Wireless networks, diversity and space-time codes

We apply the idea of space-time coding devised for multiple-antenna systems to the problem of communications over wireless relay networks. A two-stage protocol is used, 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 proposed system has a diversity of order α₀ min{T, R}, with T the coherence interval, R the number of relay nodes, and α₀ the solution to the equation α + logα/logP = 1 - loglogP/logP, where P is the total transmit power in the network. In particular, we show that the pairwise error probability (PEP) decays no slower than (logP/P)^min{T,R}. Thus, apart from the log P factor and assuming T ≥ R, the system has the same diversity as a multiple-antenna system with R transmit antennas and one receive antenna, which is the same as assuming that the R relay nodes can fully cooperate and have full knowledge of the transmit 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 multiple-antenna systems. However, at intermediate SNR, it can be quite different. We discuss some of the ramifications of using different space-time codes and finally verify our analysis through the simulation or randomly generated distributed space-time codes.