radar:doppler
Differences
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| radar:doppler [2018/06/01 23:34] – masrour | radar:doppler [2026/04/28 15:13] (current) – external edit 127.0.0.1 | ||
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| The characteristic feature of coherent MTI radar is that the transmitted signal must be coherent (in phase) with the reference signal in the receiver. This is accomplished by the coho signal. The function of the Stalo is to provide the necessary frequency translation from the IF to the transmitted RF frequency. Any Stalo phase shift is canceled on reception. | The characteristic feature of coherent MTI radar is that the transmitted signal must be coherent (in phase) with the reference signal in the receiver. This is accomplished by the coho signal. The function of the Stalo is to provide the necessary frequency translation from the IF to the transmitted RF frequency. Any Stalo phase shift is canceled on reception. | ||
| - | The reference signal from the coho and the IF echo signal | + | The reference signal from the coho and the IF echo signal |
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| **Delay Lines and cancelers** | **Delay Lines and cancelers** | ||
| - | The simple delay-line canceler is limited in its ability to do all that might be desired of an MTI filter. | + | The **simple delay-line canceler** is limited in its ability to do all that might be desired of an MTI filter. |
| The delay line must introduce a delay equal to the pulse-repetition interval. | The delay line must introduce a delay equal to the pulse-repetition interval. | ||
| One of the advantages of a time-domain delay-line canceler, as compared to the more conventional frequency-domain filter, is that a single network operates at all ranges and does not require a separate filter for each range resolution cell. Frequency-domain doppler filter- banks are of interest in some forms of MTI and pulse-doppler radar. | One of the advantages of a time-domain delay-line canceler, as compared to the more conventional frequency-domain filter, is that a single network operates at all ranges and does not require a separate filter for each range resolution cell. Frequency-domain doppler filter- banks are of interest in some forms of MTI and pulse-doppler radar. | ||
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| \end{equation} | \end{equation} | ||
| - | It is assumed that the gain through the delay-line canceler is unity. The output from the canceler ($Eq.16$) consists of a cosine wave at the Doppler frequency $f_d$ with an amplitude ($k.sin \pi{f_d}T$): | + | It is assumed that the gain through the delay-line canceler is unity. The output from the canceler ($Eq.16$) consists of a cosine wave at the Doppler frequency $f_d$ with an amplitude ($k.sin \pi{f_d}T$): |
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| \end{equation} | \end{equation} | ||
| - | where $n$ = $0, 1, 2, ..$, and $f_r$ = pulse repetition frequency. The delay-line canceler, not only eliminates the d-c component caused by clutter ($n = 0$), it also rejects any moving target whose doppler frequency happens to be the same as the prf or a multiple thereof. Those relative target velocities which result in zero MTI response are called blind speeds are given by | + | where $n$ = $0, 1, 2, ..$, and $f_r$ = pulse repetition frequency. The delay-line canceler, not only eliminates the DC component caused by clutter ($n = 0$), it also rejects any moving target whose doppler frequency happens to be the same as the PRF or a multiple thereof. Those relative target velocities which result in zero MTI response are called blind speeds are given by |
| \begin{equation} | \begin{equation} | ||
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| where $n = 1, | where $n = 1, | ||
| - | and $v_n$ is the nth blind speed. If $λ$ is measured in [m], $f_r$ in [Hz], and the relative velocity in knots, the blind speeds are | + | |
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| - | The frequency response of a single-delay-line canceler $Fig.29$ does not always have as broad a clutter-rejection null as might be desired in the vicinity of D-C which limits their rejection of clutter and clutter does not have a zero width spectrum, Adding more cancellers sharpens the nulls. | + | The frequency response of a single-delay-line canceler $Fig.27$ does not always have as broad a clutter-rejection null as might be desired in the vicinity of D-C which limits their rejection of clutter and clutter does not have a zero width spectrum, Adding more cancellers sharpens the nulls. |
| - | The two-delay-line configuration of the next $Fig$ has the same frequency-response characteristic as the double-delay-line canceler. The operation of the device is as follows. A signal $f(t)$ is inserted into the adder along with the signal from the preceding pulse period, with its amplitude weighted by the factor - 2, plus the signal from two pulse periods previous. The output of the adder is therefore | + | The two-delay-line configuration of $Fig.28b$ has the same frequency-response characteristic as the double-delay-line canceler. The operation of the device is as follows. A signal $f(t)$ is inserted into the adder along with the signal from the preceding pulse period, with its amplitude weighted by the factor - 2, plus the signal from two pulse periods previous. The output of the adder is therefore |
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| These have the same frequency response: which is the square of the single canceller response | These have the same frequency response: which is the square of the single canceller response | ||
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| **Transversal filter** | **Transversal filter** | ||
| - | These are basically a tapped delay line, It is also sometimes known as a feed forward-filter, | + | These are basically a tapped |
| - | The,frequency response function is proportional to $sin^2 π f_d T$, three delay lines whose weights are $1, -3, 3, -1$ gives a $sin^3 π f_d T$ response. This is a four-pulse canceler. | + | |
| + | The weights $w_i$ for a three-pulse canceler utilizing two delay lines arranged as a transversal filter are $ 1, -2, 1 $. | ||
| + | The frequency response function is proportional to $sin^2 π f_d T$, three delay lines whose weights are $ 1, -3, 3, -1 $ gives a $sin^3 π f_d T$ response. This is a four-pulse canceler. | ||
| * Note the potentially confusing nomenclature. A cascade configuration of three delay lines, each connected as a single canceler, is called a triple canceler but **when connected as a transversal filter it is called a four-pulse canceler**. | * Note the potentially confusing nomenclature. A cascade configuration of three delay lines, each connected as a single canceler, is called a triple canceler but **when connected as a transversal filter it is called a four-pulse canceler**. | ||
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| \end{equation} | \end{equation} | ||
| - | where $(S/ | + | where $(S/ |
| - | The ideal MTI filter should be shaped to reject the clutter at d-c and around the prf and its harmonics, but have a flat response over the region where no clutter is expected. That is, it would be desirable to have the freedom to shape the filter response, just as with any conventional filter. The ability to shape the frequency response depends to a large degree on the number of pulses used. The more pulses, the more flexibility in the filter design. | + | Which can be expressed as |
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| + | \begin{equation} | ||
| + | I _C = \frac{(S)_{out}}{(S)_{in}}\times CA=(CA)\times G_{N} | ||
| + | \end{equation} | ||
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| + | where $CA$ is the clutter attenuation and $G_N$ is called Noise Gain. | ||
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| + | The ideal MTI filter should be shaped to reject the clutter at D-C and around the PRF and its harmonics, but have a flat response over the region where no clutter is expected. That is, it would be desirable to have the freedom to shape the filter response, just as with any conventional filter. The ability to shape the frequency response depends to a large degree on the number of pulses used. The more pulses, the more flexibility in the filter design. | ||
| Unfortunately, | Unfortunately, | ||
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| - | The figure | + | $Fig.31$ |
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| Non-recursive filters employ only feedforward loops. | Non-recursive filters employ only feedforward loops. | ||
| - | Feedforward (finite impulse response or FIR) filters have only poles (one per delay). | + | Feedforward (finite impulse response or **FIR**) filters have only poles (one per delay). |
| More flexibility in filter design can be obtained if we use recursive or feedback filters ( also known as infinite impulse response or IIR filters ) | More flexibility in filter design can be obtained if we use recursive or feedback filters ( also known as infinite impulse response or IIR filters ) | ||
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| + | **Multiple and staggered PRFs** | ||
| An alternative is to use multiple PRFs because the blind speeds (and hence the shape of the filter response) depends on the PRF and, combining two or more PRFs offers an opportunity to shape the overall response. | An alternative is to use multiple PRFs because the blind speeds (and hence the shape of the filter response) depends on the PRF and, combining two or more PRFs offers an opportunity to shape the overall response. | ||
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| The closer the ratio $T_1$: $T_2$ approaches unity, the greater will be the value of the first blind speed. However, the first null in the vicinity of $f_d$ = $1 /T_1$ becomes deeper. Thus the choice of $T_1/T_2$ is a compromise between the value of the first blind speed and the depth of the nulls within the filter passband. The depth of the nulls can be reduced and the first blind speed increased by operating with more than two interpulse periods. | The closer the ratio $T_1$: $T_2$ approaches unity, the greater will be the value of the first blind speed. However, the first null in the vicinity of $f_d$ = $1 /T_1$ becomes deeper. Thus the choice of $T_1/T_2$ is a compromise between the value of the first blind speed and the depth of the nulls within the filter passband. The depth of the nulls can be reduced and the first blind speed increased by operating with more than two interpulse periods. | ||
| - | $Fig.36$ shows the response of a five-pulse stagger (four periods) that might be used with a long-range air traffic control radar.' | + | $Fig.34$ shows the response of a five-pulse stagger (four periods) that might be used with a long-range air traffic control radar. In this example, the periods are in the ratio $ 25: 30: 27: 31$ and the first blind speed is $28.25$ times that of a constant PRF waveform with the same average period. |
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| - | **Digital Signal Processing** | + | **Digital |
| The convenience of digital means that multiple delay-line cancellers with tailored frequency-response characteristics can be readily achieved. And Most of the advantages of a digital MTI processor are due to its use of digital delay lines. | The convenience of digital means that multiple delay-line cancellers with tailored frequency-response characteristics can be readily achieved. And Most of the advantages of a digital MTI processor are due to its use of digital delay lines. | ||
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| - | * Note: The quadrature channel removes blind phases and the requirements for the A/D are not very difficult to meet with today’s technology. | + | * Note: The **quadrature channel** removes blind phases and the requirements for the A/D are not very difficult to meet with today’s technology. |
| - | 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__ |
| Assuming an antenna rotation period of $12$ s ($5$rpm) the storage required would be only $12$ Mbytes/ | Assuming an antenna rotation period of $12$ s ($5$rpm) the storage required would be only $12$ Mbytes/ | ||
| - | Quantization Noise : | + | __Quantization Noise__ |
| The A/D introduces noise because it quantizes the signal. | The A/D introduces noise because it quantizes the signal. | ||
| - | The **Improvement Factor** can be limited by the quantization noise the limit being: | + | The **Improvement Factor** |
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| In practice one or more extra bits to achieve the desired performance. | In practice one or more extra bits to achieve the desired performance. | ||
| - | Dynamic Range: | + | __Dynamic Range__: |
| - | This is the maximum signal to noise ratio that can be handled by the A/D without saturation | + | the maximum signal to noise ratio that can be handled by the A/D without saturation |
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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 $10$ bit A/D gives a dynamic range of $45.2$ dB. | + | * Note: A $10$-bit A/D gives a dynamic range of $45.2$ dB. |
| - | **Blind speed in an MTI radar** | + | **Blind speed in a MTI radar** |
| 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 | + | By using both **I**n-phase and **Q**uadrature |
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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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| - | 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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| ===== Moving Target Detector ===== | ===== Moving Target Detector ===== | ||
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| - | 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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| - | **Limitation | + | **Limitation |
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| - | | + | * **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** ($SCV$): |
| 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 ($V_{OC}$)** : |
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| 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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| - | 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 " | + | 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 " |
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| - | 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{ | + | 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{ | + | S_a = G_0 exp [-{\frac{ |
| \end{equation} | \end{equation} | ||
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| \begin{equation} | \begin{equation} | ||
| - | S_a = K exp [\frac{ | + | S_a = K exp [-{\frac{ |
| \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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| 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 |
| Unfortunately, | Unfortunately, | ||
| - | 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 | + | 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 |
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| + | **Termination of Moving Target Detection** | ||
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| + | The **M**oving **T**arget **D**etector, | ||
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| + | 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, | ||
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| + | 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. | ||
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| + | 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. | ||
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| + | 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** | + | * |
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