Interference and noise reduction by beamforming in cognitive networks
We consider beamforming in a cognitive network with multiple primary users and a secondary user sharing the same spectrum. Each primary and secondary user consists of a transmitter and a receiver. In particular, we assume that the secondary transmitter has Nt antennas and transmits data to its single-antenna receiver using beamforming. The beamformer is designed to maximize the cognitive signal-to-interference ratio (CSIR). Using mathematical tools from random matrix theory, we derive both lower and upper bounds on the average interference created by the cognitive transmitter at the primary receivers and the average CSIR of the cognitive user. We further analyze and prove the convergence of these two performance measures asymptotically as the number of antennas Nt or primary users Np increases. Specifically, we show that the average interference per primary receiver converges to E[d-α], the expected value of the path loss in the network, whereas the average CSIR decays as 1/c when c = Np/Nt → ∞. In the special case of Nt ≥ Np, the lower bound of the average total interference approaches 0 and the upper bound of the average CSIR approaches NtE[d-α] /σC2c where σC2c is the noise variance at the cognitive receiver. © 2009 IEEE.
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