Robust cognitive beamforming with partial channel state information

This paper considers a spectrum sharing based cognitive radio (CR) communication system, which consists of a secondary user (SU) having multiple transmit antennas and a single receive antenna and a primary user (PU) having a single receive antenna. The channel state information (CSI) on the link of the SU is assumed to be perfectly known at the SU transmitter (SU-Tx). However, due to loose cooperation between the SU and the PU, only partial CSI of the link between the SU-Tx and the PU is available at the SU-Tx. With the partial CSI and a prescribed transmit power constraint, our design objective is to determine the transmit signal covariance matrix that maximizes the rate of the SU while keeping the interference power to the PU below a threshold for all the possible channel realizations within an uncertainty set. This problem, termed the robust cognitive beamforming problem, can be naturally formulated as a semi-infinite programming (SIP) problem with infinitely many constraints.We first transform this problem into a second order cone programming (SOCP) problem and then solve it via a standard interior point algorithm. Then, an analytical solution with significantly reduced complexity is developed from a geometric perspective. It is shown that both algorithms yield the same optimal solution. Simulation examples are presented to validate the effectiveness of the proposed algorithms.