The joint estimation of signal and noise from the sum envelope

The separate estimation of carrier strength and of narrowband additive noise strength from envelope samples is considered. The mathematical problem is one of the joint estimation of the two parameters in the Rice probability-density function. The estimation is useful, for example, in the radar analysis of targets containing both specular and distributed components. In the mathematical analysis, theoretical Cramér-Rao lower bounds on the standard deviation in unbiased estimation are first determined. Estimation procedures based upon the method of maximum likelihood and two simple methods of moments are then developed. An error analysis for each procedure is performed by Monte Carlo simulation. For the purpose of comparison, two direct averaging methods are also analyzed. Results are extended to the case where an additional noise is also present, but with known strength. It is also shown that the time average of a slowly-varying carrier strength can be estimated despite the presence of noise.