Sherman-Morrison Regularization for ELAA Iterative Linear Precoding

The design of iterative linear precoding is recently challenged by extremely large aperture array (ELAA) systems, where conventional preconditioning techniques could hardly improve the channel condition. In this paper, it is proposed to regularize the extreme singular values to improve the channel condition by deducting a rank-one matrix from the Wishart matrix of the channel. Our analysis proves the feasibility to reduce the largest singular value or to increase multiple small singular values with a rank-one matrix when the singular value decomposition of the channel is available. Knowing the feasibility, we propose a low-complexity approach where an approximation of the regularization matrix can be obtained based on the statistical property of the channel. It is demonstrated, through simulation results, that the proposed low-complexity approach significantly outperforms current preconditioning techniques in terms of reduced iteration number for more than $10\%$ in both ELAA systems as well as symmetric multi-antenna (i.e., MIMO) systems when the channel is i.i.d. Rayleigh fading.