Page 255 - Fundamentals of Radar Signal Processing
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Suppose the radar can be expected to receive significant clutter returns at ranges

               up  to P · t , and consider the clutter component of the slow-time signal for a
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               given range bin in the pulse-by-pulse processing viewpoint. When the range bin
               of  interest  is  sampled  at  delay t   < T after the first pulse is transmitted, only
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               clutter  echoes  from  the  corresponding  range ct /2  will  be  sampled  at  the
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               receiver. When the range bin is sampled again after the second pulse, the clutter
               component will include echoes from the second pulse and range ct /2 as well as
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               from  the  first  pulse  and  range c/2(t   + T).  These  two  contributions  represent
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               echo from two physically different patches of clutter scatterers. The first slow-
               time  sample,  which  includes  echoes  from  only  the  nearer  patch,  may  differ
               significantly  in  power  and  statistical  behavior  from  the  second  slow-time
               sample,  which  includes  echoes  from  both.  The Pth and subsequent slow-time
               samples will contain contributions from all P contributing range intervals and
               therefore  exhibit  the  consistent  clutter  power  levels  and  statistical  behavior

               needed  for  effective  clutter  filtering  and  target  detection.  Extending  the
               transmitted waveform to M + P – 1 pulses as above therefore allows collection
               of M steady-state clutter measurements. In Chap. 5 these additional pulses will
               be  called  “clutter  fill”  pulses.  The  first P  –  1  slow-time  samples  will  be
               discarded in each range bin and only the remaining M samples will be used in
               clutter filtering, coherent integration, and detection processing.



               4.5.4   Doppler Response of the Pulse Burst Waveform
               To consider the effect of a Doppler mismatch on the pulse burst waveform and
               its matched filter, consider a target moving toward the radar at velocity v meters
               per second so that its range is R  – vt meters at time t. Assume that the “stop-
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               and-hop” approximation is valid and that the target motion does not exceed one
               range bin over the CPI, that is, MvT < cτ/2; this ensures that all echoes from a
               given  target  appear  in  the  same  range  bin  over  the  course  of  a  CPI.  The

               demodulated echoes will have a phase shift of –(4π/λ)R(t) = –(4π/λ)(R   – vt).
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               Adopting  the  pulse-by-pulse  processing  viewpoint  and  absorbing  the  phase
               exp(–j4πR /λ) due to the nominal range R  into the overall gain, the individual
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               matched filtered outputs for each pulse become







                                                                                                       (4.67)

               The corresponding slow-time sequence is








                                                                                                       (4.68)
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