Robust beamformer design for underlay cognitive radio network 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. 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. We consider a scenario where all transmitters have multiple antennas and all primary and secondary receivers are equipped with a single antenna. Individual transmit powers of the transmitters are limited and interference power constraints to the primary receivers guarantee the performance of the primary network. Imperfect channel state information (CSI) in all relevant channels are considered and bounded ellipsoidal uncertainty model is used to model the CSI errors. We recast the problem in the form of semi-definite program and an iterative algorithm is proposed to achieve the optimal solution. Numerical simulation are conducted to show the effectiveness of the proposed method against the non-robust design.