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We study simultaneous channel sharing of collocated primary and secondary networks at three different levels of coexistence: pure interference, asymmetric, and symmetric. At the pure interference level, both networks operate simultaneously in the same frequency band regardless of their interference to each other. At the asymmetric level, only the secondary network performs user scheduling based on various degrees of interference and channel gain knowledge while at the symmetric level both networks do so. Using a lemma on the asymptotic behavior of the largest order statistic and a proposition on the asymptotic sum of lower order statistics, we derive asymptotic primary and secondary sum-rates under simultaneous channel sharing at each coexistence level. As a baseline comparison, time-division (TD) channel sharing is considered. While maintaining the same asymptotic primary sum-rate, the asymptotic secondary sum-rate under TD is compared with that achievable by simultaneous channel sharing. The results indicate that simultaneous channel sharing at both asymmetric and symmetric co-existence levels can outperform TD. Furthermore, this enhancement is achievable asymptotically when user scheduling in uplink mode is based only on the interference gains to the opposite network and not on a network's own channel gains.

Asymptotic Scheduling Gains in Point-to-Multipoint Cognitive Networks