Hybrid Precoding for Physical Layer Multicasting

This work investigates the problem of downlink transmit precoding for physical layer multicasting with a limited number of radio-frequency (RF) chains. To tackle the RF hardware constraint, we consider a hybrid precoder that is partitioned into a high-dimensional RF precoder and a low-dimensional baseband precoder. Considering a total transmit power constraint over the RF chains, the goal is to maximize the minimum (maxmin) received signal-to-noise ratio (SNR) among all users. We propose a low complexity algorithm to compute the RF precoder that achieves near-optimal max-min performance. Moreover, we derive a simple condition under which the hybrid precoding driven by a limited number of RF chains incurs no loss of optimality with respect to the fully digital precoding case. Finally, numerical results validate the effectiveness of the proposed algorithm and theoretical findings.