The errors produced by a least square type singl-Doppler velocity retrieval scheme based on variational analaysis are studied. It is found that the retrieved azimuthal wind is always underestimated, due to the discrete nature of the radar observations. The underestimation occurs when the time period between two radar scans (dt), is greater than dx/u, where dx is the radar's spatial resolution and u is the speed of the observed weather system. This condition is often true for today's Doppler radar operational modes, which implies that the wind speed underestimation becomes inevitable. Using an optimized moving frame to conduct the retrieval can reduce this kind of error. The experiments also reveal that the condition under which the moving frame can be found is somewhat relaxed, and can be fulfilled by the current operational Doppler radar. The results predicted by the theoretical analyses are confirmed by a real case study.