Joint Multicast Beamforming and Antenna Selection

Multicast beamforming exploits subscriber channel state information at the base station to steer the transmission power towards the subscribers, while minimizing interference to other users and systems. Such functionality has been provisioned in the long-term evolution (LTE) enhanced multimedia broadcast multicast service (EMBMS). As antennas become smaller and cheaper relative to up-conversion chains, transmit antenna selection at the base station becomes increasingly appealing in this context. This paper addresses the problem of joint multicast beamforming and antenna selection for multiple co-channel multicast groups. Whereas this problem (and even plain multicast beamforming) is NP-hard, it is shown that the mixed $\\ell_{1,\\infty}$-norm squared is a prudent group-sparsity inducing convex regularization, in that it naturally yields a suitable semidefinite relaxation, which is further shown to be the Lagrange bi-dual of the original NP-hard problem. Careful simulations indicate that the proposed algorithm significantly reduces the number of antennas required to meet prescribed service levels, at relatively small excess transmission power. Furthermore, its performance is close to that attained by exhaustive search, at far lower complexity. Extensions to max-min-fair, robust, and capacity-achieving designs are also considered.