We study three relay selection schemes for uniformly distributed wireless sensor networks: 1) optimal selection where the relays that maximize the signal-to-noise ratio (SNR) at the destination are selected, 2) geometry-based, which is based on selecting the closest nodes to the source, and 3) random selection in which the nodes are selected randomly from a certain neighborhood of the source. In all schemes, we assume that all relays operate in the amplify-and-forward mode and transmit with equal average powers and each relay has only access to its backward channel and location. For each relay selection strategy, we propose a decentralized protocol whereby proper nodes choose to act as relays without requiring any central coordinating entity or any inter-node information transfer. We derive expressions for the average SNR at the relays and destination while assuming that the source-node distances and the inter-terminal channel links are completely random. We show that, for all proposed schemes, the SNR variance at the destination converges to zero as the number of relays increases. While each selection scheme has its pros and cons, we derive a sufficient condition under which the average SNR at the destination becomes independent of the selection scheme employed. 2012 IEEE.
