Asymptotic Analysis of Multi-Antenna Cognitive Radio Systems Using Extreme Value Theory

TL;DR

This paper analyzes the asymptotic behavior of multi-antenna cognitive radio systems using extreme value theory, deriving capacity expressions that scale with the number of antennas under interference and power constraints.

Contribution

It provides a novel asymptotic analysis of spectrum-sharing cognitive radio systems with antenna selection, using extreme value theory to derive capacity scaling laws.

Findings

Capacity scales as log(N) under interference constraints

Capacity scales as log(log(N)) under power constraints

Asymptotic results closely match exact capacities for large N

Abstract

We consider a spectrum-sharing cognitive radio system with antenna selection applied at the secondary transmitter (ST). Based on the extreme value theory, we deduce a simple and accurate expression for the asymptotic distribution of the signal to interference plus noise ratio at the secondary receiver. Using this result, the asymptotic mean capacity and the outage capacity for the secondary user (SU) are derived. The obtained asymptotic capacities approach the exact results as the number of transmit antennas $N$ increases. Results indicate that the rate of the SU scales as $\log(N)$ when the transmit power of the ST is limited by the maximum allowable interference level, while rate scales as $\log(\log(N))$ if ST is limited by the maximum transmit power.