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This paper studies the optimal beamforming design for a cognitive relay network in which a secondary network transmits its data using a multi-antenna relay simultaneously with the primary users over the same spectrum. An optimal beamforming approach is proposed to maximize the received signal-to-noise ratio (SNR) of the secondary users, whereas the received interference power at the primary user is kept below a predefined threshold. The maximization of the SNR at the secondary users is derived as an objective function to fumulate a constrained beamforming optimization problem, and the optimization problem can be transformed into a Rayleigh-Ritz ratio problem which is then solved by the generalized singularvalue decomposition in a closed form. In response to the practical problem that perfect instantaneous channel state information (CSI) is difficult to be available, we assume that partial CSI is available in the proposed method. Simulation results show that the performance can be further improved by either decreasing the uncertainty in channel coefficients or increasing the number of relay antennas.

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