The increasing complexity of heterogeneous cellular networks (HetNets) due to the irregular deployment of small cells demands significant rethinking in the way cellular networks are perceived, modeled and analyzed. In addition to threatening the relevance of classical models, this new network paradigm also raises questions regarding the feasibility of state-of-the-art simulation-based approach for system design. This dissertation proposes a fundamentally new approach based on random spatial models that is not only tractable but also captures current deployment trends fairly accurately. First, this dissertation presents a general baseline model for HetNets consisting of K different types of base stations (BSs) that may differ in terms of transmit power, deployment density and target rate. Modeling the locations of each class of BSs as an independent Poisson Point Process (PPP) allows the derivation of surprisingly simple expressions for coverage probability and average rate. One interpretation of these results is that adding more BSs or tiers does not necessarily change the coverage probability, which indicates that fears of "interference overload" in HetNets are probably overblown. Second, a flexible notion of BS load is incorporated by introducing a new idea of conditionally thinning the interference field. For this generalized model, the coverage probability is shown to increase when lightly loaded small cells are added to the existing macrocellular networks. This is due to the fact that owing to the smaller loads, small cells typically transmit less often than macrocells, thus contributing less to the interference power. The same idea of conditional thinning is also shown to be useful in modeling the non-uniform user distributions, especially when the users lie closer to the BSs. Third, the baseline model is extended to study multi-antenna HetNets, where BSs across tiers may additionally differ in terms of the number of transmit antennas, number of users served and the multi-antenna transmission strategy. Using novel tools from stochastic orders, a tractable framework is developed to compare the performance of various multi-antenna transmission strategies for a fairly general spatial model, where the BSs may follow any general stationary distribution. The analysis shows that for a given total number of transmit antennas in the network, it is preferable to spread them across many single-antenna BSs vs. fewer multi-antenna BSs. Fourth, accounting for the load on the serving BS, downlink rate distribution is derived for a generalized cell selection model, where shadowing, following any general distribution, impacts cell selection while fading does not. This generalizes the baseline model and all its extensions, which either ignore the impact of channel randomness on cell selection or lumps all the sources of randomness into a single random variable. As an application of these results, it is shown that in certain regimes, shadowing naturally balances load across various tiers and hence reduces the need for artificial cell selection bias. Fifth and last, a slightly futuristic scenario of self-powered HetNets is considered, where each BS is powered solely by a self-contained energy harvesting module that may differ across tiers in terms of the energy harvesting rate and energy storage capacity. Since a BS may not always have sufficient energy, it may not always be available to serve users. This leads to a notion of availability region, which characterizes the fraction of time each type of BS can be made available under variety of strategies. One interpretation of this result is that the self-powered BSs do not suffer performance degradation due to the unreliability associated with energy harvesting if the availability vector corresponding to the optimal system performance lies in the availability region. / text

Device-to-device (D2D) networking enables direct discovery and communication between cellular subscribers that are in proximity, thus bypassing the base stations (BSs). In principle, exploiting direct communication between nearby mobile devices will improve spectrum utilization, overall throughput, and energy consumption, while enabling new peer-to-peer and location-based applications and services. D2D-enabled broadband communication technology is also required by public safety networks that must function when cellular networks are not available. Integrating D2D into cellular networks, however, poses many challenges and risks to the long-standing cellular architecture, which is centered around the BSs. This dissertation identifies outstanding technical challenges in D2D-enabled cellular networks and addresses them with novel models and fundamental analysis. First, this dissertation develops a baseline hybrid network model consisting of both ad hoc nodes and cellular infrastructure. This model uses Poisson point processes to model the random and unpredictable locations of mobile users. It also captures key features of multicast D2D including multicast receiver heterogeneity and retransmissions while being tractable for analytical purpose. Several important multicast D2D metrics including coverage probability, mean number of covered receivers per multicast session, and multicast throughput are analytically characterized under the proposed model. Second, D2D mode selection which means that a potential D2D pair can switch between direct and cellular modes is incorporated into the hybrid network model. The extended model is applied to study spectrum sharing between cellular and D2D communications. Two spectrum sharing models, overlay and underlay, are investigated under a unified analytical framework. Analytical rate expressions are derived and applied to optimize the design of spectrum sharing. It is found that, from an overall mean-rate perspective, both overlay and underlay bring performance improvements (vs. pure cellular). Third, the single-antenna hybrid network model is extended to multi-antenna transmission to study the interplay between massive MIMO (multi-input multiple-output) and underlaid D2D networking. The spectral efficiency of such multi-antenna hybrid networks is investigated under both perfect and imperfect channel state information (CSI) assumptions. Compared to the case without D2D, there is a loss in cellular spectral efficiency due to D2D underlay. With perfect CSI, the loss can be completely overcome if the number of canceled D2D interfering signals is scaled appropriately. With imperfect CSI, in addition to pilot contamination, a new asymptotic underlay contamination effect arises. Finally, motivated by the fact that transmissions in D2D discovery are usually not or imperfectly synchronized, this dissertation studies the effect of asynchronous multicarrier transmission and proposes a tractable signal-to-interference-plus-noise ratio (SINR) model. The proposed model is used to analytically characterize system-level performance of asynchronous wireless networks. The loss from lack of synchronization is quantified, and several solutions are proposed and compared to mitigate the loss. / text

On étudie une équation différentielle stochastique animée par un processus ponctuel de Poisson, qui modélise un changement continu de lénvironnement d'une population et la fixation stochastique de mutations bénéfiques pour compenser ce changement. La probabilité de fixation d'une mutation augmente dès que le retard phénotypique $X_t$ entre la population et l'optimum augmente. On suppose que les mutations favorables se fixent instantanément induisant un saut adaptatif. En premier lieu, on a étudié le comportement à long terme de la solution de cette équation sachant qu'on ne considère qu'un seul trait phénotypique de la population et on a trouvé les conditions sous lesquelles $X_t$ est récurrent (possibilité de survie) ou transient (extinction inévitable). Ensuite, on a généralisé nos résultats en considérant un vecteur de traits phénotypiques de la population, essentiellement dans $mathbb R^2$. A la fin, on introduit une limite des petits sauts pour caractériser et comprendre le cas récurrent. / We study a stochastic differential equation driven by a Poisson point process, which models continuous changes in a population's environment, as well as the stochastic fixation of beneficial mutations that might compensate for this change. The fixation probability of a given mutation increases as the phenotypic lag $X_t$ between the population and the optimum grows larger, and successful mutations are assumed to fix instantaneously (leading to an adaptive jump). First, we study the large time behavior of the solution of this SDE taking into consideration one phenotypic trait of the population and we find the conditions under which $X_t$ is recurrent (possibility of survival) or transient (doomed to exctinction).Then we generalize our results to the case of a phenotypic traits vector, essentially in $R^2$. Finally, we introduce a small jumps limit to characterize and understand the recurrent case.

Abstract In this thesis we study the spatial throughput of interference-limited wireless networks from different perspectives, considering that the spatial distribution of nodes follows a 2-dimensional homogeneous Poisson point process and transmitters employ Gaussian point-to-point codes. To carry out this analysis, we model the interrelations between network elements using concepts from stochastic geometry, communication theory and information theory. We derive closed-form equations to compute/approximate the performance metric that is chosen to evaluate the system for each given specific scenario. Our first contribution is an investigation about whether it is preferable to have a large number of short single-hop links or a small number of long hops in multi-hop wireless networks, using a newly proposed metric denominated aggregate multi-hop information efficiency. For single-hop systems, we revisit the transmission capacity framework to study medium access protocols that use asynchronous transmissions and allow for packet retransmissions, showing when a carrier sensing capability is more suitable than synchronous transmissions, and vice-versa. We also cast the effective link throughput and the network spatial throughput optimization problems to find the combination of medium access probability, coding rate and maximum number of retransmissions that maximize each metric under packet loss and queue stability constraints, evincing when they do (and do not) have the same solution. Furthermore we analyze the expected maximum achievable sum rates over a given area – or spatial capacity – based on the capacity regions of Gaussian point-to-point codes for two decoding rules, namely (i) treating interference as noise (IAN) and (ii) jointly detecting the strongest interfering signals treating the others as noise (OPT), proving the advantages of the second. We additionally demonstrate that, when the same decoding rule and network density are considered, the spatial-capacity-achieving scheme always outperforms the spatial throughput obtained with the best predetermined fixed rate strategy. With those results in hand, we discuss general guidelines on the construction of ad hoc adaptive algorithms that would improve the information flow throughout the interference network, respecting the nodes’ internal and external constraints. / Tiivistelmä Tässä työssä tutkitaan häiriörajoitteisten langattomien verkkojen tila-alueen suorituskykyä, olettaen verkkosolmujen sijoittuvan 2-ulotteisen Poissonin pisteprosessin mukaisesti, sekä olettaen lähettimien hyödyntävän Gaussisia pisteestä-pisteeseen -koodeja. Suorituskykyanalyysi pohjautuu stokastiseen geometriaan, tietoliikenneteoriaan sekä informaatioteoriaan. Suljetun muodon suorituskyky-yhtälöitä hyödyntäen arvioidaan suorityskykymetriikoita eri skenaarioissa. Työn aluksi esitetään uusi monihyppyverkkojen informaatiotehokkuuteen perustuva metriikka. Sen avulla voidaan tutkia onko tehokkaampaa käyttää useita lyhyen hypyn linkkejä vai pienempää määrää pidempien hyppyjen linkkejä. Yhden hypyn verkoissa tutkitaan mediaanpääsyprotokollia asynkronisissa verkoissa pakettien uudelleenlähetykseen perustuen ja verrataan tätä synkroniseen lähetykseen ilman vapaan kanavan tunnistusmekanismia. Työssä tutkitaan myös linkin efektiivisen suorituskyvyn ja verkon tila-alueen suorituskyvyn optimointia, jotta sopiva yhdistelmä mediaan pääsyn todennäköisyydelle, koodausnopeudelle ja uudelleenlähetysten maksimilukumäärälle löytyisi ja samalla maksimoisi jokaisen käytetyn metriikan ehdollistettuna paketin menetyksille ja jonon stabiilisuudelle. Lisäksi arvioidaan maksimaalista odotettavaa nettosiirtonopeutta tietyllä alueella, eli tila-alueen kapasiteettia, Gaussimaisen pisteestä-pisteeseen koodien kapasiteettialueisiin perustuen kahta eri dekoodaussääntöä hyödyntäen: (i) olettaen häiriön olevan kohinaa tai (ii) ilmaisemalla voimakkaimmat häiriösignaalit ja olettaen muiden olevan kohinaa. Jälkimmäinen osoittautui tehokkaammaksi menetelmäksi. Työssä osoitetaan myös, että samalla dekoodaussäännöllä ja verkon tiheydellä tila-alueen kapasiteetin saavuttava menetelmä on aina tehokkaampi kuin tavanomainen tila-alueen suorituskykyyn perustuva kiinteän siirtonopeuden menetelmä. Saavutettujen tulosten valossa työssä esitetään yleisiä suunnittelumenetelmiä mukautuville ad hoc -algoritmeille, joiden avulla voidaan parantaa tiedonsiirtoa häiriörajoitteisissa verkoissa, ehdollistettuna verkon solmujen sisäisille ja ulkoisille rajoitteille.

L’objectif principal de cette thèse est l’analyse des performances des réseaux LTE-A (Long Term Evolution- Advanced) au travers de la géométrie stochastique. L’analyse mathématique des réseaux cellulaires est un problème difficile, pour lesquels ils existent déjà un certain nombre de résultats mais qui demande encore des efforts et des contributions sur le long terme. L’utilisation de la géométrie aléatoire et des processus ponctuels de Poisson (PPP) s’est avérée être une approche permettant une modélisation pertinente des réseaux cellulaires et d’une complexité faible (tractable). Dans cette thèse, nous nous intéressons tout particulièrement à des modèles s’appuyant sur ces processus de Poisson : PPP-based abstraction. Nous développons un cadre mathématique qui permet le calcul de quantités reflétant les performances des réseaux LTE-A, tels que la probabilité d’erreur, la probabilité et le taux de couverture, pour plusieurs scénarios couvrant entre autres le sens montant et descendant. Nous considérons également des transmissions multi-antennes, des déploiements hétérogènes, et des systèmes de commande de puissance de la liaison montante. L’ensemble de ces propositions a été validé par un grand nombre de simulations. Le cadre mathématique développé dans cette thèse se veut général, et doit pouvoir s’appliquer à un nombre d’autres scénarios importants. L’intérêt de l’approche proposée est de permettre une évaluation des performances au travers de l’évaluation des formules, et permettent en conséquences d’éviter des simulations qui peuvent prendre énormément de temps en terme de développement ou d’exécution. / The main focus of this thesis is on performance analysis and system optimization of Long Term Evolution - Advanced (LTE-A) cellular networks by using stochastic geometry. Mathematical analysis of cellular networks is a long-lasting difficult problem. Modeling the network elements as points in a Poisson Point Process (PPP) has been proven to be a tractable yet accurate approach to the performance analysis in cellular networks, by leveraging the powerful mathematical tools such as stochastic geometry. In particular, relying on the PPP-based abstraction model, this thesis develops the mathematical frameworks to the computations of important performance measures such as error probability, coverage probability and average rate in several application scenarios in both uplink and downlink of LTE-A cellular networks, for example, multi-antenna transmissions, heterogeneous deployments, uplink power control schemes, etc. The mathematical frameworks developed in this thesis are general enough and the accuracy has been validated against extensive Monte Carlo simulations. Insights on performance trends and system optimization can be done by directly evaluating the formulas to avoid the time-consuming numerical simulations.

Cette thèse porte principalement sur la modélisation, l'évaluation des performances et l'optimisation au niveau système des réseaux cellulaires de nouvelle génération à l'aide de la géométrie stochastique. En plus, la technologie émergente des surfaces intelligentes reconfigurables (RISs) est étudiée pour l'application aux futurs réseaux sans fil. En particulier, reposant sur un modèle d’abstraction basé sur la loi de Poisson pour la distribution spatiale des nœuds et des points d’accès, cette thèse développe un ensemble de nouveaux cadres analytiques pour le calcul d’importantes métriques de performance, telles que la probabilité de couverture et l'efficacité spectrale potentielle, qui peuvent être utilisés pour l'analyse et l'optimisation au niveau système. Plus spécifiquement, une nouvelle méthodologie d'analyse pour l'analyse de réseaux cellulaires tridimensionnels est introduite et utilisée pour l'optimisation du système. Un nouveau problème d’allocation de ressources est formulé et résolu en combinant pour la première fois géométrie stochastique et programmation non linéaire mixte en nombres entiers. L'impact du déploiement de surfaces réfléchissantes intelligentes sur un réseau sans fil est quantifié à l'aide de processus ponctuels, et les avantages potentiels des RISs contre le relais sont étudiés à l'aide de simulations numériques. / The main focus of this thesis is on modeling, performance evaluation and system-level optimization of next-generation cellular networks by using stochastic geometry. In addition, the emerging technology of Reconfigurable Intelligent Surfaces (RISs) is investigated for application to future wireless networks. In particular, relying on a Poisson-based abstraction model for the spatial distribution of nodes and access points, this thesis develops a set of new analytical frameworks for the computation of important performance metrics, such as the coverage probability and potential spectral efficiency, which can be used for system-level analysis and optimization. More specifically, a new analytical methodology for the analysis of three-dimensional cellular networks is introduced and employed for system optimization. A novel resource allocation problem is formulated and solved by jointly combining for the first time stochastic geometry and mixed-integer non-linear programming. The impact of deploying intelligent reflecting surfaces throughout a wireless network is quantified with the aid of line point processes, and the potential benefits of RISs against relaying are investigated with the aid of numerical simulations.

In this thesis, new methods for proving concentration inequalities for Poisson functionals are developed. The focus is on techniques that are based on logarithmic Sobolev inequalities, but also results that are based on the convex distance for Poisson processes are presented. The general methods are applied to a variety of functionals associated with random geometric graphs. In particular, concentration inequalities for subgraph and component counts are proved. Finally, the established concentration results are used to derive strong laws of large numbers for subgraph and component counts associated with random geometric graphs.

We construct and investigate random geometric structures that are based on a homogeneous Poisson point process. We investigate the random Vietoris-Rips complex constructed as the clique complex of the well known gilbert graph as an infinite random simplicial complex and prove that every realizable finite sub-complex will occur infinitely many times almost sure as isolated complex and also in the case of percolations connected to the unique giant component. Similar results are derived for the Cech complex. We derive limit theorems for the f-vector of the Vietoris-Rips complex on the unit cube centered at the origin and provide a central limit theorem and a Poisson limit theorem based on the model parameters. Finally we investigate random polytopes that are given as convex hulls of a Poisson point process in a smooth convex body. We establish a central limit theorem for certain linear combinations of intrinsic volumes. A multivariate limit theorem involving the sequence of intrinsic volumes and the number of i-dimensional faces is derived. We derive the asymptotic normality of the oracle estimator of minimal variance for estimation of the volume of a convex body.

With the increasing maturity of unmanned aerial vehicles (UAVs), also known as drones, wireless ecosystem is experiencing an unprecedented paradigm shift. These aerial platforms are specifically appealing for a variety of applications due to their rapid and flexible deployment, cost-effectiveness, and high chance of forming line-of-sight (LoS) links to the ground nodes. As with any new technology, the benefits of incorporating UAVs in existing cellular networks cannot be characterized without completely exploring the underlying trade space. This requires a detailed system-level analysis of drone cellular networks by taking the unique features of UAVs into account, which is the main objective of this dissertation. We first focus on a static setup and characterize the performance of a three-dimensional (3D) two-hop cellular network in which terrestrial base stations (BSs) coexist with UAVs to serve a set of ground user equipment (UE). In particular, a UE connects either directly to its serving terrestrial BS by an access link or connects first to its serving UAV which is then wirelessly backhauled to a terrestrial BS (joint access and backhaul). We consider realistic antenna radiation patterns for both BSs and UAVs using practical models developed by the third generation partnership project (3GPP). We assume a probabilistic channel model for the air-to-ground transmission, which incorporates both LoS and non-LoS links. Assuming the max-power association policy, we study the performance of the network in both amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. Using tools from stochastic geometry, we analyze the joint distribution of distance and zenith angle of the closest (and serving) UAV to the origin in a 3D setting. Further, we identify and extensively study key mathematical constructs as the building blocks of characterizing the received signal-to-interference-plus-noise ratio (SINR) distribution. Using these results, we obtain exact mathematical expressions for the coverage probability in both AF and DF relaying protocols. Furthermore, considering the fact that backhaul links could be quite weak because of the downtilted antennas at the BSs, we propose and analyze the addition of a directional uptilted antenna at the BS that is solely used for backhaul purposes. The superiority of having directional antennas with wirelessly backhauled UAVs is further demonstrated via extensive simulations. Second, we turn our attention to a mobile setup and characterize the performance of several canonical mobility models in a drone cellular network in which UAV base stations serve UEs on the ground. In particular, we consider the following four mobility models: (i) straight line (SL), (ii) random stop (RS), (iii) random walk (RW), and (iv) random waypoint (RWP), among which the SL mobility model is inspired by the simulation models used by the 3GPP for the placement and trajectory of UAVs, while the other three are well-known canonical models (or their variants) that offer a useful balance between realism and tractability. Assuming the nearest-neighbor association policy, we consider two service models for the UEs: (i) UE independent model (UIM), and (ii) UE dependent model (UDM). While the serving UAV follows the same mobility model as the other UAVs in the UIM, it is assumed to fly towards the UE of interest in the UDM and hover above its location after reaching there. We then present a unified approach to characterize the point process of UAVs for all the mobility and service models. Using this, we provide exact mathematical expressions for the average received rate and the session rate as seen by the typical UE. Further, using tools from the calculus of variations, we concretely demonstrate that the simple SL mobility model provides a lower bound on the performance of other general mobility models (including the ones in which UAVs follow curved trajectories) as long as the movement of each UAV in these models is independent and identically distributed (i.i.d.). Continuing our analysis on mobile setups, we analyze the handover probability in a drone cellular network, where the initial positions of the UAVs serving the ground UEs are modeled by a homogeneous Poisson point process (PPP). Inspired by the mobility model considered in the 3GPP studies, we assume that all the UAVs follow the SL mobility model, i.e., move along straight lines in random directions. We further consider two different scenarios for the UAV speeds: (i) same speed model (SSM), and (ii) different speed model (DSM). Assuming nearest-neighbor association policy, we characterize the handover probability of this network for both mobility scenarios. For the SSM, we compute the exact handover probability by establishing equivalence with a single-tier terrestrial cellular network, in which the BSs are static while the UEs are mobile. We then derive a lower bound for the handover probability in the DSM by characterizing the evolution of the spatial distribution of the UAVs over time. After performing these system-level analyses on UAV networks, we focus our attention on the air-to-ground wireless channel and attempt to understand its unique features. For that, we first study the impact of UAV wobbling on the coherence time of the wireless channel between UAVs and a ground UE, using a Rician multi-path channel model. We consider two different scenarios for the number of UAVs: (i) single UAV scenario (SUS), and (ii) multiple UAV scenario (MUS). For each scenario, we model UAV wobbling by two random processes, i.e., the Wiener and sinusoidal processes, and characterize the channel autocorrelation function (ACF) which is then used to derive the coherence time of the channel. For the MUS, we further show that the UAV-UE channels for different UAVs are uncorrelated from each other. One key observation that is revealed from our analysis is that even for small UAV wobbling, the coherence time of the channel may degrade quickly, which may make it difficult to track the channel and establish a reliable communication link. Finally, we develop an impairments-aware air-to-ground unified channel model that incorporates the effect of both wobbling and hardware impairments, where the former is caused by random physical fluctuations of UAVs, and the latter by intrinsic radio frequency (RF) nonidealities at both the transmitter and receiver, such as phase noise, in-phase/quadrature (I/Q) imbalance, and power amplifier (PA) nonlinearity. The impact of UAV wobbling is modeled by two stochastic processes, i.e., the canonical Wiener process and the more realistic sinusoidal process. On the other hand, the aggregate impact of all hardware impairments is modeled as two multiplicative and additive distortion noise processes, which is a well-accepted model. For the sake of generality, we consider both wide-sense stationary (WSS) and nonstationary processes for the distortion noises. We then rigorously characterize the ACF of the wireless channel, using which we provide a comprehensive analysis of four key channel-related metrics: (i) power delay profile (PDP), (ii) coherence time, (iii) coherence bandwidth, and (iv) power spectral density (PSD) of the distortion-plus-noise process. Furthermore, we evaluate these metrics with reasonable UAV wobbling and hardware impairment models to obtain useful insights. Similar to our observation above, this work again demonstrates that the coherence time severely degrades at high frequencies even for small UAV wobbling, which renders air-to-ground channel estimation very difficult at these frequencies. / Doctor of Philosophy / With the increasing maturity of unmanned aerial vehicles (UAVs), also known as drones, wireless ecosystem is changing dramatically. Owing to their ease of deployment and high chance of forming direct line-of-sight (LoS) links with the other UAVs and ground users, they are very appealing for numerous wireless applications. As with any new technology, exploring the full extent of the benefits of UAVs requires careful exploration of the underlying trade space. Therefore, in this dissertation, our main focus is on the analysis of such aerial networks, their interplay with the current terrestrial networks, and the unique features of UAVs that make them different from conventional ground nodes. One important aspect of aerial communication systems is their integration into our current cellular networks. Clearly, the addition of these new aerial components has the potential of benefiting both the ground users (such as mobile users watching a concert who need cellular connectivity to share the moments) and the cellular base station (BS). Therefore, careful analysis of these ``aerial-terrestrial" networks is of utmost importance. In the first phase of this dissertation, we perform this analysis by interpreting the network as a combination of one-hop (from the BS to the user) and two-hop (from the BS to the UAV and then from the UAV to the UE) links. Since the locations of BSs, UAVs, and users are irregular in general, we use tools from stochastic geometry to carry out our analysis, which is a field of mathematics that studies random shapes and patterns. Also, because existing terrestrial BSs are primarily designed to serve the ``ground", we propose the addition of a separate set of antennas at the BS site that is solely used to serve the ``air", i.e., to communicate with the UAVs, and demonstrate the benefits of this additional infrastructure in detail. One of our assumptions in the first phase of this dissertation was that the considered network was static, i.e., the UAVs were hovering in the air and the BSs/users were also not moving. In the second phase, on the other hand, we explore the benefits and challenges of a mobile network of UAVs and characterize the performance of several canonical mobility models in a drone cellular network. In particular, one of the models that we studied extensively is the so-called straight line (SL) mobility model, which was inspired by the simulation models used by the third generation partnership project (3GPP) for the placement and trajectory of UAVs. Since the locations of UAVs could be assumed random in general, we use tools from stochastic geometry and present a unified approach to characterize the point process of UAVs, using which we obtained exact mathematical expressions for the average received rate (i.e., throughput) as seen by the users. Continuing our analysis on mobile setups and using the SL mobility model, we also analyze the handover probability in a drone cellular network, which is defined as the event when the serving UAV of a user changes. By establishing equivalence between our aerial setup with a terrestrial cellular network, we compute the exact handover probability in drone cellular networks. In the final phase of this dissertation, we focus our attention on the air-to-ground wireless channel and attempt to understand its unique features. For that, we propose an impairments-aware unified channel model for an air-to-ground wireless communication system and extensively analyze the link between a hovering UAV in the air and a static user on the ground. In particular, we consider two different types of impairments: (i) UAV wobbling, and (ii) hardware impairments, where the former is caused by random physical fluctuations, and the latter by intrinsic radio frequency (RF) nonidealities at both the transmitter and receiver. Using appropriate models for each type of impairment, we rigorously characterize the autocorrelation function (ACF) of the wireless channel, using which we provide a comprehensive analysis of key channel-related metrics, such as coherence time and coherence bandwidth. One key observation that is revealed from our analysis is that even for small UAV wobbling and low hardware impairment levels, the coherence time of the channel may degrade quickly at high frequencies, which could make it difficult to track the channel and establish a reliable communication link at these frequencies.

The success of the Internet-of-Things (IoT) paradigm relies on, among other things, developing energy-efficient communication techniques that can enable information exchange among billions of battery-operated IoT devices. With its technological capability of simultaneous information and energy transfer, ambient backscatter is quickly emerging as an appealing solution for this communication paradigm, especially for the links with low data rate requirements. However, many challenges and limitations of ambient backscatter have to be overcome for widespread adoption of the technology in future wireless networks. Motivated by this, we study the design and implementation of ambient backscatter systems, including non-coherent detection and encoding schemes, and investigate techniques such as multiple antenna interference cancellation and frequency-shift backscatter to improve the bit error rate performance of the designed ambient backscatter systems. First, the problem of coherent and semi-coherent ambient backscatter is investigated by evaluating the exact bit error rate (BER) of the system. The test statistic used for the signal detection is based on the averaging of energy of the received signal samples. It is important to highlight that the conditional distributions of this test statistic are derived using the central limit theorem (CLT) approximation in the literature. The characterization of the exact conditional distributions of the test statistic as non-central chi-squared random variable for the binary hypothesis testing problem is first handled in our study, which is a key contribution of this particular work. The evaluation of the maximum likelihood (ML) detection threshold is also explored which is found to be intractable. To overcome this, alternate strategies to approximate the ML threshold are proposed. In addition, several insights for system design and implementation are provided both from analytical and numerical standpoints. Second, the highly appealing non-coherent signal detection is explored in the context of ambient backscatter for a time-selective channel. Modeling the time-selective fading as a first-order autoregressive (AR) process, we implement a new detection architecture at the receiver based on the direct averaging of the received signal samples, which departs significantly from the energy averaging-based receivers considered in the literature. For the proposed setup, we characterize the exact asymptotic BER for both single-antenna (SA) and multi-antenna (MA) receivers, and demonstrate the robustness of the new architecture to timing errors. Our results demonstrate that the direct-link (DL) interference from the ambient power source leads to a BER floor in the SA receiver, which the MA receiver can avoid by estimating the angle of arrival (AoA) of the DL. The analysis further quantifies the effect of improved angular resolution on the BER as a function of the number of receive antennas. Third, the advantages of utilizing Manchester encoding for the data transmission in the context of non-coherent ambient backscatter have been explored. Specifically, encoding is shown to simplify the detection procedure at the receiver since the optimal decision rule is found to be independent of the system parameters. Through extensive numerical results, it is further shown that a backscatter system with Manchester encoding can achieve a signal-to-noise ratio (SNR) gain compared to the commonly used uncoded direct on-off keying (OOK) modulation, when used in conjunction with a multi-antenna receiver employing the direct-link cancellation. Fourth, the BER performance of frequency-shift ambient backscatter, which achieves the self-interference mitigation by spatially separating the reflected backscatter signal from the impending source signal, is investigated. The performance of the system is evaluated for a non-coherent receiver under slow fading in two different network setups: 1) a single interfering link coming from the ambient transmission occurring in the shifted frequency region, and 2) a large-scale network with multiple interfering signals coming from the backscatter nodes and ambient source devices transmitting in the band of interest. Modeling the interfering devices as a two dimensional Poisson point process (PPP), tools from stochastic geometry are utilized to evaluate the bit error rate for the large-scale network setup. / Doctor of Philosophy / The emerging paradigm of Internet-of-Things (IoT) has the capability of radically transforming the human experience. At the heart of this technology are the smart edge devices that will monitor everyday physical processes, communicate regularly with the other nodes in the network chain, and automatically take appropriate actions when necessary. Naturally, many challenges need to be tackled in order to realize the true potential of this technology. Most relevant to this dissertation are the problems of powering potentially billions of such devices and enabling low-power communication among them. Ambient backscatter has emerged as a useful technology to handle the aforementioned challenges of the IoT networks due to its capability to support the simultaneous transfer of information and energy. This technology allows devices to harvest energy from the ambient signals in the environment thereby making them self-sustainable, and in addition provide carrier signals for information exchange. Using these attributes of ambient backscatter, the devices can operate at very low power which is an important feature when considering the reliability requirements of the IoT networks. That said, the ambient backscatter technology needs to overcome many challenges before its widespread adoption in IoT networks. For example, the range of backscatter is limited in comparison to the conventional communication systems due to self-interference from the power source at a receiver. In addition, the probability of detecting the data in error at the receiver, characterized by the bit error rate (BER) metric, in the presence of wireless multipath is generally poor in ambient backscatter due to double path loss and fading effects observed for the backscatter link. Inspired by this, the aim of this dissertation is to come up with new architecture designs for the transmitter and receiver devices that can improve the BER performance. The key contributions of the dissertation include the analytical derivations of BER which provide insights on the system design and the main parameters impacting the system performance. The exact design of the optimal detection technique for a communication system is dependent on the channel behavior, mainly the time-varying nature in the case of a flat fading channel. Depending on the mobility of devices and scatterers present in the wireless channel, it can either be described as time-selective or time-nonselective. In the time-nonselective channels, coherent detection that requires channel state information (CSI) estimation using pilot signals can be implemented for ambient backscatter. On the other hand, non-coherent detection is preferred when the channel is time-selective since the CSI estimation is not feasible in such scenarios. In the first part of this dissertation, we analyze the performance of ambient backscatter in a point-to-point single-link system for both time-nonselective and time-selective channels. In particular, we determine the BER performance of coherent and non-coherent detection techniques for ambient backscatter systems in this line of work. In addition, we investigate the possibility of improving the BER performance using multi-antenna and coding techniques. Our analyses demonstrate that the use of multi-antenna and coding can result in tremendous improvement of the performance and simplification of the detection procedure, respectively. In the second part of the dissertation, we study the performance of ambient backscatter in a large-scale network and compare it to that of the point-to-point single-link system. By leveraging tools from stochastic geometry, we analytically characterize the BER performance of ambient backscatter in a field of interfering devices modeled as a Poisson point process.