The Ubiquitous MATCHED FILTER . . . it

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The Ubiquitous MATCHED FILTER . . . its
everywhere!!
an evening with a very important principle
thats finding exciting new applications in
modern radar
R. T. Hill AES Society an IEEE
Lecturer Dallas Chapter 25 September 2007
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How do receivers work? A brief review, then, of
network theory characterizing a receiver
by its impulse response function represent
ing radio signals reminding ourselves of
convolution in linear systems . . Wow!
. . all in twenty minutes or so! Well, first
well need a receiver block diagram ?
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characterizing a receiver (or generally, a
network) by its impulse response
function Why?
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Do you see how we can represent any signal s(t)
as a collection of impulses . .? . . the
impulse is a wonderful function, so useful
Ill make some comments about it.
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About designing our receiver . . What impulse
response function do I want?? Well, what do
we want our receiver to do . . produce
a replica of our signal? NO!! . . .
discuss . . .
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For maximum sensitivity to our own signals being
at the input, we dont need to see a copy of it
at the output . . . . we simply need, at the
output, the greatest possible indication of its
presence at the input. In other words, we need
to have an impulse response function that, when
convolved with our signal, would give the
greatest possible signal to noise ratio at
the output. Oh, yes . . did I neglect to
mention noise? ?
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This, then, is The Matched Filter A receiver
the impulse response function of which is the
complex conjugate of a particular signal will
produce the greatest possible signal-to-noise
ratio at the output when that signal is at the
input and in the presence of independent and
completely random noise . . . this receiver is
the most sensitive to the particular signal . .
. . it is matched to it.
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OK . . but just one further thought . .
Remember the childs block tower?
Consider The childs playroom is subject to a
mild earthquake (good grief!) as the blocks are
tumbled in the way we expected. White noise
. . were OK . . use the matched filter On the
other hand, what if a wind had been blowing
distinctly from, say, the west as the blocks
were tumbled in addition to the earthquakes
vibratory behavior? Not random!! Biased!
Wed better compensate for that, assuming we
can sense it. That is, we may wish to use a
whitening filter to randomize the
disturbance before the matched filter! That idea
is indeed key to much of the adaptive signal
processing so strong in todays radar literature
. . . more about that to come
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Where do we use the Matched Filter? Some
illustrations . . Pulse compression,
very common in radar . . Receive beam
steering, direction finding in antennas, the
adaptive antenna . . Space-Time
Adaptive Processing (STAP) in radar . .
Polarimetry in radar, adaptive processing,
target recognition . .
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Illustration 1 . . Pulse Compression ?
First, some remarks about pulse compression in
modern radar . . fine range resolution desired,
but still with long pulse for lots of
energy ? Achieved by modulating the
transmitted pulse, then compressing the
pulse on receive with (of course) a matched
filter ? Techniques binary phase coding
widely used typical lengths of hundreds to
one our example here? A mere four to one!
?
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A peculiar thing about binary phase coding
The idea that the tapped delay line,
backwards is indeed a conjugating matched
filter is not so clear in binary phase coding .
. adding or subtracting 180 results in the same
zero phase for that bit (all bits then being
phase aligned). Just to illustrate conjugation
more clearly, imagine that our four-segment
sequence had been 0, -30, 0, 0 terrible
autocorrelation function, but it makes our
point about phase realignment by conjugation
in this convolution process.
Compressed pulse output (here showing rather
poor range sidelobes)
Pulse expander on transmit
Pulse compressor on receive
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The Barker codes sidelobe level Length 2 -
and - 6.0 dB 3
- - 9.5 4 - and
- - 12.0 5 - -
14.0 7 - - - - 16.9
11 - - - - - - - 20.8
13 - - - - - 22.3 dB
Modulo 2 adder
Seven-stage shift register
This seven-stage shift register is used to
generate a 127-bit binary sequence that can in
turn be used to control a (0,180o) phase shifter
through which our IF signal is passed in the
pulse modulator of our waveform generator. Such
shift-register generators produce sequences of
length 2N 1 (before repeating N is the number
of stages). Today, computer programs generate
the modulation, storing sequences known to have
good autocorrelation functions, for many lengths
other than just 2Int - 1.
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Illustration 2 . . Antennas the Adaptive
Array ? First, some remarks about how antennas
form receive beams, phased arrays the simplest
and very pertinent illustration ? Next,
well observe that compensating for the
angle of arrival for an echo is indeed a form
of (you guessed it) a matched filter, this one
in angle space ? Then, well consider
(again in angle space) that the noise may
NOT be utterly random, not white
(statistically uniform) in angle . . we may
need a whitening filter before our matched
filter ?
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. . continuing . .
Can you see how the compensating phase control
in the phased array is acting as a conjugating
matched filter? Here, the segments of our
signal are NOT a function of time (as
before discussed in signal processing) but rather
a function of space, the position of each
element of the array. The same Matched Filter
principle applies, but here in a different
dimensional space than normally considered in
matched filter teaching. But what was the other
part of the principle? Ah . . that the
background noise be independent and random . .
. . necessary condition for the Matched Filter
to give best possible output (here, angle
measurement accuracy). Is our noise
stationary in angle, uniform statistically???
Perhaps not!! ?
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The Adaptive Antenna . .
Discussion ? Spatial analysis analogous
to spectral analysis ? Finding
compensating weights for each element
involves solving as many simultaneous
algebraic equations . . inverting
the covariance matrix NOT EASY ? Adapted
pattern will be inverse to the angular
distribution of noise, whitening it ?
Todays art state . . 16 DOF rather standard . .
Array signal processing . . first, spatial
analysis, then compensation to whiten
Bottom line the coherent sidelobe cancellers
(CSLC) the more elaborate adaptive
phased arrays are forms of spatial whitening
filters, here to whiten the heterogeneous
disturbance noise in angle. Why? So
that a straightforward angle matched filter can
be used most effectively.
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Illustration 3 . . Space-Time Adaptive
Processing, STAP ? Adaptive antenna processing
is Space-Adaptive. What is meant by
Space-Time Adaptive Processing? ? A few
remarks about Doppler processing in radar,
itself an application of the Matched Filter . .
Doppler filters are indeed filters matched to a
particular Doppler shift ? Many radars,
airborne ones particularly, need to do
Doppler processing when the background (noise,
continuous ground clutter) is certainly NOT
spectrally uniform . . once again, well need a
whitening filter
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Doppler filtering Theory View a
single Doppler filter as a classic Matched
Filter, that is, we
multiply (convolve) the input signal
with the conjugate of the signal
being sought.
sample 1 2
3 4 signal
x reference
product
Recall, phase angles add when complex numbers
(vectors) are multiplied that is, the signal
is rotated back in phase by the amount it might
have been progressing in phase . . To the extent
that such a component was in the input signal
will we get an output in this particular filter.
Weve built a Matched Filter for that component
(that frequency component) alone. HOWEVER, this
is best ONLY IF background noise is utterly
random in Doppler frequencies . . ?
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Illustration 4 . . The Polarimetric Matched
Filter ? First, a short general review of
polarimetry in radar, its uses, its value ?
Then, an example of the Polarimetric Whitening
Filter and how a polarimetric radar image (by
SAR) is improved just from PWF application to
the area clutter ? Of course, the whitening
to randomize the polarization state of the
surrounding area (local clutter in a scene)
permits us then to search for targets
(building, vehicles) the polarimetric
signature of which may have been estimated in
advance.
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Radar Polarimetry . . a little review ?
Polarization of an Electro-Magnetic wave is taken
as the spatial orientation of the E-field . .
most, but certainly not all, radars are
designed to operate, for various reasons, in
either horizontal or vertical (linear)
polarization, fixed by the antenna design
that is, they are not polarimetric ? A
Fully Polarimetric Radar (FPR) can, first,
transmit one polarization and separately
measure the received signal in each of two
orthogonal polarizations, then do the same,
transmitting the orthogonal polarization (e.g.,
transmit H, receive H and V then transmit
V, receive H and V) ? We learn a lot about a
target by sensing its polarimetric scattering ?
Developed well by the meteorological radar
community, some other specialty radars
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Well . . did we make it to this concluding
slide?? The Matched Filter ? The
conjugate impulse response function max
sensitivity to a signal in the presence of
white noise ? Normally taught in the context
of just temporal signal processing . .
functions of time, etc ? Should be no less
seen by students of radar as the underlying
principle to many advances, in other
dimension spaces angle (antenna patterns),
spectral analysis (Doppler filtering), polarimet
ric analysis (as in synthetic aperture radar
image enhancement) ? Todays adaptive
processes are generally the MF-related
whitening required in non-random environments
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The End More than you wanted to know about The
Matched Filter