# Differential Diversity Reception of MDPSK over Independent Rayleigh Channels with Nonidentical Branch Statistics and Asymmetric Fading Spectrum

## TL;DR

This paper analyzes the performance of differential DPSK with diversity reception over independent Rayleigh fading channels with nonidentical and asymmetric spectral characteristics, providing explicit closed-form BEP expressions.

## Contribution

It derives exact closed-form BEP expressions for differential DPSK over diverse Rayleigh channels with asymmetric fading spectra, considering nonidentical branch statistics.

## Key findings

- BEP expressions explicitly depend on system parameters.
- Performance varies with Doppler spectrum and branch asymmetry.
- Analysis applies to 8-DPSK as a specific example.

## Abstract

This paper is concerned with optimum diversity receiver structure and its performance analysis of differential phase shift keying (DPSK) with differential detection over nonselective, independent, nonidentically distributed, Rayleigh fading channels. The fading process in each branch is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth, but to have distinct, asymmetric fading power spectral density characteristic. Using 8-DPSK as an example, the average bit error probability (BEP) of the optimum diversity receiver is obtained by calculating the BEP for each of the three individual bits. The BEP results derived are given in exact, explicit, closed-form expressions which show clearly the behavior of the performance as a function of various system parameters.