  In this paper, a cognitive relay channel is considered, and
amplify-and-forward (AF) relay beamforming designs in the presence of an
eavesdropper and a primary user are studied. Our objective is to optimize the
performance of the cognitive relay beamforming system while limiting the
interference in the direction of the primary receiver and keeping the
transmitted signal secret from the eavesdropper. We show that under both total
and individual power constraints, the problem becomes a quasiconvex
optimization problem which can be solved by interior point methods. We also
propose two sub-optimal null space beamforming schemes which are obtained in a
more computationally efficient way.
