Cognitive Beamforming for Throughput Maximization With Statistical Cross Channel State Information

Throughput maximization is considered in this letter for a multiple-input multiple-output (MIMO) cognitive radio system where instantaneous cross channel state information is unavailable at the secondary transmitter. We study cognitive beamforming subject to interference expectation constraint and interference outage probability constraint at the primary receiver, respectively. For the former constraint, the beamforming problem can be formulated as a conventional MIMO transmission problem, which can be easily solved via the water-filling method. For the latter constraint, we find that the optimal beamforming matrix lies in the space spanned by the secondary channel, and that the interference power is only related to eigenvalues of the secondary covariance matrix. By exploiting the relationship between vibrations of the secondary covariance matrix and its eigenvalues, we design an algorithm for this beamforming problem. Finally, numerical results are presented to demonstrate the performance of the proposed solutions.