Optimum filtering of a noisy phase-shift keyed signal

Abstract

The recovery of a signal from noise is one of the basic problems in communication, telemetry and command. Receivers attempting to detect a particular signal are beset by a myriad of unwanted signals called noise. This noise may come from atmospheric or solar disturbances, from some other transmitter or from intentional radiation (jamming). Recovery of the desired signal from such noise is difficult. Some type of band pass filter is generally used to either eliminate the noise or to pass the signal; however, in cases for which the signal and noise occupy the same frequency band, the simple filters are ineffective. One practical method to remove a signal from noise is the use of the optimum filter proposed by Wiener and Lee. The optimum network function (h[subscript opt](t)) found by this method must conform to the requirements of a realizable network and at the same time minimize the mean squared error between the desired output and the actual output. Wiener's method can only be used when the Rep Fourier transform (S[subscript xx](ω)) of the input autocorrelation (R[subscript xx](τ)) is a factorable function of frequency (ω). ...