arXiv:2610.09172v1 Announce Type: new Abstract: The problem of fast Doppler counter-aliasing for short-dwell weather-radar measurements is addressed. The proposed approach realizes a log-periodic slow-time design by changing only the waiting time between otherwise unchanged frequency-modulated continuous-wave (FMCW) chirps. The fast-time waveform, bandwidth, and range-processing chain are preserved while the acquisition changes the Doppler ambiguity structure. We formulate a novel moment-space ambiguity function for distributed weather spectra. It measures statistical ambiguity jointly in mean Doppler velocity and spectral width and expresses the competing sidelobes through their expected relative likelihood. A complex Gaussian process (CGP) maximum-likelihood estimator reconstructs the spectrum from the measured aperiodic samples. A deterministic basin-selection and optimization strategy accelerates the same CGP likelihood without defining a different statistical estimator. Real precipitation measurements establish central-branch stability over an extended search domain. Using 64 slow-time sweeps, we compare three acquisitions and their associated estimators. Periodic data are processed by the discrete Fourier transform (DFT) and parametric spectral estimation (PSE), log-periodic data by the nonuniform discrete Fourier transform (NUDFT) and CGP, and staggered data by velocity-difference and CGP estimators. The differences become more pronounced when the dwell is reduced to 32 sweeps. The results show that aperiodic time sampling enables extended-domain branch identification without degrading spectral-width estimation.