Effects of Feedback Delay in Partial Relay Selection Over Nakagami- $m$ Fading Channels

This paper investigates the effect of feedback delay on the performance of amplify-and-forward (AF) relay selection over a Nakagami- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading environment. Spatial diversity can be improved by employing multiple relays with selection; however, this diversity gain cannot be fully realized when the feedback delay is present in the decision metric. Hence, in this paper, we quantify this detrimental effect by deriving the exact closed-form solution to outage probability, average symbol error rate (SER), and generalized higher moments of signal-to-noise ratio (SNR) for both channel state information (CSI)-assisted and fixed-gain relay. Further, an exact closed form of the ergodic capacity for CSI-assisted relay is derived, and a tight approximation is provided for the fixed-gain relay case. To have a clear picture of the diversity gain variation, we analyze the system in high SNR and obtain simple asymptotic results. Monte Carlo simulation is used to verify the analytical work.