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The paper presents design of a linear precoder for orthogonal space-time block coded orthogonal frequency division multiplexing (OFDM)-based multiple-input multiple-output (MIMO) antenna cognitive radio (CR) when operating in correlated Rayleigh fading channels. Unlike previous studies on precoder design for CR, this proposed linear precoder is capable of handling both transmit and receive correlation in a multi-carrier based CR system. The linear precoder is designed to minimize an upper bound on the average pairwise error probability, constrained to a set of per subcarrier transmit power constraints at the CR transmitter and a set of interference power thresholds at primary user receivers. The CR transmitter exploits the knowledge of transmit and receive correlation matrices while designing the precoder. It is shown that the linear precoder design problem is convex with these constraints, and convex optimization techniques are exploited to derive an efficient algorithm to obtain the optimal precoder matrices. Computer simulations are performed to investigate the performance of the proposed linear precoder in a CR system.