Worst-case transmitter design for multi-antenna cognitive radio network using Lagrange duality

The problem of optimal transmitter design to achieve the physical layer security for multi-antenna cognitive radio network (CRN) in the presence of an eavesdropper receiver (ED-Rx) is considered in this paper. The purpose of this problem is to maximize the security rate of the secondary user transmitter (SU-Tx) under the constraints of secondary user transmit power and interference limit at primary user (PU). In this paper, we propose an algorithm based on the Lagrange duality to solve this optimization problem. Compared with the existing algorithm, our proposed algorithm avoids several coarse conversions and obtains more rigorous formulas. Simulation results demonstrate that the performance of our algorithm is better than the existing algorithm distinctly when the channel covariance estimate errors stay at a high level.