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.