Multigroup Multicast Beamformer Design for MISO-OFDM With Antenna Selection

We study the problem of designing transmit beamformers for a multigroup multicasting by considering a multiple-input single-output orthogonal frequency-division multiplexing framework. The design objective involves either minimizing the total transmit power for certain guaranteed quality of service or maximizing the minimum achievable rate among the users for a given transmit power budget. The problem of interest can be formulated as a nonconvex quadratically constrained quadratic programming (QCQP) for which the prevailing semidefinite relaxation (SDR) technique is inefficient for at least two reasons. At first, the relaxed problem cannot be reformulated as a semidefinite programming. Second, even if the relaxed problem is solved, the so-called randomization procedure should be used to generate a feasible solution to the original QCQP, which is difficult to derive for the considered problem. To overcome these shortcomings, we adopt successive convex approximation framework to find multicast beamformers directly. The proposed method not only avoids the need of randomization search, but also incurs less computational complexity compared to an SDR approach. In addition, we also extend multicasting beamformer design problem with an additional constraint on the number of active elements, which is particularly relevant when the number of antennas is larger than that of radio frequency chains. Numerical results are used to demonstrate the superior performance of our proposed methods over the existing solutions.