Precoder Design for Non-Regenerative MIMO Relay Cognitive Radio Systems

In this paper, we study the problem of relay precoder design in a multi-antenna non-regenerative relay cognitive radio (CR) system assuming underlay spectrum sharing methodology with the primary users (PUs). An expression for the capacity of the secondary system is derived assuming fixed source covariance matrix. We then consider maximizing this capacity expression subject to a power constraint at the relay and an interference power constraint at the PU due to the secondary relay. We then derive the structure of the relay precoding up to a square matrix that should be chosen optimally. A constrained optimization problem is derived to find this square matrix to maximize the capacity equation. The solution to this optimization problem involves an exhaustive search and the complexity increases with the number of relay antennas. We, therefore, propose an alternative sub-optimal approach with significantly lower complexity to derive the structure of the relay precoding matrix. Through simulation, we compare the effectiveness of the optimal and the sub-optimal approaches to improve the achievable throughput of the CR system. It is shown that both approaches provide a significant improvement in the throughput of the system at different power and interference regimes.