Parallel Doppler methods may be visualized as a set of coherent stacking
operations carried out at offset Doppler frequencies (Raney, 1998b). Three
new steps are required: (1) sorting the data into Doppler bins, (2) delay
compensation, and (3) parallel Doppler summation. Consider these in turn.
(1) Doppler bins. The sounder is operated coherently as in coherent
stacking, and a sequence of undetected return waveforms is stored in memory.
This is a two-dimensional data array: delay, and pulse number. When a complete
group of returns has been collected, the data are transferred to a processor
for operations while the next group accumulates. In the processor, an along-track
fast Fourier transform (FFT) at each delay increment integrates over the
sequence of pulses. The data are thus transformed into another two-dimensional
data array: delay, and Doppler frequency. It is convenient to use a power
of two for group size. For this example, there are 32 pulse returns in the
input group, and the data are sorted into 32 output Doppler bins.
(2) Delay compensation. Within each group, Doppler frequency corresponds
to a scatterer's position along-track relative to nadir, where nadir maps
into the zero-Doppler bin. At all non-zero Doppler bins, there is an extra
delay due to its off-nadir location. The loci of these extra delays are
hyperbolae, evident in the incoherent average
example. The extra delay at each Doppler is known from the sounder's
geometry. Therefore, this extra delay can be removed, for which there are
several means to do so (Raney, 1998a). After delay compensation, the waveform
depths within all Doppler bins are in agreement.
(3) Parallel Doppler summation. The delay-compensated output waveform
in each Doppler bin is square-law detected. Recall that each Doppler bin
for each group corresponds to a particular along-track position. Thus, the
trick in parallel Doppler summation is to correctly select the corresponding
waveforms across groups. Each completed output waveform is the summation
across Ndop Doppler bins, where 1 < Ndop <= 32 for this data set.
The example of this figure is for Ndop = 3, or summation over the zero-Doppler
bin and its two adjacent neighbors. In this case, the SNR and the SSR are
approximately 3 times larger than that observed in the coherent
stacking example.