Cooperative Diversity with Mobile Nodes: Capacity Outage Rate and Duration

TL;DR

This paper derives exact and approximate expressions for the capacity outage rate and duration in mobile cooperative diversity systems, revealing how these metrics depend on system parameters and SNR.

Contribution

It introduces the first analytical expressions for AOR and AOD in mobile cooperative diversity protocols, including asymptotic high-SNR approximations.

Findings

AOR decays with SNR at a rate depending on the diversity gain.

AOD decays with SNR with a universal slope of -1/2.

High-SNR approximations provide insights into system performance.

Abstract

The outage probability is an important performance measure for cooperative diversity schemes. However, in mobile environments, the outage probability does not completely describe the behavior of cooperative diversity schemes since the mobility of the involved nodes introduces variations in the channel gains. As a result, the capacity outage events are correlated in time and second-order statistical parameters of the achievable information-theoretic capacity such as the average capacity outage rate (AOR) and the average capacity outage duration (AOD) are required to obtain a more complete description of the properties of cooperative diversity protocols. In this paper, assuming slow Rayleigh fading, we derive exact expressions for the AOR and the AOD of three well-known cooperative diversity protocols: variable-gain amplify-and-forward, decode-and-forward, and selection decode-and-forward relaying. Furthermore, we develop asymptotically tight high signal-to-noise ratio (SNR) approximations, which offer important insights into the influence of various system and channel parameters on the AOR and AOD. In particular, we show that on a double-logarithmic scale, similar to the outage probability, the AOR asymptotically decays with the SNR with a slope that depends on the diversity gain of the cooperative protocol, whereas the AOD asymptotically decays with a slope of -1/2 independent of the diversity gain.