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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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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Sampling in time domain is the process of multiplying

the wave to be sampled by a sampling waveform.

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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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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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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 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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The sample rate for individual targets is PRF

PRF cannot be increased without time to accommodate Nyquist

sampling for Doppler

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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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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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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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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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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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Each of the signal is a rotating vector completing revolutions

per second

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)(2

1sin

)(2

1cos

sincos

jj

jj

j

eej

ee

je

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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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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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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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The two signals I and Q completely represent the echo

signal

The signal processor can reconstruct the signal

magnitude and phase.

Vs2 = VI2 + VQ

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Φ = Tan-1(VQ/VI)

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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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lecture 14 target echo information extraction samplinga signal consists of five sinusoids is sampled...

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