Higher Order Statistics in Switched Diversity Systems

TL;DR

This paper investigates the higher order statistics, specifically level crossing rate and average fade duration, of output SNR in switched diversity systems, covering both colocated and distributed configurations with threshold-based strategies.

Contribution

It introduces a unified approach to analyze higher order statistics for various diversity configurations and develops an asymptotic framework for high SNR environments.

Findings

Derived general formulas for LCR and average fade duration.

Applicable to any fading distribution at the diversity branches.

Provided asymptotic expressions for high mean SNR scenarios.

Abstract

We analyze the level crossing rate (LCR) and the average fade duration of the output signal-to-noise-ratio (SNR) in generalized switched diversity systems. By using a common approach, we study these higher order statistics for two different kinds of configurations: (1) Colocated diversity, i.e. receiver equipped with multiple antennas, and (2) Distributed diversity, i.e. relaying link with multiple single-antenna threshold-based decode-and-forward (DF) relays. In both cases, we consider the switched diversity combining strategies Selection Combining and Switch \& Stay Combining (SSC). Whenever using threshold-based techniques such as DF or SSC, the output SNR is a discontinuous random process and hence classic Rice approach to calculate the LCR is not applicable. Thus, we use an alternative formulation in terms of the one and two-dimensional cumulative distribution functions of the output SNR. Our results are general, and hold for any arbitrary distribution of fading at the different diversity branches. Moreover, we develop a general asymptotic framework to calculate these higher order statistics in high mean SNR environments which only needs of the univariate probability density function.