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The authors propose a distributed robust joint signal and interference alignment design for multiple-input-multiple-output cognitive radio (CR) networks where single primary link coexists with multiple secondary links. Considering two practical challenges of interference alignment: imperfect channel state information (CSI) and finite signal-to-noise ratio, the proposed scheme aims to minimise both the leakage of interference signals and that of the desired signals, while maintaining interference to the primary user below a permissible level. Under the assumption of the ellipsoidal CSI uncertainties, the joint worst-case optimisation problem is decomposed and reformulated as semi-definite programming form by using S-lemma, orthogonal relaxation and semi-definite relaxation. Simulation results verify the effectiveness of the joint design, and robustness of the worst-case design against channel uncertainties.