Performance and Optimization of Amplify-and-Forward Cooperative Diversity Systems in Generic Noise and Interference

Cooperative diversity systems have received significant attention recently as a distributed means of exploiting the inherent spatial diversity of wireless networks. In this paper, we consider a cooperative diversity system consisting of a source, a destination, and multiple single-hop amplify-and-forward relays, and provide a mathematical framework for the asymptotic analysis of this system in generic noise and interference for high signal-to-noise ratios. Assuming independent Rayleigh fading for all links in the network and orthogonal relay-destination channels, we obtain simple and elegant closed-form expressions for the asymptotic symbol and bit error rates valid for arbitrary linear modulation formats, arbitrary numbers of relays, and arbitrary types of noise and interference with finite moments including co-channel interference, ultra-wideband interference, impulsive ε-mixture noise, generalized Gaussian noise, and Gaussian noise. Furthermore, we exploit the derived analytical error rate expressions to develop power allocation, relay selection, and relay placement schemes that are asymptotically optimal in environments with generic noise and interference. In general, the power allocation problem results in a geometric program which can be solved efficiently numerically. For the special case of only one relay, we provide a closed-form result for the optimal power allocation. Simulation results confirm our analysis and illustrate that, in non-Gaussian noise, the proposed power allocation, relay selection, and relay placement schemes lead to large performance gains compared to their conventional counterparts optimized for Gaussian noise.

I. Introduction

Cooperative diversity is a promising approach to achieve high diversity gains in distributed wireless networks where nodes are allowed to cooperate by relaying each other's messages. The main idea behind this technique is to allow idle wireless nodes to relay signals emitted by a source node to the destination node. As a result, the message transmitted by the source undergoes multiple independent fading paths and the probability of an erroneous decision at the destination is significantly reduced [1]. The two most popular relaying techniques are amplify-and-forward (AF) relaying and decode-and-forward (DF) relaying. While in DF relaying the signal received from the source is decoded and re-encoded at the relays, it is only amplified in AF relaying. Thus, AF relaying is generally considered to be less complex and is particularly well-suited for applications with simple relay units such as wireless sensor networks.