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 /spl alpha//sub 0/ min{T, R}, with T the coherence interval, R the number of relay nodes, and /spl alpha//sub 0/ the solution to the equation /spl alpha/ + log/spl alpha//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)/sup min{T,R}/. Thus, apart from the log P factor and assuming T /spl ges/ 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.

[1]  Yu Chang,et al.  Application of space-time linear block codes to parallel wireless relays in mobile ad hoc networks , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.

[2]  Elza Erkip,et al.  User cooperation diversity. Part I. System description , 2003, IEEE Trans. Commun..

[3]  Yan Mei,et al.  Wireless antennas - making wireless communications perform like wireline communications , 2003, 2003 IEEE Topical Conference on Wireless Communication Technology.

[4]  Babak Hassibi,et al.  Is broadcast plus multiaccess optimal for Gaussian wireless networks? , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.

[5]  Babak Hassibi,et al.  On the expected complexity of integer least-squares problems , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[6]  A. Robert Calderbank,et al.  Space-Time Codes for High Data Rate Wireless Communications : Performance criterion and Code Construction , 1998, IEEE Trans. Inf. Theory.

[7]  Babak Hassibi,et al.  High-rate codes that are linear in space and time , 2002, IEEE Trans. Inf. Theory.

[8]  Gerard J. Foschini,et al.  Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas , 1996, Bell Labs Technical Journal.

[9]  Thomas L. Marzetta,et al.  Unitary space-time modulation for multiple-antenna communications in Rayleigh flat fading , 2000, IEEE Trans. Inf. Theory.

[10]  Michael Gastpar,et al.  On the capacity of wireless networks: the relay case , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[11]  Thomas L. Marzetta,et al.  Capacity of a Mobile Multiple-Antenna Communication Link in Rayleigh Flat Fading , 1999, IEEE Trans. Inf. Theory.

[12]  Matthew C. Valenti,et al.  Coded transmit macrodiversity: block space-time codes over distributed antennas , 2001, IEEE VTS 53rd Vehicular Technology Conference, Spring 2001. Proceedings (Cat. No.01CH37202).

[13]  Helmut Bölcskei,et al.  Fading relay channels: performance limits and space-time signal design , 2004, IEEE Journal on Selected Areas in Communications.

[14]  Elza Erkip,et al.  User cooperation diversity. Part II. Implementation aspects and performance analysis , 2003, IEEE Trans. Commun..

[15]  Gregory W. Wornell,et al.  Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks , 2003, IEEE Trans. Inf. Theory.

[16]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[17]  Babak Hassibi,et al.  On the power efficiency of sensory and ad hoc wireless networks , 2003, IEEE Transactions on Information Theory.