The sum capacity of underlay cognitive broadcast channel

We study the sum capacity of the underlay cognitive broadcast (BC) channel with M primary receivers (PRs) and K secondary receivers (SRs). In particular, the sum capacity is investigated under an average transmit power constraint (TPC) on the SRs and multiple average or peak interference power constraints (IPCs) on the PRs. In a fading environment, the average sum capacity is obtained from the solution of a convex optimization problem. The ergodic sum capacity C is then derived from the limiting case where the number of fading state tends to infinity. Further, the asymptotic capacity is investigated in the homogeneous Rayleigh fading system for which two different asymptotic regimes are analyzed.