Approximation Bound for Semidefinite Relaxation Based Multicast Transmit Beamforming

Abstract

The max-min-fair transmit beamforming problem in multigroup broadcasting has been shown to be NP-hard in general. Recently, a polynomial time approximation approach based on semidefinite relaxation (SDR) has been proposed [1]. It was found [1], through computer simulations, that this method is capable of giving a good approximate solution in polynomial time. This paper shows that the SDR based approach can guarantee as least an 0(1/M) approximation quality, where M is the total number of receivers. The existence of such a data independent bound certifies the worst case approximation quality of the SDR algorithm for any problem instance and any number of transmit antennas.