A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels

Romain Couillet (1) , Merouane Debbah (2) , Jack W. Silverstein (3)

1 SSEC - Chaire Sciences des Systèmes et Défis Energétiques EDF/ECP/Supélec
2 Chaire Radio Flexible - Chaire Radio Flexible Alcatel-Lucent/Supélec
3 NC State - North Carolina State University [Raleigh]

This article provides novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices. These results are used to characterise the ergodic rate region of multiple antenna multiple access channels, when each point-to-point propagation channel is modelled according to the Kronecker model. We specifically provide an approximation of all rates achieved within the ergodic rate region and we provide an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water-filling algorithm to obtain these precoders. An original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides. The above results are validated by Monte Carlo simulations.

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Romain Couillet, Merouane Debbah, Jack W. Silverstein. A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels. IEEE Transactions on Information Theory, 2011, 57 (6), pp.3493-3514. ⟨10.1109/TIT.2011.2133151⟩. ⟨hal-00553676⟩