caa a22 4500 467893217 CHVBK 20180406152754.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s10955-006-9076-0 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9076-0 Capacity of Multivariate Channels with Multiplicative Noise: Random Matrix Techniques and Large-N Expansions (2) [Elektronische Daten] [A. Sengupta, Partha Mitra] We study memoryless, discrete time, matrix channels with additive white Gaussian noise and input power constraints of the form Y i = ∑ j H ij X j + Z i , where Y i , X j and Z i are complex, i = 1 m, j = 1 n, and H is a complex m× 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[H ik H * jl] = 1/n C ij D kl, 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 † 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 α; I+ β H, α,β 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. Springer Science+Business Media, Inc., 2006 Random matrix theory nationallicence multiple input nationallicence multiple output channel nationallicence capacity nationallicence large-N-matrix field theory nationallicence Sengupta A. Department of Physics and Astronomy and BioMaPS Institute, Rutgers University, 08854, Piscataway, NJ, USA aut Mitra Partha Cold Spring Harbor Laboratory, 1 Bungtown Rd., 11724, Cold Spring Harbor, USA aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/5-6(2006-12-01), 1223-1242 0022-4715 125:5-6<1223 2006 125 10955 https://doi.org/10.1007/s10955-006-9076-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9076-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sengupta A. Department of Physics and Astronomy and BioMaPS Institute, Rutgers University, 08854, Piscataway, NJ, USA aut NATIONALLICENCE 700 1- Mitra Partha Cold Spring Harbor Laboratory, 1 Bungtown Rd., 11724, Cold Spring Harbor, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/5-6(2006-12-01), 1223-1242 0022-4715 125:5-6<1223 2006 125 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer