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Vector Precoding in High Dimensions: A Replica Analysis

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3 Author(s)
Muller, R.R. ; Dept. of Electr. & Telecommun., NTNU, Trondheim ; Dongning Guo ; Moustakas, A.L.

We apply the replica method to analyze vector pre-coding, a method to reduce transmit power in antenna array communications, in the limit of an infinite number of dimensions of the signal vector. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We specialize our result to inversion of an i.i.d. channel and two cases of signal point optimization (i) 2-point lattice pre-coding and (ii) compact relaxation. In the two cases the replica symmetric transmitted energy is found to be 4.3 dB and 9.6 dB above the orthogonal case for a square channel matrix, respectively.

Published in:

Information Theory, 2007. ISIT 2007. IEEE International Symposium on

Date of Conference:

24-29 June 2007