Opportunistic cognitive radio broadcast channel: Asymptotic performance

We consider a cognitive channel where one secondary transmitter opportunistically broadcasts to n secondary nodes subject to peak interference power constraints on the primary receivers. We find asymptotic bounds for the secondary throughput, which imply that the throughput scales as Θ (log log n) for any finite interference constraint, no matter how small. Furthermore, a fundamental tradeoff between the secondary throughput and the interference on the primary is obtained, showing that the interference on the primary can be forced asymptotically to zero while maintaining a nontrivial secondary throughput. Specifically, for an arbitrary exponent 0 <; q <; 1, the interference on the primary can be made as small as (log n)^-q, while the secondary throughput scales as (1-q) log log n+O(1). Finally, if the number of primary receivers increases as Θ(n^β), the secondary system attains only a constant throughput asymptotically, for any β >; 0.