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In this study, the authors consider the problem of distributed relay beamforming in an underlay-based cognitive relay network in which a secondary network transmits its data using multiple relays under an amplify-and-forward protocol simultaneously with a primary network over the same spectrum. For such a network, assuming that the partial channel state information (CSI) is available, the authors study two different beamforming approaches to improve performance of the secondary transmissions while ensuring the quality-of-service of the primary transmissions. In the first approach, the authors obtain the beamforming weights as well as the transmit power of the secondary source such that the signal-to-interference plus noise ratio (SINR) at the secondary destination is maximised whereas the interference power from the secondary to the primary network is kept below a predefined threshold. In the second approach, the beamforming weights are obtained through minimising the received interference power at the primary receiver subject to a constraint on SINR at the secondary destination. The authors prove that both proposed approaches result in closed-form solutions. Simulation results show that as the uncertainty in CSI decreases, the proposed schemes achieve better performances. In addition, increasing the number of relays improves the overall system performance.