Performance of a Fast, Distributed Multiple Access Based Relay Selection Algorithm Under Imperfect Statistical Knowledge

Cooperative wireless systems can exploit spatial diversity by opportunistically selecting the best relay to forward data to a destination. However, determining the best relay is a challenging task and requires a selection algorithm because the relays are geographically separated and only have local channel knowledge. Selecting the best relay is equivalent to finding the relay with the largest metric, where each relay computes its metric using local channel knowledge. We analyze the performance of a fast, distributed, and scalable multiple access based selection algorithm when it assumes incorrect values for two fundamental parameters that it requires to operate efficiently - the number of available relays and the cumulative distribution function (CDF) of the metrics. Such imperfect knowledge will invariably arise in practice. We develop new expressions for the time required to select the best relay as a function of the assumed and actual parameters. We show that imperfect knowledge can significantly slow down the selection algorithm. Further, in a system that uses its observations to update its CDF estimate, we determine the minimum number of observations required to limit the performance degradation. We also develop a minimax formulation that makes the algorithm robust to uncertainties in the number of relays in the system.