Series Expansion for Interference in Wireless Networks

The spatial correlations in transmitter node locations introduced by common multiple access protocols makes the analysis of interference, outage, and other related metrics in a wireless network extremely difficult. Most works therefore assume that nodes are distributed either as a Poisson point process (PPP) or a grid, and utilize the independence properties of the PPP (or the regular structure of the grid) to analyze interference, outage and other metrics. But,the independence of node locations makes the PPP a dubious model for nontrivial MACs which intentionally introduce correlations, e.g. spatial separation, while the grid is too idealized to model real networks. In this paper, we introduce a new technique based on the factorial moment expansion of functionals of point processes to analyze functions of interference, in particular outage probability. We provide a Taylor-series type expansion of functions of interference, wherein increasing the number of terms in the series provides a better approximation at the cost of increased complexity of computation. Various examples illustrate how this new approach can be used to find outage probability in both Poisson and non-Poisson wireless networks.Comment: Submitted to IEEE Transactions on Information Theor

Design, Modeling, and Performance Analysis of Multi-Antenna Heterogeneous Cellular Networks

This paper presents a stochastic geometry-based framework for the design and analysis of downlink multi-user multiple-input multiple-output (MIMO) heterogeneous cellular networks with linear zero-forcing transmit precoding and receive combining, assuming Rayleigh fading channels and perfect channel state information. The generalized tiers of base stations may differ in terms of their Poisson point process spatial density, number of transmit antennas, transmit power, artificial-biasing weight, and number of user equipments served per resource block. The spectral efficiency of a typical user equipped with multiple receive antennas is characterized using a non-direct moment-generating-function-based methodology with closed-form expressions of the useful received signal and aggregate network interference statistics systematically derived. In addition, the area spectral efficiency is formulated under different space-division multiple-access and single-user beamforming transmission schemes. We examine the impact of different cellular network deployments, propagation conditions, antenna configurations, and MIMO setups on the achievable performance through theoretical and simulation studies. Based on the state-of-the-art system parameters, the results highlight the inherent limitations of baseline single-input single-output transmission and conventional sparse macro-cell deployment, as well as the promising potential of multi-antenna communications and small-cell solution in interference-limited cellular environments

Large deviations of the interference in the Ginibre network model

Under different assumptions on the distribution of the fading random variables, we derive large deviation estimates for the tail of the interference in a wireless network model whose nodes are placed, over a bounded region of the plane, according to the $\beta$-Ginibre process, $0<\beta\leq 1$. The family of $\beta$-Ginibre processes is formed by determinantal point processes, with different degree of repulsiveness, which converge in law to a homogeneous Poisson process, as $\beta \to 0$. In this sense the Poisson network model may be considered as the limiting uncorrelated case of the $\beta$-Ginibre network model. Our results indicate the existence of two different regimes. When the fading random variables are bounded or Weibull superexponential, large values of the interference are typically originated by the sum of several equivalent interfering contributions due to nodes in the vicinity of the receiver. In this case, the tail of the interference has, on the log-scale, the same asymptotic behavior for any value of $0<\beta\le 1$, but it differs (again on a log-scale) from the asymptotic behavior of the tail of the interference in the Poisson network model. When the fading random variables are exponential or subexponential, instead, large values of the interference are typically originated by a single dominating interferer node and, on the log-scale, the asymptotic behavior of the tail of the interference is essentially insensitive to the distribution of the nodes. As a consequence, on the log-scale, the asymptotic behavior of the tail of the interference in any $\beta$-Ginibre network model, $0<\beta\le 1$, is the same as in the Poisson network model

Design, Modeling, and Performance Analysis of Multi-Antenna Heterogeneous Cellular Networks

Abstract This paper presents a stochastic geometry-based framework for the design and analysis of downlink multi-user multipleinput multiple-output (MIMO) heterogeneous cellular networks (HetNets) with linear zero-forcing (ZF) transmit precoding and receive combining, assuming Rayleigh fading channels and perfect channel state information (CSI). The generalized tiers of base stations (BSs) may differ in terms of their Poisson point process (PPP) spatial density, number of transmit antennas, transmit power, artificial-biasing weight, and number of user equipments (UEs) served per resource block. The spectral efficiency of a typical user equipped with multiple receive antennas is characterized using a non-direct moment-generating-function (MGF)-based methodology with closed-form expressions of the useful received signal and aggregate network interference statistics systematically derived. In addition, the area spectral efficiency is formulated under different space-division multiple-access (SDMA) and single-user beamforming (SUBF) transmission schemes. We examine the impact of different cellular network deployments, propagation conditions, antenna configurations, and MIMO setups on the achievable performance through theoretical and simulation studies. Based on state-of-the-art system parameters, the results highlight the inherent limitations of baseline single-input singleoutput (SISO) transmission and conventional sparse macro-cell deployment, as well as the promising potential of multi-antenna communications and small-cell solution in interference-limited cellular environments. Index Terms Multi-antenna communications, downlink heterogeneous cellular networks, stochastic geometry theory