Capacity-achieving input covariance for single-user multi-antenna channels

Tulino, Antonia M.; Lozano Solsona, Angel; Verdú, Sergio

doi:http://dx.doi.org/10.1109/TWC.2006.1611096

Capacity-achieving input covariance for single-user multi-antenna channels

Citation

Tulino A M, Lozano A, Verdú S. Capacity-achieving input covariance for single-user multi-antenna channels. IEEE Transactions on Wireless Communications. 2006; 5(3): 662-671. DOI 10.1109/TWC.2006.1611096

Abstract

We characterize the capacity-achieving input covariance for multi-antenna channels known instantaneously at the receiver and in distribution at the transmitter. Our characterization, valid for arbitrary numbers of antennas, encompasses both the eigenvectors and the eigenvalues. The eigenvectors are found for zero-mean channels with arbitrary fading profiles and a wide range of correlation and keyhole structures. For the eigenvalues, in turn, we present necessary and sufficient conditions as well as an iterative algorithm that exhibits remarkable properties: universal applicability, robustness and rapid convergence. In addition, we identify channel structures for which an isotropic input achieves capacity.