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An interference alignment (IA) scheme is presented that allows multiple opportunistic transmitters (secondary users) to use the same frequency band of a pre-existing primary link without generating any interference. The primary and secondary transmit-receive pairs are equipped with multiple antennas. Under power constraints on the primary transmitter, the rate of the primary user is maximized by water-filling on the singular values of its channel matrix leaving some eigen modes unused, and hence, the secondary users can align their transmitted signals to produce a number of interference-free dimensions at each secondary receiver without causing any interference to the primary user. An outer bound is developed on the degrees of freedom (DoF) of the secondary users. In the case of a symmetric secondary network with time-varying channel coefficients having M antennas at each node and operating in the presence of a primary link with d0 active eigen modes, a precoding scheme is presented for the secondary transmitters that can asymptotically achieve the available (M-d0)+/2 DoF per secondary user. An iterative algorithm is also presented that utilizes channel reciprocity to achieve the proposed cognitive IA scheme. For a cognitive 3-user secondary network with constant channel coefficients, a novel closed-form solution is derived for the precoding matrices of the secondary users.