Counter-aliasing is better than De-aliasing: Application to Doppler Weather Radar with Aperiodic Pulse Train

The challenge of avoiding aliasing in the Doppler spectrum for precipitation is addressed. A novel integrative signal processing approach has been proposed to address the research gaps from various disciplines. The proposed approach consists of several steps. First, an aperiodic way of sampling the echoes (aperiodic sampling refers to aperiodic pulse train in the context of radar echoes in slow time) has been proposed by which the maximum unambiguous Doppler frequency (velocity) is enhanced. Second, the Doppler spectrum moment estimation is performed with the help of a parametric form of its covariance. The performance of the moment estimation is assessed by the bias and the variance in the estimated counterparts. The theoretical variance for the parameter estimation is also derived. An aperiodic pulse train design recommendation has been proposed for adequately and unambiguously estimating the Doppler moments for one extended target (like precipitation). Finally, a spectrum reconstruction technique is implemented after the moment estimation on simulated radar echo samples for a realistic precipitation-like event. The comparison with the other approaches proves its superiority for parameter estimation and Doppler spectrum reconstruction.