Phase codes for separation of range overlaid echoes

The systematic phase code SZ(8/64) has been implemented on the lowest two elevations scans for Doppler measurements in some volume coverage pattern of the WSR-88D network. This code tags the transmitted phases of 64 consecutive pulses so that upon reception, decoding, and processing, it is possible to separate overlaid echoes. This and similar proposed codes have sequence lengths equal to a power of two, which was chosen for efficient computation of Fourier transforms; the FFTs are used for separation of multiple trip signals in the frequency domain. The fixed number of pulses constrains the antenna rotation rate if a specific spacing of spectral moments in azimuth (radials) is desired. Although, overlapping and windowing the incoming pulse train can produce radials of spectral moments at 1 degree spacing (increments) there are additional reasons to explore modulation codes other than those that operate on sequence lengths equal to powers of two. For example, the combined effects of a data window and the desired azimuthal sampling, while keeping errors in check, might necessitate anywhere from 40 to 80 weather signal samples to maintain acceptable upper bound on the error of estimates. The purpose herein is to present other codes of the same family but which are matched to sequence lengths that are not powers of two. These codes have the following common properties: 1) The power spectrum of a coded sinusoid is periodic and so is its autocorrelation function, 2) any two complex spectral coefficients of the coded sinusoid are sufficient to determine the correct frequency of the sinusoid. In choosing separation between the spectral coefficients of the code a trade off is made between rejection of the strong trip echo and self-contamination (interference) of the reconstructed weaker trip echo.