Hybrid Precoding for MISO Broadcasting SWIPT Systems: A Stochastic Optimization Approach

This paper investigates the hybrid precoding (HP) design for simultaneous wireless information and power transfer in a multiple-input single-output broadcast channel setup where the terminals adopt the power splitting architecture. The problem of interest is the maximization of the signal-to-interference-plus-noise-ratio and the harvested power for all terminals under a total transmit power constraint. Our focus is on the derivation of frequency- and setup-agnostic low-complexity HP methods. Two baseline approaches for the determination of the analog precoder are considered. In the first one, the phases are computed via the singular value decomposition (SVD) of the channel matrix, while in the second they are selected randomly. Then, the baseband precoder is computed by applying semidefinite relaxation (SDR) to the problem under study. Alternatively, we combine the aforemen-tioned analog precoders with a fixed zero-forcing baseband pre-coder, in order to further reduce the computational load. Another proposed strategy focuses on the minimization of the Euclidean distance between the optimal fully-digital precoder, which is obtained via SDR, and the hybrid one. To this end, an alternating minimization algorithm that employs Gaussian smoothing to convexify the problem and utilizes stochastic gradient descent to update the phases is introduced. The performance of the proposed HP methods is comparatively evaluated versus the one achieved by the optimal fully-digital precoder via numerical simulations. The simulation results indicate that the stochastic optimization approach presents a favorable performance-complexity trade-off as well as substantial power gains.