Distributed space-time codes in wireless relay networks

We apply the idea of space-time coding devised for multiple antenna systems to the communication over a wireless relay network. We use a two stage protocol, where in one stage the transmitter sends information and in the other, the relay nodes encode their received signals into a "distributed" linear dispersion code, and then transmit the coded signals to the receiver. We show that for high SNR the pairwise error probability (PEP) behaves as (log P/P)^min{T,R} with T the coherence interval, R the number of relay nodes and P the total transmit power. Thus, apart from the log P factor and assuming T≥R, the system has the same diversity as a multi-antenna system with R transmit antennas, which is the same as assuming that the R relay nodes can fully cooperate and have full knowledge of the transmitted signal. We further 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 collectively expend the other half. We also show that at low and high SNR, the coding gain is the same as that of a multi-antenna system with R antennas. At intermediate SNR, it can be quite different, which has implications for the design of distributed space-time codes.