# If the clutter spectrum is too wide due to too short

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If the clutter spectrum is too wide due to too short an observation interval, theimprovement factor will be affected. This limitation is called scanning fluctuation or scanningmodulation.To find the limitation on Ic we first find the clutter attenuation CA
195Here WS(f) describes the spectrum produced by the finite time ontarget and H(f) is the MTI processor frequency response.If the antenna main beam is approximated bya Gaussian shape, the spectrum will also beGaussian. Hence the results previously derived for a Gaussian clutter spectrum can be applied.Thus equations I1cand I2capply for the antenna scanning fluctuations with the correctinterpretation of σc(the RMS spread of the spectrum about the mean).Here the voltage waveform for the clutter is modulated bythe antenna power pattern (equal to thetwo way field strength pattern), as it is rotatedNow,Where θ and θBare in degreesThereforeWhere Sa(t) is the modulation of the received signal due to theantenna patternand is the scan rate in ˚/s.The spectrum is found by taking the Fourier transformSince this is a Gaussian function we must have
196Hence,Note:This is for the voltage spectrumFor the power spectrum we have,Hence the σs due to the antenna scanning isSubstituting this for σc, we get,Note:the stepped scan antenna also is limited in MTI performance by the finite time on target.The time waveform is rectangular which gives a different improvement factor.
197Limiting in MTI Radar:A limiter is used just before the MTI processor to prevent the residue from large clutterechoes from saturating the display. Ideally an MTI radar should reduce clutter to a levelcomparable to noise. However, when I is not great enough, the clutter residue will appear on thedisplayand prevent the detection of aircraft whose radar cross section is larger than the clutterresidue. This condition can be prevented bysetting the limit L relative to the noise N equal to theMTI improvement factor I.If the limit le vel is set too high, clutter residue obscures part of the display. If the limit isset too lo w, there may be a black hole effect. The limiter provides a CFAR (Constant FalseAlarm Rate).A nonlinear limiter however causes the spectrum of strong clutter to spread intothe canceler pass band and results in the generation of additional residue which degrades theMTI performance.Figure 4.32 plots I for 2 pulse and 3 pulse cancelers with various levels of limiting. Theabscissa applies to Gaussian clutter spectrum generated by clutter motion (σv) or by antennascanning modulation (nB). Here C/L is the ratio of RMS clutter power to the IF limit level.Note:The loss of I increases with the complexity of the canceler. Limiting in a 3 pulse cancelerwill cause a 15 to 25 dB reduction in performance. A 4 pulse canceler with limiting is only 2 dBbetter than a 3 pulse canceler. Hence adding complexity is not justified in a limiting environmentLimiting is not needed if processor I is large enough to reduce the largest clutter to thenoise level (typically requires I ≈ 60 dB). This is difficult to achieve since it requires the receiverto have a linear dynamic range of at least 60 dB, the A/D must have at least 11 bits, theequipment must be stable, the processor must be designed for I = 60 dB and the number of pulsesprocessed must be sufficient to reduce the antenna scanning modulation.

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