D.C. iterations for SINR maximin multicasting in Cognitive radio

The design of transmit beamforming vectors to maximize the threshold of the signal-to-interference-plus-noise ratios (SINR) at the secondary receivers in cognitive multicast transmission is maximin optimization of quadratic fractional functions. There is no efficient solver for this hard maximin program. In the present paper, we show that the program can be effectively represented by a canonical d.c. (difference of convex functions) program of the same size. Accordingly, d.c. iterations are derived to locate its optimized solution. Our thorough numerical examples verify that the proposed algorithms offer almost global optimality whilst requiring relatively low computational load.