Bivariate probabilistic constrained programming for interference exploitation in the cognitive radio

In this paper, we study a constructive interference based cognitive radio beamforming optimization problem under perfect channel state information at the transmitter and the knowledge of data information. The beamformers are designed to minimize the worst secondary user's symbol error probability under constraints on the instantaneous total transmit power, and the power of the instantaneous interference in the primary link. The problem is formulated as a bivariate probabilistic constrained programming problem and can be solved using the barrier method. Our simulations indicate that the proposed technique offers a significantly improved performance over the conventional technique, while guaranteeing the quality of service (QoS) of primary users on an instantaneous basis, in contrast to the average QoS guarantees of conventional beamformers.