Joint multicast and unicast beamforming for the MISO downlink interference channel

In this paper, we consider the joint multicast and unicast beamforming design problem in the multi-input single-output downlink wireless network, where all base stations (BSs) potentially can cooperate (as a single virtual BS) to transmit a common multicast and multiple dedicated unicast data streams at the same time on the same frequency band. To reduce cooperation overhead (among different BSs), we prefer partial cooperation transmission such that each user's data stream (either multicast or unicast) is served by only a small subset of BSs. We formulate the problem from a (group) sparse optimization perspective and propose a branch-and-bound (BB) algorithm for solving the problem. Our proposed BB algorithm is guaranteed to find the globally optimal solution of the problem. We also propose an efficient successive linear approximation (SLA) algorithm for solving the problem. Numerical results show that the SLA algorithm can perform very close to the BB algorithm but with significantly less computational complexity. It is also shown that the proposed mixed ℓ ₂ /ℓ ₁ regularizer in the sparse formulation provides a flexible and effective tradeoff between the total transmission power cost and the cooperation cost.