On analytical expressions for the distribution of the filtered output of square envelope receivers with signal and colored Gaussian noise input

Closed-form expressions for the moment generating function (MGF) of the filtered output of square envelope receivers with signal and colored Gaussian noise input are derived. The informative signal is a binary sequence of rectangular pulses. The considered Gaussian processes are the Wiener process, a Gaussian process with linear covariance (moving average), and the Ornstein-Uhlenbeck process. The derived MGFs are then applied to the problem of finding the quantum limit for optically preamplified, direct detection receivers.