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We propose transceiver algorithms in cognitive radio networks where the cognitive users are equipped with multiple antennas. Prior work has focused on the design of precoding matrices to suppress interference to the primary receivers. This work considers designs of precoding and decoding matrices for spatial sensing to achieve two objectives: (i) to prevent interference to the primary receivers and (ii) to remove the interference, due to primary transmissions, at the secondary receiver. With single antenna primary terminals and two antenna cognitive terminals, a linear transceiver design has been introduced under a global channel state information (CSI) assumption . In this letter, multiple antenna primary and cognitive terminals and three different CSI scenarios depending upon the amount of CSI are studied: (i) local CSI, (ii) global CSI, and (iii) local CSI with side information. When local CSI is available, we leverage prior work and employ the projected-channel singular value decomposition (P-SVD). In the global CSI scenario, we propose a joint transmitter-receiver design under the assumption of full CSI of all the users at the secondary transceiver. To reduce the feedback overhead, we also propose a new iterative algorithm that exploits only local CSI with side information. In this algorithm, the secondary transmitter and receiver iteratively update precoding and decoding matrices based on the local CSI and side information (precoding/decoding matrices at the previous iteration step) to maximize the rate of the secondary link while maintaining the zero-interference constraint. Convergence is established in the special case of single stream beamforming. Numerical results confirm that the proposed joint design and the iterative algorithm show better achievable rate performance than the P-SVD technique at the expense, respectively, of CSI knowledge and side information.