Multicast beamforming with antenna selection

Multicast beamforming exploits subscriber channel state information at the base station to form multiple beams that steer radiated power towards users of interest, while minimizing leakage to other users and systems. Such functionality has been provisioned in the long-term evolution (LTE) enhanced multimedia broadcast multicast service (EMBMS). In this context, the present paper deals with joint multicast beamforming and antenna selection. Whereas this problem (and even plain multicast beamforming) is NP-hard, it is shown that using ℓ₁-norm squared (instead of ℓ₁-norm) as a surrogate for the ℓ₀-norm yields a natural semidefinite programming relaxation - something not obvious with the ℓ₁-norm. Simulations indicate that the proposed algorithm significantly reduces the number of antennas required to meet prescribed service levels, at a relatively small cost of excess transmission power. Furthermore, its performance is close to that attained by exhaustive search, at far lower complexity.