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In practice, the imperfect channel state information can degrade the optimization performance of a cognitive system, especially yielding the detrimental violation of the interference constraint perceived by the primary users. This paper investigates the linear transceiver design in cognitive downlink systems with the imperfect channel knowledge, aiming at minimizing the mean square error of the secondary network subject to both the transmit and interference power constraints. Two methods are proposed to solve the optimization problem. The first alternating method decomposes the non-convex primal problem into two subproblems. Each of them is converted to the standard convex optimization forms. The second method is based on the reformulation of the primal problem into a two-loop optimization problem in which a more efficient gradient projected method applies. We also prove the condition to achieve Karush-Kuhn-Tucker optimality. The effectiveness and robustness of the proposed solutions are validated by the simulation result.