Robust Distributed Cognitive Relay Beamforming

In this paper, we present a distributed relay beamformer design for a cognitive radio network in which a cognitive (or secondary) transmit node communicates with a secondary receive node assisted by a set of cognitive non-regenerative relays. The secondary nodes share the spectrum with a licensed primary user (PU) node, and each node is assumed to be equipped with a single transmit/receive antenna. The interference to the PU resulting from the transmission from the cognitive nodes is kept below a specified limit. The proposed robust cognitive relay beamformer design seeks to minimize the total relay transmit power while ensuring that the transceiver signal-to-interference-plus-noise ratio and PU interference constraints are satisfied. The proposed design takes into account a parameter of the error in the channel state information (CSI) to render the performance of the beamformer robust in the presence of imperfect CSI. Though the original problem is non-convex, we show that the proposed design can be reformulated as a tractable convex optimization problem that can be solved efficiently. Numerical results are provided and illustrate the performance of the proposed designs for different network operating conditions and parameters.