radar:doppler
Differences
This shows you the differences between two versions of the page.
| radar:doppler [2018/05/30 16:44] – masrour | radar:doppler [2026/04/28 15:13] (current) – external edit 127.0.0.1 | ||
|---|---|---|---|
| Line 35: | Line 35: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| )] </ | )] </ | ||
| </ | </ | ||
| Line 164: | Line 164: | ||
| 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! | ||
| Line 247: | Line 247: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| - | )] </ | + | |
| </ | </ | ||
| Line 288: | Line 287: | ||
| * 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. | ||
| | | ||
| - | * But as a Receiver bandwidth in increased noise, increases and sensitivity | + | * But as a Receiver bandwidth in increased noise, increases and sensitivity |
| * And also the Transmitted signal bandwidth is not narrow. | * And also the Transmitted signal bandwidth is not narrow. | ||
| * So Received signal bandwidth again increases. | * So Received signal bandwidth again increases. | ||
| Line 324: | Line 323: | ||
| 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$. | 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' |
| One method of determining the relative sign is: | One method of determining the relative sign is: | ||
| Line 385: | Line 384: | ||
| - | If the frequency is modulated at a rate $f_m$ over a range $Delta f$ the **beat frequency** is : | + | If the frequency is modulated at a rate $f_m$ over a range $Δf$ the beat frequency is : |
| \begin{equation} | \begin{equation} | ||
| Line 392: | Line 391: | ||
| - | 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 |
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 409: | Line 408: | ||
| \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 |
| + | |||
| Line 423: | Line 424: | ||
| < | < | ||
| </ | </ | ||
| + | |||
| + | |||
| 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. | ||
| Line 431: | Line 434: | ||
| 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**: | ||
| - | | + | |
| - | | + | |
| - | | + | |
| - | | + | |
| - | | + | |
| Line 463: | Line 466: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| - | 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: | ||
| Line 506: | Line 509: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| - | Sample waveforms (//bipolar//) | + | Sample waveforms (**bipolar**) |
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 520: | Line 523: | ||
| - | 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. | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 536: | Line 539: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| - | 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. |
| Line 547: | Line 550: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 556: | Line 559: | ||
| 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 |
| Line 568: | Line 571: | ||
| **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 |
| < | < | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| - | 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 " | ||
| Line 584: | Line 587: | ||
| **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. | ||
| Line 591: | Line 594: | ||
| **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} | ||
| Line 610: | Line 613: | ||
| \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> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| - | [(#13)]</ | + | [(cite:Image9)]</ |
| </ | </ | ||
| + | |||
| + | |||
| + | |||
| + | |||
| Line 632: | Line 639: | ||
| \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} | ||
| Line 639: | Line 646: | ||
| 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 | + | |
| Line 663: | Line 670: | ||
| - | 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} | ||
| Line 674: | Line 681: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| + | |||
| + | |||
| 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 | ||
| Line 685: | Line 694: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| + | |||
| + | |||
| + | |||
| + | |||
| Line 692: | Line 705: | ||
| **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**. | ||
| Line 707: | Line 722: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| + | |||
| + | |||
| Line 724: | Line 741: | ||
| \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, | ||
| Line 733: | Line 760: | ||
| - | The figure | + | $Fig.31$ |
| | | ||
| Line 743: | Line 770: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 749: | Line 776: | ||
| 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 ) | ||
| Line 758: | Line 785: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 773: | Line 800: | ||
| + | **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. | ||
| Line 781: | Line 808: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| + | |||
| + | |||
| 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> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 805: | Line 834: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| - | **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. | ||
| Line 818: | Line 847: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| - | * 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** |
| Line 844: | Line 873: | ||
| 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 |
| | | ||
| Line 851: | Line 880: | ||
| * $N$ = 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 |
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 875: | Line 904: | ||
| **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: |
| Line 909: | Line 938: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| - | 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.) | ||
| Line 918: | Line 947: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 925: | Line 954: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 937: | Line 966: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| + | |||
| Line 949: | Line 979: | ||
| ===== Moving Target Detector ===== | ===== Moving Target Detector ===== | ||
| + | |||
| + | |||
| Line 961: | Line 993: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| - | 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. |
| Line 975: | Line 1007: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 984: | Line 1016: | ||
| - | **Limitation | + | **Limitation |
| Line 991: | Line 1023: | ||
| - | | + | * **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. | ||
| Line 1001: | Line 1033: | ||
| $SCV = (C/S)_{in}$ | $SCV = (C/S)_{in}$ | ||
| - | | + | * **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 $P_{fa}$. | ||
| Line 1059: | Line 1091: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 1130: | Line 1162: | ||
| - | 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> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| - | 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 ($λ$). |
| Line 1161: | Line 1193: | ||
| \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} | ||
| Line 1169: | Line 1201: | ||
| \begin{equation} | \begin{equation} | ||
| - | S_a = G_0 exp [\frac{ | + | S_a = G_0 exp [-{\frac{ |
| \end{equation} | \end{equation} | ||
| Line 1178: | Line 1210: | ||
| \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 |
| Line 1199: | Line 1231: | ||
| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
| Line 1218: | Line 1250: | ||
| <figure label> | <figure label> | ||
| {{: | {{: | ||
| - | < | + | < |
| </ | </ | ||
| + | |||
| Line 1227: | Line 1260: | ||
| 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 |
| Line 1242: | Line 1275: | ||
| + | **Termination of Moving Target Detection** | ||
| + | |||
| + | |||
| + | |||
| + | 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. | ||
| + | |||
| + | |||
| + | |||
| + | <figure label> | ||
| + | {{ : | ||
| + | < | ||
| + | </ | ||
| + | |||
| + | |||
| + | |||
| + | 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.1527698695.txt.gz · Last modified: (external edit)