On optimal precoding in linear vector Gaussian channels with arbitrary input distribution

Details On optimal precoding in linear vector Gaussian channels with arbitrary input distribution On optimal precoding in linear vector Gaussian channels with arbitrary input distribution

2009-04-30

arxiv.org/abs/0904.4900v1

Computer Science

Information Theory

Proceedings of the 2009 IEEE International Symposium on Information Theory, Seoul, Korea, June 28 - July 3, 2009

Scientific paper

The design of the precoder the maximizes the mutual information in linear vector Gaussian channels with an arbitrary input distribution is studied. Precisely, the precoder optimal left singular vectors and singular values are derived. The characterization of the right singular vectors is left, in general, as an open problem whose computational complexity is then studied in three cases: Gaussian signaling, low SNR, and high SNR. For the Gaussian signaling case and the low SNR regime, the dependence of the mutual information on the right singular vectors vanishes, making the optimal precoder design problem easy to solve. In the high SNR regime, however, the dependence on the right singular vectors cannot be avoided and we show the difficulty of computing the optimal precoder through an NP-hardness analysis.

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