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Asymptotic Scheduling Gains in Point-to-Multipoint Cognitive Networks

We consider collocated primary and secondary networks that have simultaneous access to the same frequency bands. Particularly, we examine three different levels at which primary and secondary networks may coexist: pure interference, asymmetric co-existence, and symmetric co-existence. At the asymmetric co-existence level, the secondary network selectively deactivates its users based on knowledge of the interference and channel gains, whereas at the symmetric level, the primary network also schedules its users in the same way. Our aim is to derive optimal sum-rates (i.e., throughputs)of both networks at each co-existence level as the number of users grows asymptotically and evaluate how the sum-rates scale with network size. In order to find the asymptotic throughput results, we derive a key lemma on extreme order statistics and a proposition on the sum of lower order statistics. As a baseline comparison, we calculate the sum-rates for channel sharing via time-division (TD). We compare the asymptotic secondary sum-rate in TD with that under simultaneous transmission, while ensuring the primary network maintains the same throughput in both cases. The results indicate that simultaneous transmission at both asymmetric and symmetric co-existence levels can outperform TD. Furthermore, this enhancement is achievable when uplink activation or deactivation of users is based only on the interference gains to the opposite network and not on a network's own channel gains.