Robust secondary multicast transmit beamforming for cognitive radio networks under imperfect channel state information

Consider a robust downlink beamforming optimization problem for secondary multicast transmission in a multiple-input multiple-output (MIMO) spectrum sharing cognitive radio (CR) network. The minimization problem of transmit power is formulated subject to both the quality-of-service (QoS) constraints on the secondary receivers and the interference temperature constraints on the primary users, under the assumption of imperfect channel state information (CSI). The problem is non-convex quadratically constrained quadratic program (QCQP), and it is hard to achieve the global optimality. As a compromise, we present a randomized approximation algorithm for the problem via convex optimization techniques. In particular, we point out that the robust beamforming problem is efficiently solvable when the number of primary and secondary links in the CR network is not larger than three. Simulation results are presented to demonstrate the performance gains of the proposed algorithm over an existing robust design.