The Probability Density Function for Correlators With Correlated Noisy Reference Inputs

A general expression for the probability density function of the output of a correlator has been obtained and plotted using a low-pass multiplier analogy. Each of the two input channels of the correlator has a specular signal in the presence of bandlimited Gaussian noise. In the general case considered here, the noise components in the two input channels are permitted to have in-phase correlation. However, the variances of each noise component and the signal-to-noise ratio in each channel are assumed to be the same. Using the general expression, the probability density function of the output for uncorrelated noise inputs with or without the signal has also been obtained and compared with previously published results.