On the integrated cross-noise term in correlation detectors

An integrated cross-noise component frequently arises in communications and in signal processing. One typical example is the autocorrelation receiver. Integrated cross-noise generally appears when a noisy signal is recovered (detected) using correlation techniques with a noisy signal as the reference. The statistics of the integrated cross-noise component are analyzed in general for both the cases of uncorrelated and correlated noise terms in the integrand. The exact 2^nd order statistics of the integrated cross-noise are derived, and new improved expressions are derived for an approximate probability density function. Accurate computer simulations are performed to evaluate the actual probability density function of the integrated cross-noise component and these results are compared with the approximations. The convergence of the approximation to a Gaussian distribution is also discussed.