A New Approach for Mutual Information Analysis of Large Dimensional Multi-Antenna Channels

Walid Hachem 1, * Oleksiy Khorunzhiy 2 Philippe Loubaton 3 Jamal Najim 1 Leonid Pastur 4
* Auteur correspondant
1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Equipe Probablités et Statistiques
3 LIGM - Laboratoire d'Informatique Gaspard-Monge
4 Low Temperature Physics Institute, Kharkiv
Abstract : This paper adresses the behaviour of the mutual information of correlated MIMO Rayleigh channels when the numbers of transmit and receive antennas converge to infinity at the same rate. Using a new and simple approach based on Poincaré-Nash inequality and on an integration by parts formula, it is rigorously established that the mutual information converges to a Gaussian random variable whose mean and variance are evaluated. These results confirm previous evaluations based on the powerful but non rigorous replica method. It is believed that the tools that are used in this paper are simple, robust, and of interest for the communications engineering community.
Keywords : Poincaré-Nash Inequality Central Limit Theorem Correlated MIMO Channels Large Random Matrix Theory Mutual Information Poincaré-Nash Inequality.
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Article dans une revue
IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2008, 54 (9), pp.3987-4004. 〈10.1109/TIT.2008.928229〉
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Walid Hachem, Oleksiy Khorunzhiy, Philippe Loubaton, Jamal Najim, Leonid Pastur. A New Approach for Mutual Information Analysis of Large Dimensional Multi-Antenna Channels. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2008, 54 (9), pp.3987-4004. 〈10.1109/TIT.2008.928229〉. 〈hal-00120482〉

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