Chance Constrained Robust Beamforming in Cognitive Radio Networks

We propose a novel method for chance constrained robust beamforming problem in cognitive radio (CR) networks. Considering the channel estimation errors in practice, the proposed method aims to minimize the total secondary users' (SUs') transmit power under chance constraints corresponding to signal-to-interference-plus-noise ratio (SINR) and interference temperature (IT). Combining use of semidefinite relaxation and two kinds of Bernstein-type inequalities, we transform the chance constraints into deterministic forms, and reformulate the problem as a semidefinite program (SDP), which can be solved efficiently using standard interior-point methods. Simulations results verify performance improvements of the proposed method as compared to that based on the worst case method with judicious selection of the upper bounds of the channel state information (CSI) errors covariance.