  We consider a certain class of large random matrices, composed of independent
column vectors with zero mean and different covariance matrices, and derive
asymptotically tight deterministic approximations of their moments. This random
matrix model arises in several wireless communication systems of recent
interest, such as distributed antenna systems or large antenna arrays.
Computing the linear minimum mean square error (LMMSE) detector in such systems
requires the inversion of a large covariance matrix which becomes prohibitively
complex as the number of antennas and users grows. We apply the derived moment
results to the design of a low-complexity polynomial expansion detector which
approximates the matrix inverse by a matrix polynomial and study its asymptotic
performance. Simulation results corroborate the analysis and evaluate the
performance for finite system dimensions.
