Optimal precoder design for non-regenerative multiple-input multiple-output cognitive relay systems with perfect and imperfect channel state information

Abstract

This paper studies optimal precoder design for non-regenerative multiple-input multiple-output (MIMO) cognitive relay systems, where the secondary user (SU) and relay station (RS) share the same spectrum with the primary user (PU). We aim to maximize the system capacity subject to the transmit power constraints at the SU transmitter (SU-Tx) and RS, and the interference power constraint at the PU. We jointly optimize precoders for the SU-Tx and RS with perfect and imperfect channel state information (CSI) between the SU-Tx/RS and PU, where our design approach is based on the alternate optimization method. With perfect CSI, we derive the optimal structures of the RS and SU-Tx precoding matrices and develop the gradient projection algorithm to find numerical solution of the RS precoder. Under imperfect CSI, we derive equivalent conditions for the interference power constraints and convert the robust SU-Tx precoder optimization into the form of semi-definite programming. For the robust RS precoder optimization, we relax the interference power constraint related with the RS precoder to be convex by using an upper bound and apply the gradient projection algorithm to deal with it. Simulation results demonstrate the effectiveness of the proposed schemes.