Cooperative diversity in wireless relay networks with multiple-antenna nodes

In [1], the idea of distributed space-time coding was proposed to achieve a degree of cooperative diversity in a wireless relay network. In particular, for a relay network with a single-antenna transmitter and receiver and R single-antenna relays, it was shown that the pairwise error probability (PEP) decays as ((log P)/P)^R, where P is the total transmit power. In this paper, we extend the results to wireless relay networks where the transmitter, receiver, and/or relays may have multiple antennas. Assuming that the transmitter has M antennas, the receiver has N antennas, the sum of all the antennas at the relay nodes is R, and the coherence interval is long enough, we show that the PEP behaves as (1/P)^(min{M,N}R), if M ≠ N, and ((log^(1/M)P)/p)^(MR), if M=N. Therefore, for the case of M ≠ N, distributed space-time coding has the same PEP performance as a multiple-antenna system with min{M, N}R transmit and a single receive antenna. For the case of M = N, the penalty on the PEP compared to a multiple-antenna system is a log^(1/M) P factor, which is negligible at high SNR. We also show that for a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to share the other half with the power used by each relay being proportional to the number of antennas it has