On the Asymptotic Throughput of the k-th Best Secondary User Selection in Cognitive Radio Systems
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We analyze the asymptotic average and effective throughputs of a multiuser diversity scheme for a secondary multiuser network consisting of multiple secondary users (transmitters) and one secondary receiver. Considering a transmit power adaptation strategy at the secondary users to satisfy the instantaneous interference constraint at the primary receiver, the secondary receiver selects the k-th best secondary user for transmission, namely, the one with the k-th highest signal-to-noise ratio (SNR). We use extreme value theory to show that the k-th highest SNR converges uniformly in distribution to an inverse gamma random variable for a fixed k and large number of secondary users. We use this result to derive closed-form asymptotic expressions for the average and effective throughputs of the k-th best secondary user.
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