Combined Bulk and Per-Tone Relay Selection in Super Dense Wireless Networks

The combined bulk/per-tone transmit antenna selection strategy has been shown to achieve optimal diversity and coding gains for single-hop systems with multiple transmit and receive antennas. In this paper, we extend this strategy to the case in which a set of user pairs communicate via a cluster of intermediary amplify-and-forward relaying nodes. We obtain an upper bound on the outage probability of the network, and a closed-form expression for the multiuser contention probability (the probability that distinct user pairs select the same relay). Consequently, we are able to construct an upper bound on the failure probability of the network, i.e., the probability that either an outage or contention occurs. We show that there exists a critical average end-to-end SNR, above which the outage probability decays exponentially with the number of available relays. In this case, the network failure probability is dominated by the contention probability. Many of our results are of a fundamental (asymptotic) nature, but key results are verified with simulations and illustrated numerically for finite system sizes.