Robust and secure beamformer design for MIMO relaying with imperfect eavesdropper CSI

This paper presents a computationally efficient beamforming approach to combat wiretapping in a relay-based multiple-input multiple output (MIMO) communication system which is part of a cognitive radio (CR) network. The system operates in two stages, that is, multiple-access (MA) followed by broadcasting (BC) using physical layer network coding (PNC). The beamforming design is based on minimizing the mean square error (MSE) at the receiving node(s) while enforcing signal-to-interference-plus-noise ratio (SINR) constraints at the eavesdroppers. The constraints take into account uncertainty bounds on eavesdropper channel estimation errors. In each stage of communication, an optimization problem is devised and solved using an iterative procedure, considering two different types of eavesdropper functionality, i.e., selection combining and “blind” beamforming. Numerical results show the convergence of the MSE at the nodes and the SINR distributions at the eavesdroppers for both cases. Comparisons to previously suggested solutions for blind beamforming are also included showing improvements in MSE values in the MA stage and computational efficiency in both stages.