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This letter considers the multi-antenna cognitive radio (CR) network, which has a single secondary user (SU) and coexists with a primary network of multiple users. Our objective is to maximize the service probability of the SU, subject to the interference constraints on the primary users (PUs) in the form of probability. Exploiting imperfect channel state information (CSI), with its error modeled by added Gaussian noise, we address the optimization for the beamforming weights at the secondary transmitter. In particular, this letter devises an iterative algorithm that can efficiently obtain the robust optimal beamforming solution. For the case with one PU, we show that a much simpler algorithm based on a closed-form solution for the antenna weights of a given power can be presented. Numerical results reveal that the optimal solution for the constructed problem provides an effective means to tradeoff the performance between the PUs and the SU, bridging the non-robust and worstcase based systems. © 2010 IEEE.
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