Energy-Efficient Precoding for Non-Orthogonal Multicast and Unicast Transmission via First-Order Algorithm

As the demand for supporting hybrid multicast and unicast services is rapidly increasing, a non-orthogonal multiplexing transmission scheme called layered-division multiplexing (LDM) has been recognized as an effective way to provide high spectrum efficiency (SE). However, high SE is not necessarily equivalent to high energy efficiency (EE). In fact, it is still unclear how much benefit LDM would provide for hybrid multicast and unicast services under EE maximization, which belongs to the more challenging class of fractional programs. To fill this gap, we formulate the problem of energy-efficient precoding design for the LDM-based multi-user multi-input-multi-output downlink system, under both multicast and unicast multi-stream data rate constraints of each user. Although the problem is nonsmooth and nonconvex, we propose a first-order algorithm for finding both the initial point and the final solution. Since the proposed first-order algorithm involves only gradient information, it achieves very low complexity. The simulation results demonstrate that, compared with the orthogonal transmission schemes, the LDM transmission under the proposed precoding can provide a much higher EE. Moreover, the proposed first-order algorithm achieves the same EE as that of a second-order based approach, but requires much shorter computation time.