Logarithmic detection with postdetection filtering

An analysis is presented of the performance of a logarithmic detector followed by a low-pass filter, under the assumption of a large ratio of IF bandwidth to postdetection bandwidth. This allows for the probability of detection and similar quantities to be computed in a straightforward manner. The mean and variance of the filter output are found by first deriving the autocorrelation function of the logarithmic detector output and then obtaining the power spectral density. A useful engineering approximation is made for the variance which is valid for all signal-to-noise ratios.