Communication in a Poisson Field of Interferers--Part I: Interference Distribution and Error Probability

Abstract

We present a mathematical model for communication subject to both network interference and noise. We introduce a framework where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a wireless environment subject to path loss, shadowing, and multipath fading. We consider both cases of slow and fastvarying interferer positions. The paper is comprised of two separate parts. In Part I, we determine the distribution of the aggregate network interference at the output of a linear receiver. We characterize the error performance of the link, in terms of average and outage probabilities. The proposed model is valid for any linear modulation scheme (e.g., M -ary phase shift keying or M -ary quadrature amplitude modulation), and captures all the essential physical parameters that affect network interference. Our work generalizes the conventional analysis of communication in the presence of additive white Gaussian noise and fast fading, allowing the traditional results to be extended to include the effect of network interference. In Part II of the paper, we derive the capacity of the link when subject to network interference and noise, and characterize the spectrum of the aggregate interference.Index Terms-Spatial distribution, Poisson field, aggregate network interference, error probability, stable laws.

Distributed Network Secrecy

“…The DNS throughput in Nakagami-m fading channels is given by (42), shown at the top of this page, for positive integer m.…”

“…2) Distributed Network Secrecy: The DNS throughput in Nakagami-m fading channels depends on p (l) c , determined by the MAC protocol, according to (42). In particular, we consider an access protocol according to which each legitimate node randomly selects a communication channel independently of other legitimate nodes in the same level [5].…”

Wireless Communication in Dynamic Interference

“…As in [4], this leads to interference with isotropic α-stable statistics. Applying our recent characterization of the achievable rates of additive isotropic α-stable noise channels in [9], we derive a closed-form expression for the achievable rate of the typical user.…”

“…Dynamic interference in wireless networks was introduced in [4,5] by considering a fast-varying (symbol-by-symbol) active transmitter set, with locations governed by a homogeneous Poisson point process. In particular, it was shown that the interfering signal in each time slot is α-stable.…”

“…Although an expression without a closedform for the error probability in the presence of α-stable interference was derived in [4], little is known about the achievable rates and the optimal density of devices in this scenario.…”