In this paper, we present robust joint relay precoder designs and transceiver power allocations for a cognitive radio network under imperfect channel state information (CSI). The secondary (or cognitive) network consists of a pair of singleantenna transceiver nodes and a non-regenerative two-way relay with multiple antennas which aids the communication process between the transceiver pair. The secondary nodes share the
spectrum with a licensed primary user (PU) while guaranteeing that the interference to the PU receiver is maintained below a specified threshold. We consider two robust designs: the first is based on the minimization of the total transmit power of the secondary relay node required to provide the minimum quality of service, measured in terms of mean-square error (MSE) of the transceiver nodes, and the second is based on the minimization of the sum-MSE of the transceiver nodes. The robust designs are based on worst-case optimization and take into account known
parameters of the error in the CSI to render the performance immune to the presence of errors in the CSI. Though the original problem is non-convex, we show that the proposed designs can be reformulated as tractable convex optimization problems that can be solved efficiently. We illustrate the performance of the proposed designs through some selected numerical simulations.

Accepted for publication