Impact of Outdated Relay Selection on the Capacity of AF Opportunistic Relaying Systems with Adaptive Transmission over Non-Identically Distributed Links

In this paper, we derive probability density function (PDF) and cumulative distribution function (CDF) expressions for the end-to-end signal-to-noise ratio (SNR) of an opportunistic relaying amplify-and-forward (AF) cooperative diversity system over independent and non-identically distributed (i.ni.d.) Rayleigh fading links where outdated channel state information (CSI) is used for relay selection. Based on these expressions, we derive the analytical capacity and outage probability expressions for four classical adaptive transmission techniques, namely, optimal power and rate adaptation (OPRA), constant power with optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR) and truncated channel inversion with fixed rate (TIFR). Numerical evaluations results are presented showing the impact of relay selection with outdated CSI and i.ni.d. links on the performance of each adaptive transmission technique in AF opportunistic relaying systems.