Average Rate of Optimal Incremental Relaying with Selection: Analysis and Insights

Incremental relaying (IR) has been widely studied in the cooperative communications literature in order to tradeoff between the improved signal-to-noise-ratio (SNR) and spatial diversity provided by a relay, and the additional time required by it to forward data to a destination. When multiple relays are present, several variants of IR with relay selection (RS) have been proposed and analyzed. These select one among the available relays to forward data only if the SNR of the source-to-destination (SD) link is either less than a threshold or less than the end-to-end SNR of at least one of the relays. However, an in-depth analysis of the average rate of the rate-optimal RS rule for IR, which turns out to be a non-linear function of the SNR of the SD link, and insights into its behavior are not available in the literature. We derive novel, closed-form expressions for this important performance metric. We further develop an insightful asymptotic analysis that helps to quantify the rate gain over direct transmission and characterizes the effect of various system parameters. We also extensively benchmark the performance of the rate-optimal RS rule against several IR variants proposed in the literature. We present numerical results to verify the analysis and show the impact of imperfect channel state information.