Opportunistic interference alignment for multiuser cognitive radio

We present an interference alignment (IA) technique 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. We exploit the fact that 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. 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. We characterize the number of achievable degrees of freedom (DoF) for the secondary users. We also present an iterative algorithm that utilizes channel reciprocity to achieve the proposed cognitive IA scheme. For a cognitive system with 3 secondary users, we derive a closed form solution for the precoding matrices of the secondary users.