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radar:doppler [2018/06/03 20:13] – masrourradar:doppler [2026/04/28 15:13] (current) – external edit 127.0.0.1
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 <figure label> <figure label>
  {{ :media:figure_2.radar.png?500x500 }}  {{ :media:figure_2.radar.png?500x500 }}
-<caption> Doppler Effect [(cite:image1>> title: https://www.texasgateway.org ,section:Wave behaviour:the doppler effect ,publisher:Texas Education Agency 1701 ,published:2007+<caption> Doppler Effect [(cite:image1>>title: https://www.texasgateway.org ,section:Wave behaviour:the doppler effect ,publisher:Texas Education Agency 1701 ,published:2007
 )] </caption> )] </caption>
 </figure> </figure>
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 <figure label> <figure label>
 {{ :media:new_cw.png?400x400 }} {{ :media:new_cw.png?400x400 }}
-<caption> (upper . Fig) Simple CW radar block diagram ; (lower. Fig) response characteristic of beat-frequency amplifier [(cite:Image8>> title: http://nptel.ac.in/courses/101108056/module2/lecture4.pdf, section:Cw Radar:Doppler frequency shift,publisher:nptel  +<caption> (upper . Fig) Simple CW radar block diagram ; (lower. Fig) response characteristic of beat-frequency amplifier [(cite:Image8>> title: http://nptel.ac.in/courses/101108056/module2/lecture4.pdf ,section:Cw-Radar,Doppler frequency shift,publisher:nptel)] </caption>
-)] </caption>+
 </figure> </figure>
  
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 __Sampling Rate__ :  __Sampling Rate__ : 
-Assuming a resolution ($R_{res}$) of $150$m, the received signal has to be sampled at intervals of $c/2R_{res}$ = $1$μs or a sampling rate of $1$ MHz+Assuming a resolution ($R_{res}$) of $150$m, the received signal has to be sampled at intervals of $2R_{res}/c$ = $1$μs or a sampling rate of $1$ MHz
  
 __Memory Requirement__ : __Memory Requirement__ :
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   * $N$ = number of bits   * $N$ = number of bits
-  * $k$ = RMS noise level divided by the quantization interval (the larger k the lower the dynamic range but $k$<$1$ results in the reduction of sensitivity )+  * $k$ = RMS noise level divided by the quantization interval (the larger k the lower the dynamic range but $k<1$ results in the reduction of sensitivity )
  
  
  
-   * Note: A $9$ bit A/D gives a dynamic range of $52.9$ dB for 9-bit quantization.($Eq.26$)+   * Note: A $10$-bit A/D gives a dynamic range of $45.2$ dB.
  
  
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 If the PRF is double the Doppler frequency then every other pair of samples can be the same amplitude thus it will be filtered out of the signal. If the PRF is double the Doppler frequency then every other pair of samples can be the same amplitude thus it will be filtered out of the signal.
-By using both in-phase and quadrature signals, blind phases can be eliminated.+By using both **I**n-phase and **Q**uadrature signals, blind phases can be eliminated.
  
  
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 **Digital filter banks and the FFT** **Digital filter banks and the FFT**
  
-A transversal filter with N outputs (N pulses and N - 1 delay lines) can be made to form a bank of N contiguous filters covering the frequency range from $0$ to $f_p$. +A transversal filter with N outputs (N pulses and N-1 delay lines) can be made to form a bank of N contiguous filters covering the frequency range from $0$ to $f_p$. 
-Consider the transversal filter that was shown in $Fig.32$ to have N - 1 delay lines each with a delay time $T$ = $1/f_p $ . Let the weights applied to the outputs of the N taps be:+Consider the transversal filter that was shown in $Fig.30$ to have N - 1 delay lines each with a delay time $T$ = $1/f_p $ . Let the weights applied to the outputs of the N taps be:
  
  
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 <figure label> <figure label>
 {{ :media:dsp_respo.png?400 }} {{ :media:dsp_respo.png?400 }}
-<caption>MTI doppler filter bank resulting from the processing of N = $8$ pulses [(#13)]</caption>+<caption>MTI doppler filter bank resulting from the processing of N = $8$ pulses [(cite:Image9)]</caption>
  </figure>  </figure>
  
-For comparison, the improvement factor for an N-pulse canceller is shown in the next $Fig$. +For comparison, the improvement factor for an N-pulse canceller is shown in $Fig.40$. 
   * Note that the improvement factor of a two-pulse canceler is almost as good as that of the $8$-pulse doppler-filter bank. The three-pulse canceler is even better. ( Maximizing the average improvement factor might not be the only criterion used in judging the effectiveness of MTI doppler processors.)   * Note that the improvement factor of a two-pulse canceler is almost as good as that of the $8$-pulse doppler-filter bank. The three-pulse canceler is even better. ( Maximizing the average improvement factor might not be the only criterion used in judging the effectiveness of MTI doppler processors.)
  
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 <figure label> <figure label>
 {{ :media:filter_b.png?400 }} {{ :media:filter_b.png?400 }}
-<caption>Improvement factor for each filter of an $8$-pulse doppler filter bank with uniform weighting as a function of the clutter spectral width (standard deviation). The average improvement for all filters is indicated by the dotted curve.[(#13)]</caption>+<caption>Improvement factor for each filter of an $8$-pulse doppler filter bank with uniform weighting as a function of the clutter spectral width (standard deviation). The average improvement for all filters is indicated by the dotted curve.[(cite:Image9)]</caption>
  </figure>  </figure>
  
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 <figure label> <figure label>
 {{ :media:npulse_filtro.png?400 }} {{ :media:npulse_filtro.png?400 }}
-<caption> Improvement factor for an N-pulse delay-line canceler with optimum weights (solid curves) and binomial weights (dashed curves), as a function of the clutter spectral width.[(#13)]</caption>+<caption> Improvement factor for an N-pulse delay-line canceler with optimum weights (solid curves) and binomial weights (dashed curves), as a function of the clutter spectral width.[(cite:Image9)]</caption>
  </figure>  </figure>
  
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 <figure label> <figure label>
 {{ :media:double_clutter.png?300x300 }} {{ :media:double_clutter.png?300x300 }}
-<caption> Improvement factor for a $3$-pulse (double-canceler) MTI cascaded with an 8-pulse doppler filter hank. or integrator.[(#13)]</caption>+<caption> Improvement factor for a $3$-pulse (double-canceler) MTI cascaded with an 8-pulse doppler filter hank or integrator.[(cite:Image9)]</caption>
  </figure>  </figure>
 +
  
  
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 ===== Moving Target Detector ===== ===== Moving Target Detector =====
 +
 +
  
  
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 <figure label> <figure label>
 {{ :media:mtd.png?500 }} {{ :media:mtd.png?500 }}
-<caption> Simple block diagram of the Moving Target Detector (MTD) signal processor.[(#13)]</caption>+<caption> Simple block diagram of the Moving Target Detector (MTD) signal processor.[(cite:Image9)]</caption>
  </figure>  </figure>
  
  
-The input on the left is from the output of the $I$ and $Q$ A/D converters. The use of a three-pulse canceler ahead of the fi1ter: bank eliminates stationary clutter and thereby reduces the dynamic range required of the doppler filter-bank.+The input on the left is from the output of the $I$ and $Q$ A/D converters. The use of a three-pulse canceler ahead of the filter: bank eliminates stationary clutter and thereby reduces the dynamic range required of the doppler filter-bank.
  
  
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 <figure label> <figure label>
 {{ :media:prf_radio.png?300 }} {{ :media:prf_radio.png?300 }}
-<caption> Detection of aircraft in rain using two prf's with a doppler filter bank.[(#13)]</caption>+<caption> Detection of aircraft in rain using two prf's with a doppler filter bank.[(cite:Image9)]</caption>
  </figure>  </figure>
  
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-**Limitation of MTI Performance**+**Limitation to MTI Performance**
  
  
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-  * **MTI Improvement Factor** ($I_C$) : + * **MTI Improvement Factor** ($I_C$) : 
  
 The signal-to-clutter ratio at the output of the MTI system divided by the signal-to-clutter ratio at the input averaged uniformly over all target radial velocities of interest. (discussed earlier) The signal-to-clutter ratio at the output of the MTI system divided by the signal-to-clutter ratio at the input averaged uniformly over all target radial velocities of interest. (discussed earlier)
  
-  * **Subclutter Visibility** ($SCV$):+ * **Subclutter Visibility** ($SCV$):
  
 The ratio by which a signal may be weaker than the coincident clutter and can be detected with the specified $P_d$ and $P_{fa}$. All radial velocities assumed equally likely. The ratio by which a signal may be weaker than the coincident clutter and can be detected with the specified $P_d$ and $P_{fa}$. All radial velocities assumed equally likely.
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 $SCV = (C/S)_{in}$ $SCV = (C/S)_{in}$
  
-  * **Clutter Visibility Factor ($V_{OC}$)** :+ * **Clutter Visibility Factor ($V_{OC}$)** :
      
 The Signal to Clutter ratio after filtering that provides the specified $P_d$ and $P_{fa}$. The Signal to Clutter ratio after filtering that provides the specified $P_d$ and $P_{fa}$.
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 <figure label> <figure label>
  {{ :media:lim_mti.png?200 }}  {{ :media:lim_mti.png?200 }}
-<caption> Power spectra of various clutter targets.[(#13)]</caption>+<caption> Power spectra of various clutter targets.[(cite:Image9)]</caption>
  </figure>  </figure>
  
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-A plot of $Eq.32$ for the double canceler is shown in $Fig.39$ The parameter describing the curves is ${f_p}λ $. Example PRF's and frequencies are shown. Several "representative" examples of clutter are indicated, based on published data for $σ_v$, which for the most part dates back to World War II +A plot of $Eq.39$ for the double canceler is shown in $Fig.45$ The parameter describing the curves is ${f_p}λ $. Example PRF's and frequencies are shown. Several "representative" examples of clutter are indicated, based on published data for $σ_v$, which for the most part dates back to World War II 
  
  
 <figure label> <figure label>
 {{ :media:omega.png?430 }} {{ :media:omega.png?430 }}
-<caption>Plot of double-canceler clutter improvement factor [(#13)]</caption>+<caption>Plot of double-canceler clutter improvement factor [(cite:Image9)]</caption>
  </figure>  </figure>
  
  
-Its a Plot of double-canceler clutter improvement factor [Eq.$32$] as a function of $σ_c$ = rms velocity spread of the clutter. The parameter is the product of the pulse repetition frequency ($f_p$) and the radar wavelength ($λ$).+Its a Plot of double-canceler clutter improvement factor [Eq.$39$] as a function of $σ_c$ = rms velocity spread of the clutter. The parameter is the product of the pulse repetition frequency ($f_p$) and the radar wavelength ($λ$).
  
  
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 \begin{equation} \begin{equation}
-G(θ) = G_0  exp [\frac{ - 2.776{θ}^2 }{ {θ_B}^2} ]   +G(θ) = G_0  exp [-{\frac{ 2.7726{θ}^2 }{ {θ_B}^2}} ]   
 \end{equation} \end{equation}
  
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 \begin{equation} \begin{equation}
-S_a = G_0  exp [\frac{ - 2.776({θ/ \dot{\theta }_s})^2 }{ (\frac{θ_B}{\dot{\theta }_s})^2} ]   +S_a = G_0  exp [-{\frac{  2.7726({θ/ \dot{\theta }_s})^2 }{ (\frac{θ_B}{\dot{\theta }_s})^2}} ]   
 \end{equation} \end{equation}
  
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 \begin{equation} \begin{equation}
-S_a = K  exp [\frac{ - 2.776 {t^2} }{ {t_0}^2} ] = K_1 exp [ \frac{{-π^2}{f^2}{t_0}^2}{ 2.776 }]  +S_a = K  exp [-{\frac{  2.7726 {t^2} }{ {t_0}^2} }] = K_1 exp [-{ \frac{{π^2}{f^2}{t_0}^2}{ 2.7726 }}]  
 \end{equation} \end{equation}
  
  
-where $K$ = constant. Since this is a Gaussian function, the exponent is of the form $ f^2 /2{σ_f}^2 $; where $σ_f$ = standard deviation. Therefore+where $K$ = $4ln2= 2.7726$. Since this is a Gaussian function, the exponent is of the form $ f^2 /2{σ_f}^2 $; where $σ_f$ = standard deviation. Therefore
  
  
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 <figure label> <figure label>
 {{ :media:gaussian_shape.png?430 }} {{ :media:gaussian_shape.png?430 }}
-<caption> Limitation to improvement factor due to a scanning antenna. Antenna pattern assumed to be of gaussian shape.[(#13)]</caption>+<caption> Limitation to improvement factor due to a scanning antenna. Antenna pattern assumed to be of gaussian shape.[(cite:Image9)]</caption>
  </figure>  </figure>
  
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 <figure label> <figure label>
 {{:media:a11.png?311 }}{{ :media:b11.png?340}} {{:media:a11.png?311 }}{{ :media:b11.png?340}}
-<caption> Effect of limit level on the improvement factor for ($a$) two-pulse delay-line canceler and ($b$) three-pulse delay-line canceler. C/L = ratio of rms clutter power to limit level.[(#13)]</caption>+<caption> Effect of limit level on the improvement factor for ($a$) two-pulse delay-line canceler and ($b$) three-pulse delay-line canceler. $C/L$ = ratio of RMS clutter power to limit level.[(cite:Image9)]</caption>
  </figure>  </figure>
 +
  
  
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 When the MTI improvement factor is not great enough to reduce the clutter sufficiently..the clutter residue will appear on the display and prevent the detection of aircraft targets whose cross sections are larger than the clutter residue.  When the MTI improvement factor is not great enough to reduce the clutter sufficiently..the clutter residue will appear on the display and prevent the detection of aircraft targets whose cross sections are larger than the clutter residue. 
-Whereby setting the limit level $ L$, relative to the noise $ N$, equal to the MTI improvement factor $I$ or $L/N = 1$. If the limit level relative to noise is set higher than the improvement factor. clutter residue obscures part of the display and If it is set too low there may be a " black hole " effect on the display. The limiter provides a constant false alarm rate **(CFAR)** and is essential to usable MTI performance.+Whereby setting the limit level $L$, relative to the noise $N$, equal to the MTI improvement factor $I$ or $L/N = 1$. If the limit level relative to noise is set higher than the improvement factor. clutter residue obscures part of the display and If it is set too low there may be a " black hole " effect on the display. The limiter provides a **C**onstant **F**alse **A**larm **R**ate (**CFAR**)[(A **false alarm** is “an erroneous radar target detection decision caused by noise or other interfering signals exceeding the detection threshold”. In general, it is an indication of the presence of a radar target when there is no valid aim. The False Alarm Rate (FAR) is calculated using the following formula: $FAR=\frac{false targets per PRT}{Number of rangecells}$)] and is essential to usable MTI performance.
 Unfortunately, nonlinear devices such as limiters have side-effects that can degrade performance. Unfortunately, nonlinear devices such as limiters have side-effects that can degrade performance.
  
  
-An example of the effect of limiting is shown in the Figure, which plots the improvement factor for two-pulse and three-pulse cancelers within various levels of limiting. The abscissa applies to a Gaussian clutter spectrum that is generated either by clutter motion with standard deviation $ σ_v$, at a wavelength $λ$ and a prf $f_p $, or by antenna scanning modulation with a Gaussian-shaped beam and $n_B$ pulses between the half-power beamwidth of the one-way antenna pattern. The parameter $C/L$ is the ratio of the RMS clutter power to the receiver-IF limit level.+An example of the effect of limiting is shown in the $Fig.47$, which plots the improvement factor for two-pulse and three-pulse cancelers within various levels of limiting. The abscissa applies to a Gaussian clutter spectrum that is generated either by clutter motion with standard deviation $ σ_v$, at a wavelength $λ$ and a prf $f_p $, or by antenna scanning modulation with a Gaussian-shaped beam and $n_B$ pulses between the half-power beamwidth of the one-way antenna pattern. The parameter $C/L$ is the ratio of the RMS clutter power to the receiver-IF limit level.
  
  
 The loss of improvement factor increases with increasing complexity of the canceler. The loss of improvement factor increases with increasing complexity of the canceler.
-Thus the added complexity of higher-order cancelers is seldom justified in such situations. The linear analysis of MTI signal processors is therefore not adequate when limiting & employed and can lead to disappointing differences between theory and measurement of actual systems.+Thus the added complexity of higher-order cancelers is not often justified in such situations. The linear analysis of MTI signal processors is therefore not enough when limiting & employed and can lead to disappointing differences between theory and measurement of actual systems.
  
  
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 +**Termination of Moving Target Detection**
 +
 +
 +
 +The **M**oving **T**arget **D**etector, as we discussed earlier ,is able to optimize mobile targets in the presence of white addictive and clutter or improves target resolution.
 +
 +The output of the receiver is a signal, which contains the required target plus various forms of noise and clutter. In the case of the MTI output, this clutter residue is the result of imperfect cancellation due to various factors such as equipment instability, antenna modulation, lack of dynamic range or Doppler content within the clutter itself. The detection process separates the required target from the noise and clutter. Detectors are normally designed to carry out this process with a constant false alarm rate (CFAR).
 +
 +The diagram shows the location of the detector in the chain of signal processing. This device forms the information on a point like target as a digital report. The up to this point existing information about the analog value (or digital description of) of the received power in a particular binary cell will be transformed to information about the coordinates of a target. The value of the power is included in this report mostly.
 +
 +The important procedure is, that up to this point all binary cells (containing the received power) must be processed. After the detector exist only reports about selected binary cells. However, there may exist several reports about a single target, generated by adjacent binary cells. This will processed in the next device.
 +
 +
 +
 +<figure label>
 +{{ :media:termination_of_mti_mtd.png?500 }}
 +<caption> Part of block diagram(information flow)[(cite:Image3)]</caption>
 + </figure>
 +
 +
 +
 +Until now its simply discused about MTI performance limitiation ,MTD device operation and using different filters or transformation.deeper discussion on the Doppler frequency and adaptive thresholds on the different filters ,etc. __is presented in__ 
  
-More information is presented in **Modern Radar System Analysis** by **David K.Barton** chapter $6$.+    *  **Modern Radar System Analysis**, Author: David K.Barton ,chapter $6$ .  
 +    *  **Advanced radar techniques and systems**, Author: Gaspare Galati ,chapter $12$ . 
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