  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 (max-min) 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.
