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MTI, limitations to performance                                                MTI, PRF-diversity  282




                                    ln 2  f r
                                       ×
                              s  =  ------------ ---
                               fa    p  n
           is the scanning modulation spectral spread of clutter, and n is
           the number of hits per scan. Equation (1) shows the maximum
           attainable improvement factor against clutter with a Gaussian
           spectrum centered at zero frequency.
               Staggering of the PRF results in a limit to improvement
           factor due to unequal time spacing between the clutter sam-
           ples:
                                        2                         Figure M31 Phasor diagram of noncoherent MTI detector.
                                   æ 2.5n ö
                              I  =  -----------
                               ms  è g 1–  ø                        .
                                                                    The improvement factors for single-  and  double-delay
           where g is the ratio of maximum to minimum PRF.
                                                                noncoherent MTI using a square-law detector are
               The sources of equipment instability are given in Table
                                                                                         2
                                                                                                2
           M6, with the corresponding limits to improvement factor in           I m1  =  ------------------------------- » ---- 2
                                                                                             2
           decibels. To  find the attainable  improvement factor  in the             1 –  exp – (  z ) z
                                Table M6                                                21 ()             1
                                                                      I m2  =  ------------------------------------------------------------------------------------------------ » ----
                                                                                                       2
                                                                                        2
                        Instability Limitations in MTI                     1 –  ( 4 3 ¤ ) exp – (  2z ) 1 3 ¤(  ) exp – (  4z ) z 4
                                                                                          +
                                                                    In the conventional noncoherent MTI system, targets in
                                                                range cells containing no clutter are lost for want of a phase
                                                                reference. Various clutter gating procedures are used to
                                                                enable a normal  video  channel in such cells, bypassing the
                                                                canceler to avoid loss of targets. A alternative noncoherent
                                                                MTI detector uses the hard-limited output of adjacent cells as
                                                                the reference to a phase detector, such that moving targets are
                                                                detected in the absence of clutter through the random phase of
                                                                noise in the reference cells (Fig. M32).









           (from Skolnik, 1990, Table 15.4, p. 15.42, reprinted by permission of McGraw-Hill)
           presence of N different limiting factors, the improvement fac-
           tors are converted to power ratios and combined according to  Figure M32 Phase-detection circuit for noncoherent MTI (from
                                                                 Skolnik, 1970,  Fig.  59, p.  17.54, reprinted by permission of
                                    N
                                                                 McGraw-Hill).
                               – 1     1
                               I m  =  å  -------
                                       I                            Advantages  of  noncoherent MTI are simplicity and  its
                                       mi
                                    i =  1                      inherently adaptation to moving clutter. Disadvantages are
           where the individual factors include those shown in Table M6  reduced improvement factor  and  inability of most types  to
           plus I ma  and I  from inherent clutter spread, antenna scan-  operate in the absence of clutter. DKB
                       ms
           ning, and PRF stagger. SAL
                                                                Ref.: Skolnik (1980), p. 138.
           Ref.: Skolnik (1980), p. 129, (1990), p. 15.41.
                                                                The  optimum MTI uses an Urkowitz  (inverse) filter
           Noncoherent MTI uses clutter echoes from the target region  response to whiten the output interference spectrum. DKB
           as the phase (velocity) reference for detection before the can-
                                                                Ref.: Barton (1988), p. 236.
           celer or filter. One common form of noncoherent MTI uses an
                                                                PRF-diversity MTI  produces an effect  similar  to stagger-
           envelope detector at the receiver output, the output amplitude
                                                                PRF MTI, except that sequential bursts of pulses at each PRF
           of which varies at the target doppler shift as the signal phasor
                                                                are transmitted, received, and batch-processed. Addition of p
           rotates around end of the clutter phasor (Fig. M31). This
                                                                fill pulses to each batch supports cancellation of clutter from
           amplitude change component passes the canceler.
                                                                ambiguous range intervals,  R  <  R  <  (p  + 1)R , where
                                                                                                          u
                                                                                         u
                                                                                              c
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