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 N_t 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 N_t or primary users N_p increases. Specifically, we show that the average interference per primary receiver converges to E[d^-alpha], the expected value of the path loss in the network, whereas the average CSIR decays as 1/c when c = N_p/N_t rarrinfin. In the special case of N_t / N_p, the lower bound of the average total interference approaches 0 and the upper bound of the average CSIR approaches N_tE[d-^alpha]/alpha²c where alpha²c is the noise variance at the cognitive receiver.