Low-Complexity GSVD-Based Beamforming Schemes for Cognitive Radio Network

In this paper, low-complexity generalized singular value decomposition (GSVD) based beamforming schemes are proposed for cognitive radio (CR) network, in which multiple secondary users (SUs) with multiple antennas are allowed to access the spectrum of the primary network only if they do not interfere with the communication of primary users (PUs). The optimal beamforming scheme that satisfies the interference constraints at multiple PUs and maximizes signal-to-interference-plus-noise ratios (SINRs) of multiple SUs simultaneously requires a complicated iterative optimization process. To overcome the computational complexity, we develop a signal-to-leakage-plus-noise ratio (SLNR) maximizing beamforming scheme in which the weight can be obtained by GSVD without any iterations. The proposed beamforming also avoids any matrix squaring operations, and therefore, the computational complexity is drastically reduced. By modifying the proposed algorithm and introducing additional iterations but less than the number of PUs, the system performance is further improved without serious increase of the computational complexity.