Lecture 14 Target Echo Information Extraction SamplingA signal consists of five sinusoids is sampled...
Transcript of Lecture 14 Target Echo Information Extraction SamplingA signal consists of five sinusoids is sampled...
Lecture 14Target Echo Information Extraction
SamplingDr. Aamer Iqbal Bhatti
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Pulsed radars are inherently sampled data systems.
Each time the illumination energy hits a target and a
portion of echo is captured by the radar, a sample of the
target parameter is obtained.
The only information available about the target comes
from this sample.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The Nyquist sampling criterion states that in order for
information to be fully recoverable after sampling, it must
be sampled more than twice for each sinusoidal cycle of
information present.
The sample rate (fs) must be greater than twice the
highest frequency present.
fN > 2fmax
◦ fN = Nyquist sample rate.
◦ fmax = The highest frequency present in the signal.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Sampling in time domain is the process of multiplying
the wave to be sampled by a sampling waveform.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Multiplication in time domain is convolution in
frequency.
Convolution with impulses is simply a matter of copying
the wave to be convolved at the location of the impulse.
Thus the spectrum of the sampled wave is an infinite
number of copies of the spectrum of the wave sampled.
If Nyquist criterion is not considered Aliasing may occur.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
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Radar Signal Processing
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Radar Signal Processing
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
A signal consists of five sinusoids is sampled at 5500
samples per second. The five sinusoids are at frequencies
of 2400Hz, -7500Hz, 14300Hz, 22900Hz, and -31250Hz.
Find the frequencies recovered after sampling.
Highest frequency captured will be 5500/2=2750Hz
◦ 2400Hz will be recovered 2400Hz.
◦ -7500Hz will be recovered as -2000Hz (-7500+5500).
◦ 14300Hz will be recovered as -2200Hz (14300-5500*3).
◦ 22900Hz will be recovered as 900Hz (22900-5500*4).
◦ -31250Hz will be recovered as 1750Hz (-31250+5500*6)
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Information is recovered by samples by isolating the spectrum
of the original signal through filtering.
If the aliases overlap the spectrum recovery is not possible.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Radar information exist at several different rates, and
two levels of sampling take place.
First, individual targets are sampled at a rate consistent
with the information about them which is to be
recovered.
Secondly, the search volume is sampled at a rate which
resolves targets (in range) to the level desired.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The sample rate for individual targets is PRF
PRF cannot be increased without time to accommodate Nyquist
sampling for Doppler
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
A radar (No Pulse Compression) has a PRF of 3500pps and
divides its interpulse period into 512 equal range bins plus a dead
time of 55 msec between the end of last range bin and the start
of the transmit pulse (neglect the transmit pulse width). Find
a) The range resolution if the bin width matches the resolution.
b) The probable pulse width.
c) The approximate receiver bandwidth.
d) The A/D conversion rate.
e) The sample rate for range resolution.
f) The sample rate for Doppler.
g) The maximum unambiguous Doppler.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The PRF of 3500 gives an interpulse period of 285.7msec. Subtracting 55msec
leaves 230.7msec for range bins. Dividing by 512 gives a bin width of
450.6nsec.
a) If the range resolution matches the bin width of 450.6nsec (the most
common practice), the range resolution is the range equavalent of
450.6nsec, or 68m.
b) Pulse width equals the bin width, or 450.6nsec.
c) Approximate receiver bandwidth is reciprocal of the pulse width i.e.
2.22MHz.
d) There is one A/D conversion for each range bin. Sampling at 2.22MHz.
For I/Q sampling 2 A/D converter sampling at 2.22MHz.
e) The sampling rate for range resolution equals the bin rate, 2.22MHz.
f) This is the PRF, 3500 samples per second.
g) The maximum Doppler can be measured unambiguous by using one half
of PRF, or 1750Hz.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The sample rate for individual target is the PRF.
There are three main classes:
Low PRF (LPRF): in low PRF system s or modes, the
transmitted pulses are far enough apart in time so that all
targets echoes return from the last pulse return before
the transmitter fires again.
High PRF (HPRF): it occurs when the sample rate is fast
enough to sufficiently sample the Doppler shift of the
target.
Medium PRF(MPRF): a MPRF mode undersamples in
Doppler, but not badly so.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Doppler shifts in pulsed radars manifests itself as the
change in the phase of target echo signals from hit to hit.
So the system must not only sample the target at
sufficient rate but must also measure and record the
phase of each received echo
Two methods are used for this:
◦ Direct Sampling
◦ I/Q Sampling.
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Direct sampling occurs when the signal amplitude is
frozen at regular intervals and these sampled and held
voltages are either digitized or processed in analog
form.
The spectrum is two sided symmetrical containing both
positive and negative frequencies with a negative
spectral component matching each positive component.
Example of sinusoids.
Each of the signal is a rotating vector completing
revolutions per second
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Each of the signal is a rotating vector completing revolutions
per second
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Radar Signal Processing
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)(2
1sin
)(2
1cos
sincos
jj
jj
j
eej
ee
je
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The process of recovering both real and imaginary signal
component is known as I/Q demodulation or sampling.
I stands for in-phase (cosine) and Q for quadrature (sin).
In I/Q recovery the signal is multiplied by a reference
wave of same frequency and the at the reference phase .
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
In I channel the echo signal is multiplies by COHO
which at zero phase represent the cosine reference.
v1(t) = Vs Cos[2πft + Φ(t)] x Vc Cos[2πft]
Vs Cos[2πft + Φ(t)] = target echo voltage
Vc Cos[2πft] = COHO voltage.
Using trigonometric identity
v1(t) = Vs Cos[4πft + Φ(t)] + Vs Cos[Φ(t)]
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Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The first term is removed by low pass filter.
The second term becomes the I component of the
received echo.
vI(t) = Vs Cos[Φ(t)]
The signal echo is multiplies with COHO shifted +900.
In this manner Q channel is recovered.
vQ(t) = Vs Sin[Φ(t)]
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Radar Signal Processing
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The two signals I and Q completely represent the echo
signal
The signal processor can reconstruct the signal
magnitude and phase.
Vs2 = VI2 + VQ
2
Φ = Tan-1(VQ/VI)
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Radar Signal Processing
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The I and Q voltages for eight consecutive hits on an
outbound target, with one Doppler cycle in eight hits are
as under.
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Radar Signal Processing
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