Principles of Modern Radar - Volume 2 1891121537

466 CHAPTER 10 Clutter Suppression Using Space-Time Adaptive ProcessingFIGURE 10-4Pulse-to-pulsephase change over32-pulse temporalaperture for severalDoppler filters.0−5Pulse-to-Pulse Phase Change for Varying Doppler Frequency−10Phase (Radians)−15−20−25Filter 1Filter 2Filter 3Filter 4Filter 5Filter 6−305 10 15 20 25 30Pulse Numberramp and estimated slope, embodied in the FFT, leads to filter mismatch and consequentperformance loss. Using our prior notation, it is common to replace s t ( ˜f d ) and s s ( f sp )by the hypothesized responses v t ( ˜f d ) and v s ( f sp ). The processor will test the spatial andDoppler frequencies of interest for potential targets by stepping across various steeringvectors v t ( ˜f d ) and v s ( f sp ). When employing uniform sampling (i.e., constant PRI or aULA), the FFT efficiently accomplishes this task. A zero-padded FFT reduces straddleloss by decreasing the frequency bin spacing.Figure 10-4 shows the pulse-to-pulse phase change over the temporal aperture for a32-pulse CPI and several different normalized Doppler frequencies. The slope of each lineis proportional to Doppler frequency, as (10.30) indicates. The response of each Dopplerfilter given by w t is reminiscent of the antenna beampatterns given in Figure 10-3. Thedwell time, NT, determines the Doppler resolution (or Doppler beamwidth); the Dopplerresolution is fd = 1Dwell = 1NT = PRFN(10.33)where the pulse repetition frequency (PRF) is the inverse of the PRI, PRF = 1/T .10.2.3 Space-Time SignalsThe preceding discussion of spatial and temporal sampling and signal structure is integralto a description of space-time signals. In this section we describe space-time signals andtheir characteristics in terms of power spectrum, covariance matrix, and eigenspectrum.Suppose the array of sensors receives a signal with a particular Doppler frequency anddirection of arrival. This signal could, for instance, result from a scattered transmissionfrom a moving target. The space-time signal vector corresponding to the return from a