Page 256 - Fundamentals of Radar Signal Processing
P. 256

Integrating the slow-time samples gives












                                                                                                       (4.69)


               Equation (4.69) gives the system response to the pulse burst waveform in an

               arbitrary range bin l as a function of the normalized Doppler mismatch ω .
                                                                                                     D
                     This is the familiar asinc function. Figure 4.17 shows the central portion of
               the magnitude of this function. The zeros occur at intervals of 1/M cycles per
               sample in normalized frequency; thus, the Rayleigh resolution in Doppler is 1/M
               cycles  per  sample  or  1/MT  Hz. MT  is  the  duration  of  the  entire  pulse  burst

               waveform. The Doppler resolution is therefore determined by the duration of the
               entire waveform instead of the duration of a single pulse. In this manner, the
               pulse  burst  waveform  achieves  much  better  Doppler  resolution  than  a  single
               pulse of the same duration while maintaining the same range resolution. The cost
               is the time and energy required to transmit and receive M pulses instead of one
               and the computational load of integrating M samples in each range bin.

































               FIGURE 4.17   Central portion of the Doppler mismatch response of the slow-
               time signal using a pulse burst waveform.



                     Integrating the slow-time samples of the pulse burst echo corresponds to
               implementing a matched filter in slow time for a signal with zero Doppler shift;
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