Error Analysis of Pulse-Pair Estimates

Detection of hazardous atmospheric zones with a high level of turbulence is a crucial problem for weather Doppler radars. In modern weather radars it is solved via estimation of the spectrum moments of weather echoes. The most known and widely used method of spectral moment estimation is the pulse-pair processing (PPP). Only asymptotic equations for the mean and variance of the PPP estimates, obtained via the perturbation method, are known. A more rigorous statistical analysis of the PPP estimates is presented here. Explicit expressions for the mean values and the variances of spectral moment estimates are derived and compared with results of a mathematical simulation. The comparison proves good match of the analytical calculations and performed simulations in situations where the previous results fail to predict accurately the performance of the PPP estimators.