  In this work, we study the problem of relay beamforming for an underlay
cognitive radio relay network using amplify-and-forward (AF) relaying
technique. We consider a cognitive radio network consisting of single primary
and multiple secondary transmitters/receivers. In addition, there are several
relay nodes that help both primary and secondary networks. We propose a new
beamforming method for relays' transmission, in which the beamforming weights
at the relays are the solution of an optimization problem. The objective of the
optimization problem is maximizing the worst case signal to interference plus
noise ratio (SINR) at the secondary receivers (SU-RX) and the constraints are
the interference power on the primary receiver (PU-RX) and the total
transmitted power of the relay nodes. We show that the beamforming problem can
be reformulated as a second order cone programming (SOCP) problem and solved by
the bisection search method. Our simulation results show the performance
improvement as a function of the size and the power of the relay network.
