On ergodic sum capacity of underlay cognitive broadcast channels

We study the fundamental capacity limits of the underlay cognitive broadcast (BC) channel under average transmit power and average interference power constraints. In a fading environment, the sum capacity is found from a constrained water-filling solution given in [7]. This solution is investigated for different average transmit power budgets and average interference thresholds, and its specific regions are characterized. Further, capacity expressions are derived for the Rayleigh fading case. In a system with K users and Rayleigh fading channels, it is shown that the capacity scales like log(log(K)) for large K. This result indicates that the same multiuser diversity gain can be achieved in a cognitive BC system as in the conventional BC system without spectrum sharing.