Operating Characteristics of Crosscorrelator with or without Sample Mean Removal

摘要

The characteristics function of the output of a crosscorrelator, with the sample means removed from each channel, is derived in closed form. More generally, if scaled versions of the sample means are subtracted prior to multiplication of the channel inputs and summation, a closed form for the characteristic function of the correlator output is derived. These results are used to plot the exact operating characteristics of the crosscorrelator, as functions of the threshold, the general scaling factors applied to the sample means, the number of terms, N, summed to yield the output, the actual means at the inputs, and the signal-to-noise ratios of the random signal components at each of the system inputs. Programs for the various cases considered are documented and exercised. Comparisons are made with a Gaussian approximation, which can be used to extend the results to larger values of N than considered here, if needed. Asymptotic results for the exceedance distribution functions have also been derived, but they are not too useful for large N. (Author)