Optimal Signal Detectability using Discrete Fourier Transform Processing

Extracting reflectivity profiles from meteorological radar data is typically accomplished using either non-coherent power estimation or spectral-based moment estimation. Spectral processing typically combines coherent FFT-based algorithms with post-averaging of the individual power spectra to generate the power spectrum. A simple expression for the optimal FFT length to maximize signal processing gain is presented that depends only on the normalized spectral width and the time-domain weighting function. The relative signal processing gain between non-coherent power averaging and spectral processing is found to depend on a variety of parameters, including the radar wavelength, normalized spectral width, available observation time and the false alarm rate. Expressions presented for the probability of detection for non-coherent and spectral-based processing also depend on these same parameters. Results of this analysis show that FFT-based processing can provide a substantial advantage in signal processing gain and probability of detection, especially when a large number of samples is available to form the power spectrum. However, non-coherent power estimation sometimes provides superior probability of detection, especially when the spectral width is large compared to the unambiguous Doppler interval.