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In order to evaluate the impacts of swarm distribution characteristics of unmanned aerial vehicles (UAVs) and the complexity of millimeter wave (mmWave) propagations on the coverage performance of UAV networks, this paper develops a stochastic geometry-based approach for the modeling and analysis of single- and multi-swarm UAV networks with mmWave communications. We first utilize binomial point processes (BPPs) to model the locations of UAVs in a finite area as a single-swarm UAV network and allow for arbitrary user locations. Then, we define multi-BPPs and extend our model to multi-swarm UAV networks. We consider an open-access strategy, where users access the closest UAV in all swarms, and derive the distance distributions of serving and interfering UAVs. Moreover, a three-dimensional (3D) blockage model and a 3D sectorized antenna model are introduced to completely depict the characteristics of air-to-ground channel in mmWave band. Based on the distance distributions and the Laplace transform of interference, coverage probabilities in considered networks are derived. Our results reveal that, there exists optimal height and density of UAV swarms that maximize the coverage probability. When densely deployed, the interference from inter-swarm cannot be negligible in the multi-swarm UAV network. [ABSTRACT FROM AUTHOR]

In millimeter-wave (mm-wave) cellular networks, directional antenna arrays are typically adopted to mitigate the severe propagation loss. However, the interference caused by such highly directional beams may, in turn, result in a significant number of transmission failures, especially for dense networks. To tackle this problem, we propose two inter-cell interference coordination (ICIC) schemes in mm-wave bands: one is merely based on the path loss incorporating the blockage effect (PL-ICIC); the other considers both path loss and directivity gain (PG-ICIC). To fully investigate both schemes, we first derive an exact expression for the success probability (reliability) of the typical (served) user. We further provide an asymptotic analysis for the success probability and propose an effective approximation based on the asymptotic signal-to-interference ratio (SIR) gain relative to no ICIC. Secondly, to incorporate the cost of ICIC schemes, we derive the approximate normalized throughput taking into account that some users cannot be served due to limited resources. Numerical results show that the two proposed schemes provide significant reliability improvements in the low-SIR regime, and the higher the number of antennas, the wider the SIR range for which there is an improvement. In addition, compared with PL-ICIC, PG-ICIC balances the available resources among all users well. [ABSTRACT FROM AUTHOR]

Energy correlation critically affects the performance of a wirelessly powered network due to its key effect on the spatial distribution of concurrent RF-powered transmitters. This paper introduces a powerful analytical framework with foundations in stochastic geometry to characterize the energy correlation in a general wirelessly powered network. Unlike the commonly used pair correlation function (pcf)-based method, it is based on the energy correlation coefficient (ECC) and yields the energy correlation distance that gives a sufficiently small ECC. Specifically, we focus on the spatial correlation of the energy harvested from a Poisson field of RF power sources with directional beams under two cases: i) each power source points the beam in a random direction; ii) each power source points the beam to an RF-powered node located in its Voronoi cell. The results demonstrate that the energized RF-powered nodes in both cases exhibit positive correlation that is weaker than in the omni-directional case due to the introduction of energy beamforming. As an application, we provide an ECC-based method using the energy correlation distance to approximate the success probability and area spectral efficiency in the communication phase. It turns out that the ECC-based approximation matches the exact result well, and, more importantly, it can deal with the energy correlation in more general and complicated scenarios (where the pcf analysis is infeasible) due to its superior tractability. [ABSTRACT FROM AUTHOR]

In the analysis of large-scale wirelessly powered networks, the energy correlation is often ignored. While this leads to remarkably simple results for key performance metrics, it is typically not realistic and accurate. Considering the accuracy, tractability, and practicability tradeoffs, this paper introduces and promotes the Poisson disk process (PDP) as a model for the energized nodes that succeed in harvesting energy. To show that the model leads to analytically tractable results in several cases of interest, we derive its first and second moment densities, which fully characterize the PDP. Besides, we also provide tight bounds for its probability generating functional as well as its contact and nearest-neighbor distance distributions. Then, to show that the model is relevant for wirelessly powered networks—which all have positive energy correlation—we provide two approaches to fit the PDP to a given energized point process incorporating practical energy harvesting factors. Further, we derive the success probability in the information transmission phase, where the distribution of the active transmitters is modeled by a PDP. It turns out that the resulting PDP can closely model the distribution of actual energized nodes in terms of the success probability and other statistics while preserving analytical tractability. [ABSTRACT FROM AUTHOR]

Rateless coding is a promising forward error correction technique to meet both delay and reliability requirements of emerging wireless applications. However, existing works on rateless codes mostly considered finite networks or ignored the traffic dynamics. In this paper, we present a comprehensive investigation of the end-to-end performance for rateless codes in Poisson bipolar and cellular networks. Specifically, we propose the notion of the end-to-end success probability, which is the success probability given an end-to-end delay requirement, to jointly evaluate the delay performance and transmission reliability of rateless codes. To fully characterize the end-to-end delay, we divide it into two parts, namely the packet waiting time and the transmission time, and provide tractable yet accurate approximations to their statistical distributions. Compared with the previous works, the proposed general framework and the end-to-end performance metric help obtain insights on the role of scheduling, queueing, and coding scheme in practical radio access networks. The approximations are verified to be effective and reliable through simulations. Overall, the results show the significant benefits of rateless codes relative to the fixed-rate codes in terms of the transmission reliability with an end-to-end delay requirement. [ABSTRACT FROM AUTHOR]

In this paper, we consider a heterogeneous network with design of a user-centric base station cooperation. Different from traditional cellular structure that associates users with cells centered around base stations, the user-centric base station cooperation focuses more on user's service experience no matter where the user is located. Leveraging the tools from stochastic geometry, we provide an exact analytical expression and two simple yet effective approximations for the coverage probability at the typical receiver. Numerical results validate our exact analysis as well as the effectiveness of the two approximations. [ABSTRACT FROM AUTHOR]

This paper focuses on the meta distributions of the signal-to-interference-plus-noise ratio (SINR) and user-perceived rate in heterogeneous cellular networks (HCNs) with multiple tiers of base stations. On the one hand, it is desirable to offload users to small cells to alleviate the congestion in macrocells; on the other hand, such offloading would in turn cause an SINR degradation of the offloaded users, which needs to be mitigated through interference avoidance based on resource partitioning. Thus, in consideration of both aspects, we provide a general framework for modeling and analyzing joint spectrum allocation and offloading in an HCN using the $K$ -tier homogeneous-independent Poisson model. With it, we derive the per-tier and overall moments of the conditional SINR and rate distribution given the point process, based on which the exact meta distributions are given. We show that the conventional SINR or rate performance evaluated at the typical user (averaging over all tiers and links in the HCN), by itself, is insufficient, and a much sharper version provided by the meta distribution is required in conjunction with the expected value to give a thorough assessment of the benefits of joint resource partitioning and offloading in HCNs. [ABSTRACT FROM AUTHOR]

As a key enabling technology for truly sustainable operation of devices, wireless energy and information transfer (WEIT) has attracted significant attention in wireless communication networks. Previous works on WEIT network analysis mostly concentrated on the energy outage probability or the expectation of the transferred energy at the typical wirelessly powered device using stochastic geometry. These calculations are relatively straightforward, but they only provide limited information on the energy extracted by the individual devices. This paper considers a WEIT-enabled device-to-device (D2D) network with the ambient RF transmitters distributed according to a Poisson point process and focuses on the meta distribution of the transferred energy, which is the distribution of the conditional energy outage probability given the locations of the RF transmitters, to show what fraction of devices in the network satisfy the target energy outage constraint if the required transmission energy is given. Furthermore, we derive the meta distribution of the transmission rate under an energy outage constraint and introduce a new notion of transmission efficiency, termed wirelessly powered spatial transmission efficiency, which is defined as the density of concurrently active links that rely on the wireless energy transfer technique and satisfy a certain reliability constraint that has a rate greater than a predefined threshold. Our analysis provides insightful guidelines for the most efficient way to operate a WEIT-enabled self-sustainable D2D communication network. [ABSTRACT FROM AUTHOR]

Millimeter-wave (mm-wave) device-to-device (D2D) communication is considered one of the most promising enabling technologies to meet the demanding requirements of future networks. Previous works on mm-wave D2D network analysis mostly considered the case that all devices were equipped with exactly the same number of antennas, whereas real networks are more complicated due to the coexistence of diverse devices. In this paper, we present a comprehensive investigation on the interference characteristics and link performance in mm-wave D2D networks where the concurrent transmission beams are varying in width. First, we establish a general and tractable framework for the target network with Nakagami fading and directional beamforming. To fully characterize the interference, we derive the mean and variance of the interference and then provide an approximation of the interference distribution by a mixture of the inverse gamma and the log-normal distributions. More importantly, the coexistence of varied beamwidths renders their interactions and thus the interference quite complicated and sensitive to the antenna pattern, highlighting the significance of adopting an accurate model for the antenna pattern. Second, to show the impact of heterogeneous antenna arrays on the link performance, we derive the signal-to-interference-plus-noise ratio and rate distributions of the typical receiver as well as their asymptotics, bounds, and approximations to get deep insights on the performance of the network. [ABSTRACT FROM AUTHOR]

Device caching has recently been proposed as an efficient way to offload traffic from congested cellular networks. However, previous works usually ignore the fact that, in practice, the user device may not be willing to help others due to the limited battery capacity. In this paper, we introduce cooperation among the device-to-device (D2D) transmitters and propose two novel hybrid caching strategies—single-point caching combined with two-point cooperative caching with joint transmission (SPC-CCJT) or multi-stream transmission (SPC-CCMT)—aiming at saving the energy cost of content deliverers. Using tools from stochastic geometry, we propose an analytical framework of the hybrid caching strategies by modeling the locations of the D2D transmitters as a Gauss–Poisson process (GPP) to accurately capture the clustering and cooperative behaviors. First, we consider a probabilistic caching placement and optimize the caching distribution to maximize the cache hit probability. Second, to compare the performance between different content delivery strategies, we derive the success probability and per-user capacity for SPC, CCJT, and CCMT, respectively. These results are then applied to evaluate the offloading gain and the distribution of the content retrieval delay for SPC-CCJT and SPC-CCMT in the GPP-based D2D networks. It turns out that significant offloading gain and delay improvement can be achieved by hybrid caching with cooperation while the energy cost of each cooperator is kept low. [ABSTRACT FROM AUTHOR]

Enabling device-to-device (D2D) communications in millimeter-wave (mm-wave) networks is of critical importance for the next-generation mobile networks to support very high data rates (multi-gigabits-per-second) for mobile devices. In this paper, we provide a fine-grained performance analysis of the mm-wave D2D communication networks. Specifically, we first establish a general and tractable framework to investigate the performance of mm-wave D2D networks using the Poisson bipolar model integrated with several features of the mm-wave band. To show what fraction of users in the network achieve target reliability if the required signal-to-interference-plus-noise ratio (SINR) (or QoS requirement) is given, we derive the meta distributions of the SINR and the data rate. Interestingly, in mm-wave D2D networks, the standard beta approximation for the meta distribution does not work very well when highly directional antenna arrays are used or the node density is small. To resolve this issue, we provide a modified approximation by using higher moments of the conditional SINR distribution, which is shown to be closer to the exact result. On this basis, we also derive the mean local delay and spatial outage capacity to provide a comprehensive investigation on the impact of mm-wave features on the performance of D2D communication. [ABSTRACT FROM AUTHOR]

The current cellular networks have evolved to be more randomly, irregularly, and heterogeneously deployed to meet the exponential growth of mobile data traffic and the demand for seamless coverage, making the signal-to-interference ratio (SIR) distribution more challenging to analyze. Therefore, in this paper, we propose two simple approximative approaches to the SIR distribution of general heterogeneous cellular networks (HCNs) based on the ASAPPP method, which stands for “approximate SIR analysis based on the Poisson point process” and the MISR (mean interference-to-signal ratio)-based gain for each individual tier of the HCNs. Specifically, we first establish a per-tier ASAPPP approximation to general HCNs and then present an effective gain ASAPPP method as a further simplification when the path loss exponents are the same for all the tiers, that is, we give an explicit expression for the effective gain G\rm{ eff} of general HCNs such that the SIR distribution is obtained by scaling the SIR threshold \theta to \theta/G_{\rm{ eff}} . The asymptotic behavior for the tail of the SIR distribution is also given. Furthermore, to highlight the simplicity and effectiveness of the approximative approaches, we derive the exact distribution of the SIR in the two-tier HCNs modeled by \beta$-Ginibre and Poisson point processes and compare it with the approximate results. The results demonstrate that the proposed approaches give a simple yet excellent approximation for the SIR distribution. [ABSTRACT FROM AUTHOR]

Due to its tractability, a multitier model of mutually independent Poisson point processes (PPPs) for heterogeneous cellular networks (HCNs) has recently been attracting much attention. However, in reality, the locations of the BSs, within each tier and across tiers, are not fully independent. Accordingly, in this paper, we propose two HCN models with inter-tier dependence (Case 1) and intra-tier dependence (Case 2), respectively. In Case 1, the macro-base station (MBS) and the pico-base station (PBS) deployments follow a Poisson point process (PPP) and a Poisson hole process (PHP), respectively. Under this setup and conditioning on a fixed serving distance (distance between a user and its nearest serving BS), we derive bounds on the outage probabilities of both macro and pico users. We also use a fitted Poisson cluster process to approximate the PHP, which is shown to provide a good approximation of the interference and outage statistics. In Case 2, the MBSs and the PBSs follow a PPP and an independent Matern cluster process, respectively. Explicit expressions of the interference and the outage probability are derived first for fixed serving distance and second with random distance, and we derive the outage performance, the per-user capacity, and the area spectral efficiency (ASE) for both cases. It turns out that the proposed Case 2 model is a more appropriate and accurate model for a HCN with hotspot regions than the multitier independent PPP model since the latter underestimates some key performance metrics, such as the per-user capacity and the ASE, by a factor of 1.5 to 2. Overall, the two models proposed provide good tradeoffs between the accuracy, tractability, and practicability. [ABSTRACT FROM PUBLISHER]