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We analyze the asymptotic performance of a generalized multiuser diversityscheme for an interference-limited secondary multiuser network of underlaycognitive radio systems. Assuming a large number of secondary users and thatthe noise at each secondary user's receiver is negligible compared to theinterference from the primary transmitter, the secondary transmitter transmitsinformation to the $k$-th best secondary user, namely, the one with the $k$-thhighest signal-to-interference ratio (SIR). We use extreme value theory to showthat the $k$-th highest SIR converges uniformly in distribution to an inversegamma random variable for a fixed $k$ and large number of secondary users. Weuse this result to derive asymptotic expressions for the average throughput,effective throughput, average bit error rate and outage probability of the$k$-th best secondary user under continuous power adaptation at the secondarytransmitter, which ensures satisfaction of the instantaneous interferenceconstraint at the primary receiver caused by the secondary transmitter.Numerical simulations show that our derived asymptotic expressions are accuratefor different values of system parameters.

Asymptotic Performance Analysis of Generalized User Selection for Interference-Limited Multiuser Secondary Networks