Robust distributed two-way relay beamforming in cognitive radio networks

In this paper, we present distributed beamformer designs for a cognitive radio network (CRN) consisting of a pair of cognitive (or secondary) transceiver nodes communicating with each other through a set of secondary non-regenerative two-way relays. The secondary network shares the spectrum with a licensed primary user (PU), and operates under a constraint on the maximum interference to the PU, in addition to its own resource and quality of service (QoS) constraints. We propose beamformer designs assuming that the available channel state information (CSI) is imperfect, which reflects realistic scenarios. The performance of proposed designs is robust to the CSI errors. Such robustness is critical in CRNs given the difficulty in acquiring perfect CSI due to loose cooperation between the PUs and the secondary users (SUs), and the need for strict enforcement of PU interference limit. We consider a mean-square error (MSE)-constrained beamformer that minimizes the total relay transmit power and an MSE-balancing beamformer with a constraint on the total relay transmit power. We show that the proposed designs can be reformulated as convex optimization problems that can be solved efficiently. Through numerical simulations, we illustrate the improved performance of the proposed robust designs compared to non-robust designs.