A robust beamformer design for underlay cognitive radio networks using worst case optimization

We propose a robust beamforming design for underlay cognitive radio networks where multiple secondary transmitters communicate with corresponding secondary receivers and coexist with a primary network. We consider a scenario where all transmitters have multiple antennas and all primary and secondary receivers are equipped with a single antenna. The main focus is to design the optimal transmit beamforming vectors for secondary transmitters that maximize the minimum of the received signal-to-interference-plus-noise ratios of the cognitive users. The interference powers to the primary receivers are kept below a threshold to guarantee that the performance of the primary network does not degrade due to the secondary network. Imperfect channel state information (CSI) in all relevant channels are considered, and a bounded ellipsoidal uncertainty model is used to model the CSI errors. We recast the problem in the form of semidefinite program and an iterative algorithm based on the bisection method is proposed to achieve the optimal solution. Further, we propose upper and lower bounds for the optimal value of the considered problem, which provides better initialization for the algorithm. Numerical simulations are conducted to show the effectiveness of the proposed method against the non-robust design.