. The authors in [29] study far field powering issues for low-power and low-duty cycle wireless sensors with low incident power density; rectenna designs are also proposed. Work in [56] demonstrated conversion efficiencies on the order of 85% operating at 40 dBm input power. Such input power values are very infrequent in practical far field RF energy harvesting, because input power usually cannot exceed 0 to 10 dBm. Work in [57] has demonstrated efficiencies on the order of 10% at −10 dBm input power, while rectenna designs for batteryless backscatter sensor networks offering efficiency 28% at −20 dBm input power can be found in [31].

Contributions
This chapter contributes to far field RF energy harvesting in the following aspects: • For the first time in the wireless communications literature, harvested power can be modeled as an arbitrary nonlinear, continuous, and non-decreasing function of input RF power, accounting for: (i) the nonlinear efficiency of realistic rectenna and RF harvesting circuits, (ii) the zero response of energy harvesting circuit for input power below sensitivity, and (iii) the saturation effect of harvested power. Two conversion efficiency models from prior art circuits are used as examples and compared to linear (baseline) models.
• A piece-wise linear approximation of the actual harvested power is harnessed to calculate/approximate harvested power probability density function (PDF) and cumulative distribution function (CDF) statistics; harvested power is the product of the nonlinear harvesting efficiency and the input power. It is found that for choosing the data points in the utilized approximation uniformly, to achieve approximation accuracy at least ǫ, at most O( 1/ǫ) number of data points is required.
• Three performance metrics are studied: (i) expected harvested energy at the receiver, (ii) expected charging time at the receiver (time-switching scenario), and (iii) successful reception at interrogator for passive RFID tags (power-splitting scenario). What can be attributed as the most important contribution of this chapter is the demonstration that the proposed methodology offers exact performance with the real, arbitrary nonlinear energy harvesting model for all studied metrics, without requiring tuning of any parameter. On the contrary, linear RF harvesting modeling results deviate from reality, and in some cases they deviate from the real model by one order of magnitude.

Organization and Notation
The rest of this chapter is organized as follows.
, respectively. The Dirac delta function is denoted as ∆(·). The probability of event A is denoted as P(A). For a function g, domg denotes its domain.

Wireless System Model
A source of radio frequency (RF) signals illuminates with wireless power an information and far field RF energy harvesting (IEH) terminal. A dedicated power source is assumed for the source of RF signals, while the far field IEH terminal harvests RF energy from the incident signals on its antenna and can operate as information transmitter or receiver. Narrowband transmissions are considered over a quasi-static flat fading channel. The downlink received signal at the output of matched filter at IEH terminal for a single channel use is given by: where s is the transmitted symbol, with E[s] = 0 and E [|s| 2 ] = 1, P T is the average transmit power of RF source, T s is the symbol duration, h is the complex baseband channel response, L(d) is the path-loss coefficient at distance d, and w ∼ CN (0, σ 2 d ) is the additive white complex Gaussian noise at the IEH receiver. A block fading model is considered and the channel response changes independently every coherence block of T c seconds. Symbol h (n) denotes the complex baseband channel response at the n-th coherence block. Every coherence block, RF source transmits a packet whose duration spans T p seconds, which in turn spans several symbols, with T p ≤ T c .
During the n-th coherence time block, the received RF input power (simply abbreviated as input power) at the IEH terminal is given by: ). Due to the definition of channel coherence time block, RVs h (n) , across different values of n, are independent and identically distributed (IID). It is also assumed that RVs γ (n) are drawn from a continuous distribution, denoted as f γ (n) (·), supported over the non-negative reals, R + . Hence, the corresponding distribution of P (n) R has a continuous density in R + . For exposition purposes, for any natural number N, the vector of input power coefficients up to coherence block N is defined as p N P The results for the PDF and the CDF of harvested power will be offered without having in mind a specific type of fading distribution. For specific numerical results, Nakagami fading will be considered, as it can describe small-scale wireless fading under both lineof-sight (LoS) or non-line-of-sight (NLoS) scenarios. Under Nakagami fading, the PDF of γ (n) follows Gamma distribution with shape parameters m, Ω m , i.e., where Γ(x) = ∞ 0 t x−1 e −t dt denotes the Gamma function, while Nakagami parameter m has to satisfy m ≥ 1 2 . Fading power parameter Ω satisfies Ω = E h (n) 2 = E γ (n) . For the special cases of m = 1 and m = ∞, Rayleigh and no-fading is obtained, respectively. For 3) is approximated by Rice, with Rician parameter κ [27]. The corresponding CDF of γ (n) is given by:

Fundamentals of Far Field RF Energy Harvesting
This section offers fundamentals in RF energy harvesting, filling a gap largely overlooked in recent wireless communications theory prior art. The principal component of the far field RF energy harvesting circuits is the rectenna, i.e., antenna and rectifier, that converts the incoming AC RF signal to DC under a completely nonlinear operation, commonly realized by one or more diodes. The efficiency is improved by increasing the number of diodes, but at the same time, the sensitivity of the harvester is reduced. Fig. 2.2 depicts typical examples of rectifier circuits found in the literature. Matching network is responsible for reducing the transmission loss from the antenna. A boost converter usually follows the rectifier, in order to amplify the required voltage and also offer maximum power point tracking (MPPT), exactly because the output of the rectifier is a nonlinear function of the rectifier input power P (n) R . Accurately modeling the nonlinearities of the RF harvester becomes mandatory in information and wireless power transfer, and that motivates the work in chapter.  Figure 2.2: Architecture of far field RF energy harvesters. Typical rectifier circuits with a single diode [31] (upwards) or multiple diodes [58] (downwards) are also depicted, emphasizing the nonlinear relationship between harvested and input RF power.

Realistic Far Field RF Energy Harvesting Model
The harvested power at the output of the RF harvesting circuit is modeled as: is the harvesting efficiency as a function of input power, defined over the interval P in [P sen in , P sat in ]. P sen in is the harvester's sensitivity and for any input power value smaller than the sensitivity the harvested power is zero, i.e., p(x) = 0 for x ≤ P sen in . P sat in denotes the saturation power threshold of the harvester, after which the harvested power is constant.
Note that the assumptions above, even though mild, are in full accordance with harvested power curves reported in the RF energy harvesting circuits prior art, e.g., [29][30][31]59]. illustrates the harvested power as a function of input power in mWatt, for the rectenna in [31] (harvester in [59]) and the input power range marked with arrows in Fig. 2

.3-Left.
It can be clearly seen that output (harvested) power is a nonlinear function of the input power. The efficiency functions in Fig. 2.3 are represented as polynomials at the dBm domain, as follows: where x takes values in mWatt, W is the degree of the fitted polynomial in dBm, and {w i } W i=0 are the coefficients of the polynomials. The degrees of the polynomials for the fitted functions are W = 10 and W = 12 for the models in [31] and in [59], respectively (depicted in Fig. 2.3 with dotted and solid curves, respectively). Moreover, input power intervals P in = [10 −4.25 , 10 1.6 ] and P in = [10 −1.2 , 10] (both in mWatt) are utilized for the efficiency models in [31] and [59], respectively.

Prior Art (Linear) RF Energy Harvesting Models
Three baseline models are considered for comparison:

Linear (L) Energy Harvesting Model
The first baseline model is the linear (L) model adopted by a gamut of information and wireless energy transfer prior art. For the linear baseline model, the harvested power (as function of P (n) R ) is expressed as follows: (2.8) with constant η L ∈ [0, 1). The functional form of harvested power in (2.8) is depicted in Fig. 2.1 with a red solid curve. This model ignores the dependence of RF harvesting efficiency on input power, the fact that the harvester cannot operate below the sensitivity threshold, and the fact that the harvested power saturates when input power level is above a power threshold.

Constant-Linear (CL) Energy Harvesting Model
The harvested power for the constant-linear (CL) baseline model is expressed as: with constant η CL ∈ [0, 1). The harvested power curve for the CL model is depicted with a dash-dotted line in Fig. 2.1. This model takes into account the fact that the RF harvester is not able to operate below sensitivity threshold P sen in , but ignores that RF harvesting efficiency is a non-constant function of input power and that the harvested power saturates when the input power level is above P sat in .

Constant-Linear-Constant (CLC) Energy Harvesting Model
For constant-linear-constant (CLC) baseline model, harvested power is expressed as function of input power P (n) R through the following expression:

Statistics of Harvested Power
Consider the harvesting model in Eq. (2.6) where function p(·) satisfies the assumptions of Section 2.2.1. A piece-wise linear approximation of function p(·) over interval P in using a set of M + 1 points is proposed. Since harvested power P in ) is assumed. A graphical illustration of the proposed methodology is provided in Fig. 2 (2.11)

Statistics of P (n) har and Approximation Error
This section offers the PDF and CDF of P (n) har . First, the following is defined: har ∈ (v m−1 , v m ] holds. Thus, using the formula for linear transformations in [60] the following is obtained for any m ∈ [M − 1]: (2.14) Note that the last interval P Finally, in view of (2.11), P (n) har = v M with probability given by: where (a) stems from the continuity of F P (n) R (·) as an integral function of a continuous PDF [61], as well as the definition of ξ M . The overall probabilistic description of P (n) har is summarized through the following proposition.
The proposed approximation utilized for harvested power in Eq. (2.11) has PDF given by: (2.17) The corresponding CDF of P (n) har is given by:

Proposition 2.2 (Approximation Error with Uniform Point Selection). Suppose that we
, with δ M defined as above. If function p(·) is in addition continuously differentiable, then function p(·) in (2.11) restricted over P in , approximates p(·) in P in with absolute error that is bounded as: where C p is a constant independent of M.
Proof. The proof is provided in Appendix 2.5.
Thus, at most O 1 ǫ support points are required to approximate function p(·) with an accuracy of at least ǫ.

Baseline Comparison: Average Harvested Energy
For baseline comparison, the expected harvested energy is considered. Let U N N n=1 P (n) har be denoting the accumulated harvested power up to coherence block N, with which one can calculate the expected harvested energy over N coherence periods as:  [N ] are also identically distributed. Let us also denote P L,har , P CL,har , P CLC,har , and P har the expected harvested power over a single coherence block of the following models, respectively: linear in Eq. (2.8), constant-linear in Eq. (2.9), constant-linear-constant in Eq. (2.10), and proposed in Eq. (2.11).
Under Nakagami fading, the average harvested power for the baseline linear models can be expressed as: Again with the aid of Eq. (2.24), the expected harvested power over a single coherence period for the proposed nonlinear model is given by:  [31] (harvesting module in [59]).

Numerical Results
The expected harvested energy in Eq. (2.20) is calculated for the actual energy harvesting model in Eq. (2.6) (obtained through Monte Carlo experiments), as well as for the three linear baseline models and the proposed approximated nonlinear energy harvesting model.
For the evaluation, the following path-loss model is adopted: and m = 5 are set for the rectenna in [31]. It can be seen that the expected harvested energy performance of the proposed approximation in (2.11) with M + 1 = 1171 points is the same with the performance of the actual harvesting model for all studied distance scenarios of d = 4 and d = 10 meters; thus, it is deduced that the approximation with the specific number M of points is accurate. The slope of the expected harvested energy for the baseline (linear) schemes is different compared to the exact model, demonstrating their deviation from the real energy harvesting model.
In Fig. 2.5-Right, under the same small-and large-scale fading parameters as above, with M + 1 = 2201 approximation points and distance d = 3 m, it is shown that the linear model is highly inaccurate for the second harvesting circuit module; thus, the widely adopted linear model cannot capture realistic efficiency models. The performance of the other two baseline linear models is closer to the actual harvesting model. However, the slopes are different and non-negligible mismatch still exists.

Time-Switching RF Energy Harvesting Scenario: Expected Charging Time
Another important metric is the expected time for the RF harvesting circuit to charge its storage unit at the minimum required level, before operation. This is graphically illustrated in Fig. 2.6, showing time-switching RF energy harvesting and communication protocols, where the terminal (e.g., a wireless sensor) first scavenges the necessary energy required for transmission and then communicates (e.g., work in [31]). This is a very common situation in many RF harvesting protocols, since the available power density in µWatt/cm 2 regime is limited and may not be able to retain the power requirements of the overall apparatus. As a result, a duty-cycled, non-continuous operation is imperative, as depicted in Fig. 2.6. Thus, the required time to harvest the necessary energy before operation should be carefully quantified.
An energy harvesting outage event after N coherence periods will occur if the harvested energy after N coherence periods is below a threshold. The latter is determined by the capacity of the energy storage unit (e.g., capacitor C) and the operating voltage V of the harvesting circuit. Thus, the outage event is given by: where the power threshold is determined by the minimum required stored energy for operation, equal to 1 2 C V 2 , as well as the transmission duration T p , i.e., θ th harv C V 2 2 Tp . Note that the above event depends on the fading coefficients {γ (n) } n∈ [N ] .
RV N ⋆ is defined as the first coherence time index when the accumulated harvested power is above threshold θ th harv , given that there exist N ⋆ − 1 consecutive outage events; Harvesting COM Harvesting COM Figure 2.6: Time-switching operation. Necessary energy is harvested before communication, in duty-cycled, non-continuous applications (e.g., wireless sensors).
thus, the probability mass function (PMF) of RV N ⋆ can be derived as: har are independent, and step (c) employed the CDF definition. Note that the expression above requires the CDF of U N −1 , which will be offered subsequently, while PDF of P (N ) har can be given with the methodology of Section 2.3.1.
The expected value of discrete RV N ⋆ is given by: for any threshold θ th harv . Consider the rectenna model in [31], the path-loss model given in (2.26) with ν = 2.1 and d = 5 m, transmission power P T = 1.5 Watt, Nakagami parameter m = 5, while the parameters for the power threshold are set to V = 1.8 V, C = 10 µF, T p = 50 msec.   ). The number of data points to approximate harvested power in Eq. (2.11) was M + 1 = 1171 and M + 1 = 2201 data points for efficiency models in [31] and [59], respectively.

Numerical Results
For both harvesting efficiency models in [31] and [59] the expected charging time for the proposed approximation and the true harvested power model coincide, verifying the accuracy of a) the proposed approximation in Eq. (2.11) and b) the Appendix 2.5 framework.
For the baseline models, results are obtained through Monte Carlo. It is observed that although the best possible values for η L , η CL , and η CLC are chosen for the baseline models, they fail to offer the same slope with the true energy harvesting model. Consequently, the obtained N ⋆ for the linear models may deviate one order of magnitude from the true value, offering deviations from the true duty-cycle and the available resources for wireless communications. It is also noted that the presence of a boost converter at the rectifier output may also magnify the necessary time for charging, further amplifying charging time differences. The proposed methodology with the nonlinear harvesting model is clearly able to offer accurate estimation of the charging time.

RFID Tags
Next, a backscatter RFID scenario is considered where the EIH node is a passive RFID tag that splits input RF power for operation and wireless communication, simultaneously (see Fig. 2.9), as opposed to time-switching (duty-cycled) operation. Passive RFID tags typically use a simple RF switch (e.g., transistor) to communicate with an interrogator. Fig. 2.10 illustrates a typical operating block diagram of a passive RFID tag. Suppose that tag's antenna is terminated between two load values Z 0 and Z 1 . When the antenna is terminated at load Z 1 , the tag reflects the incoming signal, i.e., backscatters information (uplink), provided that it has sufficient amount of energy. On the other hand, when the antenna is terminated at load Z 0 , tag's antenna is matched to input load and the tag absorbs the power from the incident signal. The duration of the overall round-trip communication between the interrogator and the tag is assumed to last a single coherence time period. Hence, to minimize the notation we focus on a single coherence time block, omitting the index n throughout.
The parameter τ d is the fraction of time the antenna load is at Z 0 (absorbing state), while the rest 1 − τ d corresponds to the fraction of time at load Z 1 (reflection state). Assume that χ is the fraction of receiving input power (when tag's antenna load is at absorbing state) dedicated for RF energy harvesting operation; thus, a total of ζ har = χ τ d percentage of input power is dedicated for energy harvesting, with ζ har ∈ (0, 1). The rest (1 − χ)τ d of the input signal power is utilized by the tag downlink communication circuitry. Furthermore, parameter ρ u denotes the fraction of incident input power that is used for uplink (reflection) scatter radio operation. This number depends on the scattering efficiency and the fraction of time the tag antenna is terminated at load Z 1 (i.e., ρ u ≤ 1−τ d ). It is emphasized that scattering efficiency depends on reflection coefficients, which in turn are input power-independent. With monostatic architecture, the incident input power at the tag is P R = P T L(d) γ = P(d)γ. Since, only a fraction ρ u of input power is backscattered (i.e., ρ u P R ), the received power at the interrogator due to the round trip nature of the backscattering operation is given by:

Interrogator Tag
Matching Network

Control Logic
Uplink COM Figure 2.10: Monostatic backscatter architecture consisting of an interrogator and a passive RFID tag. The interrogator's antenna acts as transmitter of the illuminating signal, as well as receiver of reflected, i.e., backscattered (from the tag) information, hence the term monostatic.
The two following events are needed: A {The BER at reader is below a threshold β} and B {The harvested power is larger than tags' power consumption P c } dt is the Q-function and the expression in the last line of Eq. (2.31) is the probability of bit error under coherent maximum-likelihood detection with FM0 line coding [63], and threshold β ∈ [0, 1 2 ]. Parameter σ 2 u is the properly scaled variance of thermal AWGN noise at the receiving circuit of the interrogator. The expression in (2.31) can be further simplified with the aid of the following proposition: is monotone decreasing and invertible for x ∈ R + ; the inverse function is given by where function Q −1 (·) denotes the inverse of Q-function (with respect to composition).
Proof. The proof is given in Appendix 2.5.
The event of successful interrogator reception is denoted by S; the non-successful reception event at interrogator S C occurs if a) the harvested power is below the tag's power consumption or (b) given that the harvested power is above the tag's power consumption P c , the BER at the interrogator is above the threshold β: Thus, in view of Eq. (2.35), the probability of a successful event is expressed as: where step (a) employed the fact that function R −1 is monotone decreasing and exploited Eq. (2.30).
The corresponding probability expressions can be derived for the baseline linear models and the proposed nonlinear harvesting model. The successful reception event at the interrogator for the baseline models is denoted as S c , c ∈ {L, CL, CLC} and for the proposed model as S. The following proposition summarizes the results: Proposition 2.4. Suppose that P c > 0 and consider Nakagami fading. Let us define For the linear model, the probability of event S L is given by: ζ har }. For the constant-linear model, the probability of event S CL is given by: ζ har }. For the last baseline model (CLC), the probability of event S CLC is expressed as follows: ζ har }. Finally, for the proposed nonlinear energy harvesting model, the probability of event S is given by:  where Proof. The proof can be found in Appendix 2.5. From both figures it can be seen that the performance of the proposed approximation in Eq. (2.11) is the same as the performance of the real model in Eq. (2.6). On the other hand, the baseline models deliver different slopes compared to the nonlinear model and fail to approach its performance; this holds for both harvesting circuits, even though deviations are more obvious for the harvester in [59]; it is also noted that the selected values of η L , η CL , and η CLC were chosen so as to reduce the performance difference. It is also noted that the linear model's performance curve has completely different slope and curvature compared to the real harvesting model.

Numerical Results
Again, it can be deduced that in sharp contrast to the linear harvesting models, the proposed harvesting model and the offered methodology provide accurate results.

Appendix: Proofs of Chapter 2 Proof of Proposition 2.1
Here the CDF expression in Eq. (2.18) is shown. Using the PDF of Eq. (2.17), for any where in (a) the integral is divided in a sum of integrals associated with disjoint intervals and in (b) change of variables Note that due to the right-continuity of CDF [60], Eq. (2.41) covers the case of

Proof of Proposition 2.2
The proof of this proposition relies on polynomial interpolation theorem [64, Th. 6.2]. For any continuously differentiable function g(·) defined over an interval [x 0 , x 1 ] and a linear function g(·) that interpolates g(·) on x 0 and x 1 , for any where g ′′ (·) denotes the second order derivative of function g(·). Using the above, the absolute error is upper bounded as as well as points x 0 and x 1 . Combining the following identity with Eq. (2.44), the absolute error can be upper bounded as Next, the above framework is applied to the proposed piece-wise linear approximation function p(·). Since p(·) is continuously differentiable in P in , using the fact that p(b m ) = p(b m ), for m = 0, 1, . . . , M, applying the results above, the following is obtained | depends on set P in and the given function p(·), and is independent of M.

Numerical Density Evolution Framework for the Sum of Independent RVs
Consider a RV x which can be expressed as are independent of each other, supported by sets S (n) , n ∈ [N], respectively. It is assumed that the PDF of each individual RV x (n) is given, f x (n) (·), over the support S (n) , n ∈ [N], and each S (n) is bounded. In addition note that the support of RV x is S = S (1) + S (2) + . . . + S (N ) (set addition), due to the required convolution operation.
The idea of density evolution is to approximate numerically the PDF of RV x exploiting the fact that it can be written as the convolution of individual PDFs. To do so, consider the support set [S m , S M ] as an approximation of set N n=1 S (n) ∪ S. Note that set can be chosen so as y∈[Sm, , and the following discrete (support) set is formed Set H ∆ is a discrete approximation of support [S m , S M ] and can be also viewed as a vector with H + 1 elements, whose the j-th element is (2.49) Note that with the above definition of PDF vector v (n) f , the following approximation holds: . Next, using J FFT > H + 1 points (for efficient implementation J FFT has to be a power of 2) the fast Fourier transform (FFT) of PDF v (n) f is evaluated, which is the characteristic function of RV x (n) . The vector of characteristic function of RV x (n) is given by f . Using the following facts: (a) the sum of independent random variables is the convolution of their associated PDFs and (b) the equivalence among convolution operation and the inverse Fourier transform of the product of Fourier transforms, the final PDF of x is obtained as and is an approximation of the PDF of RV x. The CDF vector for RV x can be evaluated as Note with the above methodology the evaluation of v fx requires only O(N J FFT logJ FFT ) arithmetic operations due to the properties of FFT [65].
To evaluate Eq. (2.28) for a given threshold θ, the PDF of RV u = N −1 n=1 x (n) , v fu , is first calculated using Eq. (2.51) with N − 1. Then, the index associated with largest element of H ∆ that is smaller than θ is found, i.e., if θ * = arg max{y ∈ H ∆ : y ≤ θ} the optimal index j θ satisfies θ * = H ∆ [j θ ], and then we calculate (2.53) The overall complexity to calculate N ⋆ for the proposed model is dominated by the

Proof of Proposition 2.3
Consider two continuous monotone (invertible) functions h 1 : The proof relies on the following facts from calculus: , is also monotone and invertible with • If h 1 is monotone decreasing and h 2 monotone increasing then h = h 2 •h 1 is monotone decreasing. In addition, h −1 is monotone decreasing as well.
Using the above we now prove the proposition.

Proof of Proposition 2.4
The proof is provided for the proposed model, as the rest baseline models are special cases. The proof for the baseline models can be obtained trivially using similar reasoning. First note that since image points are selected as 0 Using similar reasoning with Eq. (2.36), the probability of successful reception at interrogator for the proposed model can be expressed as where (a) stems from the definition of θ A as well as the fact that 0 < P c < v M , while (b) relies on the definition of θ max . The result follows by plugging the CDF of P R for Nakagami fading.
For P c ≥ v M , the following hold where (a) results from the following facts: (i) P c ≥ v M and (ii) p(ζ har P R ) ≤ p(P R ), since ζ har ∈ (0, 1) and function p(·) is non-decreasing. Thus, by the monotonicity of probability measure [61], Eq.
to the definition of CDF in Eq. (2.18). Hence, for P c ≥ v M , P( S) = 0.

Chapter 3 Backscatter Radios: Fundamentals, Detection, and Channel Coding
This chapter offers the basic communication principles and physical layer receiver designs for scatter radio point-to-point systems. A detailed exposition of a scatter radio signal model is provided, incorporating all microwave, tag-related, and wireless channel parameters. The chapter in the sequel presents coherent and noncoherent detection and decoding reception schemes tailored to the scatter radio frequency shift-keying (FSK) signal model.
FSK modulation is employed as it is an ideal option for the power-limited regime. Specific small block-length channel codes are harnessed at both ends of scatter radio link to reduce the resulting bit error rate (BER) at the reader. The proposed reception algorithms are ideal for short packet communication. The latter offers reduced processing delay at the reader within practically meaningful limits and allows for large-scale multi-tag processing.
Detailed simulation study demonstrates that the BER performance gap between coherent and noncoherent reception depends on whether channel codes are employed, on the fading conditions (e.g., Rayleigh vs Rician vs no fading), as well as on the utilized coding interleaving depth; the choice of one coding scheme over the other depends on the wireless fading parameters and the design choice for extra diversity vs extra power gain. Finally, experimental outdoor results at 13 dBm transmission power corroborate the practicality of the proposed detection and decoding techniques for scatter radio systems. The material of this chapter facilitates the adoption of intelligent, low-power scatter radio devices in the sensing regime of several tens of meters, ideal for ultra-low-power Internet-of-Things applications.

Related Work
The basic ingredients of current scatter radio technology include the illuminating radio frequency (RF) emitter towards the tags, the reflecting tags (scatter radio nodes), that may be passive (i.e., powered by the illuminating RF field) or semi-passive (i.e., power by an ambient source or an external battery) and the receiving device of the backscattered (from the tags) signals, also known as the reader. In contrast to Marconi radios that consist of signal conditioning RF components, such as amplifiers, mixers or active filters, in scatter radios, the communication is accomplished by means of reflection; scattering can be achieved with a single RF transistor at each tag, significantly reducing the energy consumption and monetary cost compared to Marconi radios. Backscatter radios are embedded in a plethora of commercial devices [66] and various interfaces [67,68]. The most prominent use of scatter radio is in radio frequency identification (RFID) systems, principally utilized for inventorying, electronic tickets and people identification [66,69]. RFID is also expected to play a key role in the evolution of Internet-of-things (IoT) and related applications [70]. Typical scatter radio RFID systems are monostatic, i.e., the illuminating transmitter and the receiver are part of the same device. RFID systems suffer from limited communication range, in the order of a few meters, due to the following reasons: (a) the illuminating signal from the interrogator is used for both powering and communication of the tag, (b) the tag's circuit has limited sensitivity and RF harvesting efficiency, and (c) there are high bitrates, reducing the received energy per bit.
Semi-passive tags, i.e., tags powered by external power sources, are more suitable for increased scatter radio communication ranges [13]. As the modulation at the tags requires only the termination of the tag/sensor antenna at different loads, ultra-low-power is required for communication purposes. Such small amount of power can be available from a battery or an ambient source, such as solar, RF or their combination [23], enabling perpetual sensing [71] even at small levels of ambient power [28]. Another option to further increase communication ranges is to employ scatter radio modulations suitable for power-limited regime, such as minimum-shift keying (MSK) or frequency-shift keying (FSK). The latter can be implemented with rather simple hardware logic at the tag and allows frequency-division multiplexing (FDM), i.e., each tag backscatters over a unique portion of the spectrum and the reader can decode concurrently the superposition of FSK-modulated backscattered signals of multiple tags.
Low bitrate symbol-by-symbol noncoherent reception of MSK for monostatic scatter radio is studied in [13]. The authors in [24] studied fading and correlation of the two-way (from illuminating antennas to the tags and from the tags back to the reader) backscatter radio channel, with emphasis on multi-antenna systems. Work in [32,72], offered a detailed link budget analysis for backscatter systems incorporating microwave and tag-related parameters. Single-antenna detectors for two-collided scatter radio tags are proposed in [73], exploiting the inherent memory of FM0 line codes, used in commercial RFID.
Recent work in [63] examined the protocol utilized at Gen2 RFID tags and re-designed signal processing reception algorithms (e.g., for symbol level synchronization, channel estimation, bit duration estimation) for coherent maximum-likelihood (ML) detection at a commodity, monostatic software-defined radio (SDR) reader. Bistatic scatter radio was first experimentally demonstrated in [11,12,33]. In bistatic scatter radio the illuminating emitter and the receiver of the backscattered signals are dislocated, i.e., they are two separate devices. Signal processing reception algorithms for tags employing scatter radio on-off keying [11] or FSK [12] and SDR symbol-by-symbol noncoherent detector are offered in [33], also highlighting the additional difficulties due to the bistatic nature, e.g., carrier frequency offset (CFO) between the illuminating emitter and the receiver. Ranges one order of magnitude larger than conventional RFID were demonstrated. Small block-length error-correction channel codes for inherently resourceconstrained tags are proposed in [74] designing heuristic soft-decision metrics for noncoherent decoding with FSK and bistatic principles; compared to the uncoded case experimental communication range increase was shown. Subsequent work in [37] proposed coherent detection and decoding with small block-length cyclic channel codes for the bistatic scatter radio architecture with FSK modulation. The compound channel vector incorporated all wireless channel and microwave, tag-related parameters and was estimated through a least-squares (LS) technique, exploiting a short training packet preamble (known at the receiver). Work in [75] offered generalized-likelihood ratio testing (GLRT)-optimal noncoherent sequence detection of uncoded orthogonal signaling, also showing its relation with commercial Gen2 RFID protocols.
Scatter radio testbeds in [76] and [38] demonstrated reception of bistatic scatter radio FSK with an embedded receiver for Bluetooth and UHF frequencies, respectively. The system in [38] achieved tag-to-reader range of 250 meters. The authors in [77] generated Wi-Fi transmissions using bistatic scatter radio principles, offering 3 orders of magnitude lower power than existing Wi-Fi chipsets and the achieved tag-to-reader ranges were up to 30 meters. Another example of Wi-Fi backscatter can be found in [78], where the tags translate the original transmitted 802.11b codeword to another valid 802.11b codeword that can be decoded by the Wi-Fi receiver. The system offers up to 54 meters communication ranges with a 200 kbps throughput.

Contributions
The contributions of this chapter can be summarized as: • It is proved that the square-law symbol-by-symbol detector for uncoded scatter radio FSK, is an instance of a composite hypothesis test (CHT), and more specifically, of a hybrid CHT (HCHT).
• Noncoherent symbol-by-symbol and sequence detectors for uncoded scatter radio FSK are designed based on GLRT.
• A noncoherent HCHT decoding rule is designed for coded scatter radio FSK signals, ideal for small packet and small block-length channel codes.
• It is found that a fully interleaved system under coherent ML decoding for backscatter FSK, offers probability of bit error (BER) that decays with the minimum distance of the utilized code. This is the same diversity order as the text-book coherent ML decoders.
• An extensive BER performance evaluation of the proposed scatter radio receivers is offered under Rician, Rayleigh or no fading, assuming fixed energy per packet. It is found that for the uncoded case, noncoherent reception may outperform coherent reception under fixed energy per packet, accounting in the coherent case the energy spent at the preamble bits for channel estimation. For the coded case, the performance gap between coherent and noncoherent decoding depends on the fading conditions (e.g., Rayleigh vs Rician vs no fading), the depth of utilized interleaver, that determines the diversity gain.
• Experimental outdoor measurements (with scatter radio testbed) corroborate the practicality of the proposed detection and decoding techniques for scatter radio.

Organization and Notation
The rest of this chapter is organized as follows: Section 3.1 presents the system model, showing how the bistatic signal model can also describe the monostatic, and describes the utilized modulation scheme. Section 3.2 designs noncoherent receivers for scatter radio FSK incorporated in the bistatic setup. Section 3.3 reviews the channel estimation procedure in scatter radio and offer the maximum-likelihood (ML) coherent detectors and decoders. Simulation and experimental results are offered in Section 3.4 and 3.5, respectively.
Symbols (·) ⊤ , (·) H , (·) * will denote the transpose, Hermitian, and complex conjugate, respectively, of a vector or matrix. Real-part and imaginary-part operations are denoted by ℜ{·} and ℑ{·}, respectively. The phase of a complex number z is denoted as z. The distribution of a proper complex Gaussian N × 1 vector x with mean µ and covariance b) and N (µ, σ 2 ) denote, respectively, the uniform distribution in [a, b) and the Gaussian distribution with mean µ and variance σ 2 . Notation f x|θ (·|·) stands for the conditional probability density function (PDF) of random vector x parameterized by a random or deterministic vector θ. The expectation operator associated with conditional PDF f x|θ (·|·) of any function

Scatter Radio Signal Model
Bistatic scatter radio consists of a carrier emitter (CE), a RF tag, and a software-defined radio (SDR) reader (a graphical illustration is provided in Fig. 3.1). Due to relatively small bitrate (in the order of kilo-bits per second), or equivalently large nominal bit period T , along with the small channel delay spread, frequency non-selective (flat) fading channel [79] is assumed, with complex baseband response given by: where a CR , a CT , a TR ∈ R + denote the channel attenuation parameters of the corresponding links and φ CR , φ CT , φ TR ∈ [0, 2π) the respective phases. Due to the bistatic setup in Rician parameter κ m stands for the ratio between the power in the direct path and the power in the scattered paths of link m ∈ {CR, CT, TR}. The distribution of channel

Carrier Emitter
Tag SDR Reader amplitude a m for link m ∈ {CR, CT, TR} is Rice, given by: where I 0 (·) is the modified Bessel of the first kind and order zero [80, p. 47]. It is noted that for κ m = 0, Rayleigh fading is obtained, while for κ m = ∞, Gaussian channel is obtained with the parameter a m being deterministic constant, i.e., a m = σ m , m ∈ {CR, CT, TR}.
It is noted that the channel power of link m, given by E [|h m | 2 ] = σ 2 m , is independent of κ m . For exposition purposes and without loss of generality, σ 2 m = 1, m ∈ {CR, CT, TR}, is assumed hereafter.
CE transmits a continuous sinusoid wave at carrier frequency F car whose complex baseband representation is where P C is the carrier transmission power at passband, ∆F and ∆φ model the carrier frequency and carrier phase offset between CE and SDR reader, respectively. ∆φ is modeled as a uniform RV in [0, 2π). The carrier wave c(t), propagated through wireless channel h CT , illuminates the antenna of the tag. The incident signal at tag is attenuated and rotated due to the channel gain a CT e −jφ CT . Portion of the incident signal is reflected back; the specific attenuation is related to the tag's scattering efficiency. Let s be denoting the scattering efficiency attenuation, which is considered constant for a duration of a packet. For two distinct tag load values (i.e., binary modulation at the tag), the baseband scattered waveform from tag is [33]: is a DC constant depending on the (load-independent) tag antenna structural mode A s [81] and the (tag load-dependent) tag reflection coefficients Γ 0 and Γ 1 . As the scatter radio modulator at each tag does not include any type of signal conditioning units (e.g., amplifiers, filters or mixers) there is no noise term in Eq. (3.5). The absence of signal conditioning at each tag offers low-power consumption and is the main advantage of scatter radio.
In this work FSK modulation is employed at tags, thus, for FSK modulation, waveform b i (t) represents the fundamental frequency component of a 50% duty cycle square where Π T (t) is the rectangular pulse of bit duration T , given by: (3.7) Φ i ∼ U[0, 2π) models the phase mismatch between tag and SDR reader when bit i ∈ B is transmitted, assumed constant for a duration of a packet. RVs Φ 0 and Φ 1 are assumed independent of each other. In addition, vector Φ [Φ 0 Φ 1 ] ⊤ is also defined.
For the duration of single bit, T , the received demodulated complex baseband signal at the SDR reader is given by the superposition of the CE sinusoid and the backscattered 1 It can be shown that the fundamental frequency component holds ≈ 80% of the total power of the 50% duty cycle square pulse [13].
tag signal propagated through wireless channels h CR and h TR , respectively, i.e., where n(t) is a complex, circularly symmetric, additive Gaussian noise process with power spectral density given by: where W SDR denotes the SDR receiver bandwidth and N 0 = k b T θ , where k b and T θ are the Boltzmann constant and receiver temperature, respectively. The signal in Eq. (3.8) contains carrier frequency offset (CFO) ∆F , which can be directly estimated using periodogram-based techniques, and subsequently, compensated. It is apparent in Eq. (3.8) that CFO depends on all terms, including the DC terms. Therefore, tag-dependent parameters such as A s , typically overlooked in the literature, do play important role in the CFO estimation step. SDR reader applies CFO compensation, and then eliminates the DC terms of the signal in (3.8) by estimation and removal of the received signal's time average [33]. Assuming perfect synchronization and CFO estimation, the DC-blocked received signal of Eq. (3.8) over a bit period T , can be simplified to: where the following abbreviations are utilized: Expanding the cosine term in (3.10) it follows that: with scalar h a e −jφ (3.14) be denoting the compound channel parameter including some phase and wireless channel fading parameters.
, the instantaneous received energy per bit is defined as: The average received energy per bit and the average received SNR are defined as: For each bit i ∈ B, the received signal in (3.13) contains two exponential frequencies ±F i and not one; thus, a classic FSK demodulator for conventional (Marconi) radio loses half of the signal and results in a 3-dB BER performance loss for bistatic FSK [33]. It is not difficult to see that for constitutes a 4-dimensional orthonormal basis, that can be used for expansion of the received signal in (3.13). The next theorem exploits the above 4-dimensional basis and offers the discrete baseband equivalent scatter radio FSK signal model.
T ≪ W SDR , the baseband equivalent signal over a bit duration T is given by the following 4-dimensional complex vector Symbol ⊙ denotes the component-wise (Hadamard) product and 4-dimensional complex, circularly symmetric Gaussian noise vector n is distributed according to: Proof. The proof is given in Appendix 3.6.
It is noted that the system model above has been verified experimentally [11,12,17,33,82,83]. It is also noted that it is general enough to describe monostatic scatter radio (where illuminating carrier emitter and receiver belong to the same reader unit) as a special case, with h CR (and appropriate κ CR , σ CR ) modeling the leakage from the transmit to the receive RF chain of the reader.

Uncoded Symbol-By-Symbol Detection
The optimal noncoherent symbol-by-symbol detector in terms of bit error rate (BER), is the maximum-likelihood (ML) detector, expressed as: Note that due to Eqs. (3.18) and (3.19), For the bistatic scatter radio signal model, the ML rule in (3.20) does not admit closed-form expression for Rician parameters κ CT , κ TR ∈ [0, +∞), and thus, alternative noncoherent detection rules should be designed.

Symbol FSK Detection
The first proposed noncoherent symbol-by-symbol detection rule is the NC-HCHT detector that treats the unknowns Φ 0 and Φ 1 as random parameters, while h is viewed as a nonrandom parameter; thus, NC-HCHT detector is given by: .
Lemma 3.1. The noncoherent detector of Eq. (3.22) is channel-agnostic and is equivalent to: i.e., the detector in (3.22) is the square-law detector.
Proof. For hypothesis i = 0, x 0 (Φ) depends solely on Φ 0 , i.e., x 0 (Φ 0 ), and for the innermost maximization in (3.22) deterministic parameter h is eliminated as: As a result, plugging the optimal h back: Only the last term in (3.25) depends on Φ 0 , and thus, applying expectation with respect to Φ in the last term in (3.25) offers where Eq. (3.26) relies on the fact that Φ 0 ∼ U[0, 2π). Therefore, applying expectation with respect to Φ in (3.25) the last term is eliminated. Since Φ 1 ∼ U[0, 2π), applying similar reasoning for hypothesis i = 1, the detection rule of Eq. (3.23) is obtained after some elementary algebra.
Interestingly, the above square-law detector has been also proposed in [33] as a heuristic noncoherent detection rule.

Noncoherent Generalized Likelihood-Ratio Test (NC-GLRT) Symbol-By-Symbol FSK Detection
The NC-GLRT symbol-by-symbol detection rule treats the unknowns Φ 0 , Φ 1 and h as deterministic parameters and can be expressed as: (3.28) The detector of Eq. (3.28) is channel-agnostic and is equivalent to: Proof. The proof relies on fact that for any complex number α, Using Lemma 3.1, for i = 0, the innermost maximization in (3.28) is simplified to Eq. (3.25), depending solely on Φ 0 . Applying maximization with respect to vector Φ ∈ [0, 2π) 2 in (3.25) affects only the last term Eq. (3.25); thus, in view of (3.30), the following holds: max Working similarly for i = 1, the result in (3.29) follows after elementary algebra.

Uncoded Sequence Detection
It is a well-known fact that when bit period T is smaller than channel coherence time T coh noncoherent symbol-by-symbol detection is not BER-optimal in flat fading and instead, noncoherent sequence detection must be employed (e.g., [85] and references therein). For static (immobile) scatter radio sensor networks, the above scenario of T coh ≫ T is possible. However, classic noncoherent sequence detection based on exhaustive search may be prohibitive, due to its exponential (in the sequence length) complexity. In this section, recent results in noncoherent sequence detection with log-linear complexity for orthogonal modulations are revisited from [85], in order to to design a noncoherent GLRT sequence detection for backscatter FSK, denoted as NC-GLRT. Let T coh = N coh T , where N coh denotes the number of symbols affected by the same channel coefficient and let N coh ∈ N, for simplicity. Transmission of a bit sequence consisting of N s information bits is considered, denoted as The associated received sequence, over a duration of N s bits consists of the concatenation of N s received vectors r 1 , r 2 , . . . , r Ns ; each of them can be further expanded as in (3.18): ⊤ stands for the 4-dimensional received vector for the nth time instant and .., N s . Using the same reasoning with (3.19), the noise statistics in Eq. (3.33) and the noise statistics above, the following is obtained, implying that r 1 , r 2 , .., r Ns are conditionally independent of each other given parameters h, Φ, and any transmitted sequence i. As in Section 3.2.1, the NC-GLRT detection metric over the sequence i can be expressed as: where Eq. (3.37) was obtained by plugging in the optimal h, h opt = and dropping out terms that do not affect the optimization problem. Thus, using Eq.
By sorting the above points in ascending order, i.e., the decision i(Φ, ϕ) remains constant in each one of the following 2N s intervals: with θ 0 = 0. It is noted that the interval [θ 2Ns , 2π) is ignored because it corresponds to the same sequence i(Φ, ϕ) with J 0 . Thus, for fixed Φ ∈ [0, 2π) 2 , our objective is the identification of the 2N s sequences i(Φ, 0), i(Φ, θ 1 ), . . . , i(Φ, θ 2Ns−1 ), one of which offers the largest metric of interest, i.e., the left-hand side of Eq. (3.38). The procedure of finding the best sequence i ⋆ (Φ) i(Φ, θ opt ) is given in Algorithm 1. For given Φ ∈ [0, 2π) 2 , the algorithm offers the GLRT-optimal sequence following the same principles with sequence detection algorithm developed in [85], with complexity O(N s logN s ).
After obtaining the sequence i ⋆ (Φ) the optimal phase pair Φ ⋆ is given by: and satisfies the following: There is no readily available closed-form solution of problem in Eq. (3.46), thus, the following approach is instead utilized. As a practical intuitive alternative, a natural number M ∈ N is chosen and the following set is formed: (3.48) and instead of solving the problem in Eq. (3.46), the following optimization problem is formed:

Noncoherent Coded Reception/Decoding
It is very challenging to apply error-correction channel coding in scatter radios due to the following reasons: • scatter radio tags are inherently resource-constrained, and thus, encoding at each tag/sensor must be computationally affordable, and • SDR reader must also employ low-complexity detection and decoding, in order to concurrently serve as many as possible frequency-modulated tags in a given spectrum band.

Encoding
The transmitter encodes a sequence of K information bits to a sequence of N c ≥ K coded bits through a linear function over the binary field. Specifically, a linear block code C over the field B is a K-dimensional subspace of B Nc . A binary N c -tuple is a codeword of C if and only if there exists a binary K-tuple that can generate this N c -tuple from G, i.e., 2 c ∈ C ⇐⇒ ∃ b ∈ B K : c = bG. (3.50) The ratio R C K Nc defines the rate of the code C, while the minimum distance d C min of C is the smallest Hamming weight w H (i.e., the number of non-zero components) of any non-zero codeword in C, i.e., d C min = min c∈C\{0} w H (c). Hereafter, a code will be abbreviated by the triplet (N c , K, d C min ).

Soft-Decision Noncoherent Hybrid Composite Hypothesis-Testing (NC-HCHT) Decoding
As already mentioned, the inherently resource-constrained tags render the utilization of small block-length channel codes mandatory. However, a major obstacle for small blocklength channel codes over wireless environments is the fact that errors usually occur in long bursts when the channel is in deep fade [79]. 3 When wireless channel fading affects a sheer amount of bits, the use of channel codes with small block-length is not appropriate, due to their small error-correction capability. The interleaving technique in conjunction with linear block codes (of relatively small length, i.e., short packet) overcomes this difficulty [80]. The transmitter stores a block of D codewords in a D × N c matrix and transmits the information column-wise (where D is the interleaving depth of the interleaver), i.e., it transmits the first coded bit of each of the D codewords and then the second bit of each of the D codewords and so forth, until the N c -th coded bit. The receiver stores DN c received symbols and performs decoding row-wise, i.e., it decodes symbol sequences corresponding to actual codewords. In that way, long errors in consecutive coded bits are avoided due to the fact that burst errors are now affecting coded bits from different codewords [79]. It can be shown that a fully interleaved coded system (i.e., DT ≥ T coh ), with classic FSK and Rayleigh fading, achieves diversity order d C min under ML noncoherent decoding [80]. For the scatter radio case, each tag backscatters a packet of DN c coded bits. After DC-blocking, CFO estimation/compensation and symbol synchronization, SDR reader processes DN c received symbols. Let c = [c 1 c 2 . . . c Nc ] ∈ C be a codeword corresponding to a specific row of the interleaving matrix; according to (3.18), the discrete baseband signal, associated with that row of interleaving matrix, is given by: where w n |r + 1 (n)| 2 + |r − 1 (n)| 2 − |r + 0 (n)| 2 + |r − 0 (n)| 2 , n = 1, 2, . . . , N c are the softdecision variables.
Proof. The proof can be found in Appendix 3.6.
The receiver forms the vector w = {w n } Nc n=1 of "soft decisions" for each row of interleaving matrix and applies the rule in (3.53) D times. In practice we apply the rule of Eq. (3.53) for any value of D (even when DT < T coh ) due to its inherent simplicity. Softdecision decoding offers smaller BER performance compared to hard-decision decoding, where the receiver applies first detection on a symbol-by-symbol basis and then applies decoding on the bit sequence. The optimization problem in (3.53) requires O(2 K N c ) arithmetic operations, which is exponential complexity on the number of information bits, K.
However, such computational cost is not very high for SDR reader if relatively small block-length N c (and thus small K) is utilized. For simulation results, small block-length, cyclic Bose-Chaudhuri-Hocquenghem (BCH), as well as Reed-Muller (RM) channel codes are studied [87].

Coherent Scatter Radio Reception
For coherent reception let us define

Channel
To coherently detect the received signal by Eq. (3.55), both the compound channel h as well as the random phases Φ i , i ∈ {0, 1} need to be estimated. Following a training based technique, an priori known at the transmitter/receiver training signal is periodically backscattered from the tag and the SDR reader then applies least-squares (LS) estimation to obtain an estimate for compound vector channel g. Such pilot signal could be the preamble, typically used for packet and/or symbol synchronization. More specifically, once during the channel coherence time T coh , N tr training bits b itr , i tr = 1, . . . , N tr , are transmitted by the tag. After CFO estimation, DC blocking, synchronization, and demodulation the vector representation of the received training signal over one bit period T can be written equivalently as with where e k , k = 1, . . . , 4, denotes the k-th column of the I 4 identity matrix.
Thus, for the duration of N tr training symbols, the receiver applies column-wise concatenation of the vector representations of the N tr bits in the training sequence and forms vector y ∈ C 4Ntr : To jointly estimate the compound channel h and phases Φ i , i ∈ {0, 1}, the receiver obtains the LS estimate of vector g: Although the LS estimate g is ignoring the dependencies in vector g, it adheres to a simple closed-form expression.

Maximum-Likelihood Detection and Decoding
For the baseband signal in (3.55) the reader treats channel estimate g as the true channel vector and applies coherent ML detection: where in (a) we exploited the fact that f r|i,g (r|i, g) ≡ CN ( g ⊙ s i , N 0 I 4 ). For decoding without interleaving technique utilized, i.e. D = 1, suppose that a codeword c = [c 1 c 2 . . . c Nc ] ∈ C (where C is a linear block code) is backscattered from the tag towards the SDR reader. The baseband signal associated with the sequence of bits in the codeword is given in (3.33). For a given the channel estimate g, the ML decoder can be simplified to where (a) exploits that The complexity to find the optimal codeword c ML is O(2 K N c ), which is exponential on the number of information bits. However, for relatively small codeword lengths N c , such complexity is affordable to SDR reader. The final result in coherent receiver pertains to the diversity order achieved by coherent ML decoding in a fully interleaved system. Proof. In Appendix 3.6.
However, the interleaving technique introduces delay and requires additional memory, since both the scatter radio tag/sensor, as well as the receiver process a block of D codewords upon transmission and reception, respectively. Since the tag is equipped with limited memory, the interleaving technique as presented for both coherent and noncoherent coded reception schemes may be a practical option only for relatively small values of D.

Simulation Results
Simulations for the bistatic scatter radio system model assume backscatter binary FSK transmissions with T = 1 msec bit duration, over quasi-static flat fading channel with coherence time T coh = 100 msec; Rayleigh fading (κ CT = κ TR = 0), Rician fading with κ CT = 20, κ TR = 10 and no fading, i.e., Gaussian channel (κ CT = κ TR −→ ∞) are studied. 4 In all simulated cases, perfect symbol synchronization and CFO estimation/compensation are also assumed. For comparison purposes, coherent detection and decoding schemes are also included with N tr = 30 training bits for channel estimation.
In all cases, the average received SNR per information bit is given by Eq. (3.17), while packet length and energy consumption per transmitted packet are both fixed for comparison fairness. Hence, noncoherent receivers (without using a dedicated sequence of training bits in the packet for channel estimation) offer for equal packet lengths higher energy per information bit than their coherent counterparts.

Uncoded BER Performance
For uncoded bistatic scatter radio system, the noncoherent symbol-by-symbol and se-  herent case) for channel estimation. The NC-GLRT sequence detector capitalizes upon that, exploiting correlation (due to the unknown channel) between consecutive symbols and offers blind detection, i.e., no requirement for overhead (training) channel estimation bits. It is also noted that increasing parameter M beyond 6, offers negligible extra performance gain for the NC-GLRT sequence detector. comparison makes a lot of sense. It can be seen that as parameters κ CT and κ TR increase, i.e., the channel becomes more deterministic, the BER gap between the two detection schemes is reduced with increasing SNR. It is observed that as the fading becomes more deterministic, the power gain dominates the BER performance in moderate and high SNR regime. Interestingly, for the Gaussian channel case (no fading, deterministic channel), NC-HCHT detector outperforms Coh-ML detector for SNR values greater than 12. As discussed above, this stems from the fact that noncoherent schemes have a higher power gain (E vs 7 10 E Joules per bit) compared to coherent one. This is highly important in typical scatter radio scenarios, with strong line-of-sight (LOS).  the higher energy per information bit, compared to the coherent receiver, due to fixed energy per packet and no need for training/overhead bits for channel estimation. Both

Coded BER Performance
Using code C(N c , K, d C min ) along with interleaving, the proposed NC-HCHT decoder of Eq. (3.53) and the ML coherent decoder in Eq. (3.61) with LS channel estimation (Coh-ML) are compared in terms of BER. Two small block-length channel codes are studied: the cyclic (31, 11, 11) BCH code C BCH and the (32,16,8) RM channel code C RM ; the first has smaller rate but higher error-correction capability than the second. As in the uncoded case, a total energy budget constraint per packet is considered assuming packets of DN c coded bits (i.e., (K/N c )DN c information bits). Thus, for noncoherent coded setups the total energy per packet is DN c x, where x is the energy cost per bit, while for coherent coded setups the total energy per packet is [DN c + L coh N tr ] x, where integer  can be seen that as fading parameters κ CT , κ TR decrease, the BER for both decoding schemes increases. That is due to the higher randomness of fading for smaller values of κ CT and κ TR and the limited error-correction capability due to the small block-length of the utilized codes. It is also noted that as κ CT , κ TR , and SNR increase, the performance of noncoherent coded system approaches the performance of coherent one.  interesting observation emerges: while for Rayleigh fading BCH-coded outperforms RMcoded system, for Rician fading they offer similar BER performance, whereas for no fading RM offers slightly smaller BER compared to BCH. This means that when κ CT and κ TR are small, i.e., in highly random fading scenarios, diversity gain (that depends on d C min ) plays more important role in BER performance than energy gain (that depends on R C ), while the opposite holds in more deterministic fading scenarios.

Experimental Results
Outdoors measurements were conducted with the experimental setup depicted in Fig. 3.8.
An embedded carrier emitter (CE) was employed transmitting at frequency of 868 MHz with transmit power 13 dBm. A custom 8-bit microcontroller-based, scatter radio tag was utilized at 1 kbps with binary FSK and switching (subcarrier) frequencies of F 0 = 125 kHz and F 1 = 250 kHz. A commodity (USRP2) SDR with Flex-900 front-end radio card was utilized as the receiver, connected to a laptop running the noncoherent and coherent detection/decoding algorithms. All radio modules were equipped with omnidirectional antennas, at height of 1.70 meters. Channel coherence time of 50 to 100 msec was observed during the experimental results, due to immobility. For the considered experimental scenario, CE was placed between tag and SDR reader, co-linearly ( Fig. 3.8).
A packet of 47 bits was utilized for both coherent and noncoherent setups.
Periodogram-based CFO estimation was applied using the whole received signal, 5 and energy-based symbol and packet synchronization was also employed. The (last) 31 bits constitute a BCH codeword (i.e., N c = 31), utilized at both coherent and noncoherent setups for detection and decoding, while the remaining 16 bits were exploited only at the coherent case, for LS channel estimation. The following schemes were compared in terms of BER: • uncoded NC-HCHT symbol-by-symbol detector, • uncoded GLRT symbol-by-symbol detector, • uncoded GLRT sequence detector with N s = 31 and M = 6, • uncoded Coh-ML detector, • coded NC-HCHT decoder, and • coded Coh-ML decoder. 5 The periodogram is the maximum-likelihood estimate (MLE) of ∆F , whose mean-squared error (MSE) decays asymptotically with the cubic power of the number of utilized samples [88].  D = 1 was utilized, i.e., coding schemes did not utilize interleaving. In addition, the energy per bit was held fixed, i.e., total energy per packet was not fixed among the different schemes (favoring coded vs uncoded or coherent vs noncoherent reception). Fig. 3.9 offers the experimental BER of the above schemes as a function of the tagto-reader distance. It can be seen that both coherent and noncoherent uncoded receivers achieve ranges in the order of 145m with BER ≤ 3%, while coded receivers achieve ranges of 148 and 141 meters approximately, at BER ≤ 4% and 0, respectively. It is observed that uncoded coh-ML detector offers similar BER with uncoded (noncoherent) GLRT sequence detector and both of them outperform by approximately one meter the symbol-by-symbol noncoherent detectors (under unequal total energy cost per packet). Interestingly, it can be shown that the proposed noncoherent coded receiver achieves comparable BER performance with the coded coherent one, even though the latter spends extra bits (and energy) for channel estimation; thus, potential energy gains are available for the noncoherent setup. It is worth emphasizing that the reported BER, in the order of 1%-5%, is acceptable for low bitrate sensing applications.

Appendix: Proofs of Chapter 3 Proof of Theorem 3.1
Under the orthogonality criterion for noncoherent FSK: |F 1 − F 0 | = k T , k ∈ N, and for F i ≫ 1 T , any two exponentials of frequencies F 0 , F 1 will be orthogonal: where the integration is performed over one bit period T . Thus, the set 1 constitutes a 4-dimensional orthonormal basis, that can be used for expansion of the received signal in Eq. (13) in the manuscript. Specifically, for bit duration T , a bank of correlators processes the received signal y(t) as where (a) follows from the fact that the integral of the "fast" exponential with frequency F i + F 0 is approximated by zero since F i ≫ 1 T , i ∈ B, and (b) follows from the definition of E in Eq. (15) of the manuscript. Similarly, The complex exponentials are time-limited in [0, T ), and thus, for F i + 20 T ≪ W SDR , the orthonormal basis 1

Proof of Proposition 3.1
Given hypothesis i = 0 and h, Φ 0 , Φ 1 , random variable (RV) z 1 |r + 1 | 2 + |r − 1 | 2 is the sum of 4 independent, squared, zero-mean Gaussians, each of variance σ 2 N 0 /2 and thus, z 1 follows a Chi-squared distribution with 4 degrees of freedom and probability density function (PDF) given by [80, p. 45]: f z 1 |i (x|0) = x 4σ 4 e − x 2σ 2 , x ≥ 0, and corresponding cumulative distribution function (CDF) given by: Similarly, given hypothesis i = 0 and h, Φ 0 , Φ 1 , random variable z 0 |r + 0 | 2 + |r − 0 | 2 is the sum of 4 independent squared non-zero-mean Gaussian RVs, each of variance σ 2 and thus, z 0 follows noncentral Chi-squared with 4 degrees of freedom with noncentrality parameter E |h| 2 = E a 2 that do not depend on RV Φ 0 . The conditional PDF of z 0 is given by [80, p. 46]: where I 1 (·) is the modified Bessel of the first kind and order one [80, p. 47]. Under hypothesis i = 0, error occurs if z 0 < z 1 . Applying the law of iterated expectation [89], the probability of that event can be calculated as follows: (3.67) In view of Eq. (3.65), the inner expectation in Eq. (3.67) is given by: Substituting SNR = E/(2σ 2 ) in Eq. (3.68) , and applying expectation with respect to a = a CT a TR under independent Rayleigh fading, offers the following: Applying expectation with respect to Φ 0 and Φ 1 in (3.71), the following is obtained: where completing the proof.

Proof of Theorem 3.4
To achieve a fully interleaved system for the coherent case the value of depth D is set The transmitter stores D codewords belonging to a linear block code C in a D ×N c matrix and transmits the information column-wise. For each D bits (each column of interleaving matrix), N tr training bits are utilized for channel estimation. Thus, the transmitter sends at total N c (D + N tr ) bits.
The receiver has N c (D + N tr ) received symbols; N c N tr of them correspond to training bits to estimate the random channel vectors associated with each column of interleaving matrix. Let g 1 , g 2 , . . . , g Nc be the actual compound channel vectors associated with the symbols of the 1st, 2nd, . . ., N c -th column of interleaving matrix, respectively. Due to Eq. (3.76) the compound channel vectors are independent of each other (and identically distributed).
We conclude that in fully interleaved system the receiver decodes symbol sequences that correspond to codewords with coded bits experiencing independent fading. Accordingly with Eq. (3.51), the received signal for a single row of interleaving matrix can be expressed as with c = [c 1 c 2 . . . c Nc ] ∈ C denoting the transmitted codeword associated with the specific row of interleaving matrix and Assuming perfect knowledge of g 1 , . . . , g Nc , and exploiting their independence, the average probability of decoding error is given by (3.78) . . g ⊤ Nc ] ⊤ for simplicity. For each i = 1, . . . , N c , the log-likelihood ratio associated with vector r i (which is a proper complex Gaussian given c i , g i ) can be written as After some algebra and using Eqs (3.11) and (3.17), the conditional PDF of l i can be expressed as where the parameters a CT,i , a TR,i are associated with compound channel g i , i = 1, 2, . . . , N c . Thus, for the channel described by (3.77), the following is satisfied: and the channel is memoryless given g 1:Nc ; thus, it can be considered as a binary-input symmetric-output channel [90]. Under equiprobable signaling, due to the linearity of block code C and the memoryless The symmetry of channel (Eq. (3.82)) ensures that no loss of optimality is incurred by considering the all-zeros codeword in the pairwise error probability at the right-hand side of (3.83).
Under the assumption of all-zeros codeword and for given g 1: where RVs a CT,i and a TR,i are independent and follow Rayleigh distribution with unit power, due to the assumption that κ CT = κ TR = 0. In view of Eqs. (3.83) and (3.85) the conditional probability of decoding error satisfies

Chapter 4 Extended Scatter Radio Coverage for Low-Power Internet-of-Things
Building upon the results presented in chapter 3, this chapter explores scatter radio from a networking point of view, trying to evaluate and contrast, in terms of several multi-tag performance metrics, the most prominent scatter radio network architectures, i.e., the monostatic and the multi-bistatic (multistatic) architectures. In monostatic architecture, the reader consists of both the illuminating transmitter and the receiver of signals scattered back from the tags/sensors. The multistatic architecture includes several ultra-lowcost illuminating carrier emitters and a single reader. The chapter analyses performance metrics such as, maximum-likelihood coherent and noncoherent bit error rate (BER), diversity order, average information and energy outage probability, under dyadic Nakagami fading. The latter is the most realistic small-scale fading wireless channel model for backscatter communications. The theoretical and simulation results revealed the following: (i) multistatic architecture outperforms monostatic one in terms of diversity order and BER performance, (ii) for passive tags with radio frequency (RF) energy harvesting, energy outage events are more infrequent in multistatic than monostatic architecture, and (iii) multistatic coverage is higher than monostatic. The chapter is closed with some experimental results attributed to [40]. A proof-of-concept digital multistatic backscatter sensor network (BSN) was demonstrated with a single receiver, four low-cost emitters and multiple ambiently-powered, low bitrate tags. The outcome of this research can be applied in the industries of wireless sensor networks (WSNs) and emerging Internet-of-things (IoT) applications.

Related Work
In environmental monitoring and precision agriculture, as well as in many other Internetof-Things (IoT) applications from healthcare domain and smart homes (with many examples found in [1] and references therein), the reader (receiver) must be able to decode multiple sensors' signals for ranges that may be larger than conventional ranges in radio frequency identification (RFID) systems. In such situations one potential solution would be the adoption of conventional (Marconi) radios for multi-sensor communication. However, radio frequency (RF) front-ends in Marconi radios typically require signal conditioning units, such as mixers, active filters, and amplifiers, increasing complexity, power consumption, and monetary cost per IoT device. On the contrary, backscattering, i.e., communication by means of reflection, can be realized with a single RF transistor at each scatter radio node, and thus, power consumption and monetary cost per IoT device can be maintained at ultra-low levels.
There are two different architectures for scatter radio networks, namely the monostatic and the multi-bistatic (multistatic) architectures, depicted in Fig 4.1. In monostatic architecture [93], the reader consists of both the illuminating transmitter and the receiver of signals reflected back from the tags. In the bistatic architecture [33], the illuminating carrier emitter (CE) and the receiver of the reflected (backscattered) signals are distinct units, located at different positions, offering flexible network topologies. In the multistatic architecture, several low-cost CEs are available, two orders of magnitude cheaper than the reader. The latter can be a low-cost, commodity software-defined radio (SDR).
Before presenting any theoretical or simulation result, simple intuition indicates that due to the morphology of the multistatic architecture, each tag can be close to a CE with high probability, offering two desired implications: (a) the tag-to-reader coverage is increased with high probability and (b) using passive tags that harvest RF energy from the illuminating emitters, the probability of energy outage during the energy harvesting phase can be decreased. Proof-of-concept multistatic backscatter sensor network (BSN) examples with analog FM principles can be found in [17] and [19], for environmental humidity and soil moisture, respectively, while work in [18] used bistatic scatter radio to convey the electric potential of several plants and each BSN terminal was powered by the plant itself, capitalizing upon the ultra-low power requirements of scatter radio.
This first concrete step towards increased range digital scatter radio systems operating with multiple tags was done in [13], where frequency-based modulations were advocated for frequency-based multiple access and a monostatic reader was built to decode noncoherently minimum-shift keying (MSK)-modulated backscattered, low bitrate sig-nals. Subsequent work in [94] conducted coverage analysis assuming tags backscattering frequency-modulated signals over orthogonal subcarriers. The required number of RF sources to obtain interference-free communication connectivity for wireless sensor networks consisting of passive devices was studied in [95]. The authors in [96] propose a network architecture that enables device-to-device (D2D) communication between passive nodes by simultaneously integrating backscatter communication along with wireless power transfer.

Contributions
The contributions of this chapter are summarized as follows: • A multi-tag signal model based on joint time-and frequency-division multiplexing (joint TDM-FDM) for both multistatic and monostatic systems is proposed, exploiting existing results on scatter radio prior art. The signal model accounts for (large-scale) path-loss and small-scale fading, based on, realistic for scatter radio signal model, dyadic Nakagami fading.  be exploited to a network level analysis. It is found that the bistatic architecture has higher diversity order than the monostatic architecture. Additionally, it is found that the multistatic analysis covers asymmetric cases, where the fading statistics of links emitter-to-tag and tag-to-reader are different.
• Information outage probability and tight Jensen-based upper bounds are provided for Rayleigh fading. In addition, for the case of passive tags, closed-form expressions for energy outage are derived for Nakagami fading.
• Numerical results demonstrate that multistatic architecture outperforms the monostatic one for every studied metric. Topology-free information and energy outage expressions are evaluated over the class of square grid topologies (related to the spatial distribution of the tags).
• A digital, multistatic BSN is experimentally demonstrated and contrasted to a monostatic counterpart, corroborating the theoretical findings and offering a concrete proof-of-concept. These experimental results are contributed from [40] and are presented in this thesis to offer a complete comparison between the two studied scatter radio architectures.

Organization and Notation
The rest of this document is organized as follows: Section 4.1 presents the model of the monostatic and multistatic architectures. Section 4.2 presents the single user (i.e., tag) error probability analysis and Section 4.3 offers the outage probability analysis for multiple tags and presents how to model the spatial distribution of tags. Next, Section 4.4 offers energy outage analytical results. Numerical and experimental (outdoor) results are presented in Sections 4.5 and 4.6, respectively.
Notation: Symbols B, N, R, and C denote the set of binary, natural, real, and complex numbers, respectively. 0 N and I N , denote, respectively, the all-zeros vector and identity matrix of size N. The phase of a complex number z is denoted as z. The distribution of a proper complex Gaussian N ×1 vector x with mean µ and covariance matrix Σ is denoted by CN (µ, Σ) U[a, b) denotes the uniform distribution in [a, b). Expectation of function g(·) of random variable x with probability density function (PDF) The probability of event A is denoted as P(A).

Network Architecture
We For TDMA operation, the l-th CE transmits at the l-th time slot using a common carrier frequency, whereas for FDMA operation, the l-th CE transmits at the l-th frequency slot, i.e., carrier frequency centered at a frequency band orthogonal to the bands of the other simultaneously (in-time) transmitting CEs. The wireless channel is assumed quasi-static, changing independently across different (time or frequency) slots. For the l-th (time or frequency) slot, 2N +1 unidirectional links exist (N CE-to-tag links, N tag-to-SDR reader links and the CE-to-SDR reader link). The distance between the l-th CE and the n-th tag is denoted by d C l Tn , the distance between the n-th tag and the reader is denoted as d TnR with n ∈ N and the distance between the l-th CE and the SDR reader is denoted as d C l R (Fig. 4.2). Under the assumptions of this work, it will be shown that TDMA and FDMA operations for CEs offer equivalent signal representations.
In the monostatic BSN architecture the single-antenna reader operates as both the receiver and the CW emitter, in full-duplex mode. Specifically, the tags are illuminated by the illuminating CE emitted from the SDR reader. The incident CE signal is modulated and backscattered towards the SDR reader. For fair comparison to the multistatic system, transmission across L time slots will be also assumed, with wireless channel changing independently between time or frequency slots. In this architecture N bidirectional links exist between the reader and the N tags ( Fig. 4.1-Left). The distance between the reader and the n-th tag is denoted by d k , where k ∈ {T n R, RT n } denotes the unidirectional tag-to-reader, reader-to-tag link, respectively. The positions of n-th tag, l-th CE, and SDR reader are denoted u Tn , n ∈ N , u C l , l ∈ L, and u R , respectively.

Channel Model
The adopted path-loss model is [27]: where k ∈ {C l R, C l T n , T n R} for multistatic and k ∈ {T n R, RT n } for monostatic architecture, d 0 is a reference distance (assumed unit thereinafter), λ is the carrier emission wavelength and ν k is the path-loss exponent for link k.
Tag communication bandwidth and channel delay spread are assumed relatively small and thus, frequency non-selective (flat) fading is assumed. The complex channel gain for the l-th (time or frequency) slot is denoted as h l,k = a l,k e −jφ l,k , where a l,k ∈ R + , φ l,k ∈ [0, 2π), k ∈ {C l R, C l T n , T n R} and k ∈ {T n R, RT n } for multistatic and monostatic architecture, respectively, with E[|h l,k | 2 ] ≡ E a 2 l,k = 1. It is emphasized that for CEs in TDMA or FDMA mode, h l 1 ,k is statistically independent to h l 2 ,k for any l 1 = l 2 . Moreover, at the monostatic architecture reciprocity implies h l,TnR = h l,RTn , while at the multistatic architecture, {h l,k } are independent (and not necessarily identically distributed) for different k ∈ {C l R, C l T n , T n R}. 1 Due to potentially strong line-of-sight (LoS) signals in scatter radio environments, Nakagami small-scale fading is a valid assumption for small-scale fading at each scatter 1 Results can be easily extended to the multi-antenna reader case. radio link (with E a 2 l,k = 1) [27, p. 79]: where M k ≥ 1 2 is the Nakagami parameter and function Γ(x) = ∞ 0 t x−1 e −t dt is the Gamma function. For the special cases of M k = 1 and M k = ∞, Rayleigh and no-fading (i.e., a l,k = 1) is obtained, respectively. For M k = (κ k +1) 2 2κ k +1 , the distribution in (4.2) approximates Rice with Rician parameter κ k [27].

Signal Model Multistatic
Following the scatter radio signal model in Section 3.1, the l-th CE transmits a CW at the l-th (time or frequency) slot, with complex baseband c l (t) = 2P C l e −j(2π∆F l t+∆φ l ) , where P C l is the l-th CE transmission power, while ∆F l and ∆φ l model the carrier frequency offset (CFO) and phase offset between the l-th CE and the SDR reader, respectively, due to the fact that CE and the SDR reader do not share the same oscillator.
Each tag n ∈ N is illuminated by the carrier wave c l (t). The tag's information is binary-modulated on the incident CW by switching the antenna load between two loads, associated with two distinct reflection coefficients: Γ n,0 and Γ n,1 for bit "0" and bit "1", respectively. Binary frequency-shift keying (FSK) modulation is employed, where each tag switches between the two loads using a 50% duty cycle square waveform of duration T per bit (nominal bit duration), fundamental frequency F n,i , and random initial phase Φ n,i , for bit i ∈ B {0, 1} (cf. Eq. (3.6)); in other words, modulation occurs with different switching frequency between tag antenna loads, utilizing switching (also coined as subcarrier) frequency F n,0 for bit "0" and F n,1 for bit "1", without any type of signal conditioning, such as filtering, amplification or mixing [13]. Fig. 4.3 depicts the measured spectrum at a spectrum analyzer when a signal's generator's CW at F s = 868 MHz illuminates tag n that utilizes binary FSK with |F n,1 − F n,0 | = 122.5 kHz. In contrast to conventional Marconi-radio FSK, frequencies F s − F n,0 and F s −F n,1 also contribute to the total received signal (in addition to F s +F n,0 and F s +F n,1 ), and thus, backscatter FSK modulation uses 4 frequencies, ±F n,in , i n ∈ B. Consequently, the optimal demodulator requires 4 matched filters and not 2, as in classic FSK demodulation.
A set of unique subcarrier frequencies F n,in , i n ∈ B, are employed at tag n to scatter its data. At the network level, the 4N frequencies {±F n,in } , ∀(i n , n) ∈ B×N must satisfy  the orthogonality criterion, which for coherent FSK adheres to the following: 2 Under the above orthogonality criteria the system of N tags scattering simultaneously can be divided into N parallel orthogonal channels, where each can be received separately, without collision. Such single-tag processing techniques have been extensively covered in [13,33,37,39,97]. In view of Eq. (3.18), for the point-to-point backscatter system associated with the n-th tag during the l-th slot, the CFO-free, DC-blocked received baseband signal at the reader over a bit period T is given by l,n x n + w l,n , n ∈ N , (4.4) where the vector x n is given by: x n 1 2 e +jΦ n,0 e −jΦ n,0 e +jΦ n,1 e −jΦ n,1 ⊤ ⊙ s in , n ∈ N , (4.5) and is the four-dimensional transmitted symbol of the n-th tag corresponding to transmitted bit i n ∈ B. Φ n,0 (Φ n,1 ) is implementation-specific phase mismatch between tag n and reader for bit 0 (bit 1), assumed constant for the L slots. Symbol ⊙ denotes the component-wise (Hadamard) product. According to Theorem 3.1 for F n,in + 20 T ≪ W SDR , where W SDR is the SDR receiver baseband bandwidth, w l,n ∼ CN (0 4 , N 0 I 4 ). Compound channel parameter h [b] l,n in Eq. (4.4) is given by: l,n e −jφ [b] l,n , (4.6) a [b] l,n = a l,C l Tn a l,TnR , l,n = φ l,C l Tn + φ l,TnR + ∆φ l + Γ n,0 − Γ n,1 .
l,n denotes the average energy per bit for the n-th tag over the l-th slot and, accordingly with Eq. (3.16), is given by: taking into account that RVs a l,C l Tn and a l,TnR are independent with unit power. Parameter µ l,n above incorporates the compound scatter radio link path-losses and tag-related parameters, i.e., with s n modeling the n-th tag's (real) scattering efficiency, assumed constant over the L slots. The average received SNR of tag n at the l-th slot for multistatic system associated with the system in Eq. (4.4) is given by SNR l,n /N 0 . As already mentioned, for CEs in TDMA or FDMA mode, h l 1 ,k is statistically independent to h l 2 ,k for any l 1 = l 2 . Under this assumption, tools developed in this work can in principle accommodate both CE modes. For simpler presentation and concise comparison with the monostatic architecture, we will assume hereinafter CEs in TDMA mode.

Monostatic
In monostatic case CFO ∆F l and phase offset ∆φ l are zero, due to the fact that the receiver and the emitter share the same oscillator. Using Eq. (4.4) and the reciprocity of the channel between the reader and each tag, the DC-blocked, demodulated received signal for tag n in the monostatic architecture at time slot l is given by: l,n = 2φ l,TnR + Γ n,0 − Γ n,1 . (4.13) The average received energy per bit for monostatic system for the n-th tag over the l-th time slot, E [m] n , is expressed as: The average received SNR of tag n at the l-th time slot for monostatic system is given

In the monostatic case above, quantities E [m]
n and SNR [m] n do not depend on time index l, because they are functions of path loss L TnR ; the latter is constant during the L slots.
On the contrary, E l,n and SNR [b] l,n in the multistatic case, are both functions of path loss L C l Tn , which depends on the slot index l, since different CE corresponds to each slot.
In addition, it is noted that due to the nature of FSK modulation, the discrete baseband signal expressions in Eqs. (4.4) and (4.11) depend solely on links C l T n and T n R due to DC-blocking operation, and thus, the analysis is continued with link T n R for monostatic and links C l T n and T n R for bistatic (one CE) or multistatic (multiple CEs) architecture, ∀(l, n) ∈ L × N .

Distribution of Fading Amplitudes
It can be observed that RVs (a l,C l Tn ) 2 and (a l,TnR ) 2 are independent following Gamma distribution with parameters M C l Tn , 1 M C l Tn and M TnR , 1 M TnR , respectively [60, p. 242], i.e., the probability density function (PDF) of RVs (a l,k ) 2 is given by: The above distribution reflects the power distribution of each small-scale fading scatter radio link for both monostatic and multistatic architectures and will be used as a building block to derive closed-form expressions for the metrics of interest. For simplified notation, the following abbreviations are used: M C l Tn = M ln and M TnR = M n . l,n ) and phase parameters Φ n,0 , Φ n,1 , the conditional bit error rate (BER) for tag n over time slot l under ML coherent detection depends solely on amplitude a [m] l,n [37], and is given by [79, p. 508]:

BER Analysis with ML
n , (4.18) where U(·, ·, ·) is the confluent hypergeometric function [84,Eq. (13.4.4)]. In step (a) above, the Chernoff bound for Q function was exploited and in step (b), [ n of tag n, which in turn, depends on Eq. (4.14); the latter is a function of tag's n location through Eq. (4.15).
Thus, the above BER expression depends on the topology of the tags. The following proposition offers an important, topology-independent metric: Proposition 4.1. Under Rayleigh fading, i.e., M n = 1, mono-static architecture offers diversity order equal to 1/2 for any (l, n) ∈ L × N .
Proof. The proof is given in Appendix 4.7.
The above result indicates that for any slot and Rayleigh fading, monostatic BER decays inversely proportional with square root of SNR at the high SNR regime. It is shown below that the decay is faster in the multistatic case.

Multistatic
Exploiting Eq. (4.7) along with the formula in [60, p. 302, Eq. 6.148], the PDF of the product g l,n 2 = (a l,C l Tn ) 2 (a l,TnR ) 2 admits closed-form:  19) can be found in [98], while a derivation of Eq. (4.19) in the special case of M ln = M n is given in [99].
In the multistatic case, according to Eq. (4.4), the conditional BER for tag n over the l-th time slot is given by: l,n | a l,n , (4.20) which with the use of Chernoff bound is upper bounded as Q a Hence, BER over the l-th slot for the n-th tag is upper bounded as follows: where U(·, ·, ·) is the confluent hypergeometric function [84,Eq. (13.4.4)]. In Step ( Proof. The proof is immediate from the last proof in Appendix 3.6.
Thus, it is concluded that under Rayleigh fading, the multistatic BER drops faster compared to the monostatic, at the high SNR regime, even for a single, fixed slot.

Noncoherent
To better highlight the importance of the expressions derived in Eqs. l,n , as well as phase offsets Φ n,0 and Φ n,1 , and unknown dyadic backscatter channel angles φ [m] l,n and φ [b] l,n , it can be shown that the ML reception rule for orthogonal signaling is based on envelope detection [80, Eq. 4.5-32] of the 4 × 1 complex received vector r l,n which can be expressed as: l,n [4] , (4.22) where x = m, x = b, for monostatic and multistatic system, respectively. Note that the above rule requires the received signal vector r [x] l,n and the tag n implementationspecific phases Φ n,0 and Φ n,1 , while it is different than the square-law detector: |r l,n [ for monostatic and multistatic system, respectively. Note that the above expressions coincide with the upper bounds of conditional error probabilities given in Eq. (4.17) and (4.20). In other words, the expressions in (4.18) and (4.21) reflect the exact BER performance under noncoherent envelope detection in monostatic and multistatic architecture, respectively. 4

Information Outage Analysis
In Section 4.1 we assumed that all subcarrier frequencies used by the tags adhere to the orthogonality criterion provided in Eq. (4.3). In practice, this is not always the case, due to frequency generation constraints (e.g., clock drifts, lack of phase-locked loops). As a result, the allocated subcarrier frequencies at tags may cause adjacent channel interference. An adjacent in frequency tag j, i.e., tag with pair of subcarrier frequencies (F j,0 , F j,1 ) relatively close to (F n,0 , F n,1 ), may be received with significantly higher power than the tag of interest n; thus, any deviation from the orthogonality criterion may cause interference. Therefore, the relative spatial location of one tag versus the other, i.e., the network topology, as well as the subcarrier frequency allocation (denoted as C) of N available pairs of subcarrier frequencies to N tags does affect overall performance in practice. Notice that there are N! possible subcarrier frequency assignments to N tags. A(n) denotes the set of tags interfering the reception of tag n, while g [m] l,n = a l,n = a For simplification purposes, we assume that dyadic channels g l,n and g l,j are statistically independent among different tags (n = j) and any l ∈ L.

Monostatic
For a given subcarrier frequency assignment C, incorporating imperfections mentioned above, the instantaneous signal-to-interference-plus-noise ratio (SINR) of tag n at the l-th time slot is defined as by: where parameter ρ nj (C) is inversely proportional to the assigned subcarrier frequencies separation between tag n and tag j ∈ A(n) [13]. It depends on the spectral efficiency of the specific binary modulation implemented at each tag and the filtering functions at the reader: where F C n,in is the subcarrier frequency allocated under assignment C at tag n for bit i n ∈ B; parameter ε n,j is a constant depending on the utilized modulation and pulse shaping, as well as the mismatch between the clocks of tag n and j. Subcarrier frequency difference raised at the second power, as opposed to the fourth power, is due to the power spectral density of FSK implemented at each tag, as opposed to (continuous phase) MSK [13].
The average received SINR for any (l, n) ∈ L × N can be expressed as: Under Rayleigh fading, i.e., M n = 1, for given subcarrier frequency assignment C and fixed monostatic topology, outage probability for specific tag n and given slot l ∈ L, can be upper bounded as: Proof. See Appendix 4.7.
It is worth emphasizing that the above outcome depends on both network topology (through E [m] n ), as well as subcarrier frequency assignment C (through parameter ρ(C) above).
As the dyadic fading channel parameters change independently among different slots, i.e., g l,n and g l ′ ,n are statistically independent for any l = l ′ ∈ L, we can offer outage expressions for operation over the L slots. Specifically, for a fixed subcarrier frequency assignment C, the monostatic information outage event for the n-th tag over L attempts (time slots) is the probability that n-th tag's SINR is below threshold θ over all L slots, i.e., where (a) is due to the fact that {g

Multistatic
For given subcarrier frequency channel assignment C, the instantaneous SINR of tag n for the l-th time slot is (4.29) The average SINR for multistatic case for any (l, n) ∈ L × N is given by: and subcarrier frequency assignment C, outage probability for tag n and slot l ∈ L is upper bounded as: l,n (C) Proof. The proof is provided in Appendix 4.7.
It is noted again that the above bound depends on tag location and network topology (through E l,n ), subcarrier frequency assignment C (through parameter ρ(C) above) and slot l (in contrast to the monostatic case), since at each slot different CE emits.
Accordingly with the monostatic case, for fixed subcarrier frequency assignment C and given threshold θ, the multistatic information outage probability of tag n operating over L time slots becomes: l,n (C) where (a) exploited the independence of SINR

Average Probability over Random Square Grids
In order to obtain topology-independent outage probabilities, expressions that average over possible topologies have to be obtained. Since, there are infinite classes of topologies to choose from, attention is restricted to the class of square M ×M grid network topologies used in practice. For simplicity, it is assumed that grid resolution ∆ divides M, i.e., M/∆ = K ∈ N and the set of 2-dimensional (2D) square grid points is denoted as follows: K,N is practically enormous, especially for large K, the averaging in this work is applied through Monte-Carlo, i.e., for a relatively large number of times, the following experiment is repeated: uniformly and random select a topology T

RF Harvesting
In contrast to the semi-passive tags assumed so-far, passive tags do not have a dedicated (ambient or not) energy source. Instead, passive tags harvest RF energy from the illuminating carrier(s).
For fixed CE, tag n, and SDR reader positions at the l-th time slot, the input power at the RF harvesting circuit of tag n is given by: h,l,n = P R L TnR (a l,TnR ) 2 , (4.35) h,l,n = P C l L C l Tn (a l,C l Tn ) 2 , (4.36) for monostatic and multistatic architecture, respectively. Energy outage (EO) event at tag n occurs when for all L time slots the received input power at tag n RF circuitry is below a threshold θ h , which models the sensitivity of the RF harvesting circuit, i.e., the input power threshold below which RF harvester offers zero power. 6 Mathematically, the EO event is defined as: h,l,n ≤ θ h ,  Table I]. Thus, energy outage event in (4.37) is given by: where γ(a, x) = x 0 t a−1 e −t dt is the lower incomplete gamma function. For the multistatic architecture, P [b] h,l,n is a Gamma RV with parameters M ln , h,l,n } l∈L are independent; as a result, the energy outage event in (4.38) can be simplified to: .
The average across all tags energy outage event is by taking the average of Eqs. (4.37) and (4.38) across all tags, i.e., (4.41) Another important metric that measures the worst-case energy outage is the maximum energy outage across all tags, i.e., It is emphasized again that the above outage probabilities depend on a specific multistatic or monostatic topology. Energy outage expressions that are topology-independent can be offered using averaging over the ensemble of square grid topologies as in Section 4.3.3.

Simulation Results
First the BER performance of monostatic and bistatic systems is examined for L = 1 slot and N = 1 tag. Rician fading parameters κ n = 10 and κ ln = 9 are used, setting M n = (κn+1) 2 2κn+1 = 5.7619 and M ln = (κ ln +1) 2 2κ ln +1 = 5.2632. Fig. 4.4-Left illustrates the exact BER performance under coherent and noncoherent reception for the two scatter radio architectures. Common SNR = SNR n is assumed, resulting to monostatic reader transmission power P R and bistatic carrier emitter power P C l related according to Eqs. (4.9), (4.14) P R = L C l ,Tn L Tn,R MnP C l Mn+1 . Any monostatic or bistatic topology offering the specific SNR is applicable to this plot. Upper bounds derived in Eq. (4.18) and Eq. (4.21) are also plotted. It can be seen that the bistatic architecture outperforms the monostatic and high-SNR slope is clearly different among the two architectures, as expected. Also, the derived upper bounds for coherent ML detection schemes coincide with the curves of noncoherent detection. Fig. 4.4-Right studies the BER performance as a function of SNR for a scenario where the tag is far-away from CE (possibly a few kilometers) but the tag-to-reader distance is relatively small (a few feet). This is a Rayleigh-Nakagami (Rice) scenario, that could be the case when the tag is illuminated by broadcasting stations and the receiver is close to the tag. In such scenario, the monostatic architecture is not applicable. Due to the large CE-to-tag distance, the link from CE-to-tag is assumed NLoS, i.e., κ ln = 0 and thus M ln = (κ ln +1) 2 2κ ln +1 = 1, while tag-to-reader link has strong LoS, thus, κ n = 10 with Fc m |Γ n,0 − Γ n,1 | = 2, ∀n s n = 0.1, ∀n M n = (κn+1) 2 2κn+1 = 5.7619. In such extreme case, where the monostatic architecture cannot be defined, the bistatic BER is less than 1% for received SNR values less than 17 dB (20 dB) under coherent (noncoherent) detection. The above demonstrate the potential benefits and flexibility of multistatic architecture in cases where CE is far away from tag.  Table 4.1. It can be seen that the average BER performance of a randomly placed tag (evaluated over several possible tag locations) is smaller in the bistatic architecture. It is also observed that the BER decay is faster in the bistatic compared to the monostatic architecture, corroborating the diversity gains offered by the bistatic system.  (Table 4.1). After sampling the grid topology, random PLEs ν ln ∼ U[2, 2.5] and ν n ∼ U[2, 2.5] are generated for link from l-th CE to n-th tag and link from n-th tag to SDR reader, respectively. In addition, to offer robustness against channel fading, after sampling the topology in the Nakagami fading scenarios, Nakagami parameters are randomly generated as follows: M ln ∼ U [1,5] and M n ∼ U [1,5], for link from l-th CE to n-th tag and link from n-th tag to SDR reader, respectively. For a fair comparison, equal transmission power for monostatic and multistatic architecture is utilized, setting P tx = P R = P C l , ∀l ∈ L. Considering a passive-tag BSN scenario, the topology-independent average and maximum energy outage probability is plotted in Fig. 4.7 (by averaging Eqs. (4.41) and (4.42) over several sampled grid topologies) as a function of harvesting threshold θ h under Nakagami fading, with P tx = 35 dBm and N = 8 tags. It is noted that the probability for a tag to be placed near a CE is higher in the multistatic architecture and thus, energy outage events are more frequent in the monostatic architecture. Energy outage is a performance bound for networks consisting of passive tags, since harvesting adequate energy is necessary for the tag to operate. It is worth noting that for energy outage probability of 10%, the multistatic architecture outperforms the monostatic by 4.5 dB for average and maximum outage performance. Finally, information outage is evaluated for a network of semi-passive tags. Since expressions in Eqs. (4.27) and (4.32) do not admit a closed-form, an extra Monte Carlo step is conducted after sampling the grid tag topology. Specifically, in the extra Monte Carlo phase, Rayleigh (M n = M ln = 1) and Nakagami small-scale fading coefficients are generated, as well as a random subcarrier assignment to the tags. For an allocation C, the c-th frequency pair is assigned to tag n if c = p C (n) ∈ N , where p C denotes the permutation associated with assignment C. The following parameters are utilized: T = 1 msec (i.e., 1 Kbps bitrate), ε n,j = 2 πT for all n, j ∈ N with n = j, and the subcarrier frequency pair for the n-th tag, F C n,0 , F C n,1 , is given by F C n,0 = (0.1 + c F sp ) MHz and F C n,1 = (0.1 + c F sp + F sp /5) MHz with F sp = 0.01 MHz, c = 1, 2, . . . , N. Hence, for a given channel assignment C, the coefficients in Eq.    Fig. 4.8 shows that for information outage 10% multistatic system outperforms monostatic by 3 dB in Rayleigh fading scenario, while for Nakagami fading the gap approaches 8 dB. The performance gap increases as threshold θ decreases. It can be also seen that the proposed bounds after averaging over all sampled tag locations are tight, especially for the multistatic architecture. It is clear again that the multistatic architecture offers higher reliability, as well as better coverage for scatter radio WSNs.

Experimental Results
Capitalizing upon the above promising results, a digital multistatic BSN is constructed, targeting on environmental and agriculture applications for ultra low-cost, microclimate monitoring around each plant [40]. The measured environmental quantities were: airhumidity, soil moisture, and temperature; all of them vary slowly as a function of time and thus, low bitrate (1 Kbps) per sensor was adequate. The communication among the tags and the reader was through subcarrier (switching) frequency division multiplexing (FDM), as explained in Section II; the CEs emitted a CW sinusoid in time division multiplexing (TDM) basis with transmission power 13 dBm over 868 MHz carrier frequency band.  Each prototype tag consisted of two distinct boards, the communication and the power board ( Fig. 4.9a). The communication board was applying the communication and sensing operations, including a 8-bit mixed-signal micro-controller unit (MCU) with analogto-digital converter, an RF transistor and input/output (I/O) pins for sensors' inputs. Binary scatter radio FSK modulation was implemented at the tags; 30 distinct orthogonal subcarrier frequency pairs could be produced. In order to increase the total number of tags while sustaining low-power operation, a "sleep" mode was implemented in all tags, with random "wake up". Thus, multiple tags could share the same pair of subcarrier frequencies with very small collision probability, increasing the total number of tags in the network, exploiting the utilized "sleep-scatter" duty cycle. In addition, a rate 1/2 Reed-Muller encoder was implemented at each MCU [74]. The tag was able to operate with a small solar panel during the daytime and a small coin cell battery during the night. The battery can be easily replaced by a super-capacitor at the power board [17], [101], [19].
Furthermore, in order to emulate a monostatic reader, the SDR reader and the CE were placed on the opposite sides of a metallic box. This structure provided good isolation between the transmit and the receive antennas, without using a circulator. The monostatic setup is depicted in Fig. 4.9b.
The outdoor measurement campaign consisted of two campaigns. In the first one, the maximum ranges of the tag-to-SDR links were found. The maximum range was determined when the BER was up to 5%. The multistatic architecture achieved tag-to-SDR reader ranges over 140 m, with CE-to-tag range in the order of 10 m. The maximum tag-to-SDR range for the monostatic system was in the order of 15 m, one order of magnitude smaller than the multistatic.
In the second campaign, coverage was examined in a field of 3500 m 2 area. For the multistatic architecture, two network topologies were deployed, one with three and one  with four CEs. In the first topology (shown in Fig. 4.10a), the SDR reader was placed at the right field corner, maximizing the tag-to-SDR reader distance, while the three CEs were placed around the field. In the second topology the reader was placed at the field center and the four CEs located as shown in Fig. 4.10b. For the monostatic architecture, multiple readers/CEs were deployed. Since the monostatic architecture's ranges were shorter, a total of eight readers were utilized, as shown in Fig. 4.10c. It should be remarked that using only four monostatic SDR readers at the same locations, at the same location where CEs were placed in the multistatic case, would offer a smaller monostatic coverage of 4 · π · 15 2 = 2827 m 2 .
From the second campaign we deduce that both architectures can cover similar areas provided that the monostatic architecture utilizes additional readers, incurring higher monetary cost. In sharp contrast, the multistatic architecture is more flexible and can offer greater ranges, even with one SDR reader and multiple low-cost CEs. Equivalently, with only one reader, the monostatic architecture would offer much smaller field coverage, compared to the multistatic, as clearly shown in Fig. 4.10a, Fig. 4.10b and Fig. 4.10c.

Appendix: Proofs of Chapter 4 Proof of Proposition 4.1
For Rayleigh fading, i.e., M n = 1, RV a [m] l,n = (a l,TnR ) 2 follows exponential distribution. Using Eq. (4.17), the unconditional probability of error over the l-th slot for the n-th tag is given by: By applying the rule of L'Hospital: Applying again the rule of L'Hospital:

Proof of Proposition 4.3
The PDF of RV g l,n = (a l,TnR ) 2 , which follows Gamma distribution with PDF given in Eq. (4.16). Using the formula in [60, p. 199], the required PDF for x ≥ 0 is l,n is simplified to f g [m] l,n (x) = 1 2 √ x e − √ x , x ≥ 0. The corresponding cumulative distribution function (CDF) is given by The monostatic outage probability for M n = 1 follows: l,n |I l,n 2 θ n (C) . (4.49) In (a), total interference at tag n for the monostatic system at the l-th time slot was defined as I [m] l,n (C) j∈A(n) ρ nj (C) g [m] l,j E

[m]
j ; step (b1) exploited the law of iterated expectation [89]; step (b2) exploited the assumed statistical independence between g [m] l,n and g [m] l,j for any j = n; step (c) utilized Jensen's inequality, taking into account the concavity of CDF in Eq. l,n for Rayleigh fading is needed, as well as proof of its concavity. Using M ln = M n = 1 in Eq. (4.19), the PDF is simplified to f g [b] l,n can be calculated as follows: l,n l,n l,n is shown by differentiating twice the CDF F g [b] l,n (x) and utilizing [84,Eq. (10.29.3)]: l,n l,n is concave and Eq. (4.31) follows using the same reasoning as in Proposition 4.3.

Resource Allocation in Multi-Cell Backscatter Sensor Networks
The topic of this chapter is devoted on alternative ultra-low-power, large-scale wireless sensor networks (WSNs) relying on scatter radio principles. The notion of multi-cell backscatter sensor networks (BSNs) is proposed: a few interrogators (or cores) that act as fusion centers and tags/sensors that are responsible for measuring environmental quantities, and transmitting the sensed information towards the cores constitute a multi-cell BSN. Cores use the conventional Marconi radio technology with front-ends consisting of active filters, mixers, and amplifiers, whereas tags/sensors use scatter principle to convey wirelessly the sensed information. To realize extended coverage with prolonged network sensor batteries lifetime, the ultimate goal in this chapter is to build multi-cell BSNs where the tag-to-core achievable range is maximized. First, a complete baseband multicell signal model is presented incorporating all scatter radio wireless channel parameters over dyadic Rician fading channel. A multi-tag channel estimation closed-form solution is proposed based on linear minimum mean-squared error (LMMSE) estimator. The average signal-to-interference-plus-noise ratio (SINR) of maximum-ratio combining (MRC) and zero-forcing (ZF) linear detectors is found and harnessed for frequency sub-channel allocation at tags. The proposed resource allocation algorithm, called Max-Sum algorithm, adheres to simple message-passing update rules and is executed over a factor graph at each core independently. The algorithm is very lightweight and converges to the optimal solution within very few iteration steps. Judicious simulation study reveals that ZF detector is more suitable for large-scale BSNs, capable to cancel out the intra-cell interference. The proposed sub-channel-tag allocation algorithm offers remarkable convergence-complexity trade-off. The outcome of this research can be used for practical receiver design and resource allocation in ultra-low-power, large-scale WSNs.

Related Work
Over the recent years, wireless communications and signal processing research on scatter radios has focused on point-to-point scenarios, where the reader decodes backscattered signals from a single tag. Very few works have offered concrete solutions on multi-tag scenarios, where the reader has to decode signals from multiple tags backscattering concurrently. To the best of our knowledge, no work has offered reception algorithms for multi-cell scatter radio network architectures, where multiple readers (or cores) aggregate sensed information from multiple tags in their vicinity. The last problem becomes even more complicated if one accounts the scatter radio aspect of the sensors/tags. Each tag in the field is illuminated by the superposition of cores' emitted carrier waves and backscattered to the nearby cores. The interference experienced at each core after the reception of multiple backscattered signals is from the tags within the cell formed by the core (i.e., intra-cell interference) as well as from the tags from other cells (i.e., inter-cell interference). To mitigate the resulting interference and efficiently assign frequency/time resources to receiver-less tags, sophisticated resource allocation algorithms accounting for the idiosyncrasies of scatter radio need to be designed at the cores.
Multi-tag reception algorithms found in scatter radio prior art are primarily designed for passive radio frequency (RF) tags and focus on single cell reception with a single receiver, e.g., radio frequency identification (RFID) systems, where an interrogator reads/decodes backscattered signals from tags in its vicinity. The first example of reliable backscatter communication with cell-like flavor is found in [17,83]. Work in [102] studied joint decoding algorithms for multi-tag reception based on clustering and expectationmaximization framework. Work in [103] designed reception algorithms for channel estimation and detection from multi-tag RFID signals exploiting multiple receive antennas at interrogator. Subsequent work [104] proposed multi-packet RFID reception algorithms for estimating the difference in delay and the tags frequency dispersion and then multi-tag detection was applied. Multi-tag decoding algorithms based on compressive sensing are designed in [105] exploiting several collisions at the receiver side.
Backscatter sensor networks (BSNs) are extremely power-limited due to the roundtrip nature of backscatter communication; even for free-space propagation loss, received power decays with the forth-power as a function of core-to-tag distance [32]. Especially, for passive tags the maximum achieved ranges is on the order of two to five metersfar from standards of large-scale, low-cost, ubiquitous sensing applications. As a result, increasing the coverage, or equivalently, increasing core-to-tag communication range, is of principle importance in low-cost, low-power BSNs. The authors in [94] offered coverage analysis for high-density, multi-cell BSNs and discovered that high coverage is feasible only if frequency-oriented modulation is harnessed at the tags. Coverage and capacity analysis for multi-cell BSNs using random Poisson cluster point processes is offered in [96].

Contributions
This chapter proposes a multi-cell BSN architecture with joint time-frequency multipleaccess following the guidelines from [13] and exploiting the know-how and the experimental experience of our group [11,12,17,33,37,39,82,83,86,106]. Several multi-antenna cores emit continuous sinusoid waves illuminating the tags in the field. A set of available orthogonal frequency sub-bands (also called sub-frequencies) is assumed available and each tag backscatters a packet of training (for channel estimation and synchronization) and data symbols modulated over a specific frequency sub-band. The packet is received and decoded at the closest core. To alleviate intra-cell interference during the training phase, the training sequences are orthogonal of each other and the tags using the same training sequence are configured to backscatter over different frequency sub-bands. A measurement phase is also considered where cores conduct signal-to-interference-plus-noise ratio (SINR) measurements with the tags in their cell. The frequency sub-channel allocation at tags changes during the measurement phase and the goal at each core is to assess the average SINR for each pair of neighboring tag-frequency sub-band. Subsequently, resource allocation based on a specific metric involving a function of estimated average SINR is applied to find the optimal assignment. Using the above multi-cell BSN framework, the contributions of this chapter can be summarized as: • • Using the average received SINR measurements associated with both linear detection techniques a generic formulation for resource allocation in BSNs is proposed. The formulated problem is attacked with a message-passing inference algorithm with simple update rules and convergence to the desired solution within very few steps.
The proposed algorithm is an instance of the Max-Sum algorithm.
• Judicious simulation study reveals that ZF generally outperforms MRC in terms of both bit error rate (BER) and outage probability. It is found that orthogonal training transmissions are mandatory to maintain good channel estimation accuracy. The proposed Max-Sum algorithm [107] offers the same optimal performance with classic convex optimization methods with reduced computational cost, measured in terms of execution time in large-scale BSNs.

Organization and Notation
The rest of this work is organized as follows. Section 5.1 presents the adopted wireless scatter radio channel model, Section 5.2 offers the multi-tag baseband signal model, while the proposed channel estimation closed-form solution along with the average SINR calculation for MRC and ZF linear detectors is provided in Section 5.3. Section 5.4 formulates the resource allocation optimization problem and designs the simple Max-Sum algorithm associated with the problem. Finally, simulation results are presented in Section 5.5.

Wireless Scatter Radio System Model
We consider a static multi-cell backscatter sensor network (BSN) consisting of B cores and K sensors/tags, an example is given in Fig. 5.1. Each core is a Marconi radio with separate transmit and receive antennas, e.g., a software define radio (SDR) reader. It is assumed that each core has N T transmit and N R receive antennas. Note that for simplification purposes monostatic architecture (with different transmit and receive antennas) is employed at each cell. Although, the proposed reception techniques can be also applied to the case of multistatic multi-cell architecture.
Due to relatively small delay spread, frequency non-selective (flat) fading channel [27] is assumed across all links (b, k) and (k, b), b ∈ B, k ∈ K. Moreover, for outdoor environments, common in wireless sensor network applications, there exist possible strong line-of-sight propagation paths. Hence, incorporating all the above in wireless channel model, the baseband complex channel response for links (b, k) and (k, b) is given by where κ d bk and κ u kb denote the ratio between the power in the direct path and the power in the scattered paths of core-to-tag link (b, k) and tag-to-core link (k, b), respectively, e d bk and e u bk are the antenna steering vectors at core b for the transmit and received antennas, respectively, depending on antenna array geometry with e d where ϕ d bk and ϕ u kb denote the angle-of-departure (AoD) for link (b, k) and angle-of-arrival (AoA) for link (k, b), respectively, λ denotes the propagation wavelength, and D y is the antenna spacing (usually D y = λ 2 ). The normalized channel powers σ 2 kb and σ 2 kb depend on large-scale path-gain (inverse of path-loss) which, due to reciprocity theorem, is the same for links (b, k) and (k, b), i.e., σ bk = σ kb .
When a tag k ∈ K reflects information, it backscatters a packet of M symbols, where each symbol within packet takes values {±1}. A fraction τ tr of total packet duration is dedicated for channel estimation while the rest 1 − τ tr is used for data transmission, i.e., the total number of training symbols is M tr = τ tr M ∈ N, while the rest M d = M − M tr are data symbols and depend on the sensed information. There is a set of available pilot sequences X tr = x (1) , x (2) , . . . , x (Mtr) ⊂ {±1} Mtr , i.e., set X tr contains M tr sequences, each of dimension M tr . The sequences in set X tr are orthogonal, i.e., The sequence assigned to tag k has been decided a-priori and is assumed fixed. In a practical scenario, to reduce the interference, the same sequence has to be reused across To obtain accurate resource allocation exploiting long-term information, a periodic measurement process is conducted divided in several time frames; each frame has duration equal to the channel coherence time. During the measurement process each core conducts (independently from the rest ones) signal-to-interference-plus-noise ratio (SINR) measurements with tags in its vicinity. Frequency sub-band allocation changes from frame to frame while tag sequence assignment is assumed fixed across all frames for simplicity in implementation. Section 5.3.2 offers a detailed exposition on the proposed average SINR estimation procedure.
The following sets are defined K Mtr (m) k ∈ K : tag k uses training sequence x (m) , (5.6) It is not difficult to see that set K can be partitioned as To minimize intra-cell interference, during the training phase for each frame of the measurements, we consider orthogonal training transmissions, i.e., tags sharing the same training sequence are configured to transmit at different frequency sub-bands. In other words, tags within the same cell are assigned to a unique pair (m, c) ∈ M tr × C, i.e., |K bmc | ≤ 1. The goal at each core b is to estimate the average SINR for each pair (k, c) ∈ K B (b)×C, by changing tag-channel allocation (i.e., set K C (c)) across different frames.

Multi-Cell and Multi-tag Processing
Each core b ∈ B emits from each transmit antenna a continuous sinusoid wave with baseband representation P b N T e jφ b , where P b is the total transmission power and φ b is the phase mismatch between transmit and receive circuitry at core b and is assumed fixed and known. The superposition of cores' emitted signals, propagated across downlink channels {h d bk } b∈B , incidents at the antenna of tag k, i.e., tag k receives B Using similar ideas developed in [12,37,39] each tag k employees joint frequency and amplitude modulation and backscatters towards core b where η k is the scattering efficiency, remaining constant within packet duration, Γ k,0 and Γ k,1 are the (load-dependent) reflection coefficients, DC k is a DC term depending on antenna structural mode as well as on reflection coefficients Γ k,0 and Γ k,1 and does not depend on time t, and v kb (t) is the reflected waveform of tag k. Waveform v kb (t) is the fundamental frequency component of a 50% duty cycle square waveform of period is the sum-indicator function of statement X. f k and Φ kb in (5.10) are the generated frequency of tag k and the random phase mismatch between tag k and core b, respectively.
Phases Φ kb are modeled as uniform RVs in [0, 2π), assumed independent and identically distributed (IID) across different k. If the m-th training sequence and the c-th frequency sub-channel are assigned to tag k, then {x k,i } Mtr i=1 = x (m) ∈ X tr and f k = f (c) . Tag frequency sub-channels satisfy the following for some l c ∈ N, implying that for Random phase mismatch, as well as the uplink and downlink channels are independent of each other. Moreover, all data symbols are independent across all tags and time instants and P(x k,i = ±1) = 1 2 , ∀k ∈ K, ∀i ∈ M d . Core b receives the superposition of {u kb (t)} k∈K , propagated by uplink channels {h u kb } k∈K , i.e., where the components of w b (t) are independent circularly symmetric, complex Gaussian noise processes with flat power spectral density (PSD) N 0 over [−W b , W b ] frequency band, and zero otherwise, i.e., where F{·} denote the Fourier transform, applied element-wise, and parameter W b denotes the receiver bandwidth at core b.
Signal in (5.13) contains DC terms, thus, the time average is removed. After DCblocking filtering, signal y b (t) = y b (t) − T 0 y b (t)dt is formed, where [0, MT ) ⊆ T 0 , and T 0 is the time processing interval. Note that T 0 y b (t)dt ≈ k∈K h u kb DC k holds true, due to (a) the linearity of integration, (b) a+T a cos(2πf k t + Φ kb ) dt = 0 for every a ∈ R since f k = l T , for some l ∈ N, and (c) the fact that the components of w b (t) are zero-mean random processes. Hence, abbreviating ∀k ∈ K and plugging Eq. (5.10) in (5.9) and then substituting in (5.13), the DC-blocked signal y b (t) can be written as x k,i cos(2πf k (t − (i − 1)T )+Φ kb ) Π T (t + (i − 1)T ) + w b (t). (5.16) Theorem 5.1. For W b ≫ 1 T , when multiple tags are backscattering, the baseband equivalent signal at core b, associated with c-th frequency sub-band, at the i-th time instant is given by r where ξ is the compound (uplink) channel between tag k ∈ K and core b at the output of c-th frequency matched filter, incorporating microwave and wireless propagation parameters, while noise vector n Proof. The proof is provided in Appendix 5.6.
By the independence of small-scale fading coefficients and Φ kb across all tags k ∈ K, compound uplink channel vectors {ξ (c) kb } k∈K are independent of each other. In addition, for a tag k ∈ K bmc vector ξ (c) kb is trivially independent from the rest {ξ

Channel Estimation and SINR Calculation
Assuming that the first M tr symbols correspond to the pilot sequence, the training signal associated with the c-th sub-band at core b can be expressed compactly as Thus, due to the orthogonality of {x (m) } m∈Mtr , the training signal associated with tag k ∈ K bmc at core b can be written as . It is remarked that training signal r (c) b,tr associated with tag k ∈ K bmc does not contain intra-cell interference terms, including only interference from tags of neighboring cells utilizing the same pair (m, c) with tag k.
Before proceeding to the proposed channel estimator the following proposition is needed.

Proposition 5.1. For vectors {ξ
In this work the linear minimum mean-squared error (LMMSE) estimator for parameter vector ξ (c) kb is used.
In addition, vector ξ (c) kb and error vector ǫ kb are uncorrelated. The mean and the covariance of vector ǫ Proof.
where the sum over the set K C (c) is decomposed across two terms, the first pertains to intra-cell interference, i.e., the tags in K C (c) within cell b (i.e., k ∈ K B (b) ∩ K C (c) = m ′ ∈Mtr K bm ′ c ), while the second one accounts for the inter-cell interference associated with tags in K C (c) that do not belong in cell b (i.e., k ∈ b ′ =b m ′ ∈Mtr K b ′ m ′ c ). Note that core b can estimate the corresponding ξ (c) kb for all tags in its cell, i.e., k ∈ m ′ ∈Mtr K bm ′ c and thus, by the properties of LMMSE estimator, the compound uplink channel can be written as ξ (c)

Multi-Tag Linear Detection
Core b treats the channel estimate ξ (c) kb for user k ∈ K bmc as the actual uplink compound channel and applies linear detection using ξ (c) kb . For linear detection, a linear transformation is applied on received signal and the sign of the outcome is used as the estimated symbol. Applying linear transformation a (c) kb on received vector r For each k ∈ K B (b), the estimate of x k,i is given by , where the q-th element of set K B (b) ∩ K C (c) satisfies l q = k. Note that ZF detector tries to mitigate the intra-cell interference coming from tags using the same sub-band with tag k since for kb as the true channel, and the part including the last three terms inside parenthesis of (5.24) is considered as interference and noise. Thus, using the independence of zero-mean {ǫ b,i , the received signal-to-interference-plus-noise ratio (SINR) for tag k ∈ K bmc is given by where intra-cell (I 1(c) k,b ) and inter-cell (I 2(c) k,b ) interference terms are given, respectively, by (5.28) Note that for N R ≥ K bc and ZF detection the first term in Eq. (5.27) becomes zero. In addition, it is worth-noting that SINR in (5.26) depends on estimated ξ (c) kb as well as on quantities that are known to the core and change very slowly with the time due to the staticness of the cores and the tags.

Measuring the Long-Term SINR
The SINR in (5.26) depends on ξ (c) kb which in turn changes every coherence period. To apply robust frequency allocation an average SINR across many channel and frequency allocation realizations has to be calculated. To this end, a measurement procedure is employed by all cores and tags to obtain long-term SINR information for subsequent frequency allocation.
Each tag is assigned to a fixed preamble sequence across the whole measurement phase, while the channel allocation of each tag changes in a per frame basis. Each frame has time duration equal to the channel coherence time T coh . Let us denote J the total number of frames for the measurement phase, while set J {1, 2, . . . J} denotes the set of all measurement frame indexes. For a core b and a tag k ∈ K B (b), let us denote J (c) kb the measurements indexes which tag k is assigned to sub-band f (c) . For each tag k ∈ K B (b) core b calculates the received SINR in (5.26) for the frames indexed by set J

Problem Formulation
After obtaining the average SINR estimates SINR (c) kb for all tuples {(k, b, c) ∈ K × B × C : k ∈ K B (b)} all cores try to obtain frequency sub-channel-tag assignment that maximizes a specific metric involving the estimated received SINRs. Using the average received SINR instead of instantaneous SINR, the impact of random intra-and inter-interference is averaged out, and thus, the optimization problem can be decoupled to B parallel subproblems across all cores without significant performance loss.
The proposed formulation to obtain the optimal tag-frequency sub-channel association is expressed at each core individually through the following optimization problem where g : R + −→ R is an arbitrary increasing function. Resource allocation variables v kc indicate either if tag k ∈ K backscatters on the c-th frequency sub-band (v kc = 1) or not (v kc = 0). Constraint (5.30b) imposes that a frequency sub-band f (c) can be assigned to at most one tag in K bm , ∀m ∈ M tr , For constraint (5.30c), each tag has to be assigned to one frequency sub-channel. From a practical point of view, constraint (5.30b) offers intra-cell pilot interference cancellation by assigning all tags in cell b to a unique pair (m, c) ∈ M tr × C of sequence x (m) and frequency sub-band f (c) , causing orthogonal training transmissions. In doing so, the channel estimate obtained for the tag k ∈ K bmc is contaminated only by the tags from other cells that use the same frequency sub-band f (c) along with the m-th training sequence (i.e., k ∈ For set K B (b), the corresponding assignment matrix is defined V b {v kc : ∀(k, c) ∈ K B (b) × C}. The following functions are also defined for all cores b ∈ K B (b): where the last two functions (factors) are associated with constraints (5.30b) and (5.30c), respectively; for a statement X, function I{X} is the max-indicator function defined as The integer programming problem in (5.30) belongs to the class of maximum weighted matching problems [111,112]

Factor Graph Construction
A FG expresses factorizations as the one in Eq. (5.36), consisting of factor nodes and variable nodes. Each factor node in the FG is connected through an edge to a variable node if the corresponding factor has input the specific variable. In the optimization problem (

Proposed Algorithm
For a given FG, the standard Max-Sum message-passing rules can be derived to find the optimal configuration for tag-sub-channel association matrix V b that maximizes the objective function in (5.30) and satisfies the constraints (5.30b)-(5.30d).

Convergence and Complexity Analysis
Note that the underlying FG associated with Eq. (5.36) contains cycles and generally convergence cannot be guaranteed for the FGs with cycles. Fortunately, for the class of the FGs corresponding to weighed matching problems, Max-Sum algorithm always converges to a fixed point which is also the exact solution. Invoking the convergence results derived in [114] for and O(C |K B (b)|) arithmetic operations, respectively. Thus, the overall per iteration complexity is dominated by lines (4)- (11). The algorithm iterates at most n max times, and thus, the overall computation cost of Algorithm 3 becomes O(n max (C |K B (b)| 2 + C 2 |K B (b)|)). From simulation results it is noticed that 5 to 10 iterations usually suffice for the algorithm to converge to the desired solution for all studied setups.
The problem in (5.30) can be transformed to a LP, where constraint (5.30d) is relaxed to v kc ∈ [0, 1], ∀(k, c) ∈ K B (b)×C. The relaxed LP problem can be solved through standard convex optimization interior point methods [115]. However, we choose to solve (5.30) with Max-Sum message-passing framework due to its low per-iteration cost and its fast convergence rate, observed through simulations. Simulation results also demonstrated that the proposed Max-Sum algorithm could offer the same optimal solution with classic interior point solvers requiring smaller execution time.

Simulation Results
The multi-cell BSN topology of Fig. 5.3 is studied, consisting of B = 21 cores and K = 500 tags. Cores (blue squares) are placed in a cellular setting [27] and the distance of neighboring cores is √ 3R core , where R core = 10 meters. The height of all cores (i.e., their z coordinate) is 2 meters. Tags (yellow circles) are placed randomly in the vicinity of cores. Their height is a uniform random variable in [0, 1]. The adopted path-loss model is given by [27]   where ν bk is the path-loss exponent for link (b, k) (same for (k, b)), d bk is the distance from core b to tag k, while d 0 is a reference distance. All considered wireless and noise parameters are shown in Table 5.1. For simplicity, common backscatter reflection coefficients are considered for all tags k ∈ K, with Γ k,0 = 0.92 and Γ k,1 = −0.91. The tag scattering efficiency is assumed common for all tags, given by η k = 20%, ∀k ∈ K. The random phase mismatch at each core b ∈ B is assumed zero, i.e., φ b = 0. The transmission power of each core is the same, i.e., P b = P tx , ∀b ∈ B. AoA ϕ d bk and AoD ϕ u kb are considered fixed and known for any pair (k, b) ∈ K × B. The BSN has C = 15 available frequency sub-channels and M = 8 orthogonal training sequences. Each sub-channel is given by T , with T = 0.1 msec. Finally, set X M comprises of the columns of the M × M Hadamard matrix [116].

Average BER
In the first scenario we compare ZF and MRC multi-tag linear detectors in terms of their bit error rate (BER). The corresponding average BER performance across all tags is The average BER performance is tested as a function of both transmission power and the number of receive antennas, assuming N T = 1 transmit antennas. For channel estimation phase, tags within the same cell employ unique pairs (m, c) ∈ M tr × C (orthogonal transmissions). Fig. 5.4 studies the average BER performance in Eq. (5.41) of MRC and ZF detectors as a function of transmission power P tx under different receive antennas setups. It can be observed that increasing the transmission power does not reduce the average BER performance. This stems from the fact that both useful signal power as well as interference depend linearly on transmission power (cf. Eq. (5.26)) and thus there is a saturation effect on total received SINR. Fig. 5.5 depicts the BER performance as a function of N R for P tx = 15 dBm. In contrast to transmission power, as can be seen in Fig. 5.5, the impact of receive antennas is significant in average BER performance for multi-tag system. It is observed that increasing the number of receive antennas offers diversity gains for both linear detectors, diminishing the average BER. The performance of ZF is slightly better compared to MRC because the former mitigates the interference coming from tags sharing the same frequency sub-band in the same cell, i.e., intra-cell interference.

Average Outage Probability
Next, we study the impact of orthogonal versus nonorthogonal pilot transmission on average outage performance. When a tag k ∈ K B (b) backscatters at frequency sub-band f (c) , an outage event occurs if P SINR

Performance of Max-Sum Algorithm
Using the same parameters as in previous paragraph, J = 5000 SINR measurements are obtained to estimate the average (long-term) SINR according to Eq. (5.29). The proposed θ (dB)  algorithm is executed to obtain the optimal assignment of variables {v kc } (k,c)∈K×C , using parameters g(x) = x, x ≥ 0, n max = 50, α = 0.1, and ǫ = 10 −4 . The specific value for the objective tries to maximize the sum of average SINRs, although other metrics could be employed. Fig. 5.7 compares the sum of average SINR performance across all tags as a function of transmission power. As expected, for both ZF and MRC, the proposed Max-Sum algorithm offers the same optimal performance with relaxed LP technique and both outperform orthogonal training transmissions for which tags of the same cell use unique pairs (m, c) ∈ M tr × C, i.e., an orthogonal tag-sub-channel assignment is a feasible assignment in optimization problem (5.30). The results for orthogonal tag-sub-channel assignments 5 10 15 20  have been averaged over 1000 Monte Carlo experiments. It can be remarked that the gap between ZF and MRC is negligible. This performance gap among the optimal assignment (Max-Sum and relaxed LP) and a feasible assignment (orthogonal transmissions) tends to slightly increase as the transmission power increases. Fig. 5.8 shows how fast the proposed algorithm converges to the optimal V ⋆ b and how many iterations are required until termination criterion is reached for cores 3 and 15. Only 3-4 iterations of the proposed algorithm are required for convergence to the optimal solution for both MRC and ZF linear detectors. For all cores the algorithm terminated after 10-15 iterations on the average, and for all cases the termination criterion of NMAE in soft estimates below ǫ was met. The above demonstrates the potential benefits of the proposed Max-Sum algorithm, since per iteration complexity is small and convergence is accomplished within few steps.
Finally, one important question would be why one should use the proposed algorithm instead of classic LP to solve the studied optimization problem in (5.30). To this end, the proposed algorithm was compared with CVX convex optimization solver [117] in terms of average execution time across all cores. For the simulations, MATLAB R2016a was used on a desktop computer with 32-bit operating system and Intel(R) Core(TM)2 Quad CPU at 2.83 GHz. The proposed algorithm was implemented with a custom MATLAB script, while the solution of LP relaxed problem was obtained by CVX solver. Table 5 where in (a), Fubini theorem [61] is employed along with the linearity of expectation. Equality (b) follows from the definition of the autocorrelation matrix function of complex white Gaussian noise process w b (t), C w b (t − t ′ ) = E w b (t) w b (t ′ ) H , which stems from the fact that the noise process is also wide-sense stationary [80,Chapter 2.7]. In (c), we use: (i) the definition of convolution operation given by the inverse Fourier transform

Proof of Proposition 5.1
The proof for mean value is relying on the following identity E[cos(a + Φ kb )] = 0, ∀a ∈ R, (5.50) which in turn stems from the fact that Φ kb ∼ U[0, 2π). Thus, E[ξ For the calculation of the covariance, it is noted that RV ventional scatter radio technology verifying the efficacy of the proposed scatter radio reception schemes.
It was clearly shown that the multistatic scatter radio architecture offers more reliable reception as well as better field coverage, while demonstrating smaller sensitivity to the topology of the tags, compared to the monostatic architecture. It is demonstrated under realistic Nakagami small-scale fading scenarios and path-loss models that not only the BER decay is doubled in a multistatic architecture compared to a monostatic one, but also, energy and information outage events are less frequent in multistatic systems due to the flexible morphology of the multistatic WSN architecture. A concrete experimental proof-of-concept scenario for large-scale and reliable scatter radio networks is also offered.
For the first time in the scatter radio literature a complete signal model for multicell backscatter sensor networks (BSNs) is presented, incorporating the idiosyncrasies of scatter radio wireless models under realistic Rician small-scale fading and path-loss models. A new closed-form channel estimation procedure is designed to estimate the tagto-reader compound uplink channels for every cell. The average SINR of two multi-tag linear detectors is found and harnessed for resource allocation. To allocate frequency subchannels to the tags, a generic optimization problem is formulated. The proposed resource allocation algorithm has very simple update rules and attains the performance of classic convex optimization algorithms with very small computational cost. It was shown that convergence to the desired solution can be obtained within very few iteration steps.
The dissertation concludes with a discussion of some research directions that are a natural extension of the problems considered.

SDR
Software-defined radio SINR Signal-to-interference-plus-noise ratio SNR Signal-to-noise ratio TDMA Time-division multiple access SWIPT Simultaneous wireless information and power transfer WSN Wireless sensor network ZF Zero-forcing