Statistically Robust Cognitive Radio Beamforming

We consider a cognitive radio (CR) network consisting of a secondary user transmitter (SU-Tx) equipped with multiple antennas and a secondary user receiver (SU-Rx) that share spectrum with multiple primary user transmitter (PUTx) and receiver (PU-Rx) pairs. We assume that the CR has a loose cooperation with the primary network and therefore, only partial channel state information of each of the PU-Tx to PU-Rx and SU-Tx to each PU-Rx links is available. Furthermore, we assume that the SU-Tx to SU-Rx link CSI is imperfect, with the channel error modelled as additive Gaussian noise. Under these assumptions, we propose a new statistically robust CR beamformer where the total SU-Tx transmit power is minimised subject to PU-Rx and SU-Rx outage probability constraints. We present expressions for PU-Rx and SU-Rx outage probabilities and formulate the robust beamformer optimisation problem as a convex semidefinite program (SDP). SU-Tx transmit power, PU-Rx signal-to-interference-and-noise ratio (SINR) and SU-Rx signal-to-noise (SNR) cumulative distribution functions (CDFs) are obtained through solution of our optimisation problem.