Probabilistic constrained multicast beamforming in cognitive relay systems
In this paper, multicast beamforming in cognitive relay systems is investigated with the consideration of imperfect channel state information at the transmitter (CSIT). We focus at the design of the optimal signal forwarding matrix at the cognitive relay in both centralized relay mode (CRM) and distributed relay mode (DRM). The problem is formulated aiming at minimizing the total consumed power at the relay node with suitable QoS guarantee for secondary users and strict interference control for primary users. Due to the uncertainty of transmission channel gains, constraints for QoS guarantee and interference control cannot be expressed in closed forms, making it extremely difficult to solve the problem directly. To circumvent this, we first employ the Bernstein-type inequality to convert the probabilistic constraints into closed-form expressions and then present both the semi-definite relaxation (SDR) algorithm and the penalty function (PenFun) algorithm to accomplish the non-convex problem optimization. Simulation results show that CRM is more resource efficient than DRM, and the PenFun algorithm can achieve a much better solution than the SDR algorithm at the cost of complexity. Meanwhile, compared with existing schemes which do not consider the CSIT error, the proposed schemes can support a much lower outage probability and enjoy perfect interference control for primary users.
multicast beamforming cognitive relay systems imperfect channel state bernstein-type inequality penalty function method