Probabilistic Analysis of Semidefinite Relaxation for Leakage-Based Multicasting

In this letter, we derive worst-case approximation results for rank one and rank two leakage-based multicasting (LBM) as recently proposed by Schwarz and Rupp [“Transmit optimization for the MISO multicast interference channel,” IEEE Trans. Commun., vol. 63, no. 12, pp. 4936-4949, Dec. 2015]. Specifically, we provide worst-case lower bounds on the approximation ratios achieved with rank one/two Gaussian randomization of the optimal solution as obtained from a semidefinite relaxation (SDR). We demonstrate the validity of the derived bounds through Monte Carlo simulations and we show that good approximation ratios are achieved even for very large number of multicast users and leakage constraints.