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MMSE analysis of certain large isometric random precoded systems

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4 Author(s)
Debbah, M. ; Motorola Labs.-Paris, Gif-sur-Yvette, France ; Hachem, W. ; Loubaton, P. ; de Courville, M.

Linear precoding consists in multiplying by a N×K matrix a K-dimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted. We analyse the performance of MMSE receivers for certain large random isometric precoded systems on fading channels. Using new tools, borrowed from the so-called free probability theory, it can be shown that the signal to interference plus noise ratio at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when N→+∞ and K/N→α⩽1. These asymptotic results are used to optimally balance the redundancy introduced between linear precoding and classical convolutional coding, while preserving a simple MMSE equalization scheme at the receiver

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Information Theory Workshop, 2001. Proceedings. 2001 IEEE

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