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Published October 2004 | Published
Book Section - Chapter Open

Wireless networks, diversity and space-time codes

Abstract

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 α_0 min{T, R}, with T the coherence interval, R the number of relay nodes, and α0 the solution to the equation α + (log α)/(log P) = 1 - (log log P)/(log P), where P is the total transmit power in the network. In particular, we show that the pairwise error probability (PEP) decays no slower than ((log P)/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.

Additional Information

© 2004 IEEE. This work was supported in part by the National Science Foundation under grant no. CCR-0133818, by the Office of Naval Research under grant no. N00014-02-1-0578 and by Caltech's Lee Center for Advanced Networking.

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Created:
August 19, 2023
Modified:
March 5, 2024