Sum-Rate-Optimal Statistical Precoding for FDD Massive MIMO Downlink With Deterministic Equivalents

Statisticalprecoding is considered as a promising technique to release the channel state information (CSI) acquisition overhead. This article investigates a linear precoder design for frequency-division duplexing (FDD) massive MIMO downlink with only statistical CSI. We use a beam-based statistical channel model to capture the spatial correlation characteristics of the channels. The objective of the precoder design is to maximize the ergodic sum-rate under total power constraint. Based on the minorize-maximize (MM) algorithm, a stationary solution of the ergodic sum-rate maximization problem can be obtained. The stationary solution is shown to be the same as the optimal solution to a stochastic weighted minimum mean square error (SWMMSE) problem. Further, we establish the approximations for rate expressions with deterministic equivalent. The deterministic equivalents of ergodic rates are only related to the precoding matrices and statistical CSI. According to these closed-form rate expressions, we propose a linear precoder design algorithm and obtain tractable expressions for precoding matrices. Numerical comparisons with the existing precoding approach demonstrate the significant advantages of the developed algorithm.