Capacity of multivariate channels with multiplicative noise: Random matrix techniques and large-N expansions (2)

Sengupta, A. M., Mitra, P. P. (December 2006) Capacity of multivariate channels with multiplicative noise: Random matrix techniques and large-N expansions (2). Journal of Statistical Physics, 125 (5-6). pp. 1227-1246. ISSN 0022-4715

DOI: 10.1007/s10955-006-9076-0


We study memoryless, discrete time, matrix channels with additive white Gaussian noise and input power constraints of the form Y-i=Sigma(j) HijXj+Z(i) , where Y-i , X-j and Z(i) are complex, i=1...m, j=1...n, and H is a complex m x n matrix with some degree of randomness in its entries. The additive Gaussian noise vector is assumed to have uncorrelated entries. Let H be a full matrix (non-sparse) with pairwise correlations between matrix entries of the form E[HikH*(jl)]=1/n CijDkl, where C, D are positive definite Hermitian matrices. Simplicities arise in the limit of large matrix sizes (the so called large-n limit) which allow us to obtain several exact expressions relating to the channel capacity. We study the probability distribution of the quantity f(H)=log (1+PH dagger SH) . S is non-negative definite and hermitian, with TrS=n and P being the signal power per input channel. Note that the expectation E[f(H)], maximised over S, gives the capacity of the above channel with an input power constraint in the case H is known at the receiver but not at the transmitter. For arbitrary C, D exact expressions are obtained for the expectation and variance of f(H) in the large matrix size limit. For C=D=I, where I is the identity matrix, expressions are in addition obtained for the full moment generating function for arbitrary (finite) matrix size in the large signal to noise limit. Finally, we obtain the channel capacity where the channel matrix is partly known and partly unknown and of the form alpha I+beta H, alpha,beta being known constants and entries of H i.i.d. Gaussian with variance 1/n. Channels of the form described above are of interest for wireless transmission with multiple antennae and receivers.

Item Type: Paper
Uncontrolled Keywords: random matrix theory multiple input multiple output channel capacity large N matrix field theory INFORMATION CAPACITY information capacity ANTENNA SYSTEMS antenna systems COMMUNICATION communication
Subjects: physics > noise
CSHL Authors:
Communities: CSHL labs > Mitra lab
Depositing User: CSHL Librarian
Date: December 2006
Date Deposited: 02 Apr 2012 18:41
Last Modified: 02 Apr 2012 20:29

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