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This letter studies the rate maximization problem for a cognitive (secondary) radio link communicating over the same frequency band as of a primary radio link, where both the primary and the secondary radios are equipped with multiple antennas. In contrast to the conventional interference power constraint approach to protect the primary receiver, we consider a new design paradigm for rate maximization of the secondary user (SU) under a direct constraint on the minimum primary user (PU) transmission rate subject to the SU interference. This problem is shown to be non-convex due to the newly introduced PU rate constraint. However, by approximating this rate constraint by the method of Taylor series expansion, this letter proposes an iterative algorithm to maximize the SU rate while satisfying the PU's minimum data rate requirement. The proposed scheme with the PU rate constraint is shown to outperform the conventional scheme with the interference power constraint in terms of SU's achievable rates for different target PU rates.