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

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.