Cognitive beamforming with unknown cross channel state information

Throughput maximization is considered in this paper for a multiple-input multiple-output (MIMO) cognitive radio system when no cross channel state information is available at the secondary transmitter (ST). We study cognitive beamforming subject to interference expectation constraint and interference outage probability constraint at the primary receiver (PR), respectively. We prove that with 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. With the latter constraint, we find that the interference power is related to the eigenvalues of the covariance matrix of the secondary signals, and thus it can be expressed as a linear combination of multiple chi-square distributed variables. By exploiting the impact of the eigenvalues on the interference outage probability and establishing the relationship between the vibrations of secondary covariance matrix and its eigenvalues, we design an algorithm for this beamforming problem. Finally, simulation results are presented to demonstrate the performance of the proposed beamforming solutions subject to both constraints.