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

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-tonoise 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.

On the Secrecy Performance of Generalized User Selection for Interference-Limited Multiuser Wireless Networks

“…3, we plot the SOP of the k-th best user as a function of the number of receive antennas, L, for k = 1, 2, R s = 1/2 bit/s/Hz and for different values of N . We verify the accuracy of the asymptotic SOP expressions derived in (12) and (19) by comparing them with the exact SOP result. As expected, we observe that for N = 20, the SOP increases as L increases.…”

“…where b N = C M (N − 1) and U (a; d; z) is the Tricomi hypergeometric function [18]. Proof: As shown in Proposition 2 of [19], if the random variable Z i has a CDF F (z) as in (2), then for a fixed k and N → ∞,…”

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

“…Noting that b is an increasing function of N , we have ln(1 + bP z) ≈ ln(bP z) in (21) for large N . Using this and variable transformation of u = (bP z) −1 , E R (N −k+1) |P can be further approximated as…”

“…This is different from [19], where the k-th highest SNR converges to a Log-Gamma random variable. 3 A portion of this work was accepted for publication in 2018 IEEE Vehicular Technology Conference (VTC) [21]. In [21], we only studied the asymptotic average and effective throughputs of the k-th best secondary user selection in uplink multiuser cognitive radio systems under unlimited transmit power.…”

“…3 A portion of this work was accepted for publication in 2018 IEEE Vehicular Technology Conference (VTC) [21]. In [21], we only studied the asymptotic average and effective throughputs of the k-th best secondary user selection in uplink multiuser cognitive radio systems under unlimited transmit power. The VTC paper is available online at https://arxiv.org/pdf/1804.05257v2.pdf.…”