High SNR BER Comparison of Coherent and Differentially Coherent Modulation Schemes in Lognormal Fading Channels

TL;DR

This paper compares the high SNR bit-error rate performance of coherent and differential modulation schemes in lognormal fading channels, revealing their asymptotic equivalence and quantifying the performance gap.

Contribution

It proves the asymptotic equivalence of binary differential and coherent phase-shift keying in lognormal channels and quantifies the SNR penalty for differential quaternary phase-shift keying.

Findings

Binary differential and coherent BPSK have the same asymptotic BER performance.

Differential QPSK is 2.32 dB worse than QPSK at high SNR.

The analysis uses an auxiliary random variable technique.

Abstract

Using an auxiliary random variable technique, we prove that binary differential phase-shift keying and binary phase-shift keying have the same asymptotic bit-error rate performance in lognormal fading channels. We also show that differential quaternary phase-shift keying is exactly 2.32 dB worse than quaternary phase-shift keying over the lognormal fading channels in high signal-to-noise ratio regimes.