Moments of Estimated Input Power for Finite Sample Averages of Radar Receiver Outputs

Closed-form solutions for all the estimated power moments as a function of the number of independent samples were found for the linear and logarithmic receiver. Incoming signal envelope distribution is assumed to be Rayleigh. The estimates' expected value and standard deviations are plotted and compared with those of a square-law receiver. It is shown that the bias in the expected value for both receivers depends on the number of samples. Only when the number of samples is large does the bias become constant, and the standard deviation around the unbiased mean becomes inversely proportional to the square root of the number of samples. The logarithmic receiver produces the largest standard deviation. When the input samples are dependent, an expansion of the method is suggested to obtain approximate moments.