Robust cognitive beamforming with partial channel state information

In this paper, we consider a multiple-input single-output (MISO) cognitive radio (CR) point-to-point channel coexisting with a single primary user (PU). The channel state information (CSI) between the secondary user (SU) transmitter (SU-Tx) and SU receiver (SU-Rx) is perfectly known at the SU-Tx. However, due to the less cooperation between the SU and the PU, only partial CSI between the SU-Tx and PU is obtained by the SU-Tx. Our objective is, given the transmit power constraint, to determine the optimal transmit signal covariance to maximize the rate of the SU while keeping the interference to the PU less than a threshold with high probability. This problem is termed as a robust cognitive beamforming design problem, and can be formulated as a semi-infinite programming (SIP) problem. An efficient algorithm is then proposed to transform this SIP problem into a finite constraint problem, and it is shown that the algorithm obtains the globally optimal solution. Simulation results are provided to evaluate the effectiveness of the algorithm.