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In this paper, we propose jointly-optimized beamforming algorithms for cognitive networks to maximize the achievable rates, where primary and cognitive users share the same spectrum and are equipped with multiple antennas. We consider the transmission of a single information stream in both primary and secondary links. No coordination is required between the primary and cognitive users and the interference cancellation is done at the cognitive user. Specifically, the beamforming vectors of the cognitive link are designed to maximize the achievable rate under the condition that the interference both at the primary and cognitive receivers is completely nullified. Furthermore, it is proved that the achievable rate of a general NtC × 2 (NtC transmit antennas at the cognitive transmitter and 2 receive antennas at the cognitive receiver) cognitive multiple-input multiple-output (MIMO) link employing the optimal proposed beamformers (which completely nullifies the interference to and from the primary link while maximizing its own achievable rate) is the same as the rate of an interference-free (NtC-1)×1 multiple-input single-output (MISO) link employing an optimal maximal ratio transmission beamforming vector. The sum rate performance of the proposed algorithms is evaluated by Monte Carlo simulations. The impact of the number of transmit and receive antennas on the proposed algorithm is also discussed.