Cooperative Beamforming for Cognitive Radio Systems with Multiple Primary and Secondary Receivers in Presence of Asynchronous Interferences

In this paper, we develop a cooperative beamforming technique for a cooperative cognitive radio (CR) system with multiple secondary cooperative transmitters (SCTs), secondary receivers (SRs) and primary receivers (PRs) in presence of asynchronous interferences. The objective of the beamforming technique is to maximize the minimum data rate of the SRs subject to transmission power constraints at the SCTs as well as asynchronous interference power constraints at the PRs. The optimal beamforming design is a quadratically constrained quadratic program max-min optimization problem, which is non-convex and non-linear. Therefore, we reformulate the optimal beamforming design as a quasi-convex problem by using the so-called semidefinite program (SDP) relaxation technique that can be solved using the standard SDP solvers and bisection method. However, the computational complexity of the optimal beamforming technique is high. Therefore, we study important properties of the optimization problem and propose a low complexity suboptimal beamfoming technique by using the properties.