Efficient Analog Beamforming for Max-Min Fair Multicast Transmission

This paper investigates analog beamforming with large-scale antenna arrays for single-group multicast transmission. We focus on the max-min fair (MMF) problem and aim to design the analog beamformer with infinite and finite resolution phase shifters (PSs), respectively, to maximize the minimum signal-to-noise ratio (SNR) over all users subject to a transmit power constraint. However, the constant magnitude and infinite/ finite phase constraints imposed by PSs frustrate the access of an optimal solution of analog beamformer. We thus formulate a sub-optimal MMF problem alternatively and propose a low-complexity algorithm, which iteratively determines each element of analog beamformer to conditionally maximize the minimum SNR among users. The computational complexities of our proposed algorithms are linear in the number of antennas. Simulation results illustrate that our proposed analog beamformer design can achieve satisfactory performance which is close to the full-digital case and outperform the other state-of- the-art schemes.