Performance Analysis of UAV Enabled Disaster Recovery Networks: A Stochastic Geometric Framework Based on Cluster Processes

Drone small cells (DSCs) can provide on-demand air-to-ground wireless communications in various unexpected situations, such as traffic jam or natural disasters. However, a DSC needs to face the challenges such as severe co-channel interference, limited battery capacity, and fast topology changes. Aiming to improve energy efficiency of DSCs and quality of services of customers, this paper presents a learning-based multiple drone management (LDM) framework by controlling the transmission power and the 3-dimension location of DSCs based on location data, and reference signal received power of users. Since the labeled throughput data are typically not available in emergency situations, we develop unsupervised learning DSC management techniques: 1) affinity propagation interference management scheme to mitigate interference and energy consumption, and 2) K-means position adjustment to adjust the new 3-dimension positions of drones. Our numerical results show that the proposed LDM framework combining with affinity propagation clustering and k-means clustering can enhance the energy efficiency of DSCs by 25% and the signal-to-interference-plus-noise ratio of ground users by 56%, respectively.

Spectrum sharing is a promising technology that improves the spectral utilization efficiency and provides the foundation stone to build up future drone cellular networks. This chapter presents an efficient transmission scheme and to optimally allocate resources in an underlay spectrum sharing between drone networks and cellular networks. Taking advantage of the stochastic geometry, the 3D blockage effect by random shape theory is determined. Under a blockage model with volume, the exact expression of the signal‐to‐noise ratio (SNR) meta‐distribution is derived. The chapter focuses on the deployment of aerial base stations in drone small cells (DSCs) while sharing the spectrum with cellular networks. Starting with a consideration of the spectrum sharing of single‐tier DSCs in a 3D network, the optimal DSC base station density by maximizing the DSC network throughput is derived. UAVs can act as aerial base stations or relays, namely DSCs, to provide communication services to areas after natural disasters.

The use of drone small cells (DSCs) which are aerial wireless base stations that can be mounted on flying devices such as unmanned aerial vehicles (UAVs), is emerging as an effective technique for providing wireless services to ground users in a variety of scenarios. The efficient deployment of such DSCs while optimizing the covered area is one of the key design challenges. In this paper, considering the low altitude platform (LAP), the downlink coverage performance of DSCs is investigated. The optimal DSC altitude which leads to a maximum ground coverage and minimum required transmit power for a single DSC is derived. Furthermore, the problem of providing a maximum coverage for a certain geographical area using two DSCs is investigated in two scenarios; interference free and full interference between DSCs. The impact of the distance between DSCs on the coverage area is studied and the optimal distance between DSCs resulting in maximum coverage is derived. Numerical results verify our analytical results on the existence of optimal DSCs altitude/separation distance and provide insights on the optimal deployment of DSCs to supplement wireless network coverage.

To leverage the numerous benefits offered by drone cellular networks, the third generation partnership project (3GPP) has recently included the support for drone base stations (DBSs) communications as part of the fifth generation standard. This chapter focuses on a 3GPP‐inspired drone mobility model in which the initial locations of DBSs are modeled as a homogeneous 2D Poisson point process at a constant height from the ground and each DBS moves along a straight line in a random direction, independently of the other DBSs. Given the irregularity in the locations of DBSs and user equipment (UE), the use of tools from stochastic geometry is a natural choice for modeling and analysis of aerial communication networks. The chapter characterizes the point process of the interfering DBSs for service models, using which we derive the average received rate at the typical UE. It also characterizes the handover probability for the service models.

In this paper, the design of an optimal trajectory for an energy-constrained drone operating in dynamic network environments is studied. In the considered model, a drone base station (DBS) is dispatched to provide uplink connectivity to ground users whose demand is dynamic and unpredictable. In this case, the DBS's trajectory must be adaptively adjusted to satisfy the dynamic user access requests. To this end, a meta-learning algorithm is proposed in order to adapt the DBS's trajectory when it encounters novel environments, by tuning a reinforcement learning (RL) solution. The meta-learning algorithm provides a solution that adapts the DBS in novel environments quickly based on limited former experiences. The meta-tuned RL is shown to yield a faster convergence to the optimal coverage in unseen environments with a considerably low computation complexity, compared to the baseline policy gradient algorithm. Simulation results show that, the proposed meta-learning solution yields a 25% improvement in the convergence speed, and about 10% improvement in the DBS' communication performance, compared to a baseline policy gradient algorithm. Meanwhile, the probability that the DBS serves over 50% of user requests increases about 27%, compared to the baseline policy gradient algorithm.

In this paper, the problem of user association and sub-channel allocation in integrated satellite-drone networks (ISDNs) is studied. In this model, drone base stations (DBSs) provide downlink connectivity, supplementally, to ground users whose demand cannot be satisfied by terrestrial small cell base station (SBSs). Meanwhile, a satellite system is used to satisfy the increased demand for backhaul resources stemming from DBSs and SBSs. In this case, one must jointly consider resource allocation over satellite-DBS/SBS backhaul links, terrestrial backhaul links, and DBS/SBS-user radio access links as well as user association with DBSs and SBSs. This joint backhaul and radio user association and sub-channel allocation problem is modeled using a competitive market setting in which all of the communication links are modeled as consumers while the user association outcomes and the wireless sub-channels are modeled as goods. In this competitive market, consumers seek to exchange goods to maximize their profits, in terms of users' data rates. The sum rate of communication links, defined as the social welfare in the competitive market, is maximized in a sequential manner. An optimal satellite frequency sub-channel allocation scheme is first proposed given the sub-channel allocation and user association scheme at DBSs and SBSs. Then, the problems of sub-channel allocation and user association at DBSs and SBSs are solved using a Hungarian-based solution, such that the sum rate of all communication links are maximized. Simulation results show that, the proposed algorithm can find a Walrasian equilibrium allocation scheme, at which the spectrum resources in the market is fully used, upon convergence. Meanwhile, the proposed algorithm can yield over two-fold gains in terms of the number of downlink service links with 35 Mbps rate and 3.4 times gains in the number of backhaul links with 1 Gbps rate.

As a promising multiple access technique for 5G wireless networks, sparse code multiple access (SCMA) has been put forward to support massive connectivity and enhance network performance. In this paper, we develop a theoretical framework using stochastic geometry to evaluate the performance of SCMA ad hoc networks. Under this framework, we first derive an explicit matrix form for the successful transmission probability. We then consider two area spectral efficiency (ASE) maximization problems without and with link reliability constraint to investigate the ASE gain of SCMA over OFDMA networks and the tradeoff between the ASE and link reliability, respectively. In particular, we obtain the optimal medium access probability (MAP) to solve both problems. Both numerical and simulation results exhibit that, compared to OFDMA networks, an asymptotically 160% gain in the ASE and a nearly 91% improvement in the transmission opportunity can be achieved by SCMA networks with typical settings.

This paper studies base station (BS) cooperation in nonuniform heterogeneous networks. Considering the limited capacity at BS and existence of untrusted small cell BSs (SBSs) in practical scenarios, a novel capacity- and trust-aware BS cooperation strategy is proposed. The BS cooperation is performed in a user centric manner, based on the average received signal strength at users, the capacity of BSs, and the trustworthiness of SBSs. Furthermore, with the proposed BS cooperation, the statistics of aggregate information-signal strength and interference strength are theoretically analyzed, based on stochastic geometry. Then, expressions for spectral efficiency (SE) and area SE (ASE) are analytically derived. In addition, to study the impact of the SBS density on the SE and ASE, the optimal densities of normal SBSs to maximize the SE and ASE are proved to exist and obtained. Finally, simulations and numerical evaluations validate the theoretical analysis and reveal that with the awareness of BS capacity and trustworthiness, optimal cooperative thresholds achieving the maximum SE and ASE exist, which decrease with high path-loss exponent; and in high path-loss fading environment with high existence probability of untrusted SBSs, more normal SBSs are required to be deployed to achieve the maximum SE and ASE performance.

Device-to-device (D2D) communication enables direct communication between proximate devices thereby improving the overall spectrum utilization and offloading 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: (i) 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 (ii) content of interest is available at the $k^{th}$ closest 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.

A K-tier heterogeneous downlink millimeter wave (mmWave) cellular network with user-centric small cell deployments is studied in this paper. In particular, we consider a heterogeneous network model with user equipments (UEs) being deployed according to a Poisson Cluster Process (PCP), i.e., Thomas cluster process, where the UEs are clustered around the base stations (BSs) and the distances between UEs and the BS are modeled as Gaussian distributed. In addition, distinguishing features of mmWave communications including directional beamforming and a sophisticated path loss model incorporating both line-of-sight (LOS) and non-line-of-sight (NLOS) transmissions, are taken into account. In this paper, the complementary cumulative distribution function (CCDF) and probability density function (PDF) of the path loss are provided. Also, using tools from stochastic geometry, we derive a general expression of the signal-to-interference-plus-noise ratio (SINR) coverage probability. Our results demonstrate that coverage probability can be improved by decreasing the size of UE clusters around BSs, and interference has noticeable influence on the coverage performance of our model.

Sparse code multiple access (SCMA) has been recently proposed for the future wireless networks, which allows non-orthogonal spectrum resource sharing and enables system overloading. In this paper, we apply SCMA into device-to-device (D2D) communication and cellular hybrid network, targeting at using the overload feature of SCMA to support massive device connectivity and expand network capacity. Particularly, we develop a stochastic geometry based framework to model and analyze SCMA, considering underlaid and overlaid mode. Based on the results, we analytically compare SCMA with orthogonal frequency-division multiple access (OFDMA) using area spectral efficiency (ASE) and quantify closed-form ASE gain of SCMA over OFDMA. Notably, it is shown that system ASE can be significantly improved using SCMA and the ASE gain scales linearly with the SCMA codeword dimension. Besides, we endow D2D users with an activated probability to balance cross-tier interference in the underlaid mode and derive the optimal activated probability. Meanwhile, we study resource allocation in the overlaid mode and obtain the optimal codebook allocation rule. It is interestingly found that the optimal SCMA codebook allocation rule is independent of cellular network parameters when cellular users are densely deployed. The results are helpful in the implementation of SCMA in the hybrid system.

Aerial base station (ABS) provides a flexible solution for hotspot scenarios in traditional cellular networks, where macro-cell base stations (MBSs) are challenged by overwhelming short-time traffic demands. However, due to stretched transmission distances from sky, the system performance of this ABS-scheme is sometimes questioned. In this paper, we study the system performance of ABS-assisted networks by tools from stochastic geometry. The two-tier network consisting of MBSs and ABSs is modeled as the superposition of a Poisson point process over the infinite plane and a binomial point process within an overlapped finite circular area. We consider a more general probabilistic line-of-sight and non-line-of-sight propagation model and derive coverage probability as well as area spectral efficiency. Based on the proposed analytical framework, we study the impacts of various parameters and compare the ABS-scheme with a benchmark scheme, in which network densification is realized through deploying additional ground base stations (GBSs). Simulation results unveil that: 1) the height and ABS number should be carefully designed to obtain the optimal performance and 2) when the number of assisting BSs is limited, the ABS-scheme can achieve even better performance than the GBS-scheme, which validates the feasibility of enhancing system performance through ABSs in hotspot scenarios.

From the perspective of statistical performance, this paper presents an analytical framework to handle the mutual interference between cellular networks and Device-to-Device (D2D) pairs in D2D underlaid downlink cellular networks. We assume that the D2D transmitters adopt power control and the base stations (BSs) adopt zero-forcing beamforming (ZFBF) to suppress the mutual interference. Using stochastic geometry, we derive the expressions for the coverage probability and the average data rate of users. Based on the analytical results, we discuss the optimal values of some important parameters to maximize the system area spectral efficiency (ASE) while guaranteeing the quality-of-service (QoS) of users, i.e., the coverage probability of users is above a threshold. The result shows that power control at D2D is always suboptimal for system ASE when the density of BSs is large enough.

Different from traditional static small cells, Drone Base Stations (DBSs) exhibit their own advantages, i.e., faster and cheaper to deploy, more flexibly reconfigured, and likely to have better communications channels owing to the presence of short-range line-of-sight links. Thus, applying DBSs into the cellular network has great potential to increase the throughput of the network and improve Quality of Service (QoS) of Mobile Users (MUs). In this paper, we focus on how to place the DBS (i.e., jointly determining the location and the association coverage of a DBS) in order to improve the QoS in terms of minimizing the total average latency ratio of MUs by considering the energy capacity limitation of the DBS. We formulate the DBS placement problem as an optimization problem and design a Latency aware dronE bAse station Placement (LEAP) algorithm to solve it efficiently. The performance of LEAP is demonstrated via simulations as compared to other two baseline methods.

Performance analysis of coverage-centric heterogeneous cellular networks using dual-slope path loss model