A comparison of two methods of estimating the intensity of a noisy complex process

Two methods of estimating the squared modulus or intensity of a noisy complex observation process are considered. Both use a serial combination of a linear optimal filter and a memoryless nonlinear operator; the difference between the two methods is in the order of application of the two devices. Mean-squared-error expressions are obtained for arbitrary signal and noise spectra and are evaluated numerically for the case of a first-order autoregressive signal process in white noise. A simulation study is undertaken for the same case, the results of which indicate that preceding the nonlinear device with the optimal filter yields lower mean-squared error, but the difference between the two schemes is not significant in most cases of interest