Interference Reduction by Beamforming in Cognitive Networks

We consider beamforming in a cognitive network with multiple primary users and secondary users sharing the same spectrum. In particular, we assume that each secondary transmitter has Nt antennas and transmits data to its single- antenna receiver using beamforming. The beamformer is designed to maximize the cognitive user´s signal-to-interference ratio (SIR), defined as the ratio of the received signal power at the desired cognitive receiver to the total interference created at all the primary receivers. Using mathematical tools from random matrix theory, we derive both lower and upper bounds on the average interference at the primary receivers and the average SIR 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_t increases. Specifically, the average interference per primary receiver converges to the expected value of the path loss in the network whereas the average SIR of the secondary user decays as 1/c when c = N_p/N_t rarr infin. In the special case of N_t = N_p, the average total interference approaches 0 and the average SIR approaches infin.