On Stochastic Beamforming for Ergodic Sum-Rate Maximization in Cooperative Transmission Systems

In this paper, we investigate stochastic beamforming approaches to maximize the ergodic sum-rate (ESR) for cooperative transmission systems, including both coherent and non coherent joint transmission. To this end, by utilizing the seminal weighted minimum mean square error (WMMSE) transform and adopting the stochastic successive upper-bound minimization (SSUM) framework, we first propose a stochastic WMMSE (SWMMSE) algorithm that maximizes the network’s ESR via analytically updating beamformers in an online manner. This algorithm can operate without any prior knowledge on the channel statistics and is applicable to very generic channel models with arbitrary probability distributions. Based on that, by substituting the SWMMSE update with the determinant equivalents (DEs) derived from large-dimensional random matrix theory, we further develop a DE-WMMSE algorithm. This method requires only the first- and second-order statistics of channel state information (CSI) and obviates the need for sampling channel. As will be proved, unlike the restrictions in the existing literature, our proposed DE-WMMSE algorithm can be applied to rather generic channel models beyond Rayleigh. Extensive numerical results verify the effectiveness and benefit of our proposed algorithms. Especially, the SWMMSE algorithm is highly computationally efficient for large-scale networks, while the DE-WMMSE algorithm is fast and convenient for modest-scale networks.