This paper examines the number of communication modes, that is, the degrees of freedom (DoF), in a wireless line-of-sight channel comprising a small continuous linear intelligent antenna array in the near field of a large one. The framework allows for any orientations between the arrays and any positions in a two-dimensional space, assuming that the transmitting array is placed at the origin. Therefore, apart from the length of the two continuous arrays, four key parameters determine the DoF and are hence considered in the analysis: the Cartesian coordinates of the center of the receiving array and two angles that model the rotation of each array around its center. The paper starts with the calculation of thedeterministicDoF for a generic geometric setting, which extends beyond the widely studied paraxial case. Subsequently, a stochastic geometry framework is proposed to study thestatisticalDoF, as a first step towards the investigation of system-level performance in near field networks. Numerical results applied to millimeter wave networks reveal the large number of DoF provided by near-field communications and unveil key system-level insights. A comparison of the proposed method with the singular value decomposition-based method is illustrated to validate the proposed approach.

In this paper, we propose a two-stage weighted projection method (TS-WPM) for time-difference-of-arrival (TDOA)-based localization, providing provable improvements in positioning accuracy, particularly under high geometric dilution of precision (GDOP) and low signal-to-noise ratio (SNR) conditions. TS-WPM employs a two-stage iterative refinement approach that dynamically updates both range and position estimates, effectively mitigating residual errors while maintaining computational efficiency. Additionally, we extend TS-WPM to support cooperative localization by leveraging two-way time-of-arrival (TW-TOA) measurements, which enhances positioning accuracy in scenarios with limited anchor availability. To analyze TS-WPM, we derive its error covariance matrix and mean squared error (MSE), establishing conditions for its optimality and robustness. To facilitate rigorous evaluation, we develop a 3rd Generation Partnership Project (3GPP)-compliant analytical framework, incorporating 5G New Radio (NR) physical layer aspects as well as large-scale and small-scale fading. As part of this, we derive a generalized Cramér-Rao lower bound (CRLB) for multipath propagation and introduce a novel non-line-of-sight (NLOS) bias model that accounts for propagation conditions and SNR variations. Our evaluations demonstrate that TS-WPM achieves near-CRLB performance and consistently outperforms state-of-the-art weighted nonlinear least squares (WNLS) in high GDOP and low SNR scenarios. Moreover, cooperative localization with TS-WPM significantly enhances accuracy, especially when an insufficient number of anchors (such as 2) are visible. Finally, we analyze the computational complexity of TS-WPM, showing its balanced trade-off between accuracy and efficiency, making it a scalable solution for real-time localization in next-generation networks.

Most data-driven localization approaches rely on fingerprinting-based techniques, which require labor-intensive site surveys and periodic calibration to maintain accuracy. These efforts limit the scalability of fingerprinting-based methods. This paper presents a calibration-free approach for indoor localization using crowdsourced data without requiring location labels. The statistical information of the crowdsourced data is utilized to learn the signal propagation characteristics. We apply a cumulative distribution function (CDF) conversion to map signal strength measurements to distances from access points. This CDF conversion overcomes the limitations of the conventional logdistance path loss (LDPL) model and efficiently captures the effect of shadow fading and multipath. Based on the estimated distances, the target locations are determined using an improved trilateration algorithm. Our approach is fully unsupervised, requiring no location labels, and significantly reduces the need for site surveys. Experimental results demonstrate substantial improvements in localization performance compared to LDPL-based methods. Moreover, our localization accuracy using unlabeled data approaches that of the$k$-Nearest-Neighbor algorithm, which relies on labeled fingerprints.

Understanding beamshaping in reconfigurable intelligent surfaces (RIS) is crucial for practical deployment, especially with the recent emphasis on self-configuring RISs. However, accurate beamshaping must account for factors such as mutual coupling and structural scattering. This paper proposes a beamshaping framework for physically consistent RISs using a modified signal model that bridges communication theory and multiport network theory. By focusing on desired beam and null locations, we enable pre-calculation of RIS channel gain matrices, reducing computational complexity. The optimization problems are then solved using constrained simulated annealing (CSA). Numerical simulations validate the framework by demonstrating wide beam and null formation and the necessity of discrete optimization for accurate beamshaping with less than 7 bits of discrete control. Results also reveal that ignoring mutual coupling in structural scattering leads to a notable decline in null quality.

In this paper, we derive the fundamental limits of low earth orbit (LEO) enabled localization by analyzing the available information in signals from multiple LEOs during different transmission time slots received on a multiple antennas and evaluate the utility of these signals for 9D localization (3D position, 3D orientation, and 3D velocity estimation). We start by deriving the Fisher Information Matrix (FIM) for the channel parameters that are present in the signals received from LEOs in the same or multiple constellations during multiple transmission time slots. To accomplish this, we define a system model that captures i) time offset between LEOs caused by having relatively cheap clocks, ii) frequency offset between LEOs, iii) the unknown Doppler rate caused by high mobility LEOs, and iv) multiple transmission time slots from a particular LEO. We transform the FIM for the channel parameters to the FIM for the location parameters and determine the required conditions for localization. To do this, we start with the 3D localization cases: i) 3D positioning with known velocity and orientation, ii) 3D orientation estimation with known position and velocity, and iii) 3D velocity estimation with known position and orientation. Subsequently, we derive the FIM for the full 9D localization case (3D position, 3D orientation, and 3D velocity estimation) in terms of the FIM for the 3D localization. Using these results, we determine the number of LEOs, the operating frequency, the number of transmission time slots, and the number of receive antennas that allow for different levels of location estimation. We then provide insights into the interaction between the number of LEOs, the operating frequency, the number of transmission time slots, and the number of receive antennas. One key result is that in the presence of time and frequency offsets and Doppler rate, it is possible to perform 9D localization (3D position, 3D velocity, and 3D orientation estimation) of a receiver by utilizing the signals from three LEO satellites observed during three transmission time slots received through multiple receive antennas.

Wireless positioning in Non-Line-of-Sight (NLoS) scenarios presents significant challenges due to multipath effects that lead to biased measurements and reduced positioning accuracy. This paper revisits electromagnetic field theory related to diffraction and in the context of wireless positioning and proposes a novel positioning technique that greatly improves accuracy in NLoS environments dominated by diffraction. The method is applied to a critical public safety use case: precisely locating at-risk individuals within buildings, with a particular focus on improving 3D positioning and z-axis accuracy. By leveraging the Geometrical Theory of Diffraction (GTD), the approach introduces an innovative NLoS path length model and a new NLOS positioning technique. Using Fisher information analysis, we establish the conditions required for 3D positioning and derive lower bounds on positioning performance for both 3D and z-axis estimates for the proposed NLOS positioning technique. Additionally, we propose an algorithmic implementation of the proposed NLoS positioning method using non-linear least squares estimation, which we term D-NLS. The positioning performance of our proposed NLOs positioning technique is validated using an extensive ray-tracing simulation. The numerical results highlight the superiority of our approach in outdoor-to-indoor environments, which directly estimates NLoS path lengths and delivers significant performance enhancements over existing methods for both 3D and z-axis positioning scenarios.

This paper considers a communication system where a source sends time-sensitive information to its destination via queues in tandem. We assume that the arrival process as well as the service process (of each server) are memoryless, and each of the servers has no buffer. For this setup, we develop a recursive framework to characterize the mean peak age of information (PAoI) under preemptive and non-preemptive policies with$N$servers having different service rates. For the preemptive case, the proposed framework also allows to obtain mean age of information (AoI).

In this paper, we rigorously derive the information in the signals received from low earth orbit (LEO) satellites, which are unsynchronized in time and frequency, and their utility for 3D position estimation. To enable this derivation, we define a system model that captures i) the time offset between LEOs caused by having cheap clocks, ii) the frequency offset between LEOs, and iii) multiple transmission time slots from a particular LEO. After this definition, we derive the Fisher information matrix (FIM) for the relevant channel parameters and transform the FIM for the channel parameters to the FIM for the 3D position. These derivations show the interactions between the number of LEOs, the operating frequency, the number of transmission time slots, and the number of receive antennas. Subsequently, these allow us to determine the minimal number of LEOs, the number of transmission time slots, and the number of receive antennas needed to determine the 3D position. One key result is that when the LEOs are unsynchronized in time and frequency and experience a high Doppler rate, the 3D position can be determined by observing a single LEO for four transmission time slots.

Large antenna arrays and reconfigurable intelligent surfaces (RIS) have been made available due to the use of higher frequency bands, and there is the possibility that these arrays can become disturbed. Hence, their orientation could change after deployment. Since low earth orbits (LEO) are being proposed to provide position, navigation, and timing services, and LEOs from different constellations could be unsynchronized in time and frequency and experience a high Doppler rate. We ask, "can unsynchronized LEOs provide 3D orientation for a ground receiver?" To answer this question, we introduce the Fisher information matrix (FIM) and use the FIM to quantify the available information needed for 3D orientation estimation utilizing signals received from LEOs during multiple transmission time slots across multiple receive antennas. We observe by analyzing the positive definitiveness of the FIM for the 3D orientation that irrespective of the presence or absence of both time and frequency offsets, the 3D orientation of the receiver can be estimated through the multiple TOA measurements received across the receive antennas from two LEO satellites during a single transmission time slot. We also observe by analyzing the positive definitiveness of the FIM for the 3D orientation that irrespective of the presence or absence of both time and frequency offsets, the 3D orientation of the receiver can be estimated through the multiple TOA measurements received across the receive antennas during two transmission time slots from a single LEO satellite.

We investigate a vision-aided integrated sensing and communications (ISAC) system comprising a transmitter, a receiver and a vision sensor (such as a camera) co-located with the receiver. The vision-aided ISAC system uses the vision sensor to sense the environment and share the vision data with the receiver. The receiver decodes the transmitted message using the received signal and the vision data. Even though this vision data may not completely determine the channel impulse response, some information about the environment, such as whether the transmitter is visible from the receiver, could be potentially useful for decoding. The objective of this paper is to understand the value of such information, termed channel state knowledge, using an information-theoretic formalism. We examine three scenarios in which the vision sensor provides different amounts of channel state knowledge to the receiver: perfect, imperfect, and none. Further, we analyze the mutual information for the vision-aided ISAC system using joint and sequential processing approaches and demonstrate that the system with the joint processing of vision data and communication signals has higher mutual information. This analysis provides crucial insights into the performance limits of vision-aided ISAC systems.

A novel stochastic geometry framework is proposed in this paper to study the downlink coverage performance in a millimeter wave (mmWave) cellular network by jointly considering the polar coordinates of the Base Stations (BSs) with respect to the typical user located at the origin. Specifically, both the Euclidean and the angular distances of the BSs in a maximum power-based association policy for the user equipment (UE) are considered to account for realistic beam management considerations, which have been largely ignored in the literature, especially in the cell association phase. For completeness, two other association schemes are considered and exact-form expressions for the coverage probability are derived. Subsequently, the key role of angular distances is highlighted by defining the dominant interferer using angular distance-based criteria instead of Euclidean distance-based, and conducting a dominant interferer-based coverage probability analysis. Among others, the numerical results reveal that considering angular distance-based criteria for determining both the serving and the dominant interfering BS, can approximate the coverage performance more accurately as compared to utilizing Euclidean distance-based criteria. To the best of the authors’ knowledge, this is the first work that rigorously explores the role of angular distances in the association policy and analysis of cellular networks.

This paper develops fundamental bounds for localization in orthogonal frequency division multiplexing (OFDM) systems aided by reconfigurable intelligent surfaces (RISs). Specifically, we start from the assumption that the position and orientation of a RIS can be viewed as prior information for RIS-aided localization in wireless systems and derive Bayesian bounds for the localization of a user equipment (UE). To do this, we first derive the Bayesian Fisher information matrix (FIM) for channel parameters to derive the Bayesian localization bounds. Then, to focus on the geometric channel parameters, we derive the equivalent Fisher information matrix (EFIM) and show that it has a definite structure. Subsequently, we show through the information loss associated with the EFIM that when the RIS reflection coefficients remain constant across all OFDM symbols, and there is no prior information about the nuisance parameters, the corresponding submatrix in the EFIM related to the RIS angle parameters is a zero matrix. As a result of the EFIM being a zero matrix, estimating the RIS-related angle channel parameters is not possible when the RIS reflection coefficients remain constant across all OFDM symbols. This observation is crucial for the estimation of the RIS-related angle parameters. It dictates that to estimate the RIS-related angle parameters, there must be more than one OFDM transmission with differing RIS reflection coefficients. Furthermore, due to this observation, we note that localization of a single antenna UE through the signals received from reflections from a single RIS to the UE is not feasible in the far-field when the RIS reflection coefficients remain constant across all OFDM symbols. We also show that the FIM for the RIS-related channel parameters can be decomposed into i) information provided by the receiver, ii) information provided by the transmitter, and iii) information provided by the RIS components. We then transform the Bayesian EFIM for geometric channel parameters to the Bayesian FIM for the UE position and orientation parameters and examine its specific structure under a particular class of RIS reflection coefficients.

Terahertz (THz) communication signals are susceptible to severe degradation because of the molecular interaction with the atmosphere in the form of subsequent absorption and re-radiation. Recently, reconfigurable intelligent surface (RIS) has emerged as a potential technology to assist in THz communications by boosting signal power or providing virtual line-of-sight (LOS) paths. However, the re-radiated energy has either been modeled as a scattering component or as additive Gaussian noise in the literature. Since the precise characterization is still a work in progress, this paper presents the first comparative investigation of the performance of an RIS-aided THz system under these two extreme re-radiation models. In particular, we first develop a novel parametric channel model that encompasses both models of the re-radiation through a simple parameter change, and then utilize that to design a robust block-coordinate descent (BCD) algorithmic framework which maximizes a lower bound on channel capacity while accounting for imperfect channel state information (CSI). In this framework, the original problem is split into two sub-problems: a) receive beamformer optimization, and b) RIS phase-shift optimization. As the latter sub-problem (unlike the former) has no analytical solution, we propose three approaches for it: a) semi-definite relaxation (SDR) (high complexity), b) signal alignment (SA) (low complexity), and c) gradient descent (GD) (low complexity). The time complexities associated with the proposed approaches are explicitly derived. We analytically demonstrate the limited interference suppression capability of a passive RIS by deriving the stationary points of signal-to-interference and noise ratio (SINR) of a one-element RIS system with one interferer. Our numerical results also demonstrate that slightly better throughput is achieved when the re-radiation manifests as scattering.

The use of reconfigurable intelligent surfaces (RIS) can improve wireless communication by modifying the wireless link to create virtual line-of-sight links, bypass blockages, suppress interference, and enhance localization. However, enabling the RIS to modify the wireless channel requires careful optimization of the RIS phase-shifts. Although discrete RIS is more practical given hardware limitations, continuous RIS phase-shift optimization has attracted significantly more attention than discrete RIS optimization, which suffers from issues like quantization error and scalability. To overcome these issues, we develop a comprehensive probabilistic technique to transform discrete optimization problems into optimization problems of continuous domain probability parameters by interpreting the discrete optimization variable as a categorical random vector and computing expectations with respect to those parameters. We rigorously establish that for the unconstrained case, the optimal points of the reformulation and the original problem coincide. For the constrained case, we prove that the transformed problem is a relaxation of the original problem. We apply the proposed technique to two canonical discrete RIS applications: SINR maximization and overhead-aware rate and energy efficiency (EE) maximization. The reformulation enables both stochastic and analytical interpretations of the original problems, as we demonstrate in our RIS applications. The former interpretation yields a stochastic sampling technique, whereas the latter yields an analytical gradient descent (GD) approach that employs closed-form approximations for the expectation. We have explicitly derived the worst-case computational complexities of the proposed algorithms. The numerical results demonstrate that the proposed technique is applicable to a variety of discrete RIS optimization problems and outperforms other general approaches, such as closest point projection (CPP) and semidefinite relaxation (SDR) methods.

We present a comprehensive approach to the modeling and design of clustered molecular bio-nanonetworks in which nano-machines of different clusters release an appropriate number of molecules to transmit their sensed information to their respective fusion centers. The fusion centers decode this information by counting the number of molecules received in the given time slot. Owing to the propagation properties of the biological media, this setup suffers from both inter- and intra-cluster interference that needs to be carefully modeled. We first develop a novel spatial model for this setup by modeling nano-machines as a Poisson cluster process with the fusion centers forming its parent point process. For this setup, we then derive a new set of distance distributions in the three-dimensional space, resulting in a remarkably simple result for the special case of the Thomas cluster process. Accordingly, total interference from previous symbols and different clusters is characterized and its expected value is obtained. Then, using the expected value, a simple detector suitable for biological applications is proposed. The impact of different parameters on the performance of the detector is also investigated.

This paper presents a rigorous examination of the estimation of the misorientation of a reconfigurable intelligent surface (RIS) based on the received signal when the user equipment (UE) is in the near or far fields of the RIS. The Bayesian analysis views the location of the RISs as a priori system-level information. With incorrect a priori information, the position and orientation offsets of the RISs become parameters that need to be estimated and fed back to the Base station (BS) for correction. Two key insights are obtained from our Bayesian analysis. First, the Bayesian equivalent Fisher information matrix (EFIM) for the channel parameters indicates that the RIS orientation offset cannot be estimated when there is an unknown phase offset in the received signal in the far-field propagation regime. Second, the corresponding EFIM for the channel parameters in the received signal observed in the near-field shows that this unknown phase offset does not hinder the estimation of the RIS orientation offset when the UE has more than one receive antenna.

Vehicular platooning is a promising solution to increase road capacity and ensure a seamless traffic flow. Despite its relevance in the current vehicular networks, its rigorous system-level analysis has not been performed yet. In this work, we develop a comprehensive framework to model and analyze a vehicular communication network with platooned traffic. The network of roads is modeled as a Poisson line process (PLP) and vehicles are placed on each road according to an independent Matérn cluster process (MCP) to capture platooning. The resulting point process formed by the locations of the vehicles is a Cox process driven by a PLP, which we term as the PLP-MCP. We first characterize PLP-MCP and present some of its key properties. Assuming that the cellular BSs are distributed as an independent Poisson point process (PPP), we then derive the load distribution on the typical BS of the network which is an important ingredient in the analysis of many key performance metrics, such as coverage probability and the rate distribution over the network. We then provide several system-design insights, including the impact of platooning on coverage probability.

In this paper, we present a comprehensive analytical framework for the system level analysis of THz cellular networks, which incorporates all key features of THz propagation, including blocking, directionality and scattering. This framework is particularly novel from the perspective of including the effect of scattering that has been largely ignored in such analyses thus far. We model the locations of the THz base-stations (BSs) as a homogeneous Poisson point process (PPP) and users (UEs) as another independent point process (PP). Further, the blockages and scatterers are modeled using a Boolean process and an independent PPP, respectively. The framework also incorporates distinction of line-of-sight (LOS), non-line-of-sight (NLOS) links, a realistic bounded path-loss model with absorption losses, and antenna directivity. Using the proposed framework, we first characterize the interference caused by BSs and scatterers via its Laplace transform (LT). We then derive the SINR (signal to interference plus noise ratio) coverage probability. With the help of a dummy exponential random variable (RV), we also derive the exact mean SINR. Our analysis concretely demonstrates that the scatterers have a significant impact on the coverage probability. Further, our results show that the coverage probability does not always increase with the increasing density of THz BSs.

This paper considers a communication system where a source sends time-sensitive information to its destination. We assume that both arrival and service processes of the messages are memoryless and the source has a single server with no buffer. Besides, we consider that the service is interrupted by an independent random process, which we model using an OnOff process. For this setup, we study the age of information for two queueing disciplines: 1) non-preemptive, where the messages arriving while the server is occupied are discarded, and 2) preemptive, where the in-service messages are replaced with newly arriving messages in the Off states. For these disciplines, we derive closed-form expressions for the mean peak age and mean age.

In millimeter wave (mmWave) networks, the communication link performance is heavily dependent on the directional characteristics of the transceiver beams. Under practical beam management considerations, the transmitter and receiver beams may not be perfectly aligned. We consider such a situation in the downlink of a mmWave cellular network. In this case, the received powers from the base stations (BSs) at the user equipment (UE) of interest will depend upon both the Euclidean and the angular distances (of the BSs to that UE). We develop a novel stochastic geometry framework to study maximum power-based association in this setting. To the best of our knowledge, this is the first work that rigorously explores the role of angular distances in the association policy and analysis of cellular networks. We derive exact expressions for the distributions of signal-to-interference-plus-noise ratio (SINR) and the link rate, as well as the average achievable rate. Among others, our analysis reveals that as the receiver beam becomes more directional (i) the instantaneous achievable rate improves at the expense of a significantly higher variance, and (ii) both the desired received power and the interference power decrease because of the reduced misalignment error and the reduction of the number of interfering BSs falling within in the 3 dB beamwidth of the receiver antenna pattern, respectively, and (iii) the probability of achieving a higher target rate than the average increases.

Determining optimal phases for a discrete reconfigurable intelligent surface (RIS) in RIS-aided wireless systems is known to be a challenging problem. This paper develops a novel probabilistic reformulation technique to transform such discrete optimization problems into continuous domain problems. The idea is to treat optimization variables as a categorical random vector with independent but non-identically distributed (i.n.i.d.) entries and replace the objective function with its expectation. In the unconstrained case, we rigorously establish the equivalence between the original problem’s unique optimal solution and the corresponding degenerate probability density function (PDF) of the transformed problem. Furthermore, we derive key analytical moments and gradients associated with the quadratic form and binary random vectors that are useful in the optimization of RIS-aided wireless systems. In order to concretely demonstrate the benefits of the proposed technique, we reformulate a canonical discrete RIS-aided signal-to-interference-plus-noise ratio (SINR) maximization problem and solve the reformulated problem with the gradient descent (GD) technique. Our solution includes an analytical approach that relies on closed-form approximations for the expectation, incorporating moment results, and a stochastic sampling method based on a log-derivative gradient estimator. Numerical results show that our expectation-based algorithms outperform state-of-the-art conventional algorithms, thereby demonstrating the effectiveness of our approach.

The geometry-based stochastic channel models (GSCM), which can describe realistic channel impulse responses, often rely on the existence of both local and far scatterers. However, their visibility from both the base station (BS) and mobile station (MS) depends on their relative heights and positions. For example, the condition of visibility of a scatterer from the perspective of a BS is different from that of an MS and depends on the height of the scatterer. To capture this, we propose a novel GSCM where each scatterer has dual disk visibility regions (VRs) centered on itself for both BS and MS, with their radii being our model parameters. Our model consists of short and tall scatterers, which are both modeled using independent inhomogeneous Poisson point processes (IPPPs) having distinct dual VRs. We also introduce a probability parameter to account for the varying visibility of tall scatterers from different MSs, effectively emulating their noncontiguous VRs. Using stochastic geometry, we derive the probability mass function (PMF) of the number of multipath components (MPCs), the marginal and joint distance distributions for an active scatterer, the mean time of arrival (ToA), and the mean received power through non-line-of-sight (NLoS) paths for our proposed model. By selecting appropriate model parameters, the propagation characteristics of our GSCM are demonstrated to closely emulate those of the COST-259 model.

In this paper, we study a general setting of status updating systems in which a set of source nodes provide status updates about some physical process(es) to a set of monitors. The freshness of information available at each monitor is quantified in terms of the Age of Information (AoI), and the vector of AoI processes at the monitors (or equivalently the age vector) models the continuous state of the system. While the marginal distributional properties of each AoI process have been studied for a variety of settings using the stochastic hybrid system (SHS) approach, we lack a counterpart of this approach to systematically study their joint distributional properties. Developing such a framework is the main contribution of this paper. In particular, we model the discrete state of the system as a finite-state continuous-time Markov chain, and describe the coupled evolution of the continuous and discrete states of the system by a piecewise linear SHS with linear reset maps. Using the notion of tensors, we first derive first-order linear differential equations for the temporal evolution of both the joint moments and the joint moment generating function (MGF) for an arbitrary set of age processes. We then characterize the conditions under which the derived differential equations are asymptotically stable. The generality of our framework is demonstrated by recovering several existing results as special cases. Finally, we apply our framework to derive the stationary joint MGF in a multi-source updating system under the non-preemptive in service queueing discipline.

Many modern wireless devices with accurate positioning needs have access to many vision sensors, such as a camera, radar, and Light Detection and Ranging (LiDAR). In numerous scenarios where wireless-based positioning is either inaccurate or unavailable, using information from vision sensors becomes highly desirable for determining the precise location of the wireless device. While localization utilizing vision information has been explored from different algorithmic perspectives, the underlying mathematical underpinnings of this problem space remain largely unexplored. Inspired by this, we develop a new analytical framework for vision-based localization in which error-free distance measurements in vision data are utilized to accurately determine the position of the target. Compared to wireless-based positioning, a notable differentiation of this approach is the inclusion of non-unique landmarks, such as lampposts, which may lack distinguishable features in the vision data. For instance, when the target is located close to a lamppost, it becomes challenging to precisely identify the specific lamppost (among several in the region) that is near the target. By assuming that the landmarks of various types follow a marked Poisson point process (PPP), we establish that three range measurements are sufficient for determining the correct combination of landmarks in a two-dimensional plane. When the number of measurements is less than three, there exists a potential for making errors in associating these range measurements with the corresponding landmark combination. We provide a mathematical characterization of this probability of error, which involves a novel joint distribution of key random variables.

It is our pleasure to share with you this Special Issue, which brings together a diverse set of articles dealing with various aspects of semantic and goal-oriented communications, providing a snapshot of research activities in this highly active research area. Wireless communications and networking research has traditionally focused on improving the capacity and throughput of the underlying wireless network. However, recent explosion in data-driven machine learning applications and their reliance on huge datasets collected by edge devices have raised legitimate concerns that the increasing data traffic might soon overwhelm the capacity of current networks despite ongoing efforts to increase their capacity and efficiency. Also, most of the edge intelligence applications impose stringent delay constraints, which cannot be met by naive forwarding of data samples for processing at the receiver end. This made it obvious to researchers in both academia and industry that it is essential to analyze the “value” or “relevance” of collected data, and filter and prioritize the delivery of data based on its value/relevance as well as the wireless channel and network conditions. In this context, data value will be closely connected to the underlying signals and processes that generate the data, e.g., text, image, video, or sensor data, and what the receiver intends to do with the received data. This subjectivity of data value makes semantic and goal-oriented communication a rather elusive research topic, which has led to both an increasingly rich and active area of investigation, but also a controversial one, mainly due to the lack of clear and widely agreed-upon definitions of some of the core concepts and formulations. Despite these disagreements, there is almost unanimous consensus on the importance and potential impact of this line of investigation for the design of future communication systems and networks.

Communication systems to date primarily aim at reliably communicating bit sequences. Such an approach provides efficient engineering designs that are agnostic to the meanings of the messages or to the goal that the message exchange aims to achieve. Next generation systems, however, can be potentially enriched by folding message semantics and goals of communication into their design. Further, these systems can be made cognizant of the context in which communication exchange takes place, thereby providing avenues for novel design insights. This tutorial summarizes the efforts to date, starting from its early adaptations, semantic-aware and task-oriented communications, covering the foundations, algorithms and potential implementations. The focus is on approaches that utilize information theory to provide the foundations, as well as the significant role of learning in semantics and task-aware communications.

We study a general setting of status updating systems in which a set of source nodes provide status updates about some physical process(es) to a set of monitors. The freshness of information available at each monitor is quantified in terms of the Age of Information (AoI), and the vector of AoI processes at the monitors (or equivalently the age vector) models the continuous state of the system. While the marginal distributional properties of each AoI process have been studied for a variety of settings using the stochastic hybrid system (SHS) approach, we lack a counterpart of this approach to systematically study their joint distributional properties. Developing such a framework is the main contribution of this paper. In particular, we model the discrete state of the system as a finite-state continuous-time Markov chain, and describe the coupled evolution of the continuous and discrete states of the system by a piecewise linear SHS with linear reset maps. Using the notion of tensors, we first derive first-order linear differential equations for the temporal evolution of both the joint moments and the joint moment generating function (MGF) for an arbitrary set of age processes. We then characterize the conditions under which the derived differential equations are asymptotically stable. The generality of our framework is demonstrated by recovering several existing results as special cases. Finally, we apply our framework to derive closed-form expressions of the stationary joint MGF in a multi-source updating system under non-preemptive and source-agnostic/source-aware preemptive in service queueing disciplines.

In this paper we calculate the exact cumulative distribution function (CDF) of the path distance (L1 norm) between a randomly selected intersection and the k-th nearest node of the Cox point process driven by the Manhattan Poisson line process. The CDF is expressed as a sum over the integer partition function$p\!\left(k\right)$, which allows us to numerically evaluate the CDF in a simple manner. The distance distributions can be used to study the k-coverage of broadcast signals in intelligent transportation systems (ITS) transmitted from a \ac{RSU} that is located at an intersection. They can also be insightful for network dimensioning in urban vehicle-to-everything (V2X) systems, because they can yield the exact distribution of network load within a cell, provided that the \ac{RSU} is located at an intersection. Finally, they can find useful applications in other branches of science like spatial databases, emergency response planning, and districting. We corroborate the applicability of the distance distribution model using the map of an urban area.

This paper presents a rigorous Bayesian analysis of the information in the signal (consisting of both the line-of-sight (LOS) path and reflections from multiple reconfigurable intelligent surfaces (RISs)) that originate from a single base station (BS) and is received by a user equipment (UE). For a comprehensive Bayesian analysis, both near and far field regimes are considered. The Bayesian analysis views both the location of the RISs and previous information about the UE as a priori information for UE localization. With outdated a priori information, the position and orientation offsets of the RISs become parameters that need to be estimated and fed back to the BS for correction. We first show that when the RIS elements have a half wavelength spacing, this RIS orientation offset is a factor in the pathloss of the RIS paths. Subsequently, we show through the Bayesian equivalent Fisher information matrix (EFIM) for the channel parameters that the RIS orientation offset cannot be corrected when there is an unknown phase offset in the received signal in the far-field regime. However, the corresponding EFIM for the channel parameters in the received signal observed in the near-field shows that this unknown phase offset does not hinder the estimation of the RIS orientation offset when the UE has more than one receive antenna. Furthermore, we use the EFIM for the UE location parameters to present bounds for UE localization in the presence of RIS uncertainty. We rigorously show that regardless of size and propagation regime, the RISs are only helpful for localization when there is a priori information about the location of the RISs. Finally, through numerical analysis of the EFIM and its smallest eigenvalue, we demonstrate the loss in information when the far-field model is incorrectly applied to the signals received at a UE experiencing near-field propagation.

Vehicular platooning is a promising way to facilitate efficient movement of vehicles with a shared route. Despite its relevance, the interplay of platooning and the communication performance in the resulting vehicular network (VN) is largely unexplored. Inspired by this, we develop a comprehensive approach to statistical modeling and system-level analysis of VNs with platooned traffic. Modeling the network of roads using the by-now well-accepted Poisson line process (PLP), we place vehicles on each road according to an independent Matérn cluster process (MCP) that jointly captures randomness in the locations of platoons on the roads and vehicles within each platoon. The resulting triply-stochastic point process is a PLP-driven-Cox process, which we term the PLP-MCP. We first present this new point process’s distribution and derive several fundamental properties essential for the resulting VN’s analysis. Assuming that the cellular base-stations (BSs) are distributed as a Poisson point process (PPP), we derive the distribution of the loads served by the typical BS and the BS associated with the typical user. In deriving the latter, we also present a new approach to deriving the length distribution of a tagged chord in a Poisson Voronoi tessellation. Using the derived results, we present the rate coverage of the typical user while considering partial loading of the BSs. We also provide a comparative analysis of VNs with and without platooning of traffic.

In this work, we analyze the downlink performance of a cell-free massive multiple-input-multiple-output system with finite capacity fronthaul links between the centralized baseband unit and the access point (APs). Conditioned on the user and AP locations, we first derive an achievable rate for a randomly selected user in the network that captures the effect of finite fronthaul capacity as a compression error. From this expression, we establish that for the traditional cell-free architecture where each AP serves all the users in the network, the achievable rate becomes zero as the network size grows. Hence, to have a meaningful analysis, for the traditional architecture, we model the user and AP locations as two independent binomial point processes over a finite region and provide an accurate theoretical result to determine the user rate coverage. In contrast, for an asymptotically large network, we consider a user-centric architecture where each user in the network is served by a specified number of nearest APs that limits the fronthaul load. For this architecture, we model the AP and user locations as two independent Poisson point processes (PPPs). Since the rate expression is a function of the number of users served by an AP, we statistically characterize the load in terms of the number of users per AP. As the exact derivation of the probability mass function of the load is intractable, we first present the exact expressions for the first two moments of the load. Next, we approximate the load as a negative binomial random variable through the moment matching method. Using the load results along with appropriate distance distributions of a PPP, we present an accurate theoretical expression for the rate coverage of the typical user. From the analyses, we conclude that for the traditional architecture when the AP transmit power is relatively high, a more collocated antenna deployment is preferred. Further, for the user-centric architecture, the energy efficiency of the system is a concave function of the number of antennas per AP.

This paper provides an impairments-aware unified channel model for the link between an unmanned aerial vehicle (UAV) and a ground user equipment (UE). In particular, we consider both physical and hardware impairments, where the former is unique to UAVs and refers to random physical vibrations of the UAV platform, also known as wobbling. The latter pertains to both the UAV and the UE and refers to intrinsic radio frequency (RF) impairments, such as power amplifier (PA) nonlinearity, phase noise, and in-phase/quadrature (I/Q) imbalance. We model the fluctuations of the UAV platform pitch angle (caused by wobbling) by a sinusoidal stochastic process. On the other hand, the combined effect of all hardware impairments is modeled by two wide-sense stationary (WSS) additive and multiplicative distortion noise processes, which is a well-accepted approach in the literature. Using this unified model, we characterize the autocorrelation function (ACF) of the impairments-aware channel impulse response, which further provides the coherence time of the channel. We also derive the power spectral density (PSD) of the distortion-plus-noise process of our unified channel model. To obtain useful insights from the joint impact of physical and hardware impairments on the air-to-ground wireless channel, we evaluate both of these metrics with reasonable impairment models and parameters. One key implication of our results is that the channel coherence time degrades noticeably at high frequencies even for small wobbling, which renders channel estimation of UAV links extremely challenging at these frequencies.

This paper considers a multi-source updating system in which a transmitter powered by energy harvesting (EH) sends status updates about multiple sources of information to a destination, where the freshness of status updates is measured in terms of Age of Information (AoI). The harvested energy packets and the status updates of each source are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. Our focus is on understanding the distributional properties of AoI under a source-aware preemptive in service queueing discipline (which only allows preemption between the status updates generated by the same source to enhance fairness). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the moment generating function (MGF) and average of AoI. To the best of our knowledge, this paper is the first to characterize the AoI performance under a source-aware preemptive policy for the generic case where the transmitter has an arbitrary number of sources. The generality of our results is demonstrated by recovering several existing results for EH-powered single-source systems as special cases. Our results demonstrate that the proposed source-aware preemptive policy strikes a balance between minimizing the sum of average AoI values associated with different sources (average sum-AoI) and achieving fairness among the average AoI values of different sources.

The unmanned aerial vehicle (UAV) based communication is expected to play an important role in enabling a variety of applications in future cellular networks. However, because of the mobility of the UAVs, the communications links involving UAVs undergo large-scale temporal variations in the received signal quality, which may affect the quality-of-service of the underlying application. Therefore, it is crucial to characterize the time-varying process of signal quality observed by the UAVs. In this paper, we consider a scenario in which a cellular-connected UAV acts as a user equipment (UAV-UE), where the locations of base stations (BSs) follow a Poisson point process (PPP) and the UAV-UE is moving along a 3GPP-inspired straight-line trajectory. For this setting, we study the properties of the time-varying successful transmission process that is defined in terms of the time-varying signal-to-noise ratio (SNR) observed at the UAV. In particular, we show that this process is a wide sense stationary (WSS) process and derive its first- and second-order statistics. Finally, we establish an equivalence between the successful transmission processes observed by a UAV-UE served by terrestrial BSs and a terrestrial user served by UAV mounted BSs (UAV-BSs) each moving along an independent straight-line trajectory.

We study a general setting of status updating systems in which a set of source nodes provide status updates about some physical process(es) to a set of monitors. The freshness of information available at each monitor is quantified in terms of the Age of Information (AoI), and the vector of AoI processes at the monitors (or equivalently the age vector) models the continuous state of the system. While the marginal distributional properties of each AoI process have been studied for a variety of settings using the stochastic hybrid system (SHS) approach, we lack a counterpart of this approach to systematically study their joint distributional properties. Developing such a framework is the main contribution of this paper. In particular, we model the discrete state of the system as a finite-state continuous-time Markov chain (MC), and describe the coupled evolution of the continuous and discrete states of the system by a piecewise linear SHS with linear reset maps. We start our analysis by deriving first-order linear differential equations for the temporal evolution of both the joint moments and the joint moment generating function (MGF) of all possible pairwise combinations formed by the age vector components. We then derive conditions under which the derived differential equations are asymptotically stable. Finally, we apply our framework to characterize the stationary joint MGF in a multi-source updating system under several queueing disciplines including non-preemptive and source-agnostic/source-aware preemptive in service queueing disciplines.

This paper considers a real-time status update system in which an energy harvesting (EH)-powered transmitter node observes some physical process, and sends its sensed measurements in the form ofstatus updatesto a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify thefreshnessof status updates when they reach the destination using the concept ofAge of Information (AoI). Unlike most of the existing analyses of AoI focusing on the evaluation of its average value when the transmitter is not subject to energy constraints, our analysis is focused on understanding thedistributional propertiesof AoI through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and preemptive in service/waiting strategies. Using these MGF results, we further obtain closed-form expressions for the first and second moments of AoI in each queueing discipline. We demonstrate the generality of this analysis by recovering several existing results for the corresponding system with no energy constraints as special cases of the new results. Our numerical results verify the analytical findings, and demonstrate the necessity of incorporating the higher moments of AoI in the implementation/optimization of real-time status update systems rather than just relying on its average value.

In this paper, we characterize the performance of a three-dimensional (3D) two-hop cellular network in which terrestrial base stations (BSs) coexist with unmanned aerial vehicles (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 line-of-sight (LoS) and non-line-of-sight (NLoS) 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 simulation.

This paper provides the performance characterization of a three-dimensional (3D) two-hop decode-and-forward (DF) aerial-terrestrial communication network, where unmanned aerial vehicles (UAVs) coexist with terrestrial base stations (BSs) to serve a set of user equipment (UE) on the ground. We assume that each UE connects either to a BS via access link or through a UAV to a BS via joint access and backhaul links, where the link from the UE to the UAV is an access link and from the UAV to the BS is a backhaul link. To capture the impact of directionality in practical antennas, we use a model developed by the third generation partnership project (3GPP) for the antenna radiation pattern of both BSs and UAVs. Following the nearest neighbor association policy, we obtain the joint distance and angle distribution of the serving UAV to the origin in a 3D setting using tools from stochastic geometry. Furthermore, we identify and analyze key mathematical constructs as the building blocks of characterizing the received signal-to-interference-plus-noise ratio (SINR) distribution at the typical UE for the DF relaying protocol. Using these intermediate results, we derive an exact mathematical expression for the coverage probability in UAV-assisted two-hop DF cellular networks. One key takeaway from our analysis is the existence of a mean UAV height and a 3D density of UAVs that optimize the network coverage performance.

In this paper, we consider a cellular-based Internet of things (IoT) network consisting of IoT devices that can communicate directly with each other in a device-to-device (D2D) fashion as well as send real-time status updates about some underlying physical processes observed by them. We assume that such real-time applications are supported by cellular networks where cellular base stations (BSs) collect status updates over time from a subset of the IoT devices in their vicinity. We characterize two performance metrics: i) the network throughput which quantifies the performance of D2D communications, and ii) the Age of Information which quantifies the performance of the real-time IoT-enabled applications. Concrete analytical results are derived using stochastic geometry by modeling the locations of IoT devices as a bipolar Poisson Point Process (PPP) and that of the BSs as another Independent PPP. Our results provide useful design guidelines on the efficient deployment of future IoT networks that will jointly support D2D communications and several cellular network-enabled real-time applications.

The operation of Terahertz (THz) communication can be significantly impacted by the interaction between the transmitted wave and the molecules in the atmosphere. In particular, it has been observed experimentally that the signal undergoes not only molecular absorption, but also molecular re-radiation. Two extreme modeling assumptions are prevalent in the literature, where the re-radiated energy is modeled in the first as additive Gaussian noise and in the second as a scattered component strongly correlated to the actual signal. Since the exact characterization is still an open problem, we provide in this paper the first comparative study of the performance of a reconfigurable intelligent surface (RIS) assisted THz system under these two extreme models of re-radiation. In particular, we employ an RIS to overcome the large pathloss by creating a virtual line-of-sight (LOS) path. We then develop an optimization framework for this setup and utilize the block-coordinate descent (BCD) method to iteratively optimize both RIS configuration vector and receive beamforming weight resulting in significant throughput gains for the user of interest compared to random RIS configurations. Our results reveal that a slightly better throughput is achieved under the scattering assumption for the molecular re-radiation than the noise assumption.

In this paper, we consider a large-scale wireless network consisting of source-destination (SD) pairs where the source nodes frequently send status updates about some underlying physical processes (observed by them) to their corresponding destination nodes. For this setup, we employ age of information (AoI) as a performance metric to quantify freshness of the status updates when they reach the destination nodes. While most of the existing works are focused on the analysis of the temporal mean AoI in deterministic network topologies, we aim to characterize the spatial AoI performance disparity that is inherently present in wireless networks. In particular, we treat the temporal mean AoI as a random variable over space as the update delivery rate of a wireless link is a function of the interference field observed by its receiver. Our objective is to characterize the spatial distribution of the temporal mean AoI observed by the SD pairs by modeling them as a Poisson bipolar process. We first derive accurate bounds on the moments of the successful transmission probability of a status update which are then used to derive tight bounds on the moments as well as the spatial distribution of the temporal mean peak AoI. Our results provide useful design guidelines on the appropriate selection of different system parameters to minimize the mean peak AoI.

This paper considers an energy harvesting (EH) real-time status update system in which an EH-powered transmitter node sends status updates about some physical process of interest to a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify the freshness of status updates when they reach the destination using the concept of Age of Information (AoI). Unlike most of the existing analyses of AoI that focus on characterizing its average when the transmitter has a reliable energy source and is hence not powered by EH (referred henceforth as a non-EH transmitter), our analysis is focused on understanding the distributional properties of AoI through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the MGF of AoI under both nonpreemptive and preemptive in service queueing disciplines at the transmitter. We demonstrate the generality of this analysis by recovering several known results for the corresponding system with a non-EH transmitter as special cases of the new results. Our numerical results verify the analytical findings, and demonstrate the importance of incorporating the higher moments of AoI in the implementation/optimization of real-time status update systems rather than just relying on its average value.

In this article, an unmanned aerial vehicle (UAV)-assisted wireless network is considered in which a battery-constrained UAV is assumed to move towards energy-constrained ground nodes to receive status updates about their observed processes. The UAV's flight trajectory and scheduling of status updates are jointly optimized with the objective of minimizing the normalized weighted sum of Age of Information (NWAoI) values for different physical processes at the UAV. The problem is first formulated as a mixed-integer program. Then, for a given scheduling policy, a convex optimization-based solution is proposed to derive the UAV's optimal flight trajectory and time instants on updates. However, finding the optimal scheduling policy is challenging due to the combinatorial nature of the formulated problem. Therefore, to complement the proposed convex optimization-based solution, a finite-horizon Markov decision process (MDP) is used to find the optimal scheduling policy. Since the state space of the MDP is extremely large, a novel neural combinatorial-based deep reinforcement learning (NCRL) algorithm using deep Q-network (DQN) is proposed to obtain the optimal policy. However, for large-scale scenarios with numerous nodes, the DQN architecture cannot efficiently learn the optimal scheduling policy anymore. Motivated by this, a long short-term memory (LSTM)-based autoencoder is proposed to map the state space to a fixed-size vector representation in such large-scale scenarios while capturing the spatio-temporal interdependence between the update locations and time instants. A lower bound on the minimum NWAoI is analytically derived which provides system design guidelines on the appropriate choice of importance weights for different nodes. Furthermore, an upper bound on the UAV's minimum speed is obtained to achieve this lower bound value. The numerical results also demonstrate that the proposed NCRL approach can significantly improve the achievable NWAoI per process compared to the baseline policies, such as weight-based and discretized state DQN policies.

This paper focuses on the non-coherent detection in ambient backscatter communication, which is highly appealing for systems where the trade-off between signaling overhead and the actual data transmission is very critical. Modeling the time-selective fading channel as a first-order autoregressive (AR) process, we propose a new receiver architecture based on the direct averaging of the received signal samples for detection, which departs significantly from the energy averaging-based receivers considered in the literature. For the proposed setup, we characterize the exact asymptotic bit error rate (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 while the direct-link (DL) interference from the ambient power source leads to a BER floor in the SA receiver, the MA receiver can remove this interference 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. A key intermediate result of our analysis is the derivation of a new concentration result for a general sum sequence that is central to the derivation of the conditional distributions of the received signal.

This paper considers a large-scale wireless network consisting of source-destination (SD) pairs, where the sources send time-sensitive information, termed status updates, to their corresponding destinations in a time-slotted fashion. We employ age of information (AoI) for quantifying the freshness of the status updates measured at the destination nodes under the preemptive and non-preemptive queueing disciplines with no storage facility. The non-preemptive queue drops the newly arriving updates until the update in service is successfully delivered, whereas the preemptive queue replaces the current update in service with the newly arriving update, if any. As the update delivery rate for a given link is a function of the interference field seen from the receiver, the temporal mean AoI can be treated as a random variable over space. Our goal in this paper is to characterize the spatial distribution of the mean AoI observed by the SD pairs by modeling them as a bipolar Poisson point process (PPP). Towards this objective, we first derive accurate bounds on the moments of success probability while efficiently capturing the interference-induced coupling in the activities of the SD pairs. Using this result, we then derive tight bounds on the moments as well as the spatial distribution of peak AoI (PAoI). Our numerical results verify our analytical findings and demonstrate the impact of various system design parameters on the mean PAoI.

This paper studies the interplay between device-to-device (D2D) communications and real-time monitoring systems in a cellular-based Internet of Things (IoT) network. In particular, besides the possibility that the IoT devices communicate directly with each other in a D2D fashion, we consider that they frequently send time-sensitive information/status updates (about some underlying physical processes observed by them) to their nearest cellular base stations (BSs). Specifically, we model the locations of the IoT devices as a bipolar Poisson Point Process (PPP) and that of the BSs as another independent PPP. For this setup, we characterize the performance of D2D communications using the average network throughput metric whereas the performance of the real-time applications is quantified by the Age of Information (AoI) metric. The IoT devices are considered to employ a distance-proportional fractional power control scheme while sending status updates to their serving BSs. Hence, depending upon the maximum transmission power available, the IoT devices located within a certain distance from the BSs can only send status updates. This association strategy, in turn, forms theJohnson-Mehl (JM)tessellation, such that the IoT devices located in theJM cellsare allowed to send status updates. The average network throughput is obtained by deriving the mean success probability for the D2D links. On the other hand, the temporal mean AoI of a given status update link can be treated as a random variable over space since its success delivery rate is a function of the interference field seen from its receiver. Thus, in order to capture the spatial disparity in the AoI performance, we characterize the spatial moments of the temporal mean AoI. In particular, we obtain these spatial moments by deriving the moments of both the conditional success probability and the conditional scheduling probability for status update links. Our results provide useful design guidelines on the efficient deployment of future massive IoT networks that will jointly support D2D communications and several cellular network-enabled real-time applications.

Spectrum sharing alleviates the severe shortage of spectrum in sub-6 GHz frequency bands through the harmonious coexistence of two or more wireless technologies on the same frequency resources. In this work, we study underlay radar-massive MIMO cellular coexistence in LoS/near-LoS channels, where both systems have 3D beamforming capabilities. Using mathematical tools from stochastic geometry, we derive an upper bound on the average interference power at the radar due to the 3D massive MIMO cellular downlink under the worst-case ‘cell-edge beamforming’ conditions. To overcome the technical challenges imposed by asymmetric and arbitrarily large cells, we devise a novel construction in which each Poisson Voronoi (PV) cell is bounded by its circumcircle to bound the effect of the random cell shapes on average interference. Since this model is intractable for further analysis due to the correlation between adjacent PV cells’ shapes and sizes, we propose a tractable nominal interference model, where we model each PV cell as a circular disk with an area equal to the average area of the typical cell. We quantify the gap in the average interference power between these two models and show that the upper bound is tight for realistic deployment parameters. We also compare them with a more practical but intractable MU-MIMO scheduling model to show that our worst-case interference models show the same trends and do not deviate significantly from realistic scheduler models. Under the nominal interference model, we characterize the interference distribution using the dominant interferer approximation by deriving the equi-interference contour expression when the typical receiver uses 3D beamforming. Finally, we use tractable expressions for the interference distribution to characterize radar’s spatial probability of false alarm/detection in a quasi-static target tracking scenario. Our results reveal useful trends in the average interference as a function of the deployment parameters (BS density, exclusion zone radius, antenna height, transmit power of each BS, etc.). We also provide useful system design insights using radar receiver operating characteristic (ROC) curves by applying our analytical results to design the minimum exclusion zone radius in current and future radar-cellular spectrum sharing scenarios.

Due to their inherent ability to operate without the channel state information (CSI), non-coherent receivers are highly suitable for ambient backscatter devices, allowing them to co-exist alongside the non-cooperative primary users. In this work, we analyze the performance of an ambient backscatter system employing non-coherent detection in a time-selective fading channel (modeled using the first order autoregressive (AR) process). We characterize the bit error rate (BER) of a multiantenna (MA) receiver by deriving the expression for antenna gain achievable after the direct link (DL) cancellation. In addition, the analysis also captures the additional angular resolution in a MA receiver with more than two antennas, which allows us to ensure reasonable performance even when the angles of arrival (AoAs) of the DL and backscatter link (BL) are almost similar.

Test and evaluation (T&E) is a critically important step before in-the-field deployment of radio frequency hardware in order to assure that the hardware meets its design requirements and specifications. Typically, T&E is performed either in a lab setting utilizing a software simulation environment or through real-world field testing. While the former approach is typically limited by the accuracy of the simulation models (of the anticipated hardware effects, channel conditions, etc.) and by non-real-time data rates, the latter can be extremely costly in terms of time, money, and manpower. To address these issues, this work presents the development of an FPGA-based T&E tool that allows for real-time pseudo-random signal generation for testing radio frequency receiver hardware (such as communication receivers, spectrum sensors, etc.). In particular, a framework is developed for an FPGA-based implementation of a test signal emulator that allows for user-defined randomization of test signal parameters such as center frequencies, bandwidths, start times, and durations, as well as receiver and channel effects such as additive white Gaussian noise (AWGN). To test the accuracy of the developed emulation framework, the randomization properties of the framework are analyzed to assure correct probability distributions and independence. Additionally, FPGA implementation decisions such as bit precision vs. accuracy of the generated signal and the impact on the FPGA's hardware footprint are analyzed. Ultimately, it is shown that this framework is easily extensible to other signal types and channel models.

In this paper, we study a real-time monitoring system in which multiple source nodes are responsible for sending update packets to a common destination node in order to maintain the freshness of information at the destination. Since it may not always be feasible to replace or recharge batteries in all source nodes, we consider that the nodes are powered through wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy (referred to as the age-optimal policy) that jointly optimizes WET and scheduling of update packet transmissions with the objective of minimizing the long-term average weighted sum of Age of Information (AoI) values for different physical processes (observed by the source nodes) at the destination node, referred to as the sum-AoI. To solve this optimization problem, we first model this setup as an average cost Markov decision process (MDP) with finite state and action spaces. Due to the extreme curse of dimensionality in the state space of the formulated MDP, classical reinforcement learning algorithms are no longer applicable to our problem even for reasonable-scale settings. Motivated by this, we propose a deep reinforcement learning (DRL) algorithm that can learn the age-optimal policy in a computationally-efficient manner. We further characterize the structural properties of the age-optimal policy analytically, and demonstrate that it has a threshold-based structure with respect to the AoI values for different processes. We extend our analysis to characterize the structural properties of the policy that maximizes average throughput for our system setup, referred to as the throughput-optimal policy. Afterwards, we analytically demonstrate that the structures of the age-optimal and throughput-optimal policies are different. We also numerically demonstrate these structures as well as the impact of system design parameters on the optimal achievable average weighted sum-AoI.

In this paper, we characterize the performance of several canonical mobility models in a drone cellular network in which drone base stations (DBSs) serve a set of user equipment (UE) 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 third generation partnership project (3GPP) for the placement and trajectory of drones, 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 DBS follows the same mobility model as the other DBSs in the UIM, it is assumed to fly towards the UE of interest in the UDM and hover above its location after reaching there. The main contribution of this paper is a unified approach to characterize the point process of DBSs 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 drones follow curved trajectories) as long as the movement of each drone in these models is independent and identically distributed (i.i.d.). To the best of our knowledge, this is the first work that provides a rigorous analysis of key canonical mobility models for an infinite drone cellular network and establishes useful connections between them.

In this paper, we present the downlink coverage and rate analysis of a cellular vehicle-to-everything (C-V2X) communication network where the locations of vehicular nodes and road side units (RSUs) are modeled as Cox processes driven by a Poisson line process (PLP) and the locations of cellular macro base stations (MBSs) are modeled as a 2D Poisson point process (PPP). Assuming a fixed selection bias and maximum average received power based association, we compute the probability with which a typical receiver, an arbitrarily chosen receiving node, connects to a vehicular node or an RSU and a cellular MBS. For this setup, we derive the signal-to-interference ratio (SIR)-based coverage probability of the typical receiver. One of the key challenges in the computation of coverage probability stems from the inclusion of shadowing effects. As the standard procedure of interpreting the shadowing effects as random displacement of the location of nodes is not directly applicable to the Cox process, we propose an approximation of the spatial model inspired by the asymptotic behavior of the Cox process. Using this asymptotic characterization, we derive the coverage probability in terms of the Laplace transform of interference power distribution. Further, we compute the downlink rate coverage of the typical receiver by characterizing the load on the serving vehicular nodes or RSUs and serving MBSs. We also provide several key design insights by studying the trends in the coverage probability and rate coverage as a function of network parameters. We observe that the improvement in rate coverage obtained by increasing the density of MBSs can be equivalently achieved by tuning the selection bias appropriately without the need to deploy additional MBSs.

This paper provides a comprehensive downlink analysis of non-orthogonal multiple access (NOMA) enabled cellular networks using tools from stochastic geometry. As a part of this analysis, we develop a novel 3GPP-inspired user ranking technique to construct a user cluster for the non-orthogonal transmission by grouping users from the cell center (CC) and cell edge (CE) regions. This technique allows the pairing of users with distinct link qualities, which is imperative for harnessing NOMA performance gains. The analysis is performed from the perspective of the typical cell, which is significantly different from the standard stochastic geometry-based approach of analyzing the performance of the typical user. For this setting, we first derive the moments of the meta distributions for the CC and CE users under NOMA and orthogonal multiple access (OMA). Using this, we then derive the distributions of the transmission rates and mean packet delays under non-real time (NRT) and real-time (RT) service models, respectively, for both CC and CE users. Finally, we study two resource allocation (RA) techniques to maximize the cell sum-rate (CSR) under NRT service, and the sum effective capacity (SEC) under RT service. In addition to providing several useful design insights, our results demonstrate that NOMA provides improved rate region and higher CSR as compared to OMA. In addition, we also show that NOMA provides better SEC as compared to OMA for the higher user density.

In this paper, we study a real-time Internet of Things (IoT)-enabled monitoring system in which a source node (e.g., IoTdevice or an aggregator located near a group of IoT devices) is responsible for maintaining the freshness of information status at a destination node by sending update packets. Since it may not always be feasible to replace or recharge batteries in all IoT devices, we consider that the source node is powered by wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy that minimizes the long-term average Age-of-Information (AoI), referred to as the age-optimal policy. The age- optimal policy determines whether each slot should be allocated for WET or update packet transmission while considering the dynamics of battery level, AoI, and channel state information (CSI). To solve this optimization problem, we model this setup as an average cost Markov Decision Process (MDP). After analytically establishing the monotonicity property of the value function associated with the MDP, the age-optimal policy is proven to be a thresholdbased policy with respect to each of the system state variables. We extend our analysis to characterize the structural properties of the policy that maximizes average throughput for our system setup, referred to as the throughput-optimal policy. Afterwards, we analytically demonstrate that the structures of the ageoptimal and throughput-optimal policies are different. We also numerically demonstrate these structures as well as the impact of system design parameters on the optimal achievable average AoI.

Unmanned aerial vehicles (UAVs) are expected to be a key component of the next-generation wireless systems. Due to their deployment flexibility, UAVs are being considered as an efficient solution for collecting information data from ground nodes and transmitting it wirelessly to the network. In this paper, a UAV-assisted wireless network is studied, in which energy-constrained ground nodes are deployed to observe different physical processes. In this network, a UAV that has a time constraint for its operation due to its limited battery, moves towards the ground nodes to receive status update packets about their observed processes. The flight trajectory of the UAV and scheduling of status update packets are jointly optimized with the objective of achieving the minimum weighted sum for the age- of-information (AoI) values of different processes at the UAV, referred to as weighted sum-AoI. The problem is modeled as a finite- horizon Markov decision process (MDP) with finite state and action spaces. Since the state space is extremely large, a deep reinforcement learning (RL) algorithm is proposed to obtain the optimal policy that minimizes the weighted sum-AoI, referred to as the age-optimal policy. Several simulation scenarios are considered to showcase the convergence of the proposed deep RL algorithm. Moreover, the results also demonstrate that the proposed deep RL approach can significantly improve the achievable sum- AoI per process compared to the baseline policies, such as the distance-based and random walk policies. The impact of various system design parameters on the optimal achievable sum-AoI per process is also shown through extensive simulations.

In this paper, we present the first stochastic geometry-based performance analysis of a drone cellular network in which drone base stations (DBSs) are initially distributed based on a Poisson point process (PPP) and move according to a random waypoint (RWP) mobility model. The serving DBS for a typical user equipment (UE) on the ground is selected based on the nearest neighbor association policy. We further assume two service models for the serving DBS: (i) UE independent model (UIM), and (ii) UE dependent model (UDM). All the other DBSs are considered as interfering DBSs for the typical UE. We introduce a simplified RWP (SRWP) mobility model to describe the movement of interfering DBSs and characterize its key distributional properties that are required for our analysis. Building on these results, we analyze the interference field as seen by the typical UE for both the UIM and the UDM using displacement theorem, which forms the basis for characterizing the average rate at the typical UE as a function of time. To the best of our knowledge, this is the first work that analyzes the performance of a mobile drone network in which the drones follow an RWP mobility model on an infinite plane.

This paper deals with the stochastic geometry- based characterization of the time-varying performance of a drone cellular network in which the initial locations of drone base stations (DBSs) are modeled as a Poisson point process (PPP) and each DBS is assumed to move on a straight line in a random direction. This drone placement and trajectory model closely emulates the one used by the third generation partnership project (3GPP) for drone-related studies. Assuming the nearest neighbor association policy for a typical user equipment (UE) on the ground, we consider two models for the mobility of the serving DBS: (i) UE independent model, and (ii) UE dependent model. Using displacement theorem from stochastic geometry, we characterize the time- varying interference field as seen by the typical UE, using which we derive the time-varying coverage probability and data rate at the typical UE. We also compare our model with more sophisticated mobility models where the DBSs may move in nonlinear trajectories and demonstrate that the coverage probability and rate estimated by our model act as lower bounds to these more general models. To the best of our knowledge, this is the first work to perform a rigorous analysis of the 3GPP-inspired drone mobility model and establish connection between this model and the more general non-linear mobility models.

In this paper, we consider a cellular vehicle-to-everything (C-V2X) network in which the road system is modeled by a Poisson line process (PLP) and the locations of vehicular nodes and RSUs on each road are modeled by a 1D Poisson point process (PPP), thereby forming a Poisson line Cox process (PLCP). Further, we model the locations of cellular macro base stations (MBSs) by a 2D PPP. While the PLCP model has recently been used to characterize vehicular network performance, the technical complexity induced by the doubly stochastic nature of the PLCP has deterred the inclusion of shadowing effects in these studies. In this paper, we approach towards closing this knowledge gap by computing the signal-to-interference ratio (SIR)-based coverage probability of a typical receiver in this network under log-normal shadowing. In order to enable this analysis, we first establish that the PLCP asymptotically converges to a 2D PPP and using this result, we develop an approximate yet accurate spatial model that is much more conducive to the coverage analysis in the presence of shadowing than the PLCP. Our analysis offers useful insights into the deployment of RSUs based on their impact on the coverage performance of the network under various scenarios.

Non-coherent detection is an important component of ambient backscatter communication due to the energy constrained nature of the backscatter devices. This paper provides the first comprehensive performance analysis of non- coherent detection under a fast-varying wireless channel for ambient backscatter communication. In particular, we evaluate the bit error rates (BERs) for two data encoding mechanisms under a new receiver architecture that is based on the direct averaging of the received signal samples. Our results concretely demonstrate the existence of BER floor for a single antenna receiver, which results in poor performance. We further show that a multi-antenna receiver can overcome this drawback by eliminating the interference created by the direct link from the ambient power source that considerably improves the BER of this receiver. This multi-antenna receiver exploits the fact that the time duration of the variation in angle of arrival (AoA) of the communication links in the fast-varying channel is much larger than the coherence period of the small-scale fading, allowing it to track the AoA of the direct link.

This paper presents the meta distribution analysis of the downlink two-user non-orthogonal multiple access (NOMA) in cellular networks. We propose a novel user ranking technique wherein the users from the cell center (CC) and cell edge (CE) regions are paired for the non-orthogonal transmission. Inspired by how users are partitioned in 3GPP cellular models, the CC and CE users are characterized based on the mean powers received from the serving and the dominant interfering BSs. We demonstrate that the proposed technique ranks users in an accurate order with distinct link qualities, which is imperative for the performance of NOMA system. The exact moments of the meta distributions for the CC and CE users under NOMA and orthogonal multiple access (OMA) are derived. In addition, we provide tight beta distribution approximations for the meta distributions and exact expressions of the mean local delays and the cell throughputs for the NOMA and OMA cases. To the best of our knowledge, this is the first comprehensive analysis of NOMA using stochastic geometry with 3GPP-inspired user ranking scheme that depends upon both of the link qualities from the serving and dominant interfering BSs.

The stochastic geometry-based downlink analysis of a cellular network modeled as a Poisson point process (PPP) has traditionally focused on the typical user placed at the origin, which does not lie in the typical cell. In order to characterize the performance of the typical cell, one needs to explicitly consider the point process of users scheduled in a given resource block (RB), which is dependent on the base station (BS) point process. Therefore, we model the locations of the scheduled users using the so-called Type I user process, which places one user uniformly at random in each cell. However, this dependency in the locations of the BSs and users complicates the characterization of the point process of interferers as seen by the typical user of the Type I process. In order to overcome this challenge, we present a general approach to determine the pair correlation function (pcf) of stationary point processes with respect to a reference point. This approach is used to approximate the pcf the point process of interferers with respect to the typical user of the Type I process. With the pcf in hand, we provide the tightest known approximation of the point process of interfering BSs as seen by the typical user of Type I process, which is used to derive remarkably tight expressions for the moments of the downlink signal-to-interference- ratio (SIR) meta distribution for the typical cell.

In the past few decades, the localization literature has seen many models attempting to characterize the non-line-of-sight (NLOS) bias error commonly experienced in range measurements. These models have either been based on specific measurement data or chosen due to attractive features of a particular distribution, yet to date, none have been backed by rigorous analysis. Leveraging tools from stochastic geometry, this paper attempts to fill this void by providing the first analytical backing for an NLOS bias error model. Using a Boolean model to statistically characterize the random locations, orientations, and sizes of reflectors, and assuming first-order (i.e., single-bounce) reflections, the distance traversed by the first-arriving NLOS path is characterized. Under these assumptions, this analysis reveals that NLOS bias exhibits an exponential form and can in fact be well approximated by an exponential distribution - a result consistent with previous NLOS bias error models in the literature. This analytically derived distribution is then compared to a common exponential model from the literature, revealing this distribution to be a close match in some cases and a lower bound in others. Lastly, the assumptions under which these results were derived suggest this model is aptly suited to characterize NLOS bias in 5G millimeter wave systems as well.

Inspired by the random sequential adsorption (RSA) process, we propose a new pilot assignment scheme for a distributed massive multiple-input-multiple- output (MIMO) system with desirable structural properties. In particular, this scheme ensures a minimum distance among co-pilot users to limit the effect of pilot contamination. Leveraging the rich literature of the RSA process, we analyze the statistics of the resulting co- pilot user point process when the system has only one pilot. Later, we extend the approach to obtain co-pilot user density for the scenario with multiple pilots. One of our key results is an accurate characterization of the probability of pilot assignment to a typical user in the network. Further, in order to provide a holistic overview of the performance of the proposed scheme, we compare the average user spectral efficiency (SE) of the proposed scheme with a baseline random pilot assignment scheme with no minimum distance guarantees. Our results demonstrate that the optimal distance threshold that maximizes the user SE for the proposed scheme decreases as the user density increases.

In this paper, we consider an underlay radar- massive MIMO spectrum sharing scenario in which massive MIMO base stations (BSs) with elevation beamforming capabilities are allowed to operate outside a circular exclusion zone centered at the radar. Modeling the locations of the massive MIMO BSs as a homogeneous Poisson point process (PPP), we derive an analytical expression for a tight upper bound on the average interference at the radar due to cellular transmissions. The challenge lies in bounding the worst-case elevation angle for each massive MIMO BS, for which we devise a novel construction based on the circumradius distribution of a typical Poisson-Voronoi (PV) cell. While these worst-case elevation angles are correlated for neighboring BSs due to the structure of the PV tessellation, it does not explicitly appear in our analysis because of our focus on the average interference. We also provide an estimate of the nominal average interference by approximating each cell as a circle with area equal to the average area of the typical cell. Using these results, we demonstrate that the gap between the two results remains approximately constant with respect to the exclusion zone radius. Our analysis reveals useful trends in average interference power, as a function of key deployment parameters such as radar/BS antenna heights, number of antenna elements per radar/BS, BS density, and exclusion zone radius.

Integrated access and backhaul (IAB) is an exciting new paradigm currently being investigated in the context of fifth generation (5G) millimeter wave (mm-wave) cellular networks, where the backhaul network (BN) shares the same resource and infrastructure used by the radio access network (RAN). While the IAB design will enable denser deployment of small cell base stations (SBSs) without the support of fiber backhaul, it will also lead to entirely new design challenges, e.g. the resource partitioning at the base stations (BSs) between the access and backhaul links. In order to study the design trends of this new paradigm, we develop a new stochastic geometry- based analytical framework for a two-tier mm-wave HetNet with IAB where the macro BSs (MBSs) provide wireless backhaul to the SBSs. For this network, we derive the downlink rate coverage probability. Our analysis reveals that offloading users from MBSs to SBSs may not provide significant rate improvements as it would if the SBSs were supported by fiber backhaul. We also show that due to the IAB design, there is a limit of densification of the SBSs beyond which no significant rate improvement is observed.

In wireless networks, many problems can be formulated as subset selection problems where the goal is to select a subset from the ground set with the objective of maximizing some objective function. These problems are typically NP-hard and hence solved through carefully constructed heuristics, which are themselves mostly NP-complete and thus not easily applicable to large networks. On the other hand, subset selection problems occur in slightly different context in machine learning (ML) where the goal is to select a subset of high quality yet diverse items from a ground set. This balance in quality and diversity is often maintained in the ML problems by using determinantal point process (DPP), which endows distributions on the subsets such that the probability of selecting two similar items is negatively correlated. While DPPs have been explored more generally in stochastic geometry (SG) to model inter-point repulsion, they are particularly conducive for ML applications because the parameters of their distributions can be efficiently learnt from a training set. In this paper, we introduce a novel DPP-based learning (DPPL) framework for efficiently solving subset selection problems in wireless networks. The DPPL is intended to replace the traditional optimization algorithms for subset selection by learning the quality-diversity trade-off in the optimal subsets selected by an optimization routine. As a case study, we apply DPPL to the wireless link scheduling problem, where the goal is to determine the subset of simultaneously active links which maximizes the network-wide sum-rate. We demonstrate that the proposed DPPL approaches the optimal solution with significantly lower computational complexity than the popular optimization algorithms used for this problem in the literature.

With the emergence of integrated access and backhaul (IAB) in the fifth generation (5G) of cellular networks, backhaul is no longer just a passive capacity constraint in cellular network design. In fact, this tight integration of access and backhaul is one of the key ways in which 5G millimeter wave (mm-wave) heterogeneous cellular networks (HetNets) differ from traditional settings where the backhaul network was designed independently from the radio access network (RAN). With the goal of elucidating key design trends for this new paradigm, we develop a stochastic geometry-based analytical framework for a millimeter wave (mm-wave) two-tier HetNet with IAB where only the macro BSs (MBSs) have fiber access to the core network and the small cell BSs (SBSs) are wirelessly backhauled by the MBSs over mm-wave links. For this network, we derive the downlink rate coverage probability for two types of resource allocations at the MBS: 1) integrated resource allocation (IRA): where the total bandwidth (BW) is dynamically split between access and backhaul, and 2) orthogonal resource allocation (ORA): where a static partition is defined for the access and backhaul communications. Our analysis concretely demonstrates that offloading users from the MBSs to SBSs may not provide similar rate improvements in an IAB setting as it would in a HetNet with fiber-backhauled SBS. Our analysis also shows that it is not possible to improve the user rate in an IAB setting by simply densifying the SBSs due to the bottleneck on the rate of wireless backhaul links between MBS and SBS.

Spectrum access and interference management are amongst the most challenging issues in device-to-device (D2D) cellular networks. In order to address these issues, this paper introduces spatial spectrum sensing (SSS) for D2D cellular networks to facilitate cellular spectrum sharing by D2D users while providing a quality of service guarantee for cellular users. In order to assess the performance of the proposed scheme, we adopt a stochastic geometry approach in which the locations of base stations and D2D devices are modeled as independent Poisson point processes (PPPs). Assuming that the locations of the active cellular transmitters form another independent PPP, we characterize the area spectral efficiency of D2D networks under cellular users' outage probability constraint. The use of SSS prohibits D2D transmissions around the active cellular users because of which the locations of the active D2D transmitters are modeled as a Poisson hole process driven by the PPP of active cellular user locations. Our analysis carefully accounts for this spatial separation between active cellular users and active D2D devices. Extensive simulation and numerical results are presented to verify our analysis and demonstrate the advantages of SSS-based D2D cellular networks.

In localization, an outage occurs if the positioning mean squared error (MSE) exceeds a pre-defined threshold εth. For time-of-arrival-based localization, a key factor affecting the MSE is the relative positions of the anchors with respect to the target location. From a design point of view, characterizing the distribution of the MSE over an ensemble of anchor locations as seen from the perspective of a target is essential for providing probabilistic performance guarantees against outage. To solve this difficult problem, previous works have assumed all anchor-target links to have the same SNR (i.e., SNR homogeneity), which neglects the impact of link distance variation on the SNR and the positioning error; for instance, under an inverse-square law pathloss model, the outage probability can differ by orders of magnitude when compared with the homogeneous SNR assumption. In this paper, we derive an approximate expression for the MSE distribution under an inverse-square law pathloss model when the anchors are uniformly distributed around a target. Through simulations, we verify that our approximation can be used to estimate the number of anchors needed so that the outage probability is below 1%.

In this paper, we analyze the performance of the uplink (UL) of a massive MIMO network considering an asymptotically large number of antennas at base stations (BSs). We model the locations of BSs as a homogeneous Poisson point process and assume that their service regions are limited to their respective Poisson-Voronoi cells (PVCs). Furthermore, for each PVC, based on a threshold radius, we model the cell center (CC) region as the Johnson-Mehl (JM) cell of its BS while the rest of the PVC is deemed as the cell edge (CE) region. The CC and CE users are located uniformly at random independently of each other in the JM cell and CE region, respectively. In addition, we consider fractional pilot reuse (FPR) scheme where two different sets of pilot sequences are used for CC and CE users with the objective of reducing the interference due to the pilot contamination for the CE users. Based on the above system model, we derive analytical expressions for the UL signal-tointerference-and-noise ratio (SINR) coverage probability and average spectral efficiency (SE) for randomly selected CC and CE users. In addition, we present an approximate expression for the average cell SE. One of the key intermediate results in our analysis is the approximate but accurate characterization of the distributions of the CC and CE areas of a typical cell. Another key intermediate step is the accurate characterization of the pair correlation functions of the point processes formed by the interfering CC and CE users that subsequently enables the coverage probability analysis. From our system analysis, we present a partitioning rule for the number of pilot sequences to be used for CC and CE users as a function of threshold radius that improves the average CE user SE, while achieving similar CC user SE with respect to the unity pilot reuse.

Owing to its flexibility in modeling real-world spatial configurations of users and base stations (BSs), the Poisson cluster process (PCP) has recently emerged as an appealing way to model and analyze heterogeneous cellular networks (HetNets). Despite its undisputed relevance to HetNets-corroborated by the models used in the industry-the PCP's use in performance analysis has been limited. This is primarily because of the lack of analytical tools to characterize the performance metrics, such as the coverage probability of a user connected to the strongest BS. In this paper, we develop an analytical framework for the evaluation of the coverage probability, or equivalently the complementary cumulative density function (CCDF) of signal-tointerference-and-noise ratio (SINR), of a typical user in a K-tier HetNet under a max power-based association strategy, where the BS locations of each tier follow either a Poisson point process (PPP) or a PCP. The key enabling step involves conditioning on the parent PPPs of all the PCPs, which allows us to express the coverage probability as a product of sum-product and probability generating functionals (PGFLs) of the parent PPPs. In addition to several useful insights, our analysis provides a rigorous way to study the impact of the cluster size on the SINR distribution, which was not possible using the existing PPP-based models.

Owing to the ubiquitous availability of radio- frequency (RF) signals, RF energy harvesting is a promising candidate for powering IoT devices, some of which may be deployed at difficult-to-reach places thus making it inconvenient or even impossible to replace or recharge their batteries. In this paper, we model and analyze an IoT network which harvests RF energy and receives information from the same wireless network. In order to enable this operation, each time slot is partitioned into charging and information reception phases. For this setup, we characterize two performance metrics: (i) energy coverage, and (ii) joint signal-to-interference-plus-noise (SINR) and energy coverage. This analysis is performed using a spatial model that captures coupling between the locations of the IoT devices and the nodes of the wireless network (referred henceforth as the IoT gateways), which is usually ignored in the existing literature. In particular, we model the locations of the IoT devices using a general Poisson cluster process (PCP) and assume that the IoT gateways (GWs) are located at the cluster centers. Our results concretely demonstrate that both energy and joint coverage probabilities decrease as the size of the clusters increases. As expected, the performance converges to the case of modeling the locations of the IoT devices and the GWs as two independent PPPs when the cluster sizes go to infinity.

Cache-enabled Device-to-Device (D2D) communication is widely recognized as one of the key components of the emerging fifth generation (5G) cellular network architecture. However, conventional half-duplex (HD) transmission may not be sufficient to provide fast enough content delivery over D2D links in order to meet strict latency targets of emerging D2D applications. In-band full-duplex (FD), with its capability of allowing simultaneous transmission and reception, can improve spectral efficiency and reduce latency by providing more content delivery opportunities. In this paper, we consider a finite network of D2D nodes in which each node is endowed with FD capability. We first carefully list all possible operating modes for an arbitrary device using which we compute the number of devices that are actively transmitting at any given time. We then characterize network performance in terms of the success probability, which depends on the content availability, signal-to-interference ratio (SIR) distribution, as well as the operating mode of the D2D receiver. Our analysis concretely demonstrates that caching dictates the system performance in lower target SIR thresholds whereas interference dictates the performance at the higher target SIR thresholds.

In this work, we analyze the performance of the uplink (UL) of a cellular network where the base station (BS) locations follow a homogeneous Poisson point process (PPP), and the locations of users and BSs are spatially coupled. In order to capture this coupling, we consider that users attached to a BS are located uniformly at random independently of each other in the Johnson-Mehl (JM) cell of that BS. For this system model, we derive analytical expressions for the UL signal to interference ratio (SIR) coverage probability and average spectral efficiency (SE) of a typical user in the network. One of the key intermediate steps in our analysis is the approximate, but accurate, characterization of the area distribution of a typical JM cell. Another key intermediate step is the accurate statistical characterization of the point process formed by the interfering users that subsequently enables the coverage probability analysis. We present coverage probability and SE results for a typical user and study the interplay between different system parameters.

In this paper, we study the coverage performance of vehicle-to-vehicle (V2V) communication using tools from stochastic geometry. In particular, we model the layout of roads using a Poisson line process (PLP) and the locations of vehicular nodes on each line as a 1D Poisson point process (PPP). In this Cox process of vehicular nodes, we analyze the performance of a typical receiver. In particular, assuming that the transmitting nodes employ beamforming to maximize signal power along their own roads, we first determine the probability with which the typical receiver connects to a node on the same road under a maximum average power based association scheme, using which we characterize the signal-to-interference ratio (SIR) based coverage performance under Nakagami-m fading. Key intermediate steps involve deriving the distribution of the distance between the typical receiver and the serving node (to characterize the desired signal power) and the distribution of the number of lines conditioned on the serving node (to characterize interference). Using these results, we derive an exact expression for coverage probability in terms of Laplace transform of the distribution of interference power. Our analysis reveals useful trends in coverage probability as a function of key network parameters, namely, line density and node density.

With the increasing network densification, it has become exceedingly difficult to provide traditional fiber backhaul access to each cell site, which is especially true for small cell base stations (SBSs). The increasing maturity of millimeter wave (mmWave) communication has opened up the possibility of providing high-speed wireless backhaul to such cell sites. Since mmWave is also suitable for access links, the third generation partnership project (3GPP) is envisioning an integrated access and backhaul (IAB) architecture for the fifth generation (5G) cellular networks in which the same infrastructure and spectral resources will be used for both access and backhaul. In this paper, we develop an analytical framework for IAB-enabled cellular network using which we provide an accurate characterization of its downlink rate coverage probability. Using this, we study the performance of two backhaul bandwidth (BW) partition strategies, (i) equal partition: when all SBSs obtain equal share of the backhaul BW, and (ii) load-based partition: when the backhaul BW share of an SBS is proportional to its load. Our analysis shows that depending on the choice of the partition strategy, there exists an optimal split of access and backhaul BW for which the rate coverage is maximized. Further, there exists a critical volume of cell-load (total number of users) beyond which the gains provided by the IAB-enabled network disappear and its performance converges to that of the traditional macro-only network with no SBSs.

Unbounded growth in cellular traffic is continuing to increase network power consumption meaning that the need for energy efficient cellular network design is more critical than ever. To find the trade-off between the spectral and energy efficiency, stochastic geometry has been widely employed where the cellular nodes are considered as being distributed according to a Poisson point process (PPP). Most of the prior works using stochastic geometry commonly assumed Rayleigh fading as the de facto fading model due to its tractability and simplicity. However, the propagation environments in which emerging cellular networks will operate, are diverse in nature, constituted by many different propagation phenomena which can not be fully captured by the Rayleigh distribution. To incorporate these physical attributes into the calculation of the network performance metrics, we consider κ-μ shadowed fading, which contains the majority of the well-known fading models as special cases. Using stochastic geometry, we evaluate the spectral efficiency and energy efficiency of a K-tier HetNet with K classes of BSs, differing in terms of the transmit power, BS density, shadowing and fading. Through numerical evaluation, we observe a trade-off relationship between the shadowing and fading parameters, spectral efficiency and energy efficiency, which provides important new insights into energy efficient network design.

The success of Internet-of-Things (IoT) relies on enabling the reliable exchange of data at low-rate and low-power among billions of battery-operated energy-constrained IoT devices. Ambient backscattering, with its technological capability of simultaneous information and energy transfer is quickly emerging as an appealing solution for this communication paradigm. In this paper, we investigate the detection of binary data transmitted using ambient backscatter at a receiver tracking the channel state information (CSI) of a flat-fading Rayleigh channel, and characterize the corresponding performance in terms of the bit-error probability. A binary hypothesis testing problem is formulated for the received signal and the performance of the receiver under mean threshold (MT) detection technique is analyzed. Two main contributions of the analysis that distinguish this work from the prior art are the characterization of the average signal energy in terms of the exact conditional density functions, and the characterization of average bit error rate (BER) expression for this setup. The key challenge lies in the handling of correlation between channel gains of two hypotheses for the derivation of joint probability distribution of magnitudes of channel gains that is needed for the BER analysis.

In this work, we analyze the performance of the downlink of a cell-free massive multiple-input multiple-output (mMIMO) system considering finite capacity fronthaul links. We model the locations of the remote radio heads (RRHs) and the users as two independent binomial point processes (BPPs). Conditioned on the locations of the RRHs and users, and considering imperfect channel state information (CSI) and conjugate beamforming at the RRHs, we derive an achievable rate for a randomly selected user in the network. Further, based on the dominant RRH approach, we provide an approximate but accurate expression to analytically evaluate this rate averaged over the spatial realizations of RRH and user locations. From our analysis, we arrive at the following conclusions: (1) the achievable average system sum-rate is a strictly quasi-concave function of the number of users in the network, (2) for the same number of antennas in the system, the optimal number of antennas per RRH to maximize the average user rate as well as average system sum-rate depends on the quality of the CSI. While for a high-quality CSI a more collocated system is preferred, for low-quality CSI it is better to consider a more distributed RRH deployment.

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated a variety of user and base station (BS) configurations to be considered for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models proposed by standardization bodies, such as the 3rd Generation Partnership Project (3GPP). Complementary to these simulation models, stochastic geometry-based approach, modeling the locations of the users, and the K tiers of BSs as independent and homogeneous Poisson point processes (PPPs), has gained prominence in the past few years. Despite its success in revealing useful insights, this PPP-based K-tier HetNet model is not rich enough to capture spatial coupling between user and BS locations that exists in real-world HetNet deployments and is included in 3GPP simulation models. In this paper, we demonstrate that modeling a fraction of users and arbitrary number of BS tiers alternatively with a Poisson cluster process (PCP) captures the aforementioned coupling, thus bridging the gap between the 3GPP simulation models and the PPP-based analytic model for HetNets. We further show that the downlink coverage probability of a typical user under maximum signal-tointerference-ratio (SIR) association can be expressed in terms of the sum-product functionals over PPP, PCP, and its associated offspring point process, which are all characterized as a part of our analysis. We also show that the proposed model converges to the PPP-based HetNet model as the cluster size of the PCPs tends to infinity. Finally, we specialize our analysis based on general PCPs for Thomas and Matérn cluster processes. Special instances of the proposed model closely resemble the different configurations for BS and user locations considered in 3GPP simulations.

In localization applications, the line-of-sight between anchors and targets may be blocked by obstacles in the environment. If an insufficient number of anchors are visible (i.e., have line-of-sight) to a target, then the target cannot be unambiguously localized and is, therefore, said to be in a blind spot. In this paper, we analyze the blind spot probability of a typical target by using stochastic geometry to model the randomness in the obstacle and anchor locations. In doing so, we handle correlated anchor blocking induced by the obstacles, unlike previous works that assume independent anchor blocking. We first characterize the regime over which the independent blocking assumption underestimates the blind spot probability of the typical target, which in turn is characterized as a function of the distribution of the visible area surrounding the target location. Since this distribution is difficult to exactly characterize, we formulate the nearest two-obstacle approximation, which is equivalent to considering correlated blocking for only the nearest two obstacles from the target and assuming independent blocking for the remaining obstacles. Based on this, we derive an approximate expression for the blind spot probability, which helps to determine the anchor deployment intensity needed for the blind spot probability of a typical target to be bounded above by a threshold, μ.

This paper develops a new approach to the modeling and analysis of heterogeneous cellular networks (HetNets) that accurately incorporates coupling across the locations of users and base stations, which exists due to the deployment of small cell base stations (SBSs) at the places of high user density (termed user hotspots in this paper). Modeling the locations of the geographical centers of user hotspots as a homogeneous Poisson point process (PPP), we assume that the users and SBSs are clustered around each user hotspot center independently with two different distributions. The macrocell BS locations are modeled by an independent PPP. This model is consistent with the user and SBS configurations considered by 3GPP. Using this model, we study the performance of a typical user in terms of coverage probability and throughput for two association policies: 1) Policy 1, under which a typical user is served by the open-access BS that provides maximum averaged received power and 2) Policy 2, under which the typical user is served by the small cell tier if the maximum averaged received power from the open-access SBSs is greater than a certain power threshold; and macro tier otherwise. A key intermediate step in our analysis is the derivation of distance distributions from a typical user to the open-access and closed-access interfering SBSs. Our analysis demonstrates that as the number of SBSs reusing the same resource block increases, coverage probability decreases, whereas throughput increases. Therefore, contrary to the usual assumption of orthogonal channelization, it is reasonable to assign the same resource block to multiple SBSs in a given cluster as long as the coverage probability remains acceptable. This approach to HetNet modeling and analysis significantly generalizes the state-of-the-art approaches that are based on modeling the locations of BSs and users by independent PPPs.

This paper studies the secrecy performance of a wireless network (primary network) overlaid with an ambient RF energy harvesting Internet of Things (IoT) network (secondary network). The nodes in the secondary network are assumed to be solely powered by ambient RF energy harvested from the transmissions of the primary network. We assume that the secondary nodes can eavesdrop on the primary transmissions due to which the primary network uses secrecy guard zones. The primary transmitter goes silent if any secondary receiver is detected within its guard zone. Using tools from stochastic geometry, we derive the probability of successful connection of the primary network as well as the probability of secure communication. Two conditions must be jointly satisfied in order to ensure successful connection: 1) the signal-to-interference-plus-noise ratio (SINR) at the primary receiver is above a predefined threshold, and 2) the primary transmitter is not silent. In order to ensure secure communication, the SINR value at each of the secondary nodes should be less than a predefined threshold. Clearly, when more secondary nodes are deployed, more primary transmitters will remain silent for a given guard zone radius, which will in turn impact the amount of energy harvested by the secondary network. Our results concretely show the existence of an optimal deployment density for the secondary network that maximizes the density of nodes that are able to harvest sufficient amount of energy. Furthermore, we show the dependence of this optimal deployment density on the guard zone radius of the primary network. In addition, we show that the optimal guard zone radius selected by the primary network is a function of the deployment density of the secondary network. This interesting coupling between the performance of the two networks is studied using tools from game theory. We propose an algorithm that can assist the two networks to converge to Nash equilibrium. The convergence of this algorithm is verified using simulations. Overall, this paper is one of the few concrete works that symbiotically merge tools from stochastic geometry and game theory.

Localization performance in wireless networks has traditionally been benchmarked using the Cramér–Rao lower bound (CRLB), given afixedgeometry of anchor nodes and a target. However, by endowing the target and anchor locations with distributions, this paper recasts this traditional scalar benchmark as a random variable. The goal of this paper is to derive an analytical expression for the distribution of this nowrandomCRLB, in the context of Time-of-Arrival-based positioning. To derive this distribution, this paper first analyzes how the CRLB is affected by the order statistics of the anglesbetweenconsecutive participating anchors (i.e.,internodal angles). This analysis reveals an intimate connection between the second largest internodal angle and the CRLB, which leads to an accurate approximation of the CRLB. Using this approximation, a closed-form expression for the distribution of the CRLB,conditionedon the number of participating anchors, is obtained. Next, this conditioning is eliminated to derive an analytical expression for themarginalCRLB distribution. Since this marginal distribution accounts for all target and anchor positions, across all numbers of participating anchors, it therefore statistically characterizes localization error throughout anentirewireless network. This paper concludes with a comprehensive analysis of this new network-wide-CRLB paradigm.

In this paper, we consider a vehicular network in which the wireless nodes are located on a system of roads. We model the roadways, which are predominantly straight and randomly oriented, by a Poisson line process (PLP) and the locations of nodes on each road as a homogeneous 1D Poisson point process. Assuming that each node transmits independently, the locations of transmitting and receiving nodes are given by two Cox processes driven by the same PLP. For this setup, we derive the coverage probability of a typical receiver, which is an arbitrarily chosen receiving node, assuming independent Nakagami-m fading over all wireless channels. Assuming that the typical receiver connects to its closest transmitting node in the network, we first derive the distribution of the distance between the typical receiver and the serving node to characterize the desired signal power. We then characterize coverage probability for this setup, which involves two key technical challenges. First, we need to handle several cases as the serving node can possibly be located on any line in the network and the corresponding interference experienced at the typical receiver is different in each case. Second, conditioning on the serving node imposes constraints on the spatial configuration of lines, which requires careful analysis of the conditional distribution of the lines. We address these challenges in order to characterize the interference experienced at the typical receiver. We then derive an exact expression for coverage probability in terms of the derivative of Laplace transform of interference power distribution. We analyze the trends in coverage probability as a function of the network parameters: line density and node density. We also provide some theoretical insights by studying the asymptotic characteristics of coverage probability.

With the increasing network densification, it has become exceedingly difficult to provide traditional fiber backhaul access to each cell site, which is especially true for small cell base stations (SBSs). The increasing maturity of millimeter wave (mm-wave) communication has opened up the possibility of providing high-speed wireless backhaul to such cell sites. Since mm-wave is also suitable for access links, the third generation partnership project (3GPP) is envisioning an integrated access and backhaul (IAB) architecture for the fifth generation (5G) cellular networks in which the same infrastructure and spectral resources will be used for both access and backhaul. In this paper, we develop an analytical framework for IAB-enabled cellular network using which its downlink rate coverage probability is accurately characterized. Using this framework, we study the performance of three backhaul bandwidth (BW) partition strategies: 1) equal partition: when all SBSs obtain equal share of the backhaul BW; 2) instantaneous load-based partition: when the backhaul BW share of an SBS is proportional to its instantaneous load; and 3) average load-based partition: when the backhaul BW share of an SBS is proportional to its average load. Our analysis shows that depending on the choice of the partition strategy, there exists an optimal split of access and backhaul BW for which the rate coverage is maximized. Further, there exists a critical volume of cell-load (total number of users) beyond which the gains provided by the IAB-enabled network disappear and its performance converges to that of the traditional macro-only network with no SBSs.

This paper develops a comprehensive framework for the performance analysis of user-centric capacity-driven small cell deployments, where small cell BSs (SBSs) are deployed at the places of high user density, i.e., user hotspots. In order to incorporate the correlation between user and SBS locations, we model the geographical centers of user hotspots as a homogeneous Poisson point process (PPP) around which users and SBSs are clustered following two independent general distributions. The macrocell base station (BS) locations are modeled by an independent PPP. A key intermediate step of our analysis is the derivation of a new set of distance distributions, which enable the exact characterization of coverage probability and throughput. For numerical evaluation, we specialized the setup to the case where users and SBSs are clustered with two independent normal distributions. Our analysis demonstrates that as the number of SBSs reusing the same resource block increases (higher frequency reuse), coverage probability decreases whereas throughput increases. Thus the same resource block can be aggressively reused by more SBSs as long as the coverage probability remains acceptable.

We present a general mathematical framework to characterize the performance of an arbitrarily-located reference receiver in a finite wireless network. Modeling the locations of nodes as a uniform binomial point process (BPP), we derive the general k-coverage probability, which is the distribution of the signal-to-interference ratio (SIR) at the reference receiver when it connects to its k-th closest transmitting node. This k-coverage result for an arbitrarily- located reference receiver significantly generalizes existing works on finite networks, which usually assume that the reference receiver connects to a pre-selected transmitter located at a fixed distance that may not be a part of the BPP (ad hoc network setup). A particular special case of interest is that of k=1, which can be interpreted as the downlink coverage probability in a finite cellular network modeled as a BPP. To the best of our understanding, the exact characterization of this result for finite cellular networks is not known. The mathematical analysis of k-coverage probability is enabled by the derivation of joint distance distributions from interfering and serving nodes to the reference receiver. As expected, our results demonstrate that the k-coverage probability strongly depends upon the location of the reference receiver. This observation highlights the importance of location information of the reference receiver for the accurate analysis of finite wireless networks.

This paper studies the secrecy performance in wireless networks (primary network) overlaid with an ambient RF energy harvesting network (secondary network). The nodes in the secondary network are assumed to be solely powered by ambient RF energy harvested from transmissions of the primary network. We assume that the secondary nodes can eavesdrop on the primary transmissions due to which the primary network uses secrecy guard zones. The primary transmitter goes silent if any secondary receiver is detected within its guard zone. Using tools from stochastic geometry, we first derive the optimal guard zone radius that minimizes the probability of going silent while ensuring a predefined minimum secure connection probability. Clearly, when more secondary nodes are deployed, more primary transmitters will remain silent for a given guard zone radius, thus impacting the amount of energy harvested by the secondary network. This introduces an interesting coupling between the performance of the two networks. We study this coupling using tools from game theory and propose an algorithm that can assist the two networks to converge to Nash equilibrium. Our results demonstrate the convergence of the proposed algorithm to the Nash equilibrium in finite number of iterations. Overall, this work forms one of the few concrete works that symbiotically merge tools from stochastic geometry and game theory.

In this paper, we characterize the joint coverage probability at two spatial locations in a cellular network. In particular, modeling the locations of cellular base stations (BSs) as a Poisson Point Process (PPP), we study interference correlation at two spatial locations L1and L2separated by a distance v, when user follows closest BS association policy at both spatial locations and moves from L1to L2. With this user displacement, two scenarios can occur: i) the user is handed off to a new serving BS at L2, or ii) no handoff occurs and the user is served by the same BS at both locations. After providing intermediate results such as probability of handoff and distance distributions of the serving BS at the two user locations, we derive exact expressions for the joint coverage probability for any distance separation v. The exact analysis is not straightforward and involves a careful treatment of the neighborhood of the two spatial locations and the resulting handoff scenarios. As expected, joint coverage probability decreases with the separation in the two locations.

In this work, we analyze the uplink performance of a massive multiple input multiple output network with asymptotically large number of antennas at the base stations. Following the usual approach, we first derive the characteristic function of interference and use the classical Gil-Palaez inversion theorem to obtain the coverage probability expression. However, since the resulting expression does not assume an efficient computational form, we propose our alternate approach that is based on approximate statistical characterization of interference by capturing the exact interference contribution from the dominant interferer and mean of the interference power from the rest of the interferers. Using this approximate but fairly accurate interference distribution, we derive the expressions for coverage probability and user spectral efficiency. These expressions are not only simpler to evaluate compared to other existing methods in literature, but also provide more accurate results in this line of work, which is validated through Monte Carlo simulations. One of the main outcomes of our analysis is that complete channel inversion based power control is not beneficial in terms of both ergodic spectral efficiency and outage spectral efficiency of a typical user.

In this paper we develop a comprehensive analytical framework for a cellular network enhanced with in-band device-to-device (D2D) communication capability where the D2D links reuse the downlink resources of the cellular links. The locations of the cellular base stations (BSs) are modeled as a Poisson point process (PPP). The user positions are modeled as a Thomas cluster process (TCP) to capture the inherent tendency of users to be located at close proximity to each other. The bandwidth allocated to D2D transmission is fixed and to cellular transmission is dynamic dependent on the load (the number of users) served by the macro BS. The users inside a cluster can either establish a D2D connection with a potential D2D transmitter (Tx) containing the file of interest within the same cluster if it is located closer than certain distance threshold or otherwise connects to the cellular network. By increasing this distance threshold, cellular traffic can be offloaded to D2D connections which in turn increases the interference from simultaneously active D2D Txs. We characterize the downlink rate coverage probability for this setup. Our analysis shows that there exists an optimum distance threshold for which rate coverage is maximized.

In this paper, we consider a finite network of unmanned aerial vehicles serving a given region. Modeling this network as a uniform binomial point process, we derive the downlink coverage probability of a reference receiver located at an arbitrary position on the ground assuming Nakagami-m fading for all wireless links. The reference receiver is assumed to connect to its closest transmitting node as is usually the case in cellular systems. After deriving the distribution of distances from the reference receiver to the serving and interfering nodes, we derive an exact expression for downlink coverage probability in terms of the derivative of Laplace transform of interference power distribution. In the downlink of this system, it is not unusual to encounter scenarios in which the line-of-sight component is significantly stronger than the reflected multipath components. To emulate such scenarios, we also derive the coverage probability in the absence of fading from the results of Nakagami-m fading by taking the limit m → ∞. Using asymptotic expansion of incomplete gamma function, we concretely show that this limit reduces to a redundant condition. Consequently, we derive an accurate coverage probability approximation for this case using dominant interferer-based approach in which the effect of dominant interferer is exactly captured and the residual interference from other interferers is carefully approximated. We then derive the bounds of the approximate coverage probability using Berry-Esseen theorem. Our analyses reveal several useful trends in coverage probability as a function of height of the transmitting nodes and the location of reference receiver on the ground.

Modeling the locations of nodes as a uniform binomial point process, we present a generic mathematical framework to characterize the performance of an arbitrarily located reference receiver in a finite wireless network. Different from most of the prior works where the serving transmitter (TX) is located at the fixed distance from the reference receiver, we consider two general TX-selection policies: 1) uniform TX-selection: the serving node is chosen uniformly at random from amongst all transmitting nodes and 2) k-closest TX-selection: the serving node is the kth closest node (out of all transmitting nodes) to the reference receiver. The key intermediate step in our analysis is the derivation of a new set of distance distributions that lead not only to the tractable analysis of coverage probability but also enable the analysis of wide range of classical and currently trending problems in wireless networks. Using this new set of distance distributions, we further investigate the diversity loss due to SIR correlation in a finite network. We then obtain the optimal number of links that can be simultaneously activated to maximize network spectral efficiency. Finally, we evaluate optimal caching probability to maximize the total hit probability in cache-enabled finite networks.

In this paper, we study jamming attacks against wireless networks. Specifically, we consider a network of base stations (BSs) or access points (APs) and investigate the impact of a fixed number of jammers that are randomly deployed according to a Binomial point process. We investigate the network performance in terms of: 1) the outage probability and 2) the error probability of a victim receiver in the downlink of this wireless network. We derive analytical expressions for both these metrics and discuss in detail how the jammer network must adapt to the various wireless network parameters in order to effectively attack the victim receivers. For instance, we will show that with only 1 jammer per BS/AP: 1) the outage probability of the wireless network can be increased from 1% (as seen in the non-jamming case) to 80% and 2) when retransmissions are used, the jammers cause the effective network activity factor (and hence the interference among the BSs) to be doubled. Furthermore, we show that the behavior of the jammer network as a function of the BS/AP density is not obvious. In particular, a non-trivial behavior is seen, which indicates that the number of jammers required to attack the wireless network must scale with the BS density only until a certain value beyond which it decreases. In the context of error probability of the victim receiver, we study whether or not some recent results related to jamming in the point-to-point link scenario can be extended to the case of jamming against wireless networks. Numerical results are presented to validate all the theoretical inferences presented.

Device-to-device (D2D) communications are now considered an integral part of future 5G networks, which will enable direct communication between user equipments and achieve higher throughputs than conventional cellular networks, but with the increased potential for co-channel interference. The physical channels, which constitute D2D communications, can be expected to be complex in nature, experiencing both line-ofsight (LOS) and non-LOS conditions across closely located D2D pairs. In addition to this, given the diverse range of operating environments, they may also be subject to clustering of the scattered multipath contribution, i.e., propagation characteristics which are quite dissimilar to conventional Rayleigh fading environments. To address these challenges, we consider two recently proposed generalized fading models, namely κ-μ and η-μ, to characterize the fading behavior in D2D communications. Together, these models encompass many of the most widely utilized fading models in the literature such as Rayleigh, Rice (Nakagami-n), Nakagami-m, Hoyt (Nakagami-q), and One-sided Gaussian. Using stochastic geometry, we evaluate the spectral efficiency and outage probability of D2D networks under generalized fading conditions and present new insights into the tradeoffs between the reliability, rate, and mode selection. Through numerical evaluations, we also investigate the performance gains of D2D networks and demonstrate their superiority over traditional cellular networks.

Emerging cellular technologies such as those proposed for use in 5G communications will accommodate a wide range of usage scenarios with diverse link requirements. This will necessitate operation over a versatile set of wireless channels ranging from indoor to outdoor, from line-of-sight (LOS) to non-LOS, and from circularly symmetric scattering to environments which promote the clustering of scattered multipath waves. Unfortunately, many of the conventional fading models lack the flexibility to account for such disparate signal propagation mechanisms. To bridge the gap between theory and practical channels, we consider κ-μ shadowed fading, which contains as special cases the majority of the linear fading models proposed in the open literature. In particular, we propose an analytic framework to evaluate the average of an arbitrary function of the signal-to-noise-plus-interference ratio (SINR) over κ-μ shadowed fading channels by using an orthogonal expansion with tools from stochastic geometry. Using the proposed method, we evaluate the spectral efficiency, moments of the SINR, and outage probability of a K-tier heterogeneous cellular network with K classes of base stations (BSs), differing in terms of the transmit power, BS density, shadowing, and fading characteristics. Building upon these results, we provide important new insights into the network performance of these emerging wireless applications while considering a diverse range of fading conditions and link qualities.

This paper provides an analytical framework with foundations in stochastic geometry to characterize the spatiotemporal interference correlation as well as the joint coverage probability at two spatial locations in a cellular network. In particular, modeling the locations of cellular base stations (BSs) as a Poisson point process, we study interference correlation at two spatial locations ℓ1and ℓ2separated by a distance v, when the user follows the closest BS association policy at both spatial locations and moves from ℓ1to ℓ2. With this user displacement, two scenarios can occur: i) the user is handed off to a new serving BS at ℓ2, or ii) no handoff occurs and the user is served by the same BS at both locations. After providing intermediate results, such as probability of handoff and distance distributions of the serving BS at the two user locations, we use them to derive exact expressions for spatio-temporal interference correlation coefficient and joint coverage probability for any distance separation v. We also study two different handoff strategies: i) handoff skipping, and ii) conventional handoffs, and derive the expressions of joint coverage probability for both strategies. The exact analysis is not straightforward and involves a careful treatment of the neighborhood of the two spatial locations and the resulting handoff scenarios. To provide analytical insights, we also provide easy-to-use expressions for two special cases: i) static user (v = 0) and ii) highly mobile user (v → ∞). As expected, our analysis shows that the interference correlation and joint coverage probability decrease with increasing v, with v → ∞ corresponding to a completely uncorrelated scenario. Further design insights are also provided by studying the effect of few network/channel parameters, such as BS density and path loss on the interference correlation.

One of the principal underlying assumptions of current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models is the uniform distribution of users independent of the base station (BS) locations. This assumption is not quite accurate, especially for user-centric capacity-driven small cell deployments where low-power BSs are deployed in the areas of high user density, thus inducing a natural correlation in the BS and user locations. In order to capture this correlation, we enrich the existing K-tier Poisson point process (PPP) HetNet model by considering user locations as Poisson Cluster Process with the BSs at the cluster centers. In particular, we provide the formal analysis of the downlink coverage probability in terms of a general density function describing the locations of users around the BSs. The derived results are specialized for two cases of interest: 1) Thomas cluster process, where the locations of the users around BSs are Gaussian distributed and 2) Matérn cluster process, where the users are uniformly distributed inside a disc of a given radius. Tight closed-form bounds for the coverage probability in these two cases are also derived. Our results demonstrate that the coverage probability decreases as the size of user clusters around BSs increases, ultimately collapsing to the result obtained under the assumption of PPP distribution of users independent of the BS locations when the cluster size goes to infinity. Using these results, we also handle mixed user distributions consisting of two types of users: 1) uniformly distributed and 2) clustered around certain tiers.

This paper studies the downlink performance of a cellular-based internet-of-things (IoT) network where the receiving devices are solely powered by energy harvested from the ambient radio frequency (RF). Assuming that the cellular network is the only source of RF energy, we consider a time-division based approach for power and information transfer where each time slot is partitioned into two sub-lots: (i) charging sub-slot during which the base stations (BSs) act as chargers for the devices, and (ii) information sub-slot in which the devices receive information using energy harvested during the charging sub-slot. Modeling the BS locations as a Poisson Point Process (PPP), we study a new composite outage probability metric that considers the joint effect of outages due to insufficient energy harvested during the charging sub-slot and low signal quality in the information sub-slot. Using this metric, we concretely demonstrate the existence of an optimum downlink time slot division between charging and information transmission that maximizes the average downlink throughput for a given user.

In this paper, we develop a comprehensive analytical framework to characterize the performance of device-centric content availability in device-to-device (D2D) networks. Modeling the locations of devices as a variant of Thomas cluster process, we derive the coverage probability of a typical device when its content of interest is available at its kth closest device within the same cluster. Using the coverage probability results, we characterize the area spectral efficiency (ASE) of the whole network. A key intermediate step in this analysis is the derivation of the distributions of distances from the typical device to both the intra- and inter-cluster devices. Our analysis reveals that an optimum number of D2D transmitters must be simultaneously activated per cluster in order to maximize ASE. This can be interpreted as the classical tradeoff between more aggressive frequency reuse and higher interference power. Our analysis also quantifies the best and worst case performance of the clustered D2D networks both in terms of coverage and ASE.

In this paper, we analyze jamming against wireless networks from an error probability perspective. Specifically, we investigate the impact of a fixed number of jammers against a network of base stations (BS) or access points (AP). We first derive analytical expressions for the error probability of a victim receiver in the downlink of this wireless network and later study whether or not some recent results related to jamming in the point-to-point link scenario can be extended to the case of jamming against wireless networks.

Machine-to-machine (M2M) communication's severe power limitations challenge the interconnectivity, access management, and reliable communication of data. In densely deployed M2M networks, coordinating and aggregating the generated data is critical. We propose an energy efficient data aggregation scheme for a hierarchical M2M network with truncated power control. We optimize the number of hierarchical stages and perform a coverage probability-based uplink analysis for M2M devices. Our analysis exposes the key tradeoffs between the coverage characteristics for successive and parallel transmission schemes that can be either half-duplex or full-duplex. Comparing the rate performances of the transmission models, we observe that successive and half-duplex parallel modes have better coverage characteristics compared to full-duplex parallel scheme.

Current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models assume users to be distributed according to a homogeneous Poisson Point Process (PPP) independently of the base station (BS) locations. In reality, however, current deployments are capacity-driven, which correlates the BS and user locations. In this paper, we develop tools for the downlink analysis of HetNets with general nonuniform user distributions by enriching the K-tier PPP HetNet model. Instead of being PPP distributed, the user locations are modeled by a Poisson cluster process with the cluster centers being the BSs. In particular, we provide the first formal analysis of the downlink coverage probability in terms of a general density function describing the locations of users around the BSs. All the results are specialized to a particular case of a Thomas cluster process, where the locations of the users around BSs are Gaussian distributed. Our results concretely demonstrate that the coverage probability decreases with the increasing variance of the user location distribution, ultimately collapsing to the result for the PPP user distribution when the variance goes to infinity.

To maintain tractability, interference field is often modeled as a homogeneous Poisson Point Process (PPP) in the analysis of wireless networks. While it provides meaningful first-order results, it falls short in modeling the effect of interference management techniques, which typically introduce some form of spatial interaction among transmitters. In some applications, such as cognitive radio and device-to-device networks, this interaction results in the formation of holes in an otherwise homogeneous interference field. The resulting interference field can be accurately modeled as a Poisson Hole Process (PHP). Despite the importance of PHP in modeling wireless networks, exact characterization of the interference experienced by a typical node in a PHP is an open problem. In this paper, we introduce a new approach to modeling the PHP, in which we dissolve the holes in such a way that it results in an equivalent non-homogeneous PPP, which is much more amenable to shot-noise analysis. Using this approach, we derive new lower and upper bounds on the Laplace transform of interference in a PHP. The new bounds are compared numerically to the known approaches and are shown to be very tight under various operational regimes.

This paper develops a comprehensive analytical framework with foundations in stochastic geometry to characterize the performance of cluster-centric content placement in a cache-enabled device-to-device (D2D) network. Different from device-centric content placement, cluster-centric placement focuses on placing content in each cluster, such that the collective performance of all the devices in each cluster is optimized. Modeling the locations of the devices by a Poisson cluster process, we define and analyze the performance for three general cases: 1) k-Tx case: the receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at the kth closest device to the cluster center; 2) 1-Rx case: the receiver of interest is the Ith closest device to the cluster center and its content of interest is available at a device chosen uniformly at random from the same cluster; and 3) baseline case: the receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at a device chosen independently and uniformly at random from the same cluster. Easy-to-use expressions for the key performance metrics, such as coverage probability and area spectral efficiency of the whole network, are derived for all three cases. Our analysis concretely demonstrates significant improvement in the network performance when the device on which content is cached or device requesting content from cache is biased to lie closer to the cluster center compared with the baseline case. Based on this insight, we develop and analyze a new generative model for cluster-centric D2D networks that allows to study the effect of intra-cluster interfering devices that are more likely to lie closer to the cluster center.

Machine-to-machine (M2M) communication's severe power limitations challenge the interconnectivity, access management, and reliable communication of data. In densely deployed M2M networks, controlling and aggregating the generated data is critical. We propose an energy-efficient data aggregation scheme for a hierarchical M2M network. We develop a coverage probability-based optimal data aggregation scheme for M2M devices to minimize the average total energy expenditure per unit area per unit time or simply the energy density of an M2M communication network. Our analysis exposes the key tradeoffs between the energy density of the M2M network and the coverage characteristics for successive and parallel transmission schemes that can be either half-duplex or full-duplex. Comparing the rate and energy performances of the transmission models, we observe that successive mode and half-duplex parallel mode have better coverage characteristics compared to full-duplex parallel scheme. Simulation results show that the uplink coverage characteristics dominate the trend of the energy consumption for both successive and parallel schemes.

Device-to-device (D2D) communication enables direct communication between proximate devices thereby improving the overall spectrum utilization and off-loading traffic from cellular networks. This paper develops a new spatial model for D2D networks in which the device locations are modeled as a Poisson cluster process. Using this model, we study the performance of a typical D2D receiver in terms of coverage probability under two realistic content availability setups: 1) content of interest for a typical device is available at a device chosen uniformly at random from the same cluster, which we term uniform content availability, and 2) content of interest is available at the kthclosest device from the typical device inside the same cluster, which we term k-closest content availability. Using these coverage probability results, we also characterize the area spectral efficiency (ASE) of the whole network for the two setups. A key intermediate step in this analysis is the derivation of the distributions of distances from a typical device to both the intra-and inter-cluster devices. Our analysis reveals that an optimum number of D2D transmitters must be simultaneously activated per cluster in order to maximize ASE. This can be interpreted as the classical tradeoff between more aggressive frequency reuse and higher interference power. The optimum number of simultaneously transmitting devices and the resulting ASE increase as the content is made available closer to the receivers. Our analysis also quantifies the best and worst case performance of clustered D2D networks both in terms of coverage and ASE.

When dedicated positioning systems, such as GPS, are unavailable, a mobile device has no choice but to fall back on its cellular network for localization. Due to random variations in the channel conditions to its surrounding base stations (BS), the mobile device is likely to face a mix of both favorable and unfavorable geometries for localization. Analytical studies of localization performance (e.g., using the Cramér-Rao lower bound) usually require that one fix the BS geometry, and favorable geometries have always been the preferred choice in the literature. However, not only are the resulting analytical results constrained to the selected geometry, this practice is likely to lead to overly-optimistic expectations of typical localization performance. Ideally, localization performance should be studied across all possible geometric setups, thereby also removing any selection bias. This, however, is known to be hard and has been carried out only in simulation. In this paper, we develop a new tractable approach where we endow the BS locations with a distribution by modeling them as a Poisson point process (PPP), and use tools from stochastic geometry to obtain easy-to-use expressions for key performance metrics. In particular, we focus on the probability of detecting some minimum number of BSs, which is shown to be closely coupled with a network operator's ability to obtain satisfactory localization performance (e.g., meet FCC E911 requirements). This metric is indifferent to the localization technique (e.g., TOA, TDOA, AOA, or hybrids thereof), though different techniques will presumably lead to different BS hearability requirements. In order to mitigate excessive interference due to the presence of dominant interferers in the form of other BSs, we incorporate both BS coordination and frequency reuse in the proposed framework and quantify the resulting performance gains analytically.

In this paper, we mathematically characterize the improvement in device localizability achieved by allowing collaboration among devices. Depending on the detection sensitivity of the receivers in the devices, it is not unusual for a device to be localized to lack a sufficient number of detectable positioning signals from localized devices to determine its location without ambiguity (i.e., to be uniquely localizable). This occurrence is well-known to be a limiting factor in localization performance, especially in communications systems. In cellular positioning, e.g., cellular network designers call this the hearability problem. We study the conditions required for unique localizability and use tools from stochastic geometry to derive accurate analytic expressions for the probabilities of meeting these conditions in the noncollaborative and collaborative cases. We consider the scenario without shadowing, the scenario with shadowing and universal frequency reuse, and, finally, the shadowing scenario with random frequency reuse. The results from the latter scenario, which apply particularly to cellular networks, reveal that collaboration between two devices separated by only a short distance yields drastic improvements in both devices' abilities to uniquely determine their positions. The results from this analysis are very promising and motivate delving further into techniques which enhance cellular positioning with small-scale collaborative ranging observations among nearby devices.

Interference field in wireless networks is often modeled by a homogeneous Poisson point process (PPP). While it is realistic in modeling the inherent node irregularity and provides meaningful first-order results, it falls short in modeling the effect of interference management techniques, which typically introduces some form of spatial interaction among active transmitters. In some applications, such as cognitive radio and device-to-device networks, this interaction may result in the formation of holes in an otherwise homogeneous interference field. The resulting interference field can be accurately modeled as a Poisson hole process (PHP). Despite the importance of the PHP in many applications, the exact characterization of interference experienced by a typical node in the PHP is not known. In this paper, we derive several tight upper and lower bounds on the Laplace transform of this interference. Numerical comparisons reveal that the new bounds outperform all known bounds and approximations, and are remarkably tight in all operational regimes of interest. The key in deriving these tight and yet simple bounds is to capture the local neighborhood around the typical node accurately while simplifying the far field to attain tractability. Ideas for tightening these bounds further by incorporating the effect of overlaps in the holes are also discussed. These results immediately lead to an accurate characterization of the coverage probability of the typical node in the PHP under Rayleigh fading.

This paper develops a new spatial model for device-to-device (D2D) networks in which the device locations are modeled as a Thomas cluster process. The devices inside a given cluster form D2D links amongst themselves and the direct communication across clusters is not required. This model captures the fact that the devices engaged in D2D communications need to be in close proximity of each other. For this model, we derive easy-to-use expressions for both coverage probability and area spectral efficiency (ASE) assuming that the content of interest is available at a device chosen uniformly at random from the same cluster. One of the important consequences of this analysis is that there exists an optimal number of simultaneously active D2D-Txs that maximizes the ASE. This can be interpreted as the classical tradeoff between more aggressive frequency reuse and higher interference power. Our analysis also provides insights into the effect of scattering variance of each cluster and the density of cluster centers on coverage probability and ASE.

In this paper, we study the downlink performance of a heterogeneous cellular network (HetNet) where both macro and small cells share the same spectrum and hence interfere with each other. We assume that the users are concentrated at certain areas in the cell, i.e., they form hotspots. While some of the hotspots are assumed to have a small cell in their vicinity, the others are directly served by the macrocell. Due to a relatively small area of each hotspot, the users lying in a particular hotspot appear to be almost co-located to the macrocells, which are typically deployed at some elevation. We assume a large number of antennas at the macrocell relative to the number of users simultaneously served. In this “massive MIMO” regime, the channel vectors become highly directional. We exploit this directionality in the channel vectors to obtain spatial blanking, i.e., concentrating transmission energy only in certain directions while creating transmission opportunities for the small cells lying in the other directions. In addition to this inherent interference suppression, we also develop three low-complexity interference coordination strategies: turn off small cells based on the amount of cross-tier interference they receive or cause to the scheduled macrocell hotspots; schedule hotspots such that treating interference as noise is approximately optimal for the resulting Gaussian interference channel; and offload some of the macrocell hotspots to nearby small cells to improve throughput fairness across all hotspots. For all these schemes, we study the relative merits and demerits of uniform deployment of small cells vs. deploying more small cells towards the cell center or the cell edge.

Although the Poisson point process (PPP) has been widely used to model base station (BS) locations in cellular networks, it is an idealized model that neglects the spatial correlation among BSs. This paper proposes the use of the determinantal point process (DPP) to take into account these correlations, in particular the repulsiveness among macro BS locations. DPPs are demonstrated to be analytically tractable by leveraging several unique computational properties. Specifically, we show that the empty space function, the nearest neighbor function, the mean interference, and the signal-to-interference ratio (SIR) distribution have explicit analytical representations and can be numerically evaluated for cellular networks with DPP-configured BSs. In addition, the modeling accuracy of DPPs is investigated by fitting three DPP models to real BS location data sets from two major U.S. cities. Using hypothesis testing for various performance metrics of interest, we show that these fitted DPPs are significantly more accurate than popular choices such as the PPP and the perturbed hexagonal grid model.

This paper studies the scalability of a wireless backhaul network modeled as a random extended network with multiantenna base stations (BSs), where the number of antennas per BS is allowed to scale as a function of the network size. The antenna scaling is justified by the current trend toward the use of higher carrier frequencies, which allows packing a large number of antennas in small form factors. The main goal is to study the per-BS antenna requirement that ensures scalability of this network, i.e., its ability to deliver nonvanishing rate to each source-destination pair. We first derive an information theoretic upper bound on the capacity of this network under a general propagation model, which provides a lower bound on the per-BS antenna requirement. Then, we characterize the scalability requirements for two competing strategies of interest: 1) long hop: each source-destination pair minimizes the number of hops by sacrificing multiplexing gain while achieving full beamforming (power) gain over each hop; and 2) short hop: each source-destination pair communicates through a series of short hops, each achieving full multiplexing gain. While long hop may seem more intuitive in the context of massive multiple-input-multiple-output transmission, we show that the short hop strategy is significantly more efficient in terms of per-BS antenna requirement for throughput scalability. As a part of the proof, we construct a scalable short hop strategy and show that it does not violate any fundamental limits on the spatial degrees of freedom.

We study multiple-input-multiple-output (MIMO)-based downlink heterogeneous cellular networks (HetNets) with joint transmit-receive diversity using orthogonal space-time block coding at the base stations (BSs) and maximal-ratio combining (MRC) at the users. MIMO diversity with MRC receivers is particularly appealing in cellular networks due to the relatively low hardware complexity at both the BS and the user device. Using stochastic geometry, we develop a tractable stochastic model for analyzing such HetNets taking into account the irregular and multitier BS deployment. We derive the coverage probability for both interference-blind (IB) and interference-aware (IA) MRC as a function of the relevant tier-specific system parameters such as BS density and transmit (Tx) power, number of Tx antennas, and path-loss law. Important insights arising from our analysis for typical HetNets are as follows: 1) IA-MRC becomes less favorable than IB-MRC with Tx diversity due to the smaller interference variance and increased interference correlation across receive (Rx) antennas; 2) ignoring spatial interference correlation significantly overestimates the performance of IA-MRC; and 3) for a small number of Rx antennas, selection combining may offer a better performance-complexity tradeoff than MRC.

In this paper, we study the coverage probability of a K-tier multiple-input multiple-output heterogeneous cellular network (MIMO HetNet) assuming (i) zero-forcing precoding at all the base stations (BSs), (ii) Rayleigh fading, (iii) independent Poisson Point Process (PPP) model for the locations of BSs of each tier, and (iv) general cell selection rule that maximizes average received signal-to-interference-plus-noise ratio (SINR) at the users. Our analysis highlights key differences between MIMO HetNets and the more familiar single antenna HetNets in terms of cell selection. While it is challenging to derive exact cell selection rule to maximize average downlink SINR in MIMO HetNets, we show that adding an appropriately chosen per-tier selection bias yields a close approximation. The bias value for each tier is given in closed form. One interpretation of this result is that MIMO HetNets may balance load more naturally across different tiers in certain special cases compared to single antenna HetNets where an artificial selection bias is often needed for load balancing.

The macro base station (BS) deployments in modern cellular networks are neither regular nor completely random. We use determinantal point process (DPP) models to study the repulsiveness among macro base stations observed in cellular networks. Three DPP models are fitted to base station location data sets from two major US cities. Hypothesis testing is used to validate the goodness-of-fit for these DPP models. Based on performance metrics including the K-function, the L-function and coverage probability, DPP models are shown to be accurate in modeling real BS deployments. On the contrary, the Poisson point process and perturbed hexagonal grid model are shown to be less realistic. Different DPP models are compared, and several computational properties of these models are also discussed.

In this paper, we study physical layer security for the downlink of cellular networks. In a cellular network, the confidential messages transmitted to each mobile user can be eavesdropped by the other users in the same cell and also by the users in the other cells. We model the locations of base stations and mobile users as two independent two-dimensional Poisson point processes. By combining tools from stochastic geometry and random matrix theory, we analyze the secrecy rates achievable with regularized channel inversion (RCI) precoding under Rayleigh fading. Our analysis shows that unlike isolated cells, the secrecy rate in a cellular network does not grow monotonically with the transmit power. Moreover, we find that the network tends to be in secrecy outage if the transmit power grows unbounded. Furthermore, we show that there exists an optimal value for the base station deployment density that maximizes the secrecy rate.

We derive an information theoretic upper bound on the capacity of a wireless backhaul network modeled as a classical random extended network, except that we assume the number of antennas at each base station (BS) also scales up as an arbitrary function of network size. The antenna scaling is justified because of the increasing maturity of higher transmission frequencies which enables us to pack large number of antennas in small form factors. The main technical arguments are based on the generalization of geometric exponential stripping technique of [1] to channel matrices with complex-valued channel gains. An important consequence of our result is a lower bound on the number of antennas per BS required for network scalability.

This paper considers an extended wireless network with multi-antenna nodes in line-of-sight (LoS) propagation environment. Assuming that the number of antennas at each node can be scaled as some arbitrary function of the number of nodes, we study the scalability of this network, i.e., its ability to deliver non-zero rate to each source-destination pair. Since the rank of the LoS multiple-input multiple-output (MIMO) channel starts collapsing with the increasing separation between the transmitter and the receiver, we consider two competing transmission strategies: (i) long hop: each source-destination pair minimizes the number of hops by sacrificing multiplexing gain and ideally achieving full power gain over each hop, and (ii) short hop: each source-destination pair communicates through a series of short hops each achieving full multiplexing gain. By characterizing the number of antennas required to achieve scalability in both the cases, we show that the antenna requirement is significantly less for the short hop case. These results have key applications in the design of wireless backhaul for cellular networks, where the possibility of having massive MIMO links is becoming a reality due to the increasing maturity of higher transmission frequencies, e.g., 28 and 38 GHz.

For wireless systems in which randomly arriving devices attempt to transmit a fixed payload to a central receiver, we develop a framework to characterize the system throughput as a function of arrival rate and per-device data rate. The framework considers both coordinated transmission (where devices are scheduled) and uncoordinated transmission (where devices communicate on a random access channel and a provision is made for retransmissions). Our main contribution is a novel characterization of the optimal throughput for the case of uncoordinated transmission and a strategy for achieving this throughput that relies on overlapping transmissions and joint decoding. Simulations for a noise-limited cellular network show that the optimal strategy provides a factor of four improvement in throughput compared with slotted ALOHA. We apply our framework to evaluate more general system-level designs that account for overhead signaling. We demonstrate that, for small payload sizes relevant for machine-to-machine (M2M) communications (200 bits or less), a one-stage strategy, where identity and data are transmitted optimally over the random access channel, can support at least twice the number of devices compared with a conventional strategy, where identity is established over an initial random-access stage and data transmission is scheduled.

In this paper, we study physical layer security for the downlink of cellular networks, where the confidential messages transmitted to each mobile user can be eavesdropped by both (i) the other users in the same cell and (ii) the users in the other cells. The locations of base stations and mobile users are modeled as two independent two-dimensional Poisson point processes. Using the proposed model, we analyze the secrecy rates achievable by regularized channel inversion (RCI) precoding by performing a large-system analysis that combines tools from stochastic geometry and random matrix theory. We obtain approximations for the probability of secrecy outage and the mean secrecy rate, and characterize regimes where RCI precoding achieves a nonzero secrecy rate. We find that unlike isolated cells, the secrecy rate in a cellular network does not grow monotonically with the transmit power, and the network tends to be in secrecy outage if the transmit power grows unbounded. Furthermore, we show that there is an optimal value for the base station deployment density that maximizes the secrecy rate, and this value is a decreasing function of the signal-to-noise ratio.

We model and analyze heterogeneous cellular networks with multiple antenna BSs (multi-antenna HetNets) with K classes or tiers of base stations (BSs), which may differ in terms of transmit power, deployment density, number of transmit antennas, number of users served, transmission scheme, and path loss exponent. We show that the cell selection rules in multi-antenna HetNets may differ significantly from the single-antenna HetNets due to the possible differences in multi-antenna transmission schemes across tiers. While it is challenging to derive exact cell selection rules even for maximizing signal-to-interference-plus-noise-ratio (SINR) at the receiver, we show that adding an appropriately chosen tier-dependent cell selection bias in the received power yields a close approximation. Assuming arbitrary selection bias for each tier, simple expressions for downlink coverage and rate are derived. For coverage maximization, the required selection bias for each tier is given in closed form. Due to this connection with biasing, multi-antenna HetNets may balance load more naturally across tiers in certain regimes compared to single-antenna HetNets, where a large cell selection bias is often needed to offload traffic to small cells.

Despite being ubiquitous in practice, the performance of maximal-ratio combining (MRC) in the presence of interference is not well understood. Because the interference received at each antenna originates from the same set of interferers but partially decorrelates over the fading channel, it possesses a complex correlation structure. This paper develops a realistic analytic model that accurately accounts for the interference correlation using stochastic geometry. Modeling interference by a Poisson shot noise process with independent Nakagami fading, we derive the link success probability for dual-branch interference-aware MRC. Using this result, we show that the common assumption that all receive antennas experience equal interference power underestimates the true performance, although this gap rapidly decays with increasing the Nakagami parameter mIof the interfering links. In contrast, ignoring interference correlation leads to a highly optimistic performance estimate for MRC, especially for large mI. In the low outage probability regime, our success probability expression can be considerably simplified. Observations based from the analysis include the following: 1) For small path loss exponents, MRC and minimum mean square error combining exhibit similar performance, and 2) the gains of MRC over selection combining are smaller in the interference-limited case than in the well-studied noise-limited case.

We develop a new tractable model for K-tier heterogeneous cellular networks (HetNets), where each base station (BS) is powered solely by a self-contained energy harvesting module. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power and deployment density. Since a BS may not always have enough energy, it may need to be kept OFF and allowed to recharge while nearby users are served by neighboring BSs that are ON. We show that the fraction of time a kthtier BS can be kept ON, termed availability ρk, is a fundamental metric of interest. Using tools from random walk theory, fixed point analysis and stochastic geometry, we characterize the set of K-tuples (ρ1, ρ2, ... ρK), termed the availability region, that is achievable by general uncoordinated operational strategies, where the decision to toggle the current ON/OFF state of a BS is taken independently of the other BSs. If the availability vector corresponding to the optimal system performance, e.g., in terms of rate, lies in this availability region, there is no performance loss due to the presence of unreliable energy sources. As a part of our analysis, we model the temporal dynamics of the energy level at each BS as a birth-death process, derive the energy utilization rate, and use hitting/stopping time analysis to prove that there exists a fundamental limit on ρkthat cannot be surpassed by any uncoordinated strategy.

While the performance of maximum ratio combining (MRC) is well understood for a single isolated link, the same is not true in the presence of interference, which is typically correlated across antennas due to the common locations of interferers. For tractability, prior work focuses on the two extreme cases where the interference power across antennas is either assumed to be fully correlated or fully uncorrelated. In this paper, we address this shortcoming and characterize the performance of MRC in the presence of spatially-correlated interference across antennas. Modeling the interference field as a Poisson point process, we derive the exact distribution of the signal-to-interference ratio (SIR) for the case of two receive antennas, and upper and lower bounds for the general case. Using these results, we study the diversity behavior of MRC and characterize the critical density of simultaneous transmissions for a given outage constraint. The exact SIR distribution is also useful in benchmarking simpler correlation models. We show that the full-correlation assumption is considerably pessimistic (up to 30% higher outage probability for typical values) and the no-correlation assumption is significantly optimistic compared to the true performance.

We consider a wireless time-slotted random access channel where user arrivals are characterized by a Poisson process. Each user comes with a fixed payload, which has to be transmitted in the slot in which it arrives. If the transmission is successful, the user leaves the system, else it is dropped. The receiver and users are assumed to have knowledge of the arrival rate λ, but they are not aware of the actual number of users simultaneously attempting to communicate during a given time slot. In contrast to a conventional slotted ALOHA-based strategy where the channel is partitioned into orthogonal subchannels and each user communicates on a randomly chosen subchannel, we propose a novel strategy whereby users transmit simultaneously over the entire channel resource and the receiver jointly decodes the transmissions. Under the proposed strategy, neither users nor the receiver have prior knowledge of the active user set. Our analysis concretely demonstrates that the proposed strategy is optimal in terms of maximizing the average throughput among all uncoordinated strategies. Numerical results show that the proposal provides an order of magnitude throughput improvement compared to slotted ALOHA in a single-cell environment under a 10% maximum outage constraint.

We develop a new tractable model for K-tier cellular networks, where each base station (BS) is solely powered by a self-contained energy harvesting module instead of a conventional power-line source. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power and deployment density. Since a BS may not always have enough energy, it may need to be kept OFF and allowed to recharge while its load is served by the neighboring BSs that are ON. Using tools from random walk theory and stochastic geometry, we characterize the fraction of time each type of BS can be kept ON, termed availability, for general uncoordinated strategies, where each BS toggles its ON/OFF state independently of the others. As a part of our analysis, we model the temporal dynamics of the energy level at each BS as a birth-death process, derive energy utilization rate for each BS class, and use hitting/stopping time analysis to study availabilities. We prove that there is a fundamental limit on the availabilities, which cannot be surpassed by any uncoordinated strategy. As a part of the proof, we construct the strategy that achieves this limit.

Current wireless networks are becoming increasingly heterogeneous both in terms of the radio access technologies (RATs) and the base station capabilities. Downlink rate or throughput in such heterogeneous networks is a crucial metric and has been primarily studied using system level simulations. To derive the distribution of rate analytically we develop a fairly general tractable model that consists of M different RATs, each deploying up to K different classes of access points (APs), where each class differs in transmit power, path loss exponent, and deployment density. Each class of APs is modeled as an independent Poisson point process (PPP), with mobile user locations modeled as another independent PPP, all channels further consisting of i.i.d. Rayleigh fading. Using a weighted association strategy, the distribution of rate over the entire network is derived. Further, it is shown that in a two-RAT setting there exists an optimum fraction of traffic that should be associated with each RAT to maximize rate coverage, defined as the fraction of users achieving a given rate.

Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For a K-tier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the ith tier are assumed to transmit independently with probability p%, which models the load. Assuming - reasonably - that smaller cells are more lightly loaded than macrocells, the analysis shows that adding such access points to the network always increases the coverage probability. We also observe that fully loaded models are quite pessimistic in terms of coverage.

The growing popularity of Machine-to-Machine (M2M) communications in cellular networks is driving the need to optimize networks based on the characteristics of M2M, which are significantly different from the requirements that current networks are designed to meet. First, M2M requires large number of short sessions as opposed to small number of long lived sessions required by the human generated traffic. Second, M2M constitutes a number of battery operated devices that are static in locations such as basements and tunnels, and need to transmit at elevated powers compared to the traditional devices. Third, replacing or recharging batteries of such devices may not be feasible. All these differences highlight the importance of a systematic framework to study the power and energy optimal system design in the regime of interest for M2M, which is the main focus of this paper. For a variety of coordinated and uncoordinated transmission strategies, we derive results for the optimal transmit power, energy per bit, and the maximum load supported by the base station, leading to the following design guidelines: (i) frequency division multiple access (FDMA), including equal bandwidth allocation, is sum-power optimal in the asymptotically low spectral efficiency regime, (ii) while FDMA is the best practical strategy overall, uncoordinated code division multiple access (CDMA) is almost as good when the base station is lightly loaded, (iii) the value of optimization within FDMA is not significant in the regime of interest for M2M.

We develop a general downlink model for multi-antenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signal-to-interference-ratio (SIR), deployment density, number of transmit antennas and the type of multi-antenna transmission. In particular, we consider and compare space division multiple access (SDMA), single user beamforming (SU-BF), and baseline single-input single-output (SISO) transmission. For this general model, the main contributions are: (i) ordering results for both coverage probability and per user rate in closed form for any BS distribution for the three considered techniques, using novel tools from stochastic orders, (ii) upper bounds on the coverage probability assuming a Poisson BS distribution, and (iii) a comparison of the area spectral efficiency (ASE). The analysis concretely demonstrates, for example, 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. Another observation is that SU-BF provides higher coverage and per user data rate than SDMA, but SDMA is in some cases better in terms of ASE.

Cellular uplink analysis has typically been undertaken by either a simple approach that lumps all interference into a single deterministic or random parameter in a Wyner-type model, or via complex system level simulations that often do not provide insight into why various trends are observed. This paper proposes a novel middle way using point processes that is both accurate and also results in easy-to-evaluate integral expressions based on the Laplace transform of the interference. We assume mobiles and base stations are randomly placed in the network with each mobile pairing up to its closest base station. Compared to related recent work on downlink analysis, the proposed uplink model differs in two key features. First, dependence is considered between user and base station point processes to make sure each base station serves a single mobile in the given resource block. Second, per-mobile power control is included, which further couples the transmission of mobiles due to location-dependent channel inversion. Nevertheless, we succeed in deriving the coverage (equivalently outage) probability of a typical link in the network. This model can be used to address a wide variety of system design questions in the future. In this paper we focus on the implications for power control and show that partial channel inversion should be used at low signal-to-interference-plus-noise ratio (SINR), while full power transmission is optimal at higher SINR.

Pushing data traffic from cellular to WiFi is an example of inter radio access technology (RAT) offloading. While this clearly alleviates congestion on the over-loaded cellular network, the ultimate potential of such offloading and its effect on overall system performance is not well understood. To address this, we develop a general and tractable model that consists of M different RATs, each deploying up to K different tiers of access points (APs), where each tier differs in transmit power, path loss exponent, deployment density and bandwidth. Each class of APs is modeled as an independent Poisson point process (PPP), with mobile user locations modeled as another independent PPP, all channels further consisting of i.i.d. Rayleigh fading. The distribution of rate over the entire network is then derived for a weighted association strategy, where such weights can be tuned to optimize a particular objective. We show that the optimum fraction of traffic offloaded to maximize SINR coverage is not in general the same as the one that maximizes rate coverage, defined as the fraction of users achieving a given rate.

Heterogeneous cellular networks (HCNs) are characterized by cells whose coverage areas may vary by orders of magnitude. It is natural therefore that their user populations (and hence traffic loads) will vary similarly. Yet, to date, random spatial models developed for HCNs generally assume that all base stations (BSs) are always transmitting and hence implicitly have the same load. This paper incorporates a flexible notion of BS load by conditionally thinning the interference field, conditional on the connection of a typical mobile to its serving BS. We derive the coverage probability - i.e. the Signal-to-Interference-Ratio (SIR) distribution - for a typical mobile in a K-tier HCN where each tier has an arbitrary load characterized by a traffic factor pk∈ [0, 1], where pk= 1 is fully loaded. Fully-loaded models are observed to be extremely pessimistic in terms of coverage, and the analysis shows that adding lightly loaded access points (e.g. pico or femtocells) to the macrocell network always increases the coverage probability.

The cellular uplink has typically been studied using simple Wyner-type analytical models where interference is modeled as a constant or a single random variable, or via complex system-level simulations for a given set of parameters, which are often insufficient to evaluate performance in all operational regimes. In this paper, we take a fresh look at this classic problem using tools from point process theory and stochastic geometry, and develop a new tractable model for the cellular uplink which provides easy-to-evaluate expressions for important performance metrics such as coverage probability. The main idea is to model the locations of mobiles as a realization of a Poisson Point Process where each base station (BS) is located uniformly in the Voronoi cell of the mobile it serves, thereby capturing the dependence in two spatial processes. In addition to modeling interference accurately, it provides a natural way to model per-mobile power control, which is an important aspect of the uplink and one of the reasons why uplink analysis is more involved than its downlink counterpart. We also show that the same framework can be used to study regular as well as irregular BS deployments by choosing an appropriate distribution for the distance of a mobile to its serving BS. We verify the accuracy of this framework with an actual urban/suburban cellular network.

In industry, cellular tower locations have primarily been modeled by a deterministic hexagonal grid. Since real deployments are rarely regular, the even spacing between nodes in the grid and constant Voronoi cell areas make the hexagonal grid unrealistic. In this paper we use tools from spatial statistics to show that a purely random node placement and a hexagonal grid distribution with the points perturbed also have unrealistic spatial relationships between nodes, and that pairwise interactions between nodes are necessary, and in most cases sufficient, for modeling spatial qualities of cellular networks. We detail the benefits of using pairwise point interactions in modeling both a coverage-centric tower deployment and a capacity-centric tower deployment. We propose using pairwise and saturated pairwise interaction point processes from the Gibbs process family of point processes: the Strauss Hardcore process for inhibitive point patterns and the Geyer Saturation process for clustered point patterns. Due to its relationship with the coverage areas, we also propose that the Voronoi cell area distribution can be used as a test statistic in general spatial modeling of cellular networks.

Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given \sinr, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR.

The problem of maximizing the sum-rate of a MIMO interference channel is investigated. Each receiver node is assumed to perform single user detection by treating interference from other users as Gaussian noise. It is assumed that all the users share a single frequency band and no pre-coding is performed over time. The sum-rate maximization in such a setup is a longstanding open problem due to its non-linear non-convex nature. The solution, to date, has only been approximated using the local optimization algorithms. In this paper, we couple the branch and bound strategy with the reformulation and linearization technique (BB/RLT) to develop a global optimization algorithm that finds a provably optimal solution. This problem is essentially an optimal power control problem over spatial channels and should not be confused with some recent developments such as Interference Alignment (IA) that typically require pre-coding over temporal, spectral or spatial dimensions. As a comparison with the state of the art, we compare the sum-rate achievable in the current system with the one predicted by IA and draw some interesting conclusions. It should be noted however, that even though the sum-rate achievable by IA can be predicted by assuming N/2 degrees of freedom in an N-user interference channel, the feasibility of IA over a limited number of signaling dimensions is an open problem.

In this paper, we develop a general mathematical framework to incorporate dynamic spectrum access in a multiuser MIMO network. This framework is particularly helpful in computing the maximum achievable system capacity of a resulting multiple-band multiuser MIMO network. The mathematical formulation to maximize the system capacity is shown to be quite similar to that of a well studied single-band multiuser MIMO network. It is further shown that the capacity maximization problem is equivalent to finding the optimal eigenvalues of the input symbol covariance matrices of the users in each frequency band. Due to the dependence of the eigenvalues on the physical characteristics of the system, such as orientation of the antennas and the channel conditions, it is difficult to achieve their optimal values in general. Because of this difficulty in achieving the optimal capacity, we also consider the suboptimal MIMO techniques (specifically beamforming) and study their capacity performance in a multiple-band multiuser MIMO system.