Comments on "Probabilities of Error for Adaptive Reception of M-Phase Signals"

TL;DR

This paper corrects typos in the derivation of error probability formulas for M-PSK systems, providing accurate expressions for the probability density function of correlated Gaussian variables.

Contribution

It identifies and corrects errors in previous derivations of error probabilities for M-PSK systems involving correlated Gaussian variables.

Findings

Corrected the PDF derivation for correlated Gaussian RVs

Provided detailed derivation leading to accurate error probability expressions

Clarified the mathematical foundation for M-PSK error analysis

Abstract

Paper [1] derived the probability density function (PDF) of a sum of products of two correlated complex Gaussian zero-mean random variables (RVs) that has been applied to calculate the error probabilities of a \emph{M}-ary phase shift keying (\emph{M}-PSK) system. We show that there exist some typos in the computation and we provide the detailed derivation leading to the correct expressions.