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In this paper, we theoretically analyse the uplink (UL) and downlink (DL) performance of massive multiple-input and multiple-output (mMIMO) networks, in term of coverage probability, cell spectral efficiency and network area spectral efficiency, using stochastic geometry. A sophisticated but yet practical system model is considered, taking into account a path loss model differentiating line-of-sight and non-line-of-sight transmissions, an idle mode capability at the base stations and a finite user density. Our analysis pays particular attention to the existence of a finite number of UL pilots for channel estimation and the effect of pilot contamination. We study for the first time the joint impact of the number of UL pilot sequences, the user density, and the base-station density on the pilot contamination issue in a mMIMO network, which in turn characterizes the DL and UL network performance. Moreover, using the proposed framework, we investigate two different scheduling problems—UE and pilot scheduling—, to find the optimal simultaneously scheduled UE density per time-frequency resource as well as the optimal UL pilot number to maximise the spectral efficiency. [ABSTRACT FROM AUTHOR]

We discover a new capacity scaling law in ultra-dense networks under practical system assumptions, such as a general multi-piece path loss model, a non-zero base station to user equipment antenna height difference, and a finite user equipment density. The intuition and implication of this new capacity scaling law are completely different from those found in the year 2011. That law indicated that the increase of the interference power caused by a denser network would be exactly compensated by the increase of the signal power due to the reduced distance between transmitters and receivers, and thus, network capacity should grow linearly with network densification. However, we find that both the signal and interference powers become bounded in practical ultra-dense networks, which leads to a constant capacity scaling law. Moreover, our new discovery on the constant capacity scaling law indicates three network optimization problems respectively for base station deployment, user equipment scheduling and base station coordination. These three optimization problems are justified and solved in this paper, shedding new light on the deployment and optimization of ultra-dense networks. [ABSTRACT FROM AUTHOR]

In heterogeneous networks (HetNets), the load between macrocell base stations (MBSs) and small-cell base stations (SBSs) is imbalanced due to their different transmission powers and locations. This load imbalance significantly impacts system performance and affects the experience of mobile users (MUs) with different priorities. In this paper, we aim to distributively optimize the user association in HetNets with various user priorities to solve the load balancing problem. Since the user association is a binary matching problem, which is NP-hard, we propose a distributed belief propagation (BP) algorithm to approach the optimal solution. We first develop a factor graph model, using the network topology, to represent this user association problem. With this factor graph, we propose a novel distributed BP algorithm by adopting the proportional fairness as the objective. Next, we theoretically prove the existence of the fixed point in our BP algorithm. To be more practical, we develop an approximation method to significantly reduce the computational and communication complexity of the BP algorithm. Furthermore, we analyze some properties of the factor graph relevant to the performance of the BP algorithm using the stochastic geometry. Simulation results show that 1) the proposed BP algorithm well approaches the optimal system performance and achieves a much better performance compared with other association schemes and that 2) the analytical results on the average degree distribution and sparsity of the factor graph match with those obtained from the Monte Carlo simulations. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the intercell interference coordination (ICIC) problem in heterogeneous cellular networks with randomly deployed small-cell base stations (BSs). Current research on ICIC mainly focuses on optimizing the spectrum and power allocations at BSs, whereas the user–BS association is treated as a separate issue. Nevertheless, the user–BS association problem is an important issue in ICIC and should be jointly optimized with resource allocations to achieve global optimality. In this paper, with the objective of maximizing the system sum rate in a distributed manner, we propose a novel belief propagation (BP) algorithm to jointly optimize user association, subchannel assignment, and power allocation. We first develop a factor graph model to decompose the network-wide objective and constraints into multiple local utilities. Then, we transform the maximization of local utilities into the estimations of marginal distributions and propose a distributed BP algorithm to solve the estimations. Simulations show that our distributed BP algorithm dramatically improves the performance compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]

Heterogeneous cellular networks (HCNs) with embedded small cells are considered, where multiple mobile users wish to download network content of different popularity. By caching data into the small-cell base stations, we will design distributed caching optimization algorithms via belief propagation (BP) for minimizing the downloading latency. First, we derive the delay-minimization objective function and formulate an optimization problem. Then, we develop a framework for modeling the underlying HCN topology with the aid of a factor graph. Furthermore, a distributed BP algorithm is proposed based on the network's factor graph. Next, we prove that a fixed point of convergence exists for our distributed BP algorithm. In order to reduce the complexity of the BP, we propose a heuristic BP algorithm. Furthermore, we evaluate the average downloading performance of our HCN for different numbers and locations of the base stations and mobile users, with the aid of stochastic geometry theory. By modeling the nodes distributions using a Poisson point process, we develop the expressions of the average factor graph degree distribution, as well as an upper bound of the outage probability for random caching schemes. We also improve the performance of random caching. Our simulations show that 1) the proposed distributed BP algorithm has a near-optimal delay performance, approaching that of the high-complexity exhaustive search method; 2) the modified BP offers a good delay performance at low communication complexity; 3) both the average degree distribution and the outage upper bound analysis relying on stochastic geometry match well with our Monte-Carlo simulations; and 4) the optimization based on the upper bound provides both a better outage and a better delay performance than the benchmarks. [ABSTRACT FROM PUBLISHER]