radar:doppler
Differences
This shows you the differences between two versions of the page.
| radar:doppler [2018/05/29 19:53] – masrour | radar:doppler [2026/04/28 15:13] (current) – external edit 127.0.0.1 | ||
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| - | As a transmitter | + | As a __transmitter__ |
| - | **Coherent Radar Processing** | + | **In Coherent Radar Processing** |
| - | One of the transmitting-system is the __**PAT**__ (**P**ower-**A**mplifier-**T**ransmitter). In this case, the high-power amplifier is driven by a highly stable continuous RF source, called the Waveform generator [(A waveform generator generates the transmitting signal on an IF- frequency. It permits generating predefined waveforms by driving the amplitudes and phase shifts of carried microwave signals. These signals may have a complex structure for a pulse compression. Since these signals are used as a reference for the receiver channels too, there are high requirements for the frequency stability.)] Modulating the output stage in response to the PRF [(The Pulse Repetition Frequency (PRF) of the radar system is the number of pulses that are transmitted per second | + | One of the transmitting-system is the __**PAT**__ (**P**ower-**A**mplifier-**T**ransmitter). In this case, the high-power amplifier is driven by a highly stable continuous RF source, called the Waveform generator [(A** waveform generator** generates the transmitting signal on an IF- frequency. It permits generating predefined waveforms by driving the amplitudes and phase shifts of carried microwave signals. These signals may have a complex structure for a pulse compression. Since these signals are used as a reference for the receiver channels too, there are high requirements for the frequency stability.)] Modulating the output stage in response to the PRF [(The** Pulse Repetition Frequency** (PRF) of the radar system is the number of pulses that are transmitted per second |
| Assuming the RF is a multiple of the PRF (as is normally the case), each pulse starts with the same phase. Systems, which inherently maintain a high level of phase coherence from pulse to pulse, are termed **fully coherent**. | Assuming the RF is a multiple of the PRF (as is normally the case), each pulse starts with the same phase. Systems, which inherently maintain a high level of phase coherence from pulse to pulse, are termed **fully coherent**. | ||
| It is taken to the necessary power with an amplifier such as (Amplitron, Klystron or Solid-State-Amplifier). | It is taken to the necessary power with an amplifier such as (Amplitron, Klystron or Solid-State-Amplifier). | ||
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| - | **Non-coherent Radar Processing** | + | **In Non-coherent Radar Processing** |
| The phases of the transmitted signal are random from pulse to pulse. The phases of the echoes cannot be used to predict the range of the target. | The phases of the transmitted signal are random from pulse to pulse. The phases of the echoes cannot be used to predict the range of the target. | ||
| - | One of the transmitting systems is the __**POT**__ (**P**ower **O**scillator **T**ransmitter) which is self-oscillating. When such a device is switched ON and OFF as a result of modulation by the rectangular modulating pulse, the starting phase of each pulse is not the same for the different successive pulses. The starting phase is a random function related to the startup process of the oscillator. | + | Another kind of the transmitting systems is the __**POT**__ (**P**ower **O**scillator **T**ransmitter) which is self-oscillating. When such a device is switched ON and OFF as a result of modulation by the rectangular modulating pulse, the starting phase of each pulse is not the same for the different successive pulses. The starting phase is a random function related to the startup process of the oscillator. |
| * Notice: Self-oscillating transmitter gives random phase pulse to pulse and is not coherent! | * Notice: Self-oscillating transmitter gives random phase pulse to pulse and is not coherent! | ||
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| The envelope detector produces an output signal whose level corresponds to the envelope of the **IF signal** (linear detector, square law detector, or logarithmic detector) | The envelope detector produces an output signal whose level corresponds to the envelope of the **IF signal** (linear detector, square law detector, or logarithmic detector) | ||
| - | All frequency and phase information is //lost//. | + | All frequency and phase information is lost. |
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| **Coherent** systems need //carrier phase information// | **Coherent** systems need //carrier phase information// | ||
| - | In other words, Coherency in signal processing is similar to correlation in statistics. In statistics, two random variables are correlated if there exists a linear relationship between the two. Perfectly coherent signals are signals such that one is the response of a linear system to the other applied signal. Hence there exists a linear system such that one signal is the input and the other signal is its output. Coherence is between 0 and 1. The higher the coherency is, the better one can explain the spectral content of the first signal by analyzing the spectral content of the other signal since a linear system is completely characterized by the system' | + | In other words, Coherency in signal processing is similar to correlation in statistics. In statistics, two random variables are correlated if there exists a linear relationship between the two. Perfectly coherent signals are signals such that one is the response of a linear system to the other applied signal. Hence there exists a linear system such that one signal is the input and the other signal is its output. Coherence is between |
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| **MOPA** ( **M**aster **O**scillator **P**ower **A**mplifier ) | **MOPA** ( **M**aster **O**scillator **P**ower **A**mplifier ) | ||
| - | Generation of adequate RF power is an important part of any radar system. The radar equations showed that the transmitter power varies as the fourth root of the range if all other factors are constant. To double the range, | + | Generation of adequate RF power is an important part of any radar system. The radar equations showed that the transmitter power varies as the fourth root of the range if all other factors are constant. To double the range, |
| - | There are two basic transmitter configurations used in radar. One is the self-excited oscillator, exemplified by the magnetron. The other utilizes a low - power, stable oscillator, which is in turn amplified to the required power level by one or more power amplifier tubes. An example is Klystron $Fig.7$ [( Klystron amplifiers are high power microwave vacuum tubes. Klystrons are velocity-modulated tubes that are used in some radar equipment as amplifiers. Klystrons make use of the transit-time effect by varying the velocity of an electron beam.)] | + | There are two basic transmitter configurations used in radar. One is the //self-excited// oscillator, exemplified by the magnetron. The other utilizes a //low - power stable// oscillator, which is in turn amplified to the required power level by one or more power amplifier tubes. An example is Klystron $Fig.7$ [( **Klystron amplifiers** are high power microwave vacuum tubes. Klystrons are velocity-modulated tubes that are used in some radar equipment as amplifiers. Klystrons make use of the transit-time effect by varying the velocity of an electron beam.)] |
| The latter is more stable than self - excited oscillators and are usually capable of greater average power. Self-excited power oscillators, | The latter is more stable than self - excited oscillators and are usually capable of greater average power. Self-excited power oscillators, | ||
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| The CW radar is of interest not only because of its many applications, | The CW radar is of interest not only because of its many applications, | ||
| - | consider the simple CW radar as illustrated by the block diagram of $ Fig.10$. The transmitter generates continuous (unmodulated ) oscillation of frequency $f_0$, which is radiated by the antenna. A portion of the radiated energy is intercepted by the target and is scattered, some of it in the direction of the radar, where it is collected by the receiving antenna. | + | consider the simple CW radar as illustrated by the block diagram of $ Fig.8$. The transmitter generates continuous (unmodulated ) oscillation of frequency $f_0$, which is radiated by the antenna. A portion of the radiated energy is intercepted by the target and is scattered, some of it in the direction of the radar, where it is collected by the receiving antenna. |
| If the target is in motion with a velocity $v_r$ relative to the radar, the received signal will be shifted in frequency from the transmitted frequency $f_0$ by an amount ± $f_d$ as given by the equation. | If the target is in motion with a velocity $v_r$ relative to the radar, the received signal will be shifted in frequency from the transmitted frequency $f_0$ by an amount ± $f_d$ as given by the equation. | ||
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| The minus sign (-) applies if the distance is increasing (receiving target). The received echo signal at frequency $f_0 ± f_d$ enters the radar via the antenna and is heterodyned in the detector ( mixer ) with a portion of the transmitter signal $f_0$ to produce a Doppler beat note of frequency $f_d$. The sign of $f_d$ is lost in this process. | The minus sign (-) applies if the distance is increasing (receiving target). The received echo signal at frequency $f_0 ± f_d$ enters the radar via the antenna and is heterodyned in the detector ( mixer ) with a portion of the transmitter signal $f_0$ to produce a Doppler beat note of frequency $f_d$. The sign of $f_d$ is lost in this process. | ||
| - | The purpose of the doppler amplifier is to eliminate echoes from stationary targets and to amplify the Doppler echo signal to a level where it can operate an indicating device. It might have a frequency - response characteristic similar to that of the figure. | + | **The purpose of the doppler amplifier** is to eliminate echoes from stationary targets and to amplify the Doppler echo signal to a level where it can operate an indicating device. It might have a frequency - response characteristic similar to that of the figure. |
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| - | title : Cw Radar:Doppler frequency shift | + | |
| - | publisher : nptel | + | |
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| - | The receiver of the simple CW radar of $Fig.10$ is in some respects analogous to a superheterodyne receiver. Receivers of this type are called **Homodyne** receivers, or superheterodyne receivers with Zero-IF. | + | The receiver of the simple CW radar of $Fig.8$ is in some respects analogous to a superheterodyne receiver. Receivers of this type are called **Homodyne** receivers, or **superheterodyne** receivers with Zero-IF. |
| - | The function of the local oscillator is replaced by the leaking signal from the transmitter .such a receiver is simpler than one with a more conventional intermediate frequency since no IF amplifier or local oscillator is required.however the simpler receiver is not as sensitive due to the increased noise at the lower intermediate frequencies by Flicker effect [(Flicker-Effect noise occurs in semiconductor devices such as crystal detectors and cathodes of vacuum tubes.The produced noise power varies as $1 / f_α$, where α is approximately unity.)] . | + | The function of the local oscillator is replaced by the leaking signal from the transmitter .such a receiver is simpler than one with a more conventional intermediate frequency since no IF amplifier or local oscillator is required.however the simpler receiver is not as sensitive due to the increased noise at the lower intermediate frequencies by Flicker effect [(**Flicker-Effect noise** occurs in semiconductor devices such as crystal detectors and cathodes of vacuum tubes.The produced noise power varies as $1 / f_α$, where α is approximately unity.)] . |
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| * Doppler frequency usually falls in the audio or video frequency range which is more susceptible to flicker noise. | * Doppler frequency usually falls in the audio or video frequency range which is more susceptible to flicker noise. | ||
| * Flicker noise is inversely proportional to frequency. So as we shift the Doppler frequency to IF flicker noise reduces. | * Flicker noise is inversely proportional to frequency. So as we shift the Doppler frequency to IF flicker noise reduces. | ||
| - | * Super-heterodyne receiver with non zero IF increases the receiver sensitivity above $30$ dB | + | * Super-heterodyne receiver with non zero IF increases the receiver sensitivity above **$30$** dB |
| **Receiver bandwidth** : | **Receiver bandwidth** : | ||
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| * IF amplifier should be wide enough to pass the expected range of Doppler frequencies. | * IF amplifier should be wide enough to pass the expected range of Doppler frequencies. | ||
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| - | * But as a bandwidth | + | * But as a Receiver |
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| * So Received signal bandwidth again increases. | * So Received signal bandwidth again increases. | ||
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| - | When the Doppler-shifted echo signal is known to lie somewhere within a relatively wide band of frequencies, | + | **When the Doppler-shifted echo signal is known** to lie somewhere within a relatively wide band of frequencies, |
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| - | The bandwidth of each individual filter is wide enough to accept the signal energy, but not so wide as to introduce more noise than need be. If filters are spaced with their half power points overlapped, the maximum reduction in the signal-to-noise ratio of a signal which lies midway between adjacent channels compared with the SNR at mid-band is $3$dB. | + | The bandwidth of each individual filter is wide enough to accept the signal energy, but not so wide as to introduce more noise than need be. If filters are spaced with their half power points overlapped, the maximum reduction in the signal-to-noise ratio of a signal which lies midway between adjacent channels compared with the SNR at mid-band is **$3$**dB. The more filters used to cover the band, the less will be the maximum loss experienced, |
| **Direction of target motion** : | **Direction of target motion** : | ||
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| - | ($c$) receding target.[(#13)]</ | + | ($c$) receding target.[(cite:Image9)]</ |
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| - | In some application of CW radar, it is of interest to know whether the target is approaching or receding. This might be determined with separate filters located on either side of the intermediate frequency. If echo-signal frequency lies below the carrier, the target is receding; if the echo frequency is greater than the carrier, the target is approaching $ Fig.14$. | + | In some application of CW radar, it is of interest to know whether the target is approaching or receding. This might be determined with separate filters located on either side of the intermediate frequency. If echo-signal frequency lies below the carrier, the target is receding; if the echo frequency is greater than the carrier, the target is approaching $ Fig.12$. |
| The sign of Doppler angular frequency shift ** $ω_d$ ** and the direction of the target' | The sign of Doppler angular frequency shift ** $ω_d$ ** and the direction of the target' | ||
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| - | If the output of channel B leads to the output of channel A, the Doppler shift is Positive | + | |
| - | If the output of channel B leads to the output of channel A, the Doppler shift is Negative | + | |
| + | If the output of channel B leads to the output of channel A, the Doppler shift is (Positive) Approaching Target. | ||
| + | If the output of channel B leads to the output of channel A, the Doppler shift is (Negative) Receding Target. | ||
| \begin{equation} | \begin{equation} | ||
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| * $ω_0$ = angular frequency of transmitter [rad/s] | * $ω_0$ = angular frequency of transmitter [rad/s] | ||
| * $Φ$ = a constant phase shift, which depends upon range of initial detection | * $Φ$ = a constant phase shift, which depends upon range of initial detection | ||
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| - | **Applications of CW radar with Non-zero IF**: | ||
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| - | * Police speed monitor | ||
| - | * Rate-of-climb meter (During aircraft take off) | ||
| - | * Vehicle counting | ||
| - | * As a replacement for “5th wheel speedometer” in-vehicle testing | ||
| - | * Antilock braking system | ||
| - | * Collision avoidance | ||
| - | * In railways as speedometer instead of a tachometer | ||
| - | * Advance warning system for approaching targets | ||
| - | * Docking speed measurement of large ships | ||
| - | * Intruder alarms | ||
| - | * Measurement of the velocity of missiles, baseball etc | ||
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| - | **Limitations of CW radar with Non-zero IF**: | ||
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| - | * False targets | ||
| - | * Unable to detect the range of the target | ||
| **Frequency Modulated CW radar** | **Frequency Modulated CW radar** | ||
| - | **FMCW** radar is capable to measure the relative velocity and the range of the target with the expense of bandwidth. An example of an amplitude modulation frequency is the pulse radar. | + | **FMCW** radar is capable to measure the relative velocity and the range of the target with the expense of bandwidth. An example of an amplitude modulation frequency is the **pulse radar**. |
| - | By providing timing marks into the Transmitted signal the time of transmission and the time of return can be calculated. This will increase the bandwidth. More distinct the timing, more accurate the result will be and broader will the Transmitted spectrum. Here it is done by frequency modulating the carrier and the timing mark is the change in frequency. | + | By providing |
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| Transmitted frequency increases linearly with time (solid line).Solid curve represents transmitted signal; | Transmitted frequency increases linearly with time (solid line).Solid curve represents transmitted signal; | ||
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| - | The echo signal will return after a time $T = 2R/c$ (dashed line). | + | The echo signal will return after a time $T = \frac{2R}{c}$ (dashed line). |
| - | If the echo signal is heterodyned with a portion of the transmitter signal in a nonlinear element such as a diode, a beat note $f_b$ will be produced. If there is no Doppler frequency shift, the beat note is a measure of the target' | + | If the echo signal is heterodyned with a portion of the transmitter signal in a nonlinear element such as a diode, a beat note $f_b$ will be produced. If there is no **Doppler frequency shift**, the beat note is a measure of the target' |
| \begin{equation} | \begin{equation} | ||
| f_r = {f_0}T = \frac{2R}{c} f_0 | f_r = {f_0}T = \frac{2R}{c} f_0 | ||
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| - | The reference signal from the transmitter is used to produce the beat frequency note. The beat frequency is amplified and limited to eliminate any amplitude fluctuations. The frequency of the amplitude-limited beat note is measured with a cycle counting frequency meter calibrated in distance, If the target is not stationary Doppler frequency shift will be superimposed on the $FM$ range beat note and an erroneous | + | The reference signal from the transmitter is used to produce the beat frequency note. The beat frequency is amplified and limited to eliminate any amplitude fluctuations. The frequency of the amplitude-limited beat note is measured with a cycle counting frequency meter calibrated in distance, If the target is not stationary Doppler frequency shift will be superimposed on the FM range beat note and a wrong range measurement results |
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| \end{equation} | \end{equation} | ||
| - | One-half the difference between the frequencies will yield the Doppler frequency. If there is more than one target, the range to each target may be measured by measuring the individual frequency components by using a bank of narrowband filters. If the targets are moving the task of measuring the range of each becomes complicated. | + | One-half the difference between the frequencies will yield the Doppler frequency. If there is "more than one target" |
| **FM CW Altimeter** | **FM CW Altimeter** | ||
| To measure the height above the surface of the earth FM-CW radar is used as aircraft radio altimeter. Low Transmitted power and low antenna gain are needed because of short range. Since the relative motion between the aircraft and ground is small, the effect of the Doppler frequency shift may usually be neglected. | To measure the height above the surface of the earth FM-CW radar is used as aircraft radio altimeter. Low Transmitted power and low antenna gain are needed because of short range. Since the relative motion between the aircraft and ground is small, the effect of the Doppler frequency shift may usually be neglected. | ||
| - | Frequency | + | And the frequency |
| - | Solid state Transmitted is used here. | + | Solid state Transmitted is used here. In general |
| - | High sensitive super-heterodyne | + | high sensitive super-heterodyne |
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| The output of the detector contains the beat frequency which contains doppler frequency and the range frequency. It is amplified to a level enough to actuate the frequency measuring circuits. | The output of the detector contains the beat frequency which contains doppler frequency and the range frequency. It is amplified to a level enough to actuate the frequency measuring circuits. | ||
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| and The switched frequency counter determines the Doppler velocity. The averaging frequency counter is necessary for an altimeter since the rate of change of altitude is usually small. | and The switched frequency counter determines the Doppler velocity. The averaging frequency counter is necessary for an altimeter since the rate of change of altitude is usually small. | ||
| - | In an altimeter, the echo signal from an extended target varies inversely as the square (rather than the $4th$ power) of the range, because of greater the range greater the echo area illuminated by the beam. | + | In an altimeter, the echo signal from an extended target varies inversely as the square (rather than the $4$th power) of the range, because of greater the range greater the echo area illuminated by the beam. |
| The low-frequency amplifier is a narrow band filter which is wide enough to pass the received signal energy, thus reducing the amount of noise with which the signal must compete. | The low-frequency amplifier is a narrow band filter which is wide enough to pass the received signal energy, thus reducing the amount of noise with which the signal must compete. | ||
| The average frequency counter is a cycle counter. It counts only absolute numbers. So there may be step errors or quantization errors. | The average frequency counter is a cycle counter. It counts only absolute numbers. So there may be step errors or quantization errors. | ||
| **Unwanted signals in FM altimeter**: | **Unwanted signals in FM altimeter**: | ||
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| - | The difference between simple pulse radar and pulse Doppler radar is that in pulse Doppler radar the reference signal at the receiver is derived from the transmitter, | + | The difference between simple pulse radar and pulse Doppler radar is that in pulse Doppler radar the reference signal at the receiver is derived from the transmitter, |
| Here the reference signal acts as the coherent reference needed to detect the Doppler frequency shift. The phase of the transmitted signal is preserved in the reference signal. | Here the reference signal acts as the coherent reference needed to detect the Doppler frequency shift. The phase of the transmitted signal is preserved in the reference signal. | ||
| Operation: | Operation: | ||
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| - | Sample waveforms (//bipolar//) | + | Sample waveforms (**bipolar**) |
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| - | Moving targets may be distinguished from stationary targets by observing the video output on an A-scope (amplitude vs. range). | + | Moving targets may be distinguished from stationary targets by observing the video output on an A-scope (**amplitude** vs. **range**). |
| Echoes from fixed targets remain constant throughout, but echoes from moving targets vary in amplitude from sweep to sweep at a rate corresponding to the Doppler frequency. | Echoes from fixed targets remain constant throughout, but echoes from moving targets vary in amplitude from sweep to sweep at a rate corresponding to the Doppler frequency. | ||
| - | The superposition of the successive A-scope sweeps is shown in $Fig.25$ [$b$ to $e$] The moving targets produce, with time, a " | + | The superposition of the successive A-scope sweeps is shown in $Fig.23$ [$b$ to $e$] The moving targets produce, with time, a “butterfly” effect on the A-scope. |
| It is not appropriate for display on the PPI. | It is not appropriate for display on the PPI. | ||
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| - | The delay-line canceler acts as a filter to eliminate the dc component of fixed targets and to pass the ac components of moving targets. | + | The delay-line canceler acts as a filter to eliminate the DC component of fixed targets and to pass the AC components of moving targets. |
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| The local oscillator must also be a **sta**ble oscillator and is called **Sta**lo, for the stable local oscillator. The RF echo signal is heterodyned with the Stalo signal to produce the IF signal just as in the conventional super-heterodyne receiver. | The local oscillator must also be a **sta**ble oscillator and is called **Sta**lo, for the stable local oscillator. The RF echo signal is heterodyned with the Stalo signal to produce the IF signal just as in the conventional super-heterodyne receiver. | ||
| - | 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 | + | 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 are both fed into a mixer called the phase detector. Its output is proportional to the phase difference between the two input signals. | + | The reference signal from the coho and the IF echo signal are both fed into a **mixer** called the **phase detector**. Its output is proportional to the phase difference between the two input signals. |
| Triode, Tetrode, Klystron, Traveling-wave tube, and the Crossed-field amplifier can be used as the power amplifier. | Triode, Tetrode, Klystron, Traveling-wave tube, and the Crossed-field amplifier can be used as the power amplifier. | ||
| - | A transmitter which consists of a stable low- power oscillator followed by a power amplifier is sometimes called MOPA, which stands for master- oscillator power amplifier. | + | A transmitter which consists of a stable low- power oscillator followed by a power amplifier is sometimes called |
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| **MTI radar (with power-oscillator Transmitter)** | **MTI radar (with power-oscillator Transmitter)** | ||
| - | In an oscillator, the phase of the RF bears no relationship from pulse to pulse. For this reason, the reference signal cannot be generated by a continuously running oscillator. However, a coherent reference signal may be readily obtained with the power oscillator by **readjusting | + | In an oscillator, the phase of the RF bears no relationship from pulse to pulse. For this reason, the reference signal cannot be generated by a continuously running oscillator. However, a coherent reference signal may be readily obtained with the power oscillator by remodifying |
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| - | A portion of the transmitted signal is mixed with the Stalo output to produce an IF beat signal whose phase is directly related to the phase of the transmitter. | + | A portion of the transmitted signal is mixed with the Stalo output to produce an **IF beat signal** whose phase is directly related to the phase of the transmitter. |
| This IF pulse is applied to the coho and causes the phase of the coho CW oscillation to " | This IF pulse is applied to the coho and causes the phase of the coho CW oscillation to " | ||
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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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| **Filter characteristics of the delay-line canceler** | **Filter characteristics of the delay-line canceler** | ||
| - | The delay-line canceler acts as a filter which rejects the d-c component of clutter. Because of its periodic nature, the filter also rejects energy in the vicinity of the pulse repetition frequency and its harmonics. the video signal | + | The delay-line canceler acts as a filter which rejects the DC component of clutter. Because of its periodic nature, the filter also rejects energy in the vicinity of the pulse repetition frequency and its harmonics. the video signal |
| \begin{equation} | \begin{equation} | ||
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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 | + | It is assumed that the gain through the delay-line canceler is unity. The output from the canceler |
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
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| - | [(#13)]</ | + | [(cite:Image9)]</ |
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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 |
| \begin{equation} | \begin{equation} | ||
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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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| <figure label> | <figure label> | ||
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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 |
| + | |||
| + | \begin{equation} | ||
| + | I _C = \frac{(S)_{out}}{(S)_{in}}\times CA=(CA)\times G_{N} | ||
| + | \end{equation} | ||
| + | |||
| + | where $CA$ is the clutter attenuation and $G_N$ is called Noise Gain. | ||
| + | |||
| + | |||
| + | |||
| + | 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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| <figure label> | <figure label> | ||
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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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| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
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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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| <figure label> | <figure label> | ||
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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. |
| <figure label> | <figure label> | ||
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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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| - | **Example Of An MTI Radar Processor** | ||
| + | |||
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| + | ===== Moving Target Detector ===== | ||
| + | |||
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| + | **Example Of An MTI Radar Processor** | ||
| The **M**oving **T**arget **D**etector (**MTD**) is an MTI radar processor originally developed by the MIT Lincoln Laboratory for the FAA's Airport Surveillance Radars $A S R$. | The **M**oving **T**arget **D**etector (**MTD**) is an MTI radar processor originally developed by the MIT Lincoln Laboratory for the FAA's Airport Surveillance Radars $A S R$. | ||
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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 ($V_{OC}$)** : |
| | | ||
| 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 " |
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
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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, | ||
| + | |||
| + | 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, | ||
| + | |||
| + | 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. | ||
| + | |||
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| + | <figure label> | ||
| + | {{ : | ||
| + | < | ||
| + | </ | ||
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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** | + | * |
| + | | ||
radar/doppler.1527623582.txt.gz · Last modified: (external edit)