On the Asymptotic Throughput of the k-th Best Secondary User Selection in Cognitive Radio Systems

TL;DR

This paper investigates the asymptotic throughput of the k-th best secondary user in cognitive radio systems, using extreme value theory to derive closed-form expressions for large user populations.

Contribution

It introduces a novel analysis of the k-th best user selection in cognitive radio, applying extreme value theory to derive asymptotic throughput expressions.

Findings

The k-th highest SNR converges to an inverse gamma distribution for large user numbers.

Closed-form asymptotic throughput expressions are derived for the k-th best user.

The analysis provides insights into multiuser diversity in cognitive radio networks.

Abstract

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.