United States Patent 5,486,833 Barrett January 23, 1996
Active signalling systems
Abstract
A signalling system in
time-frequency space for detecting targets in the presence of clutter and for penetrating
media, includes a transmitter antenna system, receiver and processor system.
The transmitter antenna system generates and launches into a medium containing
the targets an energy pulse (wave packet) having a predetermined duration and
frequency characteristic, and which energy pulse matches at least one of the
following: 1) the time-frequency reflection characteristics of the target(s)
but not the clutter, or 2) the penetration time-frequency dielectric window of
the medium, or 3) the time-frequency characteristics of the window of the
receiver. Preferably, the time-frequency wave packet is the complex conjugate
of the impulse response of the combined medium and target. The processor solves
the wave equation for transmissions through the medium, reflectance from the
target(s) and transmission back through the medium and causes a match of the
generated wave packet signals to both the medium and target for maximum
propagation through the medium and reflectance from the target, the wave packet
match to the medium and the target being with respect to both time and
frequency response characteristics.
Inventors: Barrett; Terence
W. (1453 Beulah Rd., Vienna, VA 22182)
Appl. No.: 042272Filed:
April 2, 1993
Current U.S. Class:342/204;
342/21; 342/22; 342/83
Intern'l Class: G01S 007/42;
G01S 007/32
Field of Search:
342/82,83,201,204,22,21
References Cited
U.S. Patent Documents
Oct., 1963 Clement
Oct., 1971 Treacy
Mar., 1973 Kelley et al
Feb., 1977 Chapman342/22.
Aug., 1980 Fowler et
al.342/196
Feb., 1991 Farhat382/15
Mar., 1992 Jehle et
al.342/21
Jun., 1992 Guerci et
al.342/204.
Sep., 1992 Guerci et
al.342/204.
Oct., 1992 Harmuth342/22.
Dec., 1992 Grieve et
al.342/82.
Jan., 1993 Kim et al.342/21.
Jun., 1993 Tang et
al.342/13.
Sep., 1993 Hughes342/22.
Primary Examiner: Barron, Jr.;
Gilberto
Attorney, Agent or Firm: Zegeer; Jim
Claims
What is claimed is:
1. A signalling system for detecting targets in a given medium, comprising:
means for generating and transmitting in said given medium a time-frequency
wave packet which is the complex (phase) conjugate of the impulse response of
the combined medium and target, and
means for solving the wave equation for transmissions through said medium,
reflectance from said target and transmission back through said medium.
2. The signalling system defined in claim 1 including means for matching said
wave packet signal to both said medium and said target for maximum propagation
through said medium and reflectance from said target, said wave packet match to
said medium and said target being with respect to both time and frequency
response characteristics.
3. The signalling system defined in claim 1 including receiver means for
receiving echoes of wave packets reflected from said targets in said medium,
time and frequency space matched filter means for preserving the instantaneous
time and frequency response characteristics of return signal echoes from said
target.
4. The signalling system defined in claim 3 wherein said receiver means
includes a TD receiver processor.
5. The signaling system defined in claim 3 wherein said receiver means is a
Homodyne.
6. The signalling system defined in claim 3 wherein said receiver means
includes means for detecting range to said target by detecting the rate of
change of energy in returned echo wave packets.
7. The signalling system defined in claim 3 wherein said receiver means
includes an independent antenna system.
8. The signalling system defined in claim 3, said receiver including means for
processing target data for target recognition purposes.
9. The signalling system defined in claim 3, said receiver including neural net
means for processing target data target imaging and display.
10. A signalling method for detecting targets in a given medium, comprising:
generating and transmitting in said given medium a time-frequency wave packet
which is the complex (phase) conjugate of the impulse response of the combined
medium and target, and
solving the wave equation for transmissions through said medium, reflectance
from said target and transmission back through said medium.
11. The signalling method defined in claim 10 including matching said wave
packet signal to both said medium and said target for maximum propagation
through said medium and reflectance from said target, said wave packet match to
said medium and said target being with respect to both time and frequency
response characteristics.
12. The signalling method defined in claim 10 including receiver means for
receiving echoes of wave packets reflected from said target in said medium,
time and frequency space matched filtering for preserving the instantaneous
time and frequency response characteristics of return signal echoes from said
target.
13. Signalling system in time-frequency space for detecting a target in the
presence of clutter and for penetrating media, comprising:
transmitter antenna means, receiver and processor means, said transmitter
antenna means having means for generating and launching into a medium
containing said target an energy pulse (wave packet) having a predetermined
duration and frequency characteristic, and which energy pulse matches one of
the following:
1) the time-frequency reflection characteristics of said target but not said
clutter, or
2) the penetration time-frequency dielectric window of said medium, or
3) the time-frequency characteristics of the window of said receiver.
14. The search apparatus defined in claim 4 wherein said means for generating
is an RF generator, includes:
a light energy activated switch, the RF energy of which follows the light
energy,
means to modulate the light energy and compress the light to said predetermined
pulse duration,
a linear semiconductor switch, and
means for applying the modulated light energy to said semiconductor switch.
15. A time-frequency space signalling method for and launching into a medium
containing a target wave packets having a predetermined duration and frequency
characteristic, and in which the wave packets match at east one of the
following:
1) the time-frequency reflection characteristics of said target but not said
clutter, or
2) the penetration time-frequency dielectric window of said medium, or
3) the time-frequency characteristics of the window of said receiver.
16. A method of analyzing wave packet transmissive solid media, comprising
generating and launching a time frequency wave packet into said solid media and
causing said wave packet to match the penetration time-frequency dielectric
window of said solid media.
17. The method defined in claim 16 including receiving wave packet reflection
echoes from said media and adjusting the time-frequency characteristics of
receiving of wave packet reflections.
18. A method of enhancing the radar cross-section of a target when using an impulse
radar system, said method comprising the steps of:
transmitting a pilot impulse radar pulse at a target, said pilot impulse radar
pulse comprising a pulse of duration shorter than the target length and
generated by an impulse radar system,
receiving a return pulse from the target, which return pulse provides
information indicative of scattering centers on the target, and wherein the
return pulse is used as a calibration signal,
processing the calibration signal corresponding to the return pulse to form a
phase conjugated transmit pulse, and
transmitting the phase conjugated transmit pulse at the target,
processing a target return signal derived from the transmitted phase conjugated
pulse,
and wherein the target return signal derived from the transmitted phase
conjugated pulse has an enhanced radar cross-section of the target since the
waveform of the transmitted phase conjugated pulse is matched to the
characteristics of the target.
19. The method defined in claim 18 wherein said phase conjugated pulse has rise
and fall times in the pico-second range.
20. An impulse radar system comprising:
a transmitter for transmitting a pilot impulse radar pulse at a target, which
pilot pulse comprises a pulse of a duration shorter than the target length,
a receiver for receiving a return impulse radar pulse from the target, which
return pulse provides information indicative of scattering centers on the
target, which return pulse provides a calibration signal, and
processing means coupled to the transmitter and receiver for processing the
calibration signal corresponding to the return impulse radar pulse to form a
phase conjugate impulse radar pulse,
wherein the transmitter is adapted to transmit the phase conjugate pulse at the
target, and wherein the receiver is adapted to process a target return signal
derived from the transmitted phase conjugate pulse, and wherein the target
return signal derived from the transmitted phase conjugated pulse enhances the
radar cross-section of the target since the waveform of the transmitted phase
conjugated pulse is matched to the characteristics of the target.
21. The system of claim 20, wherein said phase conjugated pulse has rise and
fall times on the pico-second range.
22. An impulse radar system comprising:
a transmitter for transmitting impulse radar pulses at a target, wherein said
transmitter comprises means for generating a search pulse having a duration
shorter than the target length,
a receiver for receiving return pulses from the target, which return pulses
provide information indicative of scattering centers on the target, and
processing means coupled to the transmitter and receiver for processing the
return pulses and for adaptively adjusting the phase of the transmitted pulses
that are transmitted at the target in response to the return pulses in such a
manner as to cause the radar cross-section contributed by the backward
traveling wave on the target to be made to add in phase in the received
direction, and
wherein the transmitter transmits the pulses having adaptively adjusted phases
at the target, and wherein the receiver sums the spectral components comprising
return pulses derived from the transmitted pulses having adjusted phases to
increase the radar cross-section of the target.
Description
BACKGROUND OF THE INVENTION
The present invention relates generally to active signalling systems which are
able (i) to penetrate media/instrumentation with high efficiency (optimally),
and (ii) to sense, detect or image targets with high accuracy; and more
particularly to time-frequency signalling systems which transmit wave packets
which take the form of (i) mathematical descriptions of the time-reversed
transfer characteristics of the medium and target, and (ii) physical solutions
to the equations of motion of those signals with the medium.
It is desirable to resolve a target with high accuracy, and increase the range
and the signal-to-noise ratio and the target-signal-to-non-target-signal ratio
of the returned signal, of signalling systems such as laser or light detection
and ranging (ladar or lidar), radio detection and ranging (radar), IR sensor
systems and sound detection and ranging (sonar) systems. One of the standard
methods for increasing signal detection is low signal-to-noise environments is
the used of matched filter systems in the receiver process. Such matched
filtering methods have been described often, e.g., in Minkoff (1992). These
matched filtering systems of prior art exist in the reception and processing
subsystems of the total signalling system. A common problem with the prior art
signalling systems is that the signals used in the transmission system to
penetrate, sense, detect or image targets/media are not matched to the
target/media, and the matched filter is confined to the receiver/processor-side
of the total signalling system. Therefore such systems do not achieve maximum
range to target for the energy (Joules) input to the devices, nor can such
devices resolve targets with accuracy from designated non-targets or "clutter".
Another standard method for resolving targets with high accuracy is the use of
ultrashort pulse waveforms, also known as impulse signals, or time-domain
signals, and sometimes inaccurately known as ultrawideband signals. Such
signalling systems are also not matched to the target/media and when used with
a matched filter in the receiver-processor subsystem also do not achieve
maximum range for the energy (Joules) input to the devices, not can such
devices resolve targets from clutter with accuracy.
OBJECTS OF THE INVENTION
Accordingly, it is an object of the present invention to significantly increase
the range of signalling systems, while at the same time obtaining extremely
high signal-to-noise ratios of target-to-background.
It is a further object of the present invention to provide a signalling system
which decreases the clutter in the signal returning to the system and provides
a system with "selective attention" for, or maximum reflectance from,
or discrimination of, or resolution of, designated targets.
It is a further object of the present invention to provide a signalling system
which optimally penetrates media and resolves, detects, and discriminates
targets with high accuracy by using wave packet signals, which are precisely
defined in both the time and the frequency domain, rather than primarily in the
frequency domain, or primarily in the time domain.
It is a further object of the present invention to provide a signalling system
which senses different forms of the reflectance response characteristics of the
target, rather than a single response characteristic. The response
characteristics of the target sensed by the present invention are also time and
frequency characteristics, rather than primarily time characteristics or primarily
frequency characteristics. The response characteristics of the target sensed by
the present invention are diverse, e.g., the early time (or optical), the
resonance, and the late time target responses, rather than one unitary response
characteristic detected by prior art.
It is a further object of the present invention to provide a signalling system
which senses or detects or resolves the individual scattering parts of a
target, rather than detecting targets as single point scatterers. Therefore in
the case of the present invention the target provides an
"information-rich" signal echo return, rather than a binary
presence/absence echo return. The informational "channel" between the
signalling system of the present invention and the target is an ergodic (information
preserving) channel, whereas the channels between prior art systems and the
target are nonergodic and only provide information concerning presence or
absence of the target.
Other objects, advantages, and novel features of the present invention will
become apparent from the detailed description of the invention, which follows
the summary and the accompanying drawings.
SUMMARY OF THE INVENTION
Briefly, the above and other objects of the present invention are achieved in a
high accuracy detection system for detecting targets in a given medium
comprising means for generating and transmitting in the given medium a
time-frequency wave packet (pulse) which is the complex conjugate of the
impulse response of the combined medium and target and a solution to the wave
equation for transmission through the medium, reflectance from the target, and
transmission back through the medium. The wave packet (WP) signals are matched
to both the medium and the target for maximum propagation through the medium and
maximum reflectance from the target. The wave packet match to the medium and
target is with respect to both the time and frequency response characteristics,
rather than time response characteristics alone, or frequency response
characteristics alone.
Methods are described for characterizing the target and medium in terms of
time-frequency transfer characteristics and for designing WPs matched to those
characteristics. Means are described for crafting and launching such matched
wave packets. Five different methods are described for obtaining sufficient
energy interactive with target: (1) high energy individual wave packet signals
emitters; (2) arrays of wave packet emitters; (3) wave packet signals emitted
as trains of pulses; (4) combinations of (1)-(3); and (5) signal averaging.
Means are provided for receiving echos of the WP reflected from targets in a
given medium. Matched filter means are provided in both time and frequency
space so that the "instantaneous" time and frequency response
characteristics of the return signal echo from the target are preserved, rather
than a matched filter of prior art in which only the frequency, or only the
time response characteristics are preserved. Finally, processing techniques are
provided for two modes of functioning of the present invention: (i) the matched
signal mode; and (ii) the imaging mode.
In one embodiment of the present invention, the WP signal is an expansion of
time-frequency affine elementary signals of a class known as wavelets and
developed by the inventor. In prior art (Gabor, 1946), the elementary signals
do not have the affine property. In another embodiment of the present
invention, the transmitted WP is a soliton wave packet which is a signal
matched to the time and frequency response characteristics of specific and
special media with characteristics defined below.
BRIEF DESCRIPTION OF THE DRAWINGS
The above and other objects, advantages and features of the invention will
become better understood when considered with the following specification and
accompanying drawings wherein:
FIG. 1 is a schematic diagram of one embodiment of the present invention.
FIG. 2A is a representation of the Gaussian envelope of a representative signal
in time-frequency space
FIG. 2B are time-frequency representations of a signal considered as a random
variable and as the result of a mapping (a) f=x(t) with the domain of t
restricted, and the range of f broad; (b) t=x(f) with the domain of f
restricted, and the range of t broad.
FIGS. 3A and 3B are a schematic representation of (i) the decomposition of a
complex target into individual elementary scattering components; and (ii) the
selective addressing of individual elementary scattering components by matched
signals.
FIGS. 4A, 4B, 4C, 4D and 4E are schematic representations of a signalling
system. FIG. 4A is a Graphical representation of
emitter-medium-target-medium-receiver interactions; FIG. 4B is a Simplification
of FIG. 4A representing media and target in terms of transfer function in time
and frequency; FIG. 4C is a Schematic method for he characterization and
definition of the time-frequency transfer function of both a linear and
nonlinear unknown target and medium; FIG. 4D is a Schematic method for the
characterization and definition of the time-frequency transfer function of a
linear target and medium; FIG. 4E is a Simplification of methods shown in FIGS.
4C and 4D.
FIG. 5 is an affine elementary signals or signal basis set with amplitude
modulations (1) D.sub.0 (x); (2) D.sub.1 (x); (3) D.sub.2 (x); (4) D.sub.3 (x);
and (5) D.sub.4 (x), where D.sub.n (x)=N.sub.n H.sub.n (.xi.)exp[-.xi..sup.2 ]
are Weber-Hermite functions, where N.sub.n is a constant such that
.intg.D*.sub.n (x)D.sub.n (x)=0, and H.sub.n (.xi.)=d.sup.2 D/dx.sup.2
+(.lambda.-t.sup.2)D=0. (a) of each set obeys the uncertainty products
.DELTA.f..DELTA.t=f.sub.0 t.sub.0 =(1/2)(2n+1); (b) an (c) obey
.DELTA.f.f.sub.0 =(1/2)(2n+1), where .DELTA.f is the frequency modulation
bandwidth. From Barrett, (1973, 1975, 1977).
FIGS. 6A, 6B and 6C are schematic representations of the selective addressing
of two targets by matched signals. In 1. two different targets are irradiated
by a short pulsed time-frequency signal which provides a wideband signal of
short duration. The signal echo returns are shown at a and b. In 2. the two
targets are irradiated with a signal which is the complex conjugate (time
reversed) of the response of target A to the short pulsed signal used in 1. In
3. the two targets are irradiated with a signal which is the complex conjugate
(time reversed) of the responses of target B to the short pulsed signal used in
1.
FIG. 7 is a tabulation of the affine elementary signal D.sub.0 (f)=f.sub.0
t.sub.0 =1/2; .DELTA.f.DELTA.t=1/2; f.sub.0 =4.DELTA.t; t.sub.0 =.DELTA.t/4 at
various frequencies. From Barrett, (1973, 1975, 1977).
FIG. 8 is a schematic operation of signalling system in the a posteriori mode
using an adaptive reconfigurable array. Array emits a short pulse defined in
terms of elementary signal expansion. The targets are defined in terms of the
elementary signal expansion of each targets transfer function.
FIG. 9A is a comparison of the return echo signals elicited by two signals of
identical bandwidth but different temporal duration. The top shows a signal of
duration long with respect to the target; the bottom shows a signal short with
respect to the target.
FIG. 9B is a comparison of the return echo signals obtained in the situation
described in FIG. 9A. (The information from individual scatterers is projected
on the whole body response, but doe to sampling restrictions and lacking the
sequency information contained in the interpulse arrivals t.sub.1, t.sub.2,
t.sub.3, t.sub.4, t.sub.5, its extraction is not possible).
FIG. 10 is a graphical representation of a short pulse (impulse) signal
interacting with a target, providing multiple reflections from parts of the
target separated by absolute time differences, as opposed to modulo time
differences (phase).
FIG. 11 is a graphical representation of three kinds of target echo responses:
(A. the early time or optical response; B. the resonance response; and C. the
late time response.)
FIG. 12A is a graphical representation of a time-frequency representation, the
ambiguity function representation, of a single frequency pulse. (a) 3-D view;
(b) contour-plot in the time-frequency plane; (c) left: cut at f.sub.0 (the
autocorrelation); right: cut at zero delay (the poser density spectrum).
FIG. 12B is a graphical representation of a time-frequency representation, the
ambiguity function representation, of a linear frequency modulated pulse. (a) a
3-D view; (b) contour-plot in the time-frequency plane; (c) cut at f.sub.0 (the
autocorrelation).
FIG. 12C is a graphical representation of a time-frequency representation, the
ambiguity function representation, of five coherent single-frequency constant
amplitude pulses. (a) 3-D view; (b) contour-plot in the time-frequency plane;
(c) upper: cut at f.sub.0 (the autocorrelation); lower: cut at zero delay (the
power density spectrum).
FIG. 12D is a graphical representation of a time-frequency representation, the
ambiguity function representation, of a length-7 Costas coded signal. (a) 3-D
view; (b) contour-plot in the time-frequency plane; (c) cut at zero delay (the
power density spectrum).
FIG. 13 is a graphical representation of target transfer characteristics in
time-frequency space and the matching of signal characteristics to the target
in the same space.
FIG. 14 is a representation of signal representation in .DELTA.f.DELTA.t space
at increasingly higher levels n`0,1,2,3, . . . n.
FIG. 15 is a schematic description of a representative fuselage shape (upper),
a representative wing shape (middle) and a representative aircraft shape with
wings and fuselage (lower in terms of a Weber-Hermite function expansion.
FIG. 16 is a schematic description of the method characterizing the
time-frequency characteristics of a linear system in terms of a Weber-Hermite
function basis set.
FIG. 17 is a schematic diagram of the canonical form of a frequency domain
receiver processor or superheterodyne receiver. The method of signal
acquisition uses a local oscillator and mixer. This is a simplified model
receiver processor used for discussion and comparison with a time domain
receiver shown in FIG. 18.
FIG. 18 is a schematic diagram of the canonical form of the time domain
receiver processor or homodyne receiver. The method of signal acquisition uses
coherency or autocorrelation. This is the receiver processor model used for
discussion in performance prediction.
FIG. 19 is a schematic representing in (1) the prior art of video signal
detection used in frequency domain processing using level-detection to resole
signal; in (2) time domain processing after autocorrelation and Fourier
transformation to power density spectral representation providing analysis
characterizing signal; in (3) with increase in sampling speed over that in (2)
(providing receiver gain), signal further resolution. An increase in signal
resolution or signal-to-noise characterization increases "detection"
(characterization) range. This form of receiver gain (increase in
signal-to-noise by faster sampling) shown in (2) and (3) is not available to
the prior art frequency domain threshold detection method (1).
FIG. 20 shows representations of: A. a radial frequency phasor; B. a Neper
frequency phasor; C. a complex plane signal representation; and D. an analytic
representation of signals. Whereas in the prior art a frequency domain receiver
is designed to receive phase-type signals whose signals duration can be
undefined, the time domain receiver is designed to receive analytic signals
which are causal, i.e., their initial conditions are defined and there is not
signal before t=0.
FIG. 21 Representations of the signal envelope of three signals of identical
energy (area). Signal 1 contrasts with signals 2 and 3 in being of longer
duration; signal 3 contrasts with signals 1 and 2 in being sampled with a small
sampling window. Suppose that the energy in all three signals i 5 Joules; that
the temporal length of the sampling bin (t.sub.n) for signals 1 and 2 is 20
nanosec. and for signal 3, 1 nanosec.; and that the threshold for detection for
all three signals is 3 nanosec./nanosec. Therefore, signals 1 and 2 will not be
detected, as the signal length/bin length ratio is 5/20<3/1. However, signal
3 is detected, as the signal length/bin length ratio is 5/1>3/1. Signal 3 is
also detected despite the fact that it was of the same energy as signals 1 and
2. The integrating time, t.sub.int is different in the case of signals 1 and 3,
but the duration and energy of the two signals, .DELTA.t, is the same. As
signal 3 is detected, but signal 1 is not, 1/t.sub. int .noteq.1/.DELTA.t.
FIG. 22 Time-frequency representations of the response characteristics of a
short pulse wave packet, and superheterodyne receiver. The steady state
characteristics of both are at the identical frequency but the transient
response of the signal is faster than that of the receiver.
FIG. 23 is a representation of a signal, its amplitude modulus and its
instantaneous phase. The abscissa is time. The ordinate (top) is amplitude; the
ordinate (middle) is reciprocal frequency, showing contour plots of the
amplitude modulus; the ordinate (bottom) is reciprocal frequency, showing lines
of constant phase.
FIG. 24A is a representation of a prior art system in which an unchanging
nonoptimum signal is propagated.
FIG. 24B is a representation of the present invention in which the source
technologies are matched to the target.
FIG. 25A is a representation of the two modes of functioning of the present
invention: the imaging mode, in which a short duration, side bandwidth wave
packet signal is used and the antenna emission is equivalent to a point source;
and the detection mode, in which a wave packet signal is used and the antenna
emission is a matched signal.
FIG. 25B is a representation of the two forms of signal return expected using
the imaging mode and the detection modes.
FIG. 26 is a representation of signal-to-noise gain expected when matched
signals are used and the orthogonal function expansion of the transfer function
description of the target is orthonal to the clutter.
FIG. 27 is a representation of the operation of the present invention using the
two modes of functioning. In this representation an aircraft is approaching the
surveillance and tracking system.
FIG. 28 is a representation of target and clutter in time-frequency space.
FIG. 29 is a representation of the mutual relations in the limiting factors on
performance of the present invention. Given a target of maximum length, a, and
desired minimum length to be resolved, a.sub.min, then pulse duration,
.DELTA.t, must be .DELTA.t.gtoreq.a.sub.min /c; and the receiver minimum
sampling interval, q.sub.min, must be .xi.=q/q.sub.min .ltoreq.K, where
K=a/a.sub.min. Performance is limited by four factors: (1) Top--range is
commensurate with energy (J) emitted, but with the following provisos; (2)
Left--the target must be a "target of opportunity", that is, there
must both exist a minimum structure, a.sub.min, available on the target, and
there must also be the desire on the part of the radar operator to detect that
minimum structure; (3) Top--given the designation of a.sub.min, the pulse
duration, .DELTA.t, can be defined according to the condition .DELTA.t
.gtoreq.a.sub.min /c.; (4) Right--again, given the designation of a.sub.min,
the receiver gain required can be specified according to the condition
.xi.=q/q.sub.min .ltoreq.K= a/a.sub.min. Thus performance of the present
invention cannot be predicted without designation of target fine structure and
the pulse energy is relevant within the context of pulse duration set by the
designated minimum fine structural length.
FIG. 30A and B are representations of range for K>1, G.sub.t =35 db and
K/.xi.=1. A. Range versus Source Energy--100 J maximum; B. 20 J. maximum; and
C. 2 J maximum.
FIG. 31 is a representation of some embodiments of the present invention. The
present invention is based on three generic technology areas: (1) source
technologies; (2) receiver-processor technologies; and (3) antenna and array
technologies.
FIG. 32 are representative applications of the present invention.
FIG. 32A counter-clutter, counter-multipath, counter-Raman scattering, counter-ionospheric
scattering.
FIG. 32B foliage penetration (FOPEN); weatherpen (WEATHERPEN); ground
penetration (GROUNDPEN) and ice penetration (ICEPEN). In the case of a WP of
the present invention (upper) the leading edge of the envelope of the WP excites
the molecular complex of the medium to an excited vibrational state; the
trailing edge of the envelope is passing before the relaxation time from that
excited state resulting in reemission back to the pulse. Homogeneous broadening
is assumed to be greater than inhomogeneous broadening in the medium. In the
case of a continuous wave signal of prior which is longer in duration than the
relaxation time of the molecular complex of the medium, the medium relaxes from
the excited state and the energy from the signal is absorbed.
FIG. 32C higher range resolution; sensing of higher order target diffractions
and target elementary scatterers; target imaging on the basis of an
informational rich return from target;
FIG. 32D long range surveillance;
FIG. 32E space-based surveillance, planetary rover;
FIG. 32F communication links;
FIG. 32G Sea-skimming missile detection.
FIG. 33 Representation from calculations by Crisp (1970) showing deeper
penetration through media when the wave packet is less than the relaxation time
of the medium. (a) and (b): propagation of a Gaussian pulse of length t. The
depth of penetration, z, is measured in Beer's law absorption lengths,
a.sup.-1. (c): variation of pulse energy per square centimeter with penetration
distance into the absorber of Gaussian pulses of various pulse lengths t.
FIG. 34 Time-frequency characteristics of a representative 3-stage receiver.
FIG. 35 A Schematic heterodyne receiver; B. Schematic homodyne receiver. All
amplification amplification methods have been omitted in both cases.
FIG. 36 (i) Quadrature filter; (ii) Power density spectra of real signal and
its Hilbert transform; (iii) Power density spectrum of the analytic signal.
Note the absence of negative frequencies. After Papoulis, 1965.
FIG. 37 is a graphical representation of a method for crafting RF wave packets.
FIG. 37A In this embodiment a diode laser provides a light pulse, the pulse is
lengthened and passes through a Pockels cell modulator which can be computer
controlled. The modulator conditions the pulse into the desired modulated wave
packet form; this wave packet is amplified and then passed through a compresses
the optical wave packet to the desired temporal length.
FIG. 37B The optical wave packet is then handed-off to a linear light-activated
RF switch and RF wave packet is generated with the desired time and frequency
characteristics which is then launched from an antenna.
FIG. 38 is a block diagram of an ultrashort pulse-time-frequency radar/sensor
incorporating the invention.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
The present invention is based on the transmission of WP signals defined in
time-frequency space which are matched to the medium and target by an expansion
of the time-frequency characteristics of signals, target and medium in an
affine orthogonal function basis set expansion, which captures and preserves
the instantaneous frequency, phase and amplitude relations. The expansion set
is also physical as well as mathematical, so that a matched signal can be
propagated and interact with the target/medium as the complex conjugate of the
impulse transfer characteristics of the target/medium. The convolution of the
matched signal and the target/medium's impulse response results in a unity, or,
alternatively, an optimum transfer of the signal energy to the signalling
system's receiver.
Prior art provides signal expansions, e.g., Fourier series, the general
Karhunen-Loeve expansion, but these are only mathematical descriptions and not
also expansion in terms which are also solutions to a wave equation describing
physically propagating WPs. The present invention uses a signal expansion
method developed by the inventor in a series of papers (Barrett, 1971-8) and is
a Karhunen-Loeve expansion restricted in terms of Weber-Hermite functions which
are also solutions to a wave equation. The signal basis set can be viewed as an
affine expansion in energy.times.frequency.times.time space. Each signal is
defined in terms of four signal parameters: the frequency bandwidth, .DELTA.f,
the temporal bandwidth, .DELTA.t, the midfrequency, f.sub.0, and the midperiod,
t.sub.0, and a level parameter, n, such that: f.sub.0 t.sub.0
=.DELTA.f.DELTA.t=(1/2)(2n+1), n=0,1,2,3 . . . Signals of different levels, n,
are orthogonal, with the signal modulating envelopes defined by the
Weber-Hermite functions D.sub.n (x)=N.sub.n H.sub.n (.xi.)exp[-.xi..sup.2 ],
where N.sub.n is a constant such that .intg.D*.sub.n (x)D.sub.n (x)=0, and
H.sub.n (.xi.)=d.sup.2 D/dx.sup.2 +(.lambda.-t.sup.2)D=0. As the signal
modulating envelope and modulated signal are related by the mutual relations
stated, signals, targets and media can be expanded in terms of these functions
referenced by the modulating envelopes, D.sub.n (f), where f is frequency and n
is the level or order of the function. That is, the signal, targets and media
are defined in terms of a collection of affine time-frequency filters of
varying frequency, the time-frequency windowing length of which can also vary
according to the size of n (FIG. 14). FIG. 7 shows the relations of the four
signal parameters of the basis set for only the n=0 conditions, i.e., for the
D.sub.0 (f.sub.1) modulated signals, but unlike the Gabor signals, these
D.sub.0 (f.sub.1) are affine related. In previous art, e.g., the Gabor
expansion (Gabor, 1946), the signals were defined only with respect to a two,
not four, dimensional mutual relation: .DELTA.t.DELTA.t=1/2, and hence are not
affine. Furthermore, the Gabor expansion does not permit a varying
time-frequency windowing length, i.e., n=0 for all Gabor elementary signals,
this results in a confusion concerning the initial and final conditions of a
resonance system, i.e. its transient response. For example, FIG. 22 is a
time-frequency representation of the response characteristics of a short pulse
wave packet, and a superheterodyne receiver. In this example, the short pulse
could be 1 nanosecond in duration with a midfrequency of 1 GigaHertz. The
receiver characteristics, in this example, are a steady state frequency of 1
GigaHertz but an onset response of 100 MegaHertz. Thus, the steady state
characteristics of both signal and receiver are at an identical frequency but
the transient response of the signal is faster than that of the receiver.
Therefore, the expansion of both the signal and the receiver in Weber-Hermite
function, .SIGMA..sub.n D.sub.n (f), form are in terms of the some of the same
frequencies, f, but are of different order, n. The level parameter, n, is
determined by the signal/system transient response as opposed to the steady
state response. The constant n=0 condition of prior art thus indicates an
implicit assumption that all systems, signals, targets and media are of
identical transient response, i.e., have identical onset and offset response
times. This assumption is not true in most cases.
Apart from the concise mathematical description in time-frequency form of the
varying steady state and transient response of signals, targets and media, the
signal descriptions and expansions, or affine elementary signals, used in the
present invention (FIG. 5) are solutions of a wave equation. The functions,
D.sub.n (f), which are the modulating envelopes of the functions
f.sub.0.t.sub.0 =.DELTA.f.DELTA.t=(1/2)(2n+1), n=0,1,2,3, . . . , are solutions
to Weber's equation, or the wave equation for a confined oscillator. Weber's
equation is only an approximation to the wave equation expected in real media.
Therefore the signal description given here is idealized and it is expected
that there will be modifications to, and deviations from, the idealized,
D.sub.n (f)-based description, depending on the media through which the signals
must propagate. In fact, a drastic modification is described below when soliton
propagation through special media is described.
Given that there are alternatives to the idealized Weber-Hermite function
expansion basis set of description embodiment, the major unvarying requirements
of the proposed invention remain that (1) the expansion basis must be an
orthogonal series; (2) the basis elements must be solutions to a wave equation
to ensure physicality, so that they can be emitted or launched; (3) the basis
elements must be both well-defined in the time-frequency domain for steady
state response description, and also an ordered set to describe the transient
response description; and (4) solutions must be matched to medium for optimum
propagation, and matched to target for optimum reflection. Prior art does not
address (1)-(4).
In general terms, the present invention is a system described in FIG. 1, in
which there is adaptive control between the matched filter of the
receiver-processor and the matched signal, which is physically launched to
address the medium and target. Prior art provides neither the adaptive control
nor the matched signal, but a signal which is unmatched, or matched by chance
to target. The signal of the present invention is defined in both the time and
frequency domains and its spread along the time and frequency axes will vary
depending on the characteristics of the designated target (FIG. 2A).
Ladar-lidar, IR, RF and sonar signals used n surveillance are random variables.
Conventionally, signals have been considered of the frequency domain form, in
which the domain of f is restricted, and the domain of f is broad, or of the time
domain form, in which the domain of t is restricted, and the domain of f is
broad (FIG. 2B). The signal referenced in the present invention are defined
over both the time and the frequency domain (FIG. 2A).
FIG. 2A is a representation of the Gaussian envelope of a representative signal
in time-frequency space. the frequency domain components of the signal are
represented along the x.sub.1 axis; the time domain components of the signal
are represented along the x.sub.2 axis; and the amplitude is represented in the
z or Z(x.sub.1, x.sub.2) direction. The envelope is not symmetrical but
"squeezed" so that the frequency bandwidth is wider than the time
bandwidth. This representative signal envelope could be that of a short
duration pulse called conventionally a time domain or impulse signal. If the
envelope were "squeezed" in the orthogonal direction it would be of
narrow frequency bandwidth and wide time bandwidth. For such a case a signal
would be called a frequency domain signal.
FIG. 2B are time-frequency representations of a signal considered as random
variable and as the result of a mapping (a) f=x(t) with the domain of t
restricted, and the range of f broad; (b) t=x(f) with the domain of f
restricted, and the range of t broad. If, and only if, there is no phase
modulation, then both mappings (a) and (b) are restricted (related) by the
uncertainty relation: .DELTA.f.DELTA.t=c. If the radiation-target interactions
are stationary (that is, the statistics of the radiation-matter interactions
are not affected by a shift in the time origin), then these three dimensional
plots could be reduced to two-dimensions, e.g., a single frequency-amplitude
representation. However, as initial conditions (of radiation-matter
interactions) are, in fact, important and significant in radiation-target
interactions, and therefore those statistics are nonstationary, Cauchy-Rieman
conditions apply and the signal representations cannot be reduced to two
dimensions without loss of information.
Approaches to implementation of the present invention: the a posteriori and the
a priori methods.
There are two approaches to the implementation of the preset invention which
will be referred to as the a posteriori and the a priori methods. The a
posteriori method permits the use of the a priori method.
The a posteriori method.
This method must be used if there are no known designated targets. Referring to
a specific example, FIG. 3, the target, in this case, nonmoving, is irradiated
by a short duration or impulse signal of wide bandwidth. The returning echo
signals from the target are received at different positions around the target
from various locations on the target, a, b and c. The signal received at a, is
time reversed and then used as the emit signal, instead of the short duration
impulse signal. That signal a, will be maximally reflected from one part of the
target. Similarly, the signal b, received at another location and time reversed
and used as an emit signal will be maximally reflected from another target
location, and the signal c, etc., will be maximally reflected from yet another
target location. This example demonstrates (1) that a target can be decomposed
into individual scattering components, or elementary scatters, by an emitted
signal which is shorter in temporal/physical length than the physical length of
the target, and (2) that the elementary scatterers can be individually
addressed by using a wave packet signal which is the complex conjugate of the
impulse response of that individual scatterer, i.e., the impulse response of
the individual scatterer convolved with the signal which is the complex
conjugate of the impulse response results in a near unity response or optimum
response scattering from that individual scatterer.
In system engineering terms, and referring to FIG. 4, the a posteriori
procedure described in FIG. 3 may be characterized as follows. A signalling
system emits a signal which propagates through media, interacts with and is
reflected from a target, and then propagates back through media (FIG. 4A). However,
such a series of interactions may be characterized as in FIG. 4B, in which
those interactions are shown as transfer functions and characteristics.
Furthermore, it is well-known that if the target transfer characteristics is
unknown then those characteristics can be determined by understood procedures
(cf. Wiener, 1958, Barrett, 1978, Schetzen, 1989). The procedure for
determining the transfer characteristics of a linear and a nonlinear
target/medium is to apply a comprehensive signal set of "all" frequencies,
and "all" phase relations between those frequencies, which is white
noise, decompose the same white noise, at the same time that it is being
applied to the unknown target/medium into an expansion which is ordered by
temporal delays, e.g., a Laguerre series, and then decompose the elements of
that series into an orthogonal series, e.g., the Weber-Hermite series (FIG.
4C). The return from the target/medium is then convolved with the components of
the expanded input white noise. The procedure for determining the transfer
characteristics of an unknown multilinear target/medium is simpler, only a
short wave packet pulse of broad bandwidth need be used and only the
Weber-Hermite orthogonal set is needed (FIG. 4D). Furthermore, it is known that
the difficult expansions into Laguerre and Weber-Hermite polynomial expansions
need not be attempted, because the well-known cross-correlation of emitted
signal and returned signal accomplishes the same description (FIG. 4E).
However, the analysis of FIG. 4 provides insight in that it, referring to FIG.
4D, in the case of a particular unknown target-medium the returned echo signal
maximally convolves with a certain collection of Weber-Hermite functions,
.SIGMA..sub.n D.sub.n (f), then the complex conjugate of those functions can be
used as the modulating envelope for a wave packet signal which will interact
with the target/medium resulting in a near unity, or at least an optimum,
signal return. FIG. 16 is a more explicit version of FIG. 4D. The procedure
described in system engineering terms in FIG. 4 is thus the procedure followed
practically and described in FIG. 3. A simplified version of FIG. 3 is shown in
FIG. 7, in which different targets are addressed by different signals,
indicating (i) that a signalling system can have "selective
attention" to specified targets with maximum interaction; and (ii) that
there can be minimum interaction with clutter, i.e., targets of no interest.
FIG. 6(1), described a procedure in which two targets are irradiated with a
short duration, wideband pulse or wave packet, and the return signal of each is
received. FIG. 6(2) and (3), describe a followup procedure in which either the
complex conjugate of one of the returned signals, a, from target A, is emitted,
or the complex conjugate of the other returned signal, b, from target B, is
emitted. In both cases maximum echo return is obtained from the designated
target ("selective attention") and there is minimum returning echo
from the other target.
The a priori method.
It is anticipated that in most cases, the a posteriori method will not be used,
because the general class of targets sought will be known. Therefore, the
signal emitted will, in advance, be matched loosely to the designated class. A
mode of functioning intermediate between no a priori knowledge of targets and
complete knowledge is also envisaged. In FIG. 8, a moderately short pulse of
moderate bandwidth is emitted and signal returns are obtained from four
man-made targets. After reception and processing, a target can be designated
and the emitted signal further crafted to approximate the complex conjugate of
that designated target.
Time-Frequency or wavelet analysis and relationship to present invention.
The present invention is an application of time-frequency or wavelet approaches
(cf Mallat (1988, 1989), Daubechies (1988, 1992)) but to both waveform design
and wavepacket signal propagation, as well as signal analysis. Prior art
applies the time-frequency analysis only to signal analysis. The Gabor
elementary signals (Gabor, 1946) do not possess affine properties, so they are
not wavelets, but are a related time-frequency method of processing. The
well-known ambiguity function can be placed in wavelet and group theory form
(Auslander & Tolimieri, 1985); and the Wigner-Ville distribution can be
given a wavelet smoothing (Flandrin & Rioul, 1990). Wavelets can be used
for spread spectrum with considerable advantages over other techniques such as
Fourier analysis. From a mother wavelet one can construct families of daughter
wavelets which are self-similar (Strang, 1989) and there is the capability of
"zeroing in" on very fast transients--a capability not permitted by
Fourier analysis.
Fourier transforms are acceptable disciplines for some applications, but not
appropriate for others. For example, there are cancellations of sines and
cosines at "dead spots" and the timing of a particular frequency's
predominant contribution is not apparent. Reconstruction of the original signal
is very much dependent upon phase. As Cohen has stated in his review (Cohen,
1989): ". . . the power of standard Fourier analysis is that it allows the
decomposition of a signal into individual frequency components and establishes
the relative intensity of each component. The energy spectrum does not, however,
tell us when those frequencies occurred." The prime example of signals
whose frequency content is changing rapidly is human speech and music. In fact,
the musical score with its notes positioned according to frequency and duration
is very similar to a wavelet representation. Each wavelet can be thought of as
a musical not with respect to frequency, duration and location. In essence,
wavelets permit the extraction of instantaneous frequency, instantaneous phase
and, by use of the modulus squared: the instantaneous energy.
Wavelets, or time-frequency distributions in general, specifically address
transients and track the time evolution of "frequency". They have a
self-similarity which can describe fractals (Arneodo et al, 1988). They can
also be used to distinguish targets in a dense target scenario (Naparst, 1991),
1/f type processes (Wornell, 1990) and nonstationary processes in general. (A
stationary stochastic process is one in which there is no change in the
statistics over time. A nonstationary stochastic process is one in which the
statistics changes over time.) Generally speaking: wavelets are good for
boundary detection, e.g., transitions in speech and edges in images (Combes et
al, 1990; Meyer, 1992; Ruskai et al, 1992; and Chui, 1992a, b).
The Receiver Processor Design.
There are many ways to receive a wave packet signal, e.g., a fast
sample-and-hold oscilloscope (for example, a Tektronix 602). The following
describes a preferred embodiment. In the case of frequency domain (FD)
detection of prior art, the detection of targets is based on simple threshold
amplitude detection, i.e., threshold detection is a local time event. In the
case of detection procedure of the present invention, the detection of targets
is in the time domain (TD). In the present invention the autocorrelator
produces a complex event amplitude, and it is on the basis of a global time
event (t.sub.global =c/a, where a is the maximum target length and c is the
speed of light) that such a representation is based. From the point of view of
detecting FD signals in noise of prior art, preserving the shape of the signal
is of no importance. From the point of view of detecting TD signals in noise,
on the other hand, preserving the shape of the signal is very important.
Threshold detection of prior art is a local time event because a signal
exceeding threshold levels occurs regardless of events before or after the
threshold level being exceeded. On the other hand, autocorrelation is based on
a local time event being multiplied (compared) with events occuring in prior
intervals in time. Thus autocorrelation places a local time event in a global
time context. Whereas a local time threshold detection does not preserve the
signal fine structure, a global time autocorrelation preserves and
characterizes the signal fine structure.
In the case of FD receiver design of prior art (FIG. 21) the bandwidth and the
pulse duration are grouped since the product is usually of the order of unity
in most FD pulse-radar applications. The operation of a detector in the mixing
mode results in a much lower conversion loss and is the reason for the
excellent sensitivity of the superheterodyne receiver. IF amplification is also
more stable and has a wider bandwidth than microwave amplification. Finally, for
coherent processing, the outputs of the IF amplifier may be processed by a pair
of synchronous or phase-sensitive detectors to produce in-phase (I) and
quadrature (Q) baseband Doppler signals that can be processed to extract moving
targets and reduce the effects of stationary clutter. In this case, a coherent
IF oscillator (COHO) is obtained from a coherent transmitted signal. While
coherent phase detection is not precluded from the TD processing of the present
invention, the local oscillator method of achieving it across a broad bandwidth
will be in most embodiments.
There is a fundamental difference between detection and characterization of a
target and that difference bears directly on the receiver-processor design of
the present invention. The ability of TD systems of the present invention to
characterize a target far exceeds that of FD systems of prior art--but only if
the correct receiver-processor design philosophy is adopted. In the case of TD
systems of the present invention, the probability that the signal will be
detected is the same as the probability that the amplitude of the power density
spectral line will deviate from a noise or clutter distribution by a
predetermined amount. Thus in TD analysis the power density spectrum is
paramount. TD system receivers of the present invention also achieve more than
detection--they also achieve target characterization. In characterizing the
target the power density spectral representation of the return signal requires
further processing for categorization and recognition.
Whereas in the case of TD receiver systems of prior art the probability of
false alarm is related to threshold detection levels in the case of TD receiver
systems of the present invention the probability of false alarm is related to (i)
the characterization of the returned signal in a power spectral density
representation; and (ii) the classification of that representation by, e.g.,
associative processor (neural net) methods. In the present invention,
characterization is a function of the receiver sampling speed; and
classification is a function of (a) the processor's capability of
distinguishing classes of inputs; and (b) the difference between the transfer
function of target and noise (i.e., their orthogonality).
The degree of orthogonality refers to how different the functions are which
describe the transfer function of the signal and noise. Complete orthogonality
means that those functions are perpendicular to each other in a Hilbert space
signal representation. This means that in processing, arithmetic operations can
be used which result in zero outcome when orthogonal signals are multiplied
together, thus enhancing signal-to-noise ratios between those signals. Usually,
the signal and noise are somewhat less than completely orthogonal. Thus for TD
receiver systems of the present invention the concept of detection versus false
alarm is taken out of the context of simple threshold detection and placed in a
context involving the receiver and processor capabilities, as well as the nature
of the noise (clutter).
This is not to say that signal modifications to enhance detection cannot be
employed in the time domain reception of the present invention. For example,
the detection of rapid changes in energy versus time could be used in parallel
with, or triggering a processing path which preserves the signal fine
structure. Rather, it is to emphasize that in the present invention the
processing path which preserves the signal fine structure is paramount to time
domain reception, regardless of ancillary methods used for detection.
In the case of FD surveillance of prior art, the important parameters affecting
range are the total transmitted energy, the transmitter gain, the effective
receiving aperture and the receiver minimum signal to noise ratio (FIG. 17).
The same parameters are important in TD surveillance (FIG. 18), but due to the
need to process the fine structure of the return signal, the additional
parameter of receiver gain (i.e., the increase in signal-to-noise detection
level due to fast, nondistorting sampling of the signal fine structure) assumes
central importance. The receiver gain also affects the maximum range achievable
by TD systems.
The power density spectrum presumes autocorrelation of the target return.
Autocorrelation is applicable to periodic and aperiodic signals, but whereas
autocorrelation is unnecessary in the determination of the power spectrum and
the energy density spectrum, it is the only means by which the power density
spectrum of random functions is calculated (Lee, 1960). Autocorrelation is
applicable to TD of prior art and TD random signals of the present invention,
but whereas FD signals can be detected by envelope detection threshold methods,
in a preferred embodiment TD signals must be detected by power density spectral
threshold methods, if information concerning target characterization is to be
preserved.
It should be noted that a TD signal of the present invention can be detected
without autocorrelation, but the full potential of TD surveillance would not be
utilised and this is a less preferred embodiment. Moreover, a target can be
detected using a TD signal without obtaining the power density spectrum for the
returned signal, but the complete ambiguity function or wavelet description
would not be used, information would be discarded, and therefore this would be
a less preferred embodiment. There are thus two ranges for TD surveillance of
the present invention--target detection range, and target identification range.
There are clear advantages of crosscorrelation over autocorrelation, e.g.,
crosscorrelation preserves signal phase information, but autocorrelation does
not. There is thus always the remote possibility that two return signals will
be confused of identical frequency content, but different phase relations.
Nonetheless, the crosscorrelation procedure assumes that the reflecting target
placed no information on the transmitted signal, that an information-rich
return with distinguishing contributions from the individual target scatterers
will not occur, and that the signal-target interaction will not lengthen and
"distort" the transmitted signal. Therefore, using crosscorrelation
methods is desirable in embodiments of the present invention, but the equally
desired signal-target interactive process, which provides an information-rich
return, can preclude crosscorrelation of the transmitted and the altered return
signal without information being lost due to an increased temporal length of a
returned signal. If TD surveillance is used in the detection mode only (without
target characterization), then crosscorrelation could be used to advantage and
the target described in cross spectral density terms which preserve phase,
rather than power density spectral terms which do not.
Cross-correlation can also be used in embodiments of the present invention for
correlating coded trains of emitted and received signals/pulses. Whether
autocorrelation or crosscorrelation methods are used, TD surveillance exceeds
the capabilities of FD surveillance of prior art in that after target
detection, the target can be characterized or classified, e.g., by neural net
or other methods.
If a periodic or aperiodic function of time is completely determined for every
value of the independent variable, time, the description of the function is
given for the whole set of values of the independent variable. These functions
can be described in the time domain and by means of harmonic analysis or
Fourier's theory, the same functions can be described in the frequency domain.
However, surveillance signals are not deterministic, i.e., not periodic or
aperiodic, but random. If a function is probabilistic or random, then different
problems arise with different solutions. In surveillance, from the receiver's
perspective the signal returning from a target is a probabilistic or a random
event.
In the case of point detection radars of prior art, the limited objective is to
detect a target's presence and range, not detailed information concerning the
target. In the case of ladars/lidars/radars/sonars incorporating the present
invention, there is an additional objective besides detection of presence and
range: that of the detecting the informational structure in the return signal.
Without a priori knowledge concerning the informational structure, the return
signal is a random variable or event. To detect or characterize that random
event, sampling theory constraints will necessarily limit receiver operation.
Such random variables have a phase space representation, where
"phase" is used synonymously with "state" and defined for
systems with 2N coordinates, i.e., a 2N-dimensional space. Because such signals
have random initial conditions, the signals, as ensemble averages, have a
certain well-defined power density spectral distribution.
Whereas in frequency domain receivers of prior art the random signal, as a
single local time event, i.e., an "instantaneous" threshold
detection, is compared against a probability distribution of noise random
variables; in time domain receivers the signal random variables are compared as
a distribution or global time event, i.e., a summation of temporally displaced
comparative measurements (autocorrelation), against the same probability
distribution of noise random variables. In the case of a receiver of prior art the
return signal will be detected as a threshold event. In the case of a time
domain receiver of the present invention, the return signal will be represented
or characterized as a distribution. The analog representation of the analog
returned signal as a distribution, instead of the detection of the analog
returned signal as threshold event and then digital representation, dictates
that the TD returned signal of the present invention must be sampled with
temporal windows less than the signal duration. These differences in the nature
of FD of prior art and TD signals of the present invention indicate the duality
of the paradigms or system-concepts of FD and TD receiver-processors.
The relation, as well as the differences between the two types of processors,
can be shown in the ambiguity function description in which the energy of the
signal is represented along both a time axis (the autocorrelation) and a
frequency axis (the power spectral density) (FIG. 2B). Random variables are
defined as an abstract set of experimental outcomes and not as points of a real
line in order to avoid infinitely dimensional spaces (Papoulis, 1962). The
difference between the time and frequency domain representations is due to the
differences in their mappings: f=f(t) in the case of the time domain, with the
domain of t restricted and the range of f broad; and t=f(f) in the case of the
frequency domain, with the domain of f restricted and the range of t broad. The
relation of the two mappings is due to both being restricted by the relation:
.DELTA.f.DELTA.t=constant.
For example, in the case of the FD receiver of prior art, the integrated signal
energy (target return) increases in direct proportion to the integration time.
By increasing the integration time, therefore, the signal to noise ratio can be
increased significantly.
On the other hand, in the case of TD systems of the present invention
integrating does help the process of detection, but for target characterization
and detection the signal to noise increases in direct proportion to the
sampling speed (i.e., to the decrease in sampling interval). By decreasing the
sampling time (window), therefore, the signal-to-noise ratio can be increased
significantly. For TD processing, decreased sampling time and increased
sampling speeds results in additional processing gain and therefore range is
obtained by detection of rate of change of energy. Processing gain through
detecting the rate of change of energy, rather than absolute energy, can
provide more sensitive detection and increased range for a given transmitted
energy.
In FD systems of prior art the mixer is by far the preferred front-end
component. In general, mixers are used to convert a low-power signal from one
frequency to another by combining it with a higher-power local oscillator (LO)
signal in a nonlinear device. Usually, the difference frequency between the RF
and LO signals is the desired output frequency at the intermediate frequency
(IF) at subsequent IF amplification. Mixing with local oscillators down
converts to intermediate frequencies and in the IF section narrowband filtering
is most easily and conveniently accomplished. Subsequent amplification and
detection is based on the intermediate frequency signal.
The operation of a detector in the mixing mode results in a much lower
conversion loss and is the reason for the excellent sensitivity of the
superheterodyne receiver of prior art. However, that sensitivity comes at a
price: loss of information in those radiation-target interactions in which the
Gaussian approximation of the noise statistics do not apply. The mixing action
is due to a nonlinear transfer function:
I=f(V)=a.sub.0 +a.sub.1 VG+a.sub.2 V.sup.2 +a.sub.3 V.sup.3, . . . a.sub.n
V.sup.n (1)
where I and V are the device current and voltage. If V.sub.RF sinw.sub.RF t is
the RF signal and V.sub.LO sinw.sub.LO t is the LO signal, then the mixing
products are:
I=a.sub.0 +a.sub.1 (F.sub.RF sin.omega..sub.RF t+V.sub.LO sin.omega..sub.LO
t)+a.sub.2 (V.sub.RF sin.omega..sub.RF t+V.sub.LO sin.omega..sub.LO t).sup.2
+a.sub.3 (V.sub.RF sin.omega..sub.RF t+V.sub.LO sin.omega..sub.LO t).sup.3, . .
. a.sub.n (V.sub.RF sin.omega..sub.RF t+V.sub.LO sin.omega..sub.LO t).sup.n (2)
The mixing action of receivers of prior art produces primary mixing products
which come from the second-order term. However, many other mixing products--the
intermodulation products--may be present within the IF passband. Mixing
produces not only a new signal but also its image, i.e., w.sub.LO .+-.w.sub.RF.
However, for broadband applications, especially for octave bandwidths,
filtering cannot be used for image rejection.
For example, the second-order term for a narrow band FD echo is:
a.sub.2 (V.sub.RF sin.omega..sub.RF +V.sub.LO sin.omega..sub.LO t).sup.2 ( 3)
but for a broad-band TD echo it is:
a.sub.2 (V.sub.RF1 sin.omega..sub.1RF +V.sub.RF2 sin.omega..sub.2RF +V.sub.RF3
sin.omega..sub.3F +. . . V.sub.LO sin.omega..sub.LO t).sup.2 ( 4)
The output is then:
.SIGMA..sub.ij V.sub.LOi sin.omega..sub.LOi tV.sub.RFj sin.omega..sub.jRF ( 5)
which possesses too many innermodulation products for use as an IF input.
Due to the broadband nature of the WP signal of the present invention, the
superheterodye receiver is the less preferred embodiment of TD signal receivers
of the present invention due to the number of mixing products produced. Another
reason for the superheterodyne design is less preferred is that information
about the target is lost. It has been conventional wisdom that the
supeheterodyne design and the homodyne design provide the same information
about the target--but this is only true for the assumption of a Gaussian
approximation of noise in radiation-target interactions. For pulses short with
respect to target dimensions, the Gaussian approximation is invalid. Therefore
there are also physical reasons for using homodyne receivers as a preferred
embodiment in the present invention.
A schematic representation of the two types of receivers--the FD receiver of
prior art and the TD receiver of the present invention--unburdened by
amplification methods, is shown in FIG. 35. The following definitions are taken
from optical physics (cf. Born and Wolf, 1970; Dummins and Pike, 1974), not
from radar engineering. Essentially, the heterodyne method requires a local
oscillator to be mixed with the scattered radiation; and the homodyne method is
a "self-beat" or autocorrelation method. The homodyne method is
inherently a coherent method (cf. Born and Wolf, 1970, page 256). The
heterodyne method of prior art can use autocorrelation--after the mixing
operation--but the signal acquisition and information loss has already occured.
The heterodyne method can even use a "coherent" local oscillator, but
only with a priori information and expectancies concerning target scattering. The
distinguishing feature between the two methods is that the homodyne method of
the present invention is a coherent (correlative) signal acquisition method
with no knowledge of the target (no a priori information) and the heterodyne
method of prior art is not.
[The various definitions of the heterodyne and homodyne methods are not
consistent. For example, the IEEE Standard Dictionary of Electronic Terms (Jay,
1988) defines "homodyne reception" as "zero-eat reception or a
system of reception by the aid of a locally generated voltage of carrier
frequency"; and the McGraw-Hill Dictionary of Science and Technology
(Parker, 1989) defines "homodyne reception" as "a system of
radio reception for suppressed-carrier systems of radio telephony, in which the
receiver generates a voltage having the original carrier frequency and combines
it with the incoming signal. Also known as zero-beat reception."
Essentially, these definitions refer to the generalized use of homodyning in a
receiver with more than one mixing stage. "Synchronous" detection is
achieved by a method called "homodyning", which involves mixing with
a signal for the same frequency as that being detected either by external or
internal (i.e., with a phase loop) methods. Thus, recently the term "homodyne"
has come to mean a method for the detection of narrowband signals and for
restoring a suppressed carrier signal to a modulated signal.
Clearly the waters have been muddied concerning the definitions of the
heterodyne and homodyne methods. However, the original optical physics
definitions are specific in equating heterodyning as a method of signal
acquisition using a local oscillator, and homodyning as a method of signal
acquisition using a coherent method such as autocorrelation. WP/TD signal
acquisition requires the homodyne method because it is a coherent method and
information preserving. It would not be right to coin new terms, because the
present terms live on relatively unambiguously in optical physics from whence
they came. Therefore, we shall use the terms in the optical physics sense of
those terms, but recognizing the danger of triggering the wrong associations.]
The Target-Receiver "Channel of Information"
If one views the target as a source of information about its characteristics
and a ladar/lidarradar/sonar receiver-processor as a receiver of that
information, then, in a sense, an informational channel exists between the
target and receiver-processor. The concept of an information-preserving
transformation is an ergodic transformation. From the point of view of
preserving information in this channel, i.e., from an ergodic transformation
point of view, it makes a great deal of difference whether a signal is
wideband, but of short duration, or wideband, but of long duration. That is,
two signals, of identical bandwidth, will convey different information
depending on differences in their duration. This difference is due to the
diffracting properties of the target being signal duration dependent, as well
as signal frequency bandwidth dependent.
Therefore, the information returned along the target-receiver channel is
different in the case of two signals .DELTA.f.sub.1 .DELTA.t.sub.1 and
.DELTA.f.sub.2 .DELTA.t.sub.2, even if .DELTA.f.sub.1 =.DELTA.f.sub.2 but
.DELTA.t.sub.1 .noteq..DELTA.t.sub.2. There are a number of reasons why use of
the signal of shorter duration but equivalent bandwidth should result in more
transmitted information. (We are not referring here to the well-known
time-bandwidth product relations in conventional radar, but to the physical differences
which occur in target diffraction and scattering when pulses short with respect
to target dimensions are used.) The most important one is that the use of a
short duration signal results in no interference between the resolved target
elementary scatterers, as the backscattering from each of the scatters arrives
at the receive antenna separated by definite intervals of time, whereas the use
of a longer duration signal results in the arrival of the backscattering from
all the elementary scatterers but without separation in time (cf. FIGS. 9A
& 9B). The use of a longer duration signal thus results in sampling and
aliasing problems.
The more information about the target that is transmitted to the receiver, the
more signal-to-noise gain--if that information can be accessed and displayed in
the power density spectrum. There are two ways of achieving that access, i.e.,
receiver-processor gain:
(1) Time scale conversion (Papoulis, 1965) is the process in which, by storing
samples of correlated signals and uncorrelated noise from repetitive probing of
the target, an increase in sampling rate an be achieved by repetitive sampling
of the stored returned signal. If F.sub.S and F.sub.G are the repetition
frequencies of the signal and gate (sampling) voltage for repetitive and
sequential non-real-time multiple sampling of the stored signal then a time
scale conversion factor, q, is defined:
q=F.sub.G /[F.sub.S =F.sub.G ]=F.sub.G /.DELTA.F (6)
Another way of defining F.sub.S and F.sub.G is: if .DELTA.t is the signal
duration and .DELTA.t is the duration of the sampling window, with repetitive
and sequential non-realtime multiple sampling of the stored signal, then
F.sub.S =1/.DELTA.t and F.sub.G =1/.DELTA.t.
The minimum value of q, q.sub.MIN, is:
q.sub.MIN =f.sub.0 (2+.DELTA.f..DELTA.t)/F.sub.G =2Q[(2/.DELTA.f..DELTA.t)+1]
(7)
where f.sub.0 is the signal average frequency; .DELTA.f..DELTA.t is the signal
bandwidth-duration product; and
Q=T.sub.n /.DELTA.t (8)
where T.sub.n is the interpulse interval in a repetitive train.
Reduction of the [F.sub.S -F.sub.G ] difference and multiple sampling achieves
an equivalent reduction in the sampling interval, .DELTA.t.sub.c. That is, by
sampling over .epsilon.T.sub.S intervals, where T.sub.S =1/F.sub.S and .xi.T.sub.S
=(.DELTA.t.sub.c /.DELTA.t)T.sub.S, the receiver gain is then:
.xi.=q/q.sub.MIN =.DELTA.t.sub.c /.DELTA.t=(S.sub.o /N.sub.o).sub.OUT /(S.sub.o
/N.sub.o).sub.IN (9)
(2) Increase receiver-processor initial sampling rate, .DELTA.t.sub.C, so that
q is initially large. This solution directly looks for increases in
receiver-processor real-time sampling speed without (non-real-time) time scale
conversion. FIG. 19 compares FD and TD signal processing concepts of prior art
and of the present invention.
Both methods (1) and (2) provide increased receiver-processor gain, .xi., which
accesses more information in a power density spectral representation.
Furthermore, the more detailed that representation, the greater the
signal-to-noise ratio, and the greater range to a maximum.
Ergodicity.
The word "ergodicity" is derived from the Greek words for
"work" and "path". The original ergodic hypothesis
concerning the sampling of a many phased system, was stated by J. C. Maxwell as
". . . the system, if left to itself in its actual state of motion, will
sooner or later, pass through every phase which is consistent with the equation
of energy."
It turned out, however, that a system cannot pass through every point of
space--therefore the quasi-ergodic hypothesis was adopted. This version states
that in a stationary ensemble of random functions produced by sources of
identical nature, and having a continuous range of values, the amplitudes of
the aggregate of elements of an ensemble member come infinitely close to every
point of the continuous range of possible values sooner or later, if the
ensemble member is allowed to take its natural course of fluctuation.
The ergodic hypothesis is relevant to characterizing the present invention in
two regards. Firstly, the quasi-ergodic hypothesis is sufficient justification
for the equivalence of time and ensemble averages. The autocorrelation function
for a time-domain, energy-differentiating receiver-processor is an ensemble and
time average of time domain events. The autocorrelation function for a
frequency domain, energy integrating receiver-processor is an ensemble and time
average of frequency domain events. A joint time-frequency autocorrelation
would be an ensemble and time average for both time and frequency events.
Secondly, a frequency domain surveillance surveillance system of prior art
detects but does not characterize the target. If the target is considered n
informational source (of its target characteristics) then a channel exists
between that source and the receiver. In the case of ideal frequency domain
surveillance, there is no rate of informational flow along that channel,
because the frequency domain approach is designed predominantly for detection
and ranging, but not characterization. If an ergodic transformation is an
information-preserving transformation, then the transformation from target to
receiver effected by an ideal frequency domain system is nonergodic. On the
other hand, i the case of time domain surveillance, the detailed characterization
of the target by mean of the information-rich time domain signal echo,
indicates that the transformation from target to receiver effected by an ideal
time domain system is information-preserving, and therefore is an ergodic
transformation.
That is not to say that using multiple frequency FD signals of prior art
provides some target information. Rather, it is to say that the signals of the
present invention provide more information and that information is more readily
accessible (i.e., there is a difference in degree and accessibility).
Antennas
The pulse response of a linear aperture or antenna is angle of incidence
dependent When the pulse is of short enough duration, i.e., less than the
"fill-time" of the antenna, the response consists of two delta functions
of opposite signal. The delta function responses are due to two local centers
at the end of the antenna. When such centers are isolated on an antenna due to
the shortness of the pulse duration, the familiar FD lobe pattern of the
angular dependence of the radiated field no longer exists.
The dependence on angle of incidence produces difficulty in matching emit and
receive antennas. The pulsed antenna must also possess a well-defined phase
center if dispersion is not to occur. If the antenna differentiates on transmit
and receive, the baseband signal will undergo two differentiations on the round
trip from transmitting systems to target and back. Using sinusoidal signals the
double differentiation will only show as a phase shift, but using pulse signals,
the envelope will be severely distorted. When using pulse signals, the response
of radiators in the radiating and receiving modes are not identical as they are
assumed to be when using FD signals of prior art. Due to the difference in
coupling: conductor to field for a transmit antenna,
field-at-an-angle-of-incidence to conductor for a receive antenna, the transmit
and receive antennas only obey the reciprocity principle when phased matched.
The transmit antenna performs the negative of a Hilbert transform on the input
baseband signal, and the receive antenna performs a positive Hilbert transform,
i.e., under both operations the signs of the signal is reversed. This amounts
to the antenna acting as a quadrature filter for which the only realistic, or
causal, signals are analytic signals (FIG. 36).
Another way to look at this is to consider the phase center of the antenna to
locate an imaginary time, t=0. Thus the analytic signal amounts to a
transmittance with positive, but no negative, phase lag. Then if the antennas
are not "matched", an antenna that does not distort when radiating,
will integrate when receiving. Conversely, an antenna that does not distort
when receiving, will differentiate when radiating.
Preferred embodiments of the present invention include the use of nondispersive
TEM horn antennas or nonresonant antennas (Tseng and Cheng, 1964).
Target Reflecting Characteristics: Primary, Secondary and Tertiary Diffraction
In conventional FD radar of prior art, a target is considered to be a point
scatterer. That is, the target as a scattering object is viewed as if
satisfying boundary conditions simultaneously and globally. This treatment
contrasts with that offered by WP radar of the present invention, for which the
target can be viewed as a collection of local elementary scatterers. The WP
scattered field at an arbitrary point depends on the pulse excitation only
within a space-time volume called a light cone. Thus the characteristics of
targets are decomposed into local elementary scattering responses which can be
described by superposing components of Green's functions that correspond to the
local scattering centers on those targets.
Three distinct components can be discerned in the frequency response of targets
(FIG. 11): the high frequency or optical component, the resonance component and
the Raleigh or low frequency component. The first, the optical component,
corresponds to a reflected field; the second and third, correspond to
diffraction fields. Whereas the diffraction component penetrates into the
shadow region of a target, the optical component does not.
The distinctive behavior of these field components can be studied on a model
edge diffracting problem. The situation studied is the diffraction of the
incident field on the edge of a conducting screen or wedge viewed as a linear
filter formed by the edge of the screen in two-dimensional space (the
Sommerfeld problem or the problem of boundary waves in diffraction theory). In
the case of a WP signal, i.e., a signal with a fast rise time, there is a
dependence of the diffraction component of the scattered field on the time
after the leading edge of the diffracted wave passes. This temporal dependence
is exhibited for both the light and shadow region of the conducting wedge. In contrast,
the temporal dependence is not exhibited by long duration, low frequency FD
signals of prior art.
Minimum Received Energy for: Detection; Processing and Target Characteristic
Extraction
In the case of FD processing of prior art, the detection process is based on
the assumption of discontinuities which rigger an intensity threshold.
Therefore FD processing is based on the detection of local temporal properties
of a function defining the signal echo. In the case of the TD processing of the
present invention, on the other hand, the informationally-rich return echo is
in the form of an analytic signal, with characteristic envelope, phase and
frequency. An analytic function does not possess discontinuities and is
therefore not deterministic or causal. Rather than detecting a discontinuity,
WP systems register, monitor or model a continuous process. That continuous
process is a power density spectrum.
The continuous power density spectrum registers a model of the target up to a
maximum set by the sampling speed or receiver gain and limited by the target
dimensions. Thus the minimum signal-to-noise ratio for WP systems is set in
two, not one, ways: pulse energy and receiver gain.
In order to extract target characteristic information, the pulse duration is of
consequence. Therefore the energy required for setting the signal-to-noise
ratio must be delivered within a set time, i.e., high average power is
required. However, the statement that high pulse average power is required is
ambiguous, because high power can be obtained either by increasing energy (J)
at constant pulse duration, or by decreasing the pulse duration with energy
held constant. The pulse duration will be determined by the dimensions of the
target whose characteristics are to be probed. Therefore due to the ambiguity
in power units (J/s) aforementioned, the goal is to obtain sounding pulses of
maximum energy and duration commensurate with target dimensions.
The processing of data from a spectral representation of the target for
recognition purposes is bounded by the following considerations. Firstly, the
transformation of such data is an ill-posed problem (Tikhonov and Goncharsky,
1987). An ill-posed problem is one in which the solution is unstable with
respect to small changes in initial conditions, or a unique solution to the
problem does not exist, or no solution to the problem exists. Such problems are
handled computationally by associative processors, e.g., neural nets.
Secondly, whereas processing of the early time or optical response must account
for its target aspect-dependence, processing of the late time response must
account for its aspect-independence with respect to form. Singularity expansion
methods for processing the input into pole-sink complex resonance form are of
assistance with the latter. Both response components require highly parallel
processing architectures to handle the processing rate required.
Thirdly, inverse scattering transformations are involved with the processing
for target imaging and these methods will require highly parallel processing
architectures.
Comparison of frequency domain signals of prior art and wave packet signals of
the present invention
There are major conceptual differences between the treatment of FD and WP
signals. In the case of FD signals of prior art, local time methods relate the
signal envelope to its spectrum. In the case of WP signals of the present,
global or real time methods relate the signal's fine structure to its spectrum.
The concept of noise is also interpreted differently. If a decreasing sampling
temporal window causes a large noise bandwidth in the frequency domain, that
increase in noise in the frequency domain is of no consequence if the receiver
processing is conducted in the time domain.
In the case of FD narrow band sinusoidal signals of long duration, .DELTA.t,
any point of discontinuity, .delta.t, e.g., at the beginning and end of the
signal, is small compared with the duration .DELTA.t. For such signals, local
time methods, relate the global nature of the signal, i.e., its envelope, to
its spectrum. This procedure is followed in Fourier analysis, as well as in
Taylor series and other expansions.
In contrast, in the case of WP pulse signals, any point of discontinuity, dt,
is large or of the same order compared with the signal duration .DELTA.t.
Therefore WP signals must be treated differently using real time methods to
preserve the local nature, or fine structure, of the signal. Periodic, or
aperiodic (transient), i.e., FD approaches to WP signal processing, cannot be
used due to the fact that for SP signals: .delta.t.apprxeq..DELTA.t. The
implication of this is that WP signals and their derivatives do not possess
discontinuities, indicating their analytical signal properties. Analytic
signals are not deterministic or causal but are continuous and require local,
or real time methods for characterization. Whereas the FD signal is
characterized by its harmonic frequency, the WP signal is characterized by its
instantaneous frequency.
The required signal referent for a WP/TD receiver is not the frequency (phasor)
referent of FD receivers of prior art. With w as the radian frequency of a wave
and s the phasor, or neper, frequency defining the envelope shape, a complex
signal is:
s.sub.0 =.sigma.The 0+i.omega..sub.0 (10)
and an analytic signal (also known as the preenvelope function) is (Papoulis,
1965):
(t)=S(t)+iS(t)=exp[s.sub.0 =A(t)exp[i.omega..sub.0 t+.phi.t]=exp[i.omega..sub.0
]exp[.sigma..sub.0 ] (11)
with real part
S(t)=exp[.sigma..sub.0 ]cos.omega..sub.0 t (12)
and imaginary part:
S(t)=exp[.sigma..sub.0 ]sin.omega..sub.0 t (13) ##EQU1##
Therefore, S(t) can be considered the output of a quadrature filter with input
S(t). The quadrature filter has an impulse response:
h(t)=1/(.pi.t)
and system function:
H(i.omega.)=-i, .omega.>0; i, .omega.<0
The envelope of a wave packet (also known as the absolute-value of the
preenvelope) is defined as:
envS(t)=exp[.sigma..sub.n ]=.sqroot.[S(t).sup.2 +S(t).sup.2 ](14)
and the carrier, average or midfrequency is defined as:
exp[i.omega..sub.n ]=[S(t)+iS(t)]/[.sqroot.[S(t).sup.2 +S(t).sup.2 ]](15)
For example, suppose
S(t)=A(t)cos.omega..sub.0 t,
then using the Hilbert transform the analytic signal is:
(t)=A(t)cos.omega..sub.0 t+iA(t)sin.omega..sub.0 t (16)
and the envelope of S(t) is:
envS(t)=exp[.sigma..sub.n ]=.sqroot.[(A(t)cos.omega..sub.0 t).sup.2
+(A(t)sin.omega..sub.0 t).sup.2 ]=A(t) (17)
Now the power spectra are defined:
.PHI.SS (.omega.)=.PHI..sub.SS (.omega.)H(i.omega.)=-i.PHI..sub.SS (.omega.),
.omega.>0; =i.PHI..sub.SS (.omega.), .omega.<0 (18)
Therefore:
.PHI. (.omega.)=2[.PHI.SS(.omega.)+i.PHI..sub.SS (.omega.)]=2.PHI..sub.SS
(.omega.), .omega.>0; =0.omega.<0 (19)
The relation expressed by Eq. (19) is the ultimate reason for using analytic
signals rather than complex signals in the time domain. The issue of causality
for random continuous signals dictate that the power density spectrum be zero
for negative frequencies. The analytic signals--together with the Hilbert
transform--permits this condition to be met. The use of the complex signal
(i.e., with real and imaginary part) or prior art does not, and therefore is
not suitable for use in the time domain. Causality conditions require that
inverse transforms must be zero for negative t and have to be met in order to
preserve the information i the signal (cf. Papoulis, 1962, p. 213). If the real
and imaginary parts of a Fourier integral of a function (t) satisfy the Hilbert
transform relations, ther (t) is causal.
FIG. 20 shows representations of a continuous wave (FIG. 20(A)), a wavepacket
envelope function (FIG. 20(B)), and two wave packets (FIG. 20(C) & 20(D)).
A radian frequency phasor representation is sufficient to describe a continuous
wave (FIG. 20(A)), and a neper frequency phasor is sufficient to describe the
envelope of a wave packet (FIG. 20(B)). However, a complex plane representation
of the complete wave packet (FIG. 20(C)), and a complex analytic signal
representation (FIG. 20(D)), are both nonstationary, whereas the representation
would be stationary (pointlike) for a continuous wave.
System Noise
There is a dual relation between noise in the time domain and noise in the
frequency domain, when an ideal time domain processor is used. Correct analysis
of time domain noise bears on the receiver gain. Considering the conventional
FD treatment of noise, the noise figure, F.sub.n, is defined: ##EQU2## where
F.sub.n is independent of receiver gain. The only noise in the output of an
ideal receiver would be that received from external sources. This is
represented by thermal agitation in a resistor and the thermal noise is spread
over the the entire frequency spectrum. Therefore the amount of noise appearing
in the output of an ideal receiver is proportional to the absolute temperature
of the resistor connected across its input terminals times the width of the
band of frequencies passed by the receiver--the receiver bandwidth.
The mean noise power of an ideal FD receiver of prior art is:
P.sub.IR =kT.sub.0 B.sub.R (21)
where k is Boltzmann's constant (1.38.times.10.sup.-23 Watt-sec/.degree.K.);
T.sub.0 is .degree.K., usually taken to be 290.degree. K. so k.sub.T.sub.0
becomes 4.times.10.sup.-21 Watt-sec/.degree.K.; and B.sub.R is the width of the
band of frequencies passed by the receiver (Hz).
Thus the noise mean power of a FD receiver of prior art is:
P.sub.AR =F.sub.n kT.sub.0 B.sub.R (22)
This equation includes both an estimate of external noise and internally
generated noise. Although internal noise predominates, it can be reduced
somewhat by adding a low noise preamplifier ahead of the receiver's mixer stage
and using a low noise mixer.
The total system noise is equipment noise+transmission line noise+antenna
noise. Combining these, the mean noise power for all sources is:
P.sub.AS =kT.sub.S B.sub.R (23)
where T.sub.S is the equivalent noise temperature.
To distinguish signal from noise one may either express these in terms of
energy ratios or power ratios, but if one uses power ratios, then the signal
duration must be given. Conventionally, the mean noise energy is given by:
E.sub.AS =kT.sub.S B.sub.R t.sub.n (24)
where t.sub.n is the duration of the period in which a return may be received
from any one resolvable increment of range, i.e., it is the temporal sampling
bin.
Conventionally, i.e., in the frequency domain, the noise can be reduced by
minimizing the receiver bandwidth, B.sub.R. The optimum bandwidth is:
B.sub.R %32 1/.DELTA.t (25)
where .DELTA.t is the pulse width. However, in the case of a time domain
receiver of the present invention, Equ. (24) permits another way of reducing
the noise: by reducing t.sub.n. For noise reduction:
In frequency frequency domain processing of prior art the temporal sampling bin
remains constant and the frequency bandwidth is reduced.
In the time domain processing of the present invention, on the other hand, the
frequency bandwidth remains constant but the temporal sampling bin is reduced.
Substituting (25) into (24) gives:
E.sub.AS =kT.sub.s t.sub.n /.DELTA.t (26)
Now B.sub. is conventionally defined as: the width of the band of frequencies
passed by the receiver. Therefore B.sub.R defines the band of frequencies which
are passed or acquired by the receiver. B.sub.R is not the sampling bandwidth,
which we shall label B.sub.S. From time domain point of view, Equ. (24) can be
defined as:
E.sub.AS =kT.sub.S B.sub.R /B.sub.S (27)
Returning to the FD analysis of prior art: the passband of, e.g., a Doppler
filter, is approximately equal to 1/t.sub.int, where t.sub.int is the
integrating time of the radar return, and, or course, the noise. According to
the conventional FD analysis, t.sub.int can be substituted for t.sub.n, and
1/t.sub.int for 1/.DELTA.t. Using these substituents in Eq. (26) and canceling
gives:
E.sub.AS =kT.sub.S, (Doppler radar) (28)
However, from the WP/TD perspective of the present invention, and with respect
to a time domain receiver, these substitutions and Eq. (28) are incorrect. The
duration of the pulse is not the duration of the temporal sampling bin.
Referring to the FIG. 21, Eq. (28) is valid for the first two cases, but for
the third case, which is the genuine time domain case, these substitutions are
incorrect.
Signal to Noise Ratios
In the case of frequency domain signalling of prior art and using a frequency
domain receiver of prior art, it is well known that narrowing the frequency
bandwidth around the signal decreases the noise. Alternatively, increasing the
frequency bandwidth increases the noise. However, this rule of thumb cannot be
extrapolated to the WP/TD domain. In the case of an ideal time domain receiver,
although decreasing the temporal sampling window increases the frequency
bandwidth window, noise in the time domain is not increased thereby (on the
contrary, it is decreased). Increasing the noise in the frequency domain is
immaterial to ideal time domain processing. (The converse observation is:
narrowing the bandwidth in the frequency domain, when using a frequency domain
receiver, increases noise in the time domain. But this is of no consequence if
the processing is carried out in the frequency domain). Thus, in the case of
ideal time domain processing, narrowing the temporal sampling window decreases
time domain noise.
These observations on the duality of frequency domain and time domain nose are
precisely mirrored in the phenomenon of "squeezed states" in optical
physics. Precision in the momentum, q, results in imprecision in the position,
p, and vice-versa, due to the p.q uncertainty product. Similarly, the signal of
conventional radar has gained precision by narrowing .DELTA.f and by
broadening, or placing the noise, in .DELTA.t, due to the .DELTA.f..DELTA.t
uncertainty product. The signal of time domain radar, on the other hand, gains
precision by narrowing .DELTA.t, and by broadening, or placing the noise, in
.DELTA.f, again, due to the .DELTA.f..DELTA.t uncertainty product. This
analysis applies to both ideal frequency and ideal time domain receivers. It
would not apply to a hybrid receiver which straddles both frequency and time
domains and which would accept noise from both modalities. Such a hybrid
receiver would not be optimized in either domain and its functioning level
would be determined by tradeoff in performance in those domains.
WP/TD Radar Performance Equation
Assume the transmitter and antenna radiates P.sub.t watts of power and the
energy is radiated isotropically (omnidirectionally). This means that the
source of transmitter and antenna is a point source. The power density per unit
area at a distance R from the target is found by dividing the total power,
P.sub.t, on the surface of an imaginary sphere, centered at the point source,
by the total surface area, 4.pi.R.sup.2.
Therefore, at a range, R, from the target, the power density is:
Power density=P.sub.t /4.pi.R.sup.2 W/m.sup.2 (29)
With replacement of the omnidirectional antenna with a directional antenna with
a power gain, G.sub.t, a directional beam of energy is produced. The power
density within the beam at range R is then:
Power density with antenna gain=P.sub.t G.sub.t /4.pi.R.sup.2 W/m.sup.2 ( 30)
Now, if a target is located within the directed beam at a range R from the
source, some of the energy will be reflected (backscattered) in the direction of
the source. The amount of energy reflected back is determined by both the power
density at the target and the target's backscatter radar cross section, s,
defined as 4.pi. times the ratio of the power per unit solid angle reflected by
the target in the direction of the source to the power per unit area of the
incident wave at the target, or:
.sigma.=4.pi.[{P.sub.b /4.pi.}/{P.sub.t /4.pi.R.sup.2 }]=4.pi.R.sup.2 [P.sub.b
/P.sub.t ]m.sup.2 (31)
where [1/4.pi.]P.sub.b is the power per unit solid angle reflected in the
direction of the illuminating source. Therefore, the power per unit solid angle
reradiated in the direction of the source is:
Power reradiated toward source.times.P.sub.t G.sub.t .sigma./[4'].sup.2 R.sup.2
W/steradian (32)
The power density of the backscattered wave arriving back at the source will
then be:
Power density of reflected wave arriving before source=P.sub.t G.sub.t
.sigma./[4.pi.].sup.2 R.sup.4 W/m.sup.2
The effective capture area and gain of a receiving antenna is:
G.sub.r =r.pi.A.sub.e /.lambda..sup.2 (34)
Therefore the power received back at the source for processing, P.sub.t, is:
Power received: P.sub.r =P.sub.t G.sub.t G.sub.r .lambda..sup.2
.sigma./[4.pi.].sup.3 R.sup.4 W (35)
The system loss factor at 290.degree. K. is:
F.sub.n =N.sub.o /N.sub.i ]/[S.sub.o /S.sub.i ]=(SNR).sub.i /(SNR).sub.o ( 36)
where SNR is signal-to-noise ratio.
The thermal noise at the receiver is:
N.sub.i =kTB (37)
where B is the receiver bandwidth. If L represents all signal losses, both
external and internal to the radar, and if A represents the receiver signal
power gain, then:
S.sub.o =AP.sub.r /L; N.sub.o =AF.sub.n kTB; (S.sub.o /N.sub.o)=P.sub.r
/LF.sub.n kTB (38)
Expanding the last expression, we obtain:
(S.sub.o /N.sub.o)=P.sub.t G.sub.t G.sub.r .lambda..sup.2 .sigma./[4.pi.].sup.3
R.sup.4 LF.sub.n kTB W/W (39)
The maximum detection range is then:
R.sub.max =[P.sub.t G.sub.t G.sub.r .lambda..sup.2 .sigma./[4.pi.].sup.3
LF.sub.n kTB(S.sub.o /N.sub.o).sub.min].sup.1/4 m (40)
Substituting for the receive aperture gain, gives:
R.sub.mawx =[P.sub.t G.sub.t A.sub.e .sigma./[4.pi.].sup.2 LF.sub.n kTB(S.sub.o
/N.sub.o).sub.min ].sup.1/4 m (41)
Defining this maximum range in terms of energy-on-target requires insertion of
the signal duration, .tau., explicitly in the numerator (to give P.sub.t .tau.
(W.times.time=E)), and implicitly in the S.sub.o /N.sub.o term of the
denominator (to give {W.times.time}/{W.times.time} or dimensionless number):
R.sub.max =[P.sub.t G.sub.t A.sub.e .sigma..tau./[4.pi.].sup.2 FL.sub.n
kTB(S.sub.o /N.sub.o).sub.min ].sup.1/4 m (42)
If coherent integration occurs over time, t.sub.0, the total transmitted
energy, P.sub.T t.sub.0, replaces P.sub.t t in the above expression.
In the case of WP/TD systems this equation is modified to account for the
receiver gain possible with higher sampling speeds. In FD analysis, the
important parameters affecting range are the total transmitted energy, the
transmitter gain, the effective receiving aperture and the receiver noise
figure, but not receiver gain. If q is the signal-to-noise ratio of the summed
signal (and the signal is coherently summed and the noise incoherently):
q=P.sub.SIGNAL /P.sub.NOISE (43)
then q.sub.MIN is the signal-to-noise ratio of the sampling window:
q.sub.MIN =(P.sub.SIGNAL /P.sub.NOISE).sub.MIN (44)
The ratio (Eq. 32, above):
.xi.=q/q.sub.MIN (45)
gives a receiver gain (at set wave packet duration) due to an increase in power
spectral density characterization of the target. With total transmitted energy,
E.sub.t =P.sub.t t, the radar equation for WP/TD systems is then:
R.sub.max =[E.sub.t G.sub.t.sigma.A.sub.e.xi./[ 4.pi.].sup.2 (S.sub.o
/N.sub.o).sub.min F.sub.n LkTB].sup.1/4 m (46)
and this equation is identical to the radar range equation for FD systems when
the ratio .xi.=1. However, despite this formal similarity, the interpretations
of the WP/TD and FD equations are quite different.
For example, there is a reciprocal relation between pulse duration and processing
speed, given the characteristic geometric dimensions of the target, a,
addressed. For example, a ratio, K:
K=a.sub.MAX /a.sub.MIN (47)
where a.sub.MAX is target maximum length and a.sub.MIN is target minimum
length, defines the target fine structure. Suppose the spatial extent of the TD
wave packet addressing the target is the length of the target. If K=1, then no
increase in .xi. (the receiver gain commensurate with K) will achieve greater
resolution because the target cannot be resolved into elementary scattering
components. If K=2, however, then greater target resolution and greater range
can be achieved either by a decrease in the sampling by a half or by decreasing
the duration of the signal by a half. Thus for maximum target characterization
and maximum range:
K/.xi.=1 (48)
must be achieved, and, as stated, this can be accomplished in two ways: either
by decreasing the duration of the signal, or by a decrease in the duration of
the sampling window.
In the range plots, below, processing gain is assumed possible, i.e., K>1,
and this optimum condition is assumed achieved. It should also be noted that
the pulse duration (t) does not appear in the WP/TD range equation above. This
is due to the target-sampling speed information rate reciprocity relation
aforementioned. As stated, for a set K>1, greater range can be obtained at
set energy either by decreasing the packet duration or by deceasing the
sampling window (increasing sample speed). Thus the variable .xi. is a function
of both:
.xi.=.tau./.tau..sub.s, .tau..sub.s .ltoreq..tau. (49)
where t is the pulse duration and t.sub.s is the sampling window duration.
Combining the above equations, maximum processing gain can be obtained to a
maximum given by:
K/.xi.=[a.sub.MAX /a.sub.MIN,].[.tau..sub.s /.tau.]=1, .tau..sub.s
.ltoreq..tau. (50)
In terms of ranging and detection, this definition of .xi. is satisfactory. In
terms of target characterization and imaging, however, this definition does not
do justice to the two situations of (for K>1): (1) decreasing the pulse
duration at set sampling window duration, and (2) decreasing the sampling
window at set pulse duration. In the case (1), the higher order diffraction
components of the target will be separated in the reflected signals from the target,
but the receiver will not be able to distinguish between them. In the case of
(2), the receiver can distinguish signals of the temporal order of the higher
order diffraction components, but those components will not exist in the single
signal reflected from the target due to the signal-target size ratio.
The maximum ranges obtained at increasing packet energy at various values of
.xi., are shown in FIG. 30A. The following representative values were used:
G.sub.t =47 db; A.sub.e =1 m.sup.2 ; .sigma.=0.1 m.sup.2 ;
kT=4.times.10.sup.-21 ; F.sub.n =3 db; L =4 db; (S.sub.o /N.sub.o).sub.min =13
db. The effective aperture, A.sub.e, used here does not behave in a manner
similar to that of an aperture for frequency domain signals.
The conventional FD radar performance baseline is shown as .xi.=1. Thus the
only difference between FD and TD systems is in the value of .xi., which is set
to unity for an ideal FD system. Given any amount of receiver gain (.xi.>1),
a WP/TD system will perform better than an FD system for equivalent transmitted
pulse energy. Given no amount of receiver gain (.xi.=1), a WP/TD system will do
as well as an FD system in terms of ranging for equivalent transmitted pulse
energy.
If the transmitted pulse is limited in total average energy to 2 H (over the
pulse duration .DELTA.t) and return signal averaging and a timed array are not
used, then a receiver gain of .xi.=10, still results in almost a doubling of
the range (FIG. 30B).
Detection and imaging in signalling systems of the present invention
Signalling systems of the present invention encompass two modes of functioning:
the detection (D) mode or (emission and reception) matched filter mode and the
imaging (I) mode. The D mode is equivalent to the a priori procedure previously
described and the I mode is equivalent to the a posteriori procedure. The D and
I labels accent the two functions offered signalling systems of the present
invention, rather than the procedures.
In the case of the D mode, the WP pulse emitted is matched to the target. If
the target's transfer function is ideally orthogonal, or, more generally,
relatively orthogonal to the transfer function of the designated non-target,
i.e., clutter, then the signal returning from the target, or echo, contains
more target components than clutter, or noise, components. Therefore the
signal-to-clutter or signal-to-noise increases by using the D mode (FIG. 26).
The amount of signal-to-noise increase will depend on the relative
orthogonality of target and clutter. The example of FIG. 26 exhibits a
"man-made" object as target and natural objects as clutter. The
signal-to-noise enhancement by systems of the present invention is expected to
be high. In other situations, e.g., between different man-made objects, the signal-to-nose
enhancement is expected to be less.
The polarization properties (characterized by the phase, .phi., of the
radiation), and the polarization property changes over time, d.phi./dt, of the
target versus clutter are also an important distinguishing feature which is
addressed in the D mode of functioning.
In the I mode of functioning, the signal echo return is not a unity (moncycle)
or near unity response, but rather contains the complete response of both
target and clutter to an interrogating WP pulse which is broadly defined in
both time and frequency domains. The primary, secondary and tertiary
diffraction components of the target are not simultaneously received, but are
received sequentially in time (FIG. 10). Therefore in the I mode of functioning
there is a departure from Kirchhoff's diffraction law as normally conceived.
If the returning echos from the target are received by a collection of antennas
which preserve the spatial as well as the timing separation of those echoes, it
is possible to form an image of the target using only one interrogating WP
pulse emission. Prior art systems require more than one emission, i.e.,
bistatic operation. If a frequency swept signal of prior art is used the
duration of that signal is still longer than the target length. Therefore the
returning echo is characterized by frequency and phase components. The phase
components are modulo measures (modulo 360 degrees), and therefore ambiguous.
Whereas frequency sweeping signals of prior art characterize the target in terms
of frequency, polarization and the modulo measure: phase, signals of systems of
the present invention characterize the target in terms of the absolute timing
of the separation of the returns from the target's individual scatterers, as
well as instantaneous phase, instantaneous frequency, instantaneous amplitude
and instantaneous polarization. Therefore an additional dimension of
information: absolute time of return from target individual scattering
components is available to systems of the present invention and which is
unavailable to systems of prior art. It is critical to the operation of
signalling systems of the present invention that the WP pulse length be less
than that of the target to be imaged.
In the I mode of functioning, the signalling system functions to decompose the
target response into individual scattering elements, and there will be the
three kinds of target responses shown in FIG. 11 for each individual target
scatterers.
The D mode provides range and "selective attention" for targets by an
increase in signal-to-noise or target-to-clutter. However, the D mode function
does not provide target identification, characterization and imaging. Therefore
characterization or verification of the target's identity class needs to be
performed in any continuous system target identification. In FIG. 27 is shown a
representative interaction of a signalling system of the present invention with
a target in which the target is approaching the system. Alternative switching
between D and I modes provides target identification and characterization, as
well as detection and tracking.
In the case of the D mode of functioning, a signalling system of the present
invention need not be matched to a single target, but to a class of targets,
i.e., a WP is used which addresses the features of a class of targets. In
another embodiment of the present invention, a series of WPs can be used which
address a series of target classes.
Hardware representation of WP
crafting in signalling systems of the present invention at RF
In a preferred embodiment at RF, and in the D mode of functioning of signalling
systems of the present invention, the WP signal matched-to-target is obtained
in the following way. Referring to FIG. 37A, a laser pulse is emitted from,
e.g., a diode laser strip array, or from a laser. The light pulse is passed
through a Pockel's cell which may be computer controlled to condition or craft
the light pulse into WP form and matched-to-target in fine structure, but not
in duration. The WP, which has the required fine structure, is then passed
through a compressor, e.g., a grid formation, an optical fiber, which
compresses the optical pulse to the desired temporal length (e.g., picoseconds
in length and above). This optical WP is then handed-off (FIG. 37B) to a
light-activated switch (Loubriel and Zutavern, 1992).
In one embodiment of the present invention, the optical WP, which is
matched-to-target in terms of fine structure and temporal length but for RF
wavelengths, is then passed to a linear light-activated-switch which serves as
a trigger to an RF launch system. One embodiment of such a system is shown in
FIG. 37B. The linear switch, composed, e.g., of oxygen-treated silicon, diamond
or any other semiconductor material, has a high quantum efficiency and a
recombination time such that the RF WP output from the device follows
faithfully the fine structure and duration of the WP triggering signal.
Therefore the RF WP pulse will possess the fine structure and temporal duration
of the triggering optical WP pulse.
This suggested embodiment of the present invention is different from methods
for obtaining signal crafting of prior art. One method of prior art is called
frozen Hertzian wave (FHWG) generation (Cronson, 1975; Proud and Norman, 1978;
Mathur, et al, 1982; Chang et al, 1984), which is an attempt to craft the fine
structure of a pulse but in the RF, rather than in the optical with hand-off to
RF following. The FHWG is dependent on the simultaneous triggering of multiple
switches all of which avalanche switch and without optical trigger following. A
representative description in Weber-Hermite form of the fine structure required
to match a target is exhibited in FIG. 15.
Other methods of crafting WPs matched-to-target which would express the methods
of the present invention are: arrays of emitters individually addressed;
modulation programmed free-electron laser wigglers/undulators; and controlled
and modulated spark-gap RF generators. The same principles of the present
invention apply whether the signalling system is an RF/lidar/ladar of a sonar
sensor.
Wavelets and coding in signalling systems of the present invention
The WP signals of the present invention are defined in time-frequency space.
Due to this time-frequency representation and their affine properties, the WPs
of the present invention are also wavelets. The WP signals of the present
invention also provide the capability of sampling the target at a heirarchy of
levels (FIG. 14), e.g., for levels n=0, 1, 2, 3, . . . These WP signals are
also physical solutions to a wave equation describing energy propagation in a
medium or media.
The same form of the WP representation can be given to signals, target and
receivers, i.e., any part of the total signalling system as represented
schematically in FIG. 1. and, e.g., as exhibited for a target receiver in FIG.
34. A sample wavelet (an ambiguity function) representation of a single
frequency pulse is shown in FIG. 12A, of a linear FM pulse in FIG. 12B, of five
coherent single frequency constant amplitude pulses in FIG. 12C, of a length-7
Costas-coded signal in FIG. 12D. Each of these figures can also be considered
to represent some target transfer characteristics. An object of signalling
system of the present invention (in the D mode of functioning) is to craft a
pulse which exactly matches the transfer characteristics of the target (FIG.
13).
The WP signal of the signalling system of the present invention can be matched
to the target with respect to the instantaneous frequency, instantaneous phase,
instantaneous amplitude and instantaneous polarization of the impulse response
of the target. FIG. 23 exhibits a monocycle WP and its decomposition into
instantaneous energy and phase characteristics.
Comparisons of signalling systems of prior art with signalling systems of the
present invention
There are many examples of signalling systems of prior art using matched
filtering (Moffatt and Mains, 1975; Van Blaricum and Mitra, 1978; Kennaugh,
1981; Kim et al, 1985; Rothwell et al, 1985; Chen et al, 1986; Kennaugh et al,
1986; Rothwell et al, 1987; Fok & Moffatt, 1987; Morgan, 1988). However,
the embodiment of the matched filtering concept by signalling systems of prior
art is a software and receiver expression (cf FIG. 1 and 24A). The signal of
prior art is not modified to match the target (FIG. 24A). So the matched
filtering of the receiver in signalling systems of prior art is on the basis of
a signal echo return from target which is the response of an emitted signal may
not optimally interact with the target, and, in some instances, may even more
optimally interact with the clutter. The example of prior art exhibited in FIG.
24A indicates the lack of adaptive control between the source technologies and
the receive technologies.
In contrast, FIG. 24B exhibits a signalling system which is configured
according to the present invention, and which exhibits a complete hardware and
software embodiment of matched filtering, in which the source and receiver
technologies are joined by adaptive control and the target response is
configured within that control and transmission channel, and the clutter is
adaptively configured out of the transmission channel inasmuch as it is
possible to do so. Signalling systems of prior art and the present invention
are contrasted in FIG. 25A. In the conventional, or prior art, signalling
system, FIG. 25A(A), the antenna is used as a point source of radiation. In the
signalling system of the present invention, FIG. 25A(B), the antenna is used as
a matched source. A signalling system configured according to the present
invention also has two modes of functioning: the I or imaging mode (FIG. 25B(A)
and the detection or D mode (FIG. 25B(B).
Other comparisons with prior art are:
(1) Prior art refers to a time-bandwidth product. In contrast, with signalling
systems of the present invention the range capability is a function of both the
energy as well as the receiver gain and the target velocity detection is a
function of the interpulse interval change. Thus there need be no reliance on
Doppler (a frequency-dependent measure), but ate-of-change-of-range (an
absolute time-dependent measure) determined by the interpulse interval change
of a train of WPs. Ther e is thus no time-bandwidth product to address with
signalling system of the present invention, but rather, a gain-bandwidth
product, where the gain is the receiver gain.
(2) Prior art uses a time-frequency description, the ambiguity function, but
the ambiguity function is used to address the range-Doppler plane. As stated in
(1), the range-Doppler trade no longer is applicable for signalling systems of
the present invention, so this interpretation of ambiguity function no longer
applies for signalling systems of the present invention. The ambiguity function
when used in the context of the present invention refers to the target's
frequency and time scattering response, i.e., target identification.
(3) Prior art treats the target as a point target. In the case of signalling
systems of the present invention, the target is not a point target but a
complex scatterer composed of elementary scattering components. The crafting of
the WP signal either interacts with all of these components (the I mode) or is
matched to these complex frequency-time scattering components (the D mode). In
prior art signal optimization means optimizing the signal to give the best
range-Doppler--and there is the implicit assumption in prior art that the
target scattering is either optimized or cannot be. In signalling systems of
the present invention, the scattering from the target is optimized, then the
range and rate-of-change-of range are separately optimized. Therefore, in the
case of signalling systems of he present invention there is no ambiguity between
obtaining range and rate-of-change-of-range. The ambiguity or trade of
signalling systems of the present invention is that between resolution of
target scattering components (target i.d.) and range, i.e., target
characterization and target range.
The use of the concept of matched filtering used by signalling systems of prior
art is different from that used by signalling systems of the present invention.
For example, Spafford (1968) and Stutt & Spafford (1968) describe
processing methods for distinguishing signal from noise, i.e., an optimum
filter design. However, the signal described is general and nonoptimum for
target scattering and modifying the signal to match the target is not
considered. Adaptive signal processing refers, in prior art, to a system that
continually adjusts its parameters in the course of time to meet a certain
performance criterion which is the maximization of the signal-to-interference
ratio, but without signal modification.
The ambiguity function diagram is a general mathematical technique used to
describe the target illuminating signal. Therefore, the ambiguity function
diagram for the scattered return from a particular target is a valid
description only with respect to the particular probing signal used. The target
sensed by a signalling system of the present invention can also be described in
ambiguity function form. The WP signal of a signalling system of the present
invention can also be described as the ambiguity function scattering diagram
which then defines the optimum signal waveform for the target (FIG. 13). The
optimization practiced by prior art optimized the received echo signal-to-noise
from targets probed with nonoptimum signals. That is, prior art attempts
optimization of signal return from various specific targets under the
circumstances of a general general signal. An object of signalling systems of
the present invention is to both emit the optimum signal optimized to target
and also optimize the signal-to-noise in the returned echo. Another object of
signalling systems of the present invention is that both optimizations are in
time-frequency space, not just time, and not just frequency space.
Mosca (1969) addressed the problem of detecting coherent pulse trains in the
presence of interfering signals, i.e., noise and clutter. However this is quite
a different problem from crafting signals to target as used in signalling
systems of the present invention. No modification of the signal is recommended
by Mosca. However, Mosca does identify the desired processor as the linear
filter orthogonal (in time) to nonfluctuating clutter which achieves the
maximum input-to-output signal-to-noise gain. This is also an object of
signalling systems of the present invention, but it is required of such systems
that the signal be modified to match the target's time-frequency response.
Rihaczek (1971) gives a general description of signal waveforms and described
four classes of signals defined with respect to time-bandwidth product,
ambiguity function, resolution cell size, ambiguities, and sidelobes. The
classification is valid, but does not address the target's geometry or material
composition. Moreover, the four types of signals described are general not
matched-to-target. On the other hand, signalling systems of the present invention
match signals to target. WP signals of the present invention do no readily fall
within the four categories proposed by Rihaczek, namely: constant-carrier
pulses, irregular or noiselike signals, FM signals, and repetitive signals. WP
signals of the present invention are matched in carrier (or average) frequency,
frequency bandwidth, temporal bandwidth, instantaneous frequency, phase,
amplitude and polarization to the target. In most cases, signals of the present
invention will not be constant carrier pulses, nor irregular or noiselike
signals, nor FM signals. However, signals of the present invention will be
repetitive--which is a general and not a distinguishing attribute from prior
art. The class of targets described by Rihaczek are defined within specific
range gates. That is, those signals provide a certain range resolution and a
range rate resolution with the minimum values of signal bandwidth and duration
established by these resolution requirements. Thus, the geometry/material
aspects of the targets are not discriminated by these signals. However, signals
of signalling systems of the present invention do discriminate target
geometry/materials. Furthermore, Rihaczek does not distinguish between the
qualitatively different types of target response, such as (i) early time
(optical); (ii) resonance; and (iii) late time, responses, such responses being
distinguished by signalling systems of the present invention.
Rihaczek (1971) and Rihaczek & Mitchell (1967) also addresses the classical
range-Doppler trade-off, which is not applicable to signalling systems of the
present invention. In the case of signalling systems of the present invention,
the rate-of-change-of-range is detected by the interpulse interval change of
the pulse train, and the range is detected separately by the duration interval
between emission and return of the individual pulse in a train. Thus there is
no range-Doppler trade constraint for system design in the case of signalling
systems of the present invention. Furthermore, Rihaczek uses the general
mathematical time-frequency technique to describe a range-Doppler detection
capability for signal waveforms of prior art. In the case of signal waveforms
of signalling systems of the present invention, the ambiguity diagram describes
the autocorrelation of macro/micro emitted/received pulses and the power
density spectrum of macro/micro emitted/received pulses. Thus when used in the
context of signalling systems of the present invention, the general
mathematical descriptive technique of the ambiguity function is used to
describe different radiation-target attributes than in the context of prior
art.
Wolf et al (1969) address the problem of synthesizing a waveform which has an
associated ambiguity function in the time-frequency plane. However in the case
of this prior art, (1) as discussed above, the time-frequency plane for these
authors is the range-Doppler plane, which as noted above, is not the same as
the target's time-frequency scattering matrix representation addressed by
signalling systems of the present invention; (2) the authors do not address
amplitude modulation but only phase modulation. Their reason for so doing is
because "phase modulation may be generated easier than amplitude
modulation, and since most radar systems operate in saturation for a
significant portion of the time in order to maximum average power." Thus
these authors do not address the time-frequency response of a target, but only
the frequency response.
The same can be said for the study of Holtzman & Thorp (1969), who apply
the ambiguity and define its surface in terms of probability of detection.
However, in the case of signalling systems of the present invention, in the
same situation addressed by Holtzmann & Thorp, the ambiguity surface
characterizes the reflectance characteristics of target(s) and separately
characterizes the range and rate-of-change of range which are no longer joined
in a tradeoff relation. The output of the filter Holtzmann & Thorp describe
is matched to the target's range and velocity. On the other hand, the
signalling system of the present invention embodies a filter matched (1) in WP
pulse characteristics to the scattering characteristics of the target in its
pulse shape and material composition, (2) in energy and receiver gain to the
target's range, and (3) in the WP pulse repetition rate to and detection of the
rate-of-change-of-range to the target's velocity.
Blau (1967), Delong & Hofstetter (1967, 1970), Ares (1967), Rihaczek &
Golden (1971), Kretschmer (1977), Hsiao (1976) and Mahapatra & Ramakrishna
(1977) describe only pulse trains and the range-Doppler interpretation of the
ambiguity function for point targets. Delong & Hofstetter (1969) and
Acampora (1976) describe only amplitude modulated signal forms for the
range-Doppler interpretation of the ambiguity function for point targets.
Chadwick & Cooper (1974) describe pulse width and pulse spacing but only so
that returns from clutter do not arrive at the same time as the return signal
from the target. Therefore these authors address signal forms for the
range-Doppler interpretation of the ambiguity function for point targets--an
interpretation which does not apply in the case of signalling systems of the
present invention.
Poelman (1976) describes the orthogonally polarized backscattered components of
a target, but does not address the amplitude modulation of the signal needed to
address the geometry/material of target. The acoustical study of van Trees
(1965) addresses signal forms for the range-Doppler interpretation of the
ambiguity function for point targets--an interpretation which does not apply in
the case of signalling systems of the present invention.
A signalling system of prior art has been proposed by Gjessing (1978, 1986)
which proposes to modify the emitted signal. However, the Gjessing proposal to
adapt the radar illumination as well as the processing of the received signal
to the target in an optimum manner addresses only the steady state continuous
wave frequency characteristics of targets and medium. The Gjessing signalling
system is this a frequency space system and addresses the steady state and not
the transient state of the target/medium, whereas that of the present invention
is a time-frequency space system and addresses both the steady stat and
transient state of the target/medium.
A signalling system of prior art has been proposed by Chen (1981, 1982; Chen et
al, 1981) which proposes to modify the emitted signal. However, the Chen
proposal is to synthesize a waveform of an incident radar signal which excites
the target in such a way that the return radar signal from the target contains
only a single natural resonance mode of the target. The Chen signalling system
is thus a frequency space system and addresses the steady state and not the
transient state of the target/medium, whereas that of the present invention is
a time-frequency space system and addresses both the steady state and transient
sate of the target/medium.
Counter-clutter properties of a signalling system of the present invention
Signalling systems configured according to the present invention can exploit
any orthogonality in the descriptions of the transfer characteristics, steady
state or transient, of the target and media, to obtain maximum signal-to-noise.
If the characteristics of the target and media are (relatively) orthogonal,
then increases in signal-to-noise are obtained by matching the WP signal to the
target in the D mode of functioning (FIG. 26). In many instances, a wavelet or
time-frequency representation of the target reveals that the target occupies a
different location in the time-frequency plane than the clutter (FIG. 28). The
echo from both target and clutter. While the echo from both target and clutter
using a signal of prior art could be two-dimensionally filtered (in time and
frequency) to remove the clutter, less energy from the emitted signal
interacted with the target, than with a matched WP signal of present invention.
By using a WP signal of present invention more signal energy interacts with the
target and greater signal-to-noise and target discrimination is obtained.
Media penetration using WP signals of present invention
In some instances (cf. Barrett, 1991) WP time-frequency-signals of the present
invention will penetrate media impenetrable to continuous waves.
In one instance the media must possess a relaxation time greater than that of
the WP duration, the WP must undergo a minimum of frequency dispersion, and the
WP must be of sufficient intensity so as to interact with two distinct
vibrational energy levels (an excited state and a ground state) of the medium.
FIG. 33 exhibits calculated results demonstrating increased media penetration
when the duration of the pulse, t, it less than that of the medium relaxation
time, T. The classical relaxation shown in FIG. 33 is linear due to the neglect
of system inertia, i.e., the system is assumed to commence relaxing
immediately. This classical relation becomes nonlinear when a realistic
two-level system with inertia is considered.
Because of the finite lifetime, T, of an excited dipole moment of the medium,
the emission line of a dipole will have a width equal to 1/T. This is the
homogeneous width, (homogeneous because it is the same for every similar
dipole). However, generally the dipole is coupled to the environment, and this
inhomogeneous lifetime (inhomogeneous because it can be different for every
dipole) is T*, and the spectral inhomogeneous broadening is 1/T*. A
"total" relaxation rate, T.sup.-1, can then be defined as T.sup.-1
=T.sup.1 +T*.sup.-1. The ratio of inhomogeneous to homogeneous broadening will
determine whether a pulse will break up in the medium due to destructive
overlapping of transitions causing dephasing in the WP pulse. If the medium's
inhomogeneous broadening is not greater than homogeneous broadening, i.e., the
homogeneous relaxation time is not greater than the inhomogeneous relaxation
time, the WP pulse will not have greater success than continuous waves and will
not penetrate the medium even if it is shorter in duration than the relaxation
time of the medium. But if the medium's inhomogeneous broadening is greater
than homogeneous broadening, i.e., the homogeneous relaxation time is greater
than the inhomogeneous relaxation time, and provided that all the conditions
mentioned above are met, the WP pulse will penetrate the medium, whereas
continuous waves which combined together describe the WP pulse in frequency
space, will not.
In another embodiment, the temporal length of the WP pulse, t, of the present
invention is matched to the dispersive properties of the medium/media resulting
in a propagating soliton.
In another embodiment, the temporal length of the Wp pulse, t, of the present
invention is matched to any intensity-dependent nonlinearities in the
medium/media resulting in another kind of propagating soliton.
In another embodiment, the polarization and the rate of change of polarization
of the W P pulse of the present invention is matched to the polarization
properties of the medium/media resulting in greater penetration.
In another embodiment, the Brillouin and Sommerfeld precursors (cf Barrett,
1991) elicited in the medium by the fast rise and fall times of the WP pulse of
the present invention will penetrate the medium.
Applications areas of the present invention
FIG. 32A exhibits five applications areas of time-frequency WP signalling
systems of the present invention and contrasts the capabilities of these
systems with those of frequency domain (FD) signalling systems of prior art.
The five areas are further exhibited in FIGS. 32B-E.
Additional applications exhibited are: ground-probing sensor-radar (FIG. 32G);
anti-ship missile sensor-radar (FIG. 32H); communications links (FIG. 32I).
Applications areas at optical, IR and RF frequencies as well as in sonar
include:
Ultra-high resolution sensor-radar;
Satellite media/atmosphere penetrating surveillance sensor-radar and
communications;
Ground probing sensor-radar;
Anti-ship missile defense;
Low probability of intercept (covert) surveillance and communications;
Low probability of exploitation if intercepted (secure) surveillance and
communications;
Communications links: local area networks; satellite-to-satellite;
air-to-ground; air-to-air; ground-to-air; ship-to-ship; ship-to-shore; data
transfer links;
Identification: Fried or Foe interrogating and identifying sensor-radar;
Ultra-spread spectrum communications and surveillance systems;
Foliage-penetrating sensor-radar;
Foliage-detecting and characterization sensor-radar;
Ice-penetrating sensor-radar;
Space-based surveillance sensor-radar;
Airborne surveillance sensor-radar;
Ultrahigh resolution/light weight planetary vehicle;
Long/Medium/Short range ultrahigh resolution sensor-radar;
Aircraft landing system;
Ship sensor-radar;
Ship docking system;
Imaging sensor-radar;
Atmosphere/Ionosphere/Weather penetrating sensor/radar;
Jammers and interferers.
Interference and jamming properties of the present invention
A signalling system of the present invention is a more effective interference
and jamming system than prior art. Due to the matching of WP pulsed signal
energy to the target in terms of both the target's time and frequency
characteristics, the matched WP approach of the present invention interacts
maximum signal energy with the time-frequency window response characteristics
of all the subsystems of a target receiver.
The time-frequency characteristics of a representative receiver is exhibited in
FIG. 34. A WP pulse crafted according to the method of the present invention
possesses time-frequency characteristics and distribution of energy so that
maximum interaction occurs with any receiver components. Prior art, neglecting
the temporal characteristics of the target interacts nonoptimally with the
target.
RF performance prediction of the signalling system of the present invention
The system performance of radars of prior art for transmitting constant
wavelength or FM signals can be contrasted with that of WP radars of the
present invention designed for transmitting ultrast/ultrashort packets or
pulses.
There are two major observations concerning WP radar of the present invention
performance prediction:
(1) Concerning those capabilities, e.g., ranging and detection, which can be
performed by both FD and WP systems: as the radar range equation is identical
for both types of systems for zero receiver gain, then the presence of ay
receiver-processor gain gives a WP system a clear advantage over FD systems.
Receiver-processor gain is expected in most instances.
(2) There are also capabilities which only WP systems possess, e.g., imaging on
the basis of one return echo (due to the arrival, separated in time, of the
scattering from individual scattering elements of the target), as well as an
information-rich characterization of the target based on accessible primary,
secondary and higher-order diffraction components, together with Rayleigh,
resonance and optical components. For these WP-only capabilities, there is a
clear superiority over the FD systems of prior art.
The following table gives
similarities and differences:
TABLE 1
______________________________________
Comparison of FD and WP system capabilities.
FD System WP
System
______________________________________
Range resolution capability
High range resolution capability
Detection of target
Identification of target
Detection of target character-
Identification of multiple target
istics characteristics
(ergodicity)
Doppler Rate of
change of range
No capability (single
One return echo imaging
frequency)
capability
Threshold Detection
Power Spectral Analysis
Local Oscillator Global analytic signal sequence
Signal envelope detection
Signal envelope and fine
structure detection
Harmonic frequency analysis
Instantaneous frequency analysis
Heterodyne receiver
Homodyne receiver
Global frequency decomposi-
Local and instantaneous
tion
(wavelet) representation
Total transmitted energy
Total transmitted energy and
receiver gain
No capability
Receiver gain
Receiver aperture
Receiver aperture and antenna
balance
Receiver FD noise
Receiver TD noise
Global Time Event
Local
Time Event
Return signal shape not
Return signal shape preserved
preserved
Signal repetition and integra-
Signal repetition and integration
tion over time improves signal
over
time and power density
to noise
spectral analysis
(sampling rate) over a wider
frequency range improves
signal to noise.
______________________________________
The general requirements for a WP radar system of the present invention are:
1. Pulse power source (cf. Didenko and Yushkov, 1984; Meleshko, 1987):
sufficient energy to satisfy minimum range requirements, but with fast
rise-times fall-times (low psec range) and of sufficiently short duration
(psec.s to nsec.s) to address targets of interest. Sufficient repetition rate
to satisfy signal averaging requirements and target speed detection (kHz range)
by interpulse interval change. Reliability and longevity is important for a
fieldable system.
2. Receiver: a time domain receiver is required with receiver gain either
obtained by real time methods or by a GHz sampling rate.
3. Matched emit and receive antennas: wideband, nondispersive resonant, or
wideband nonresonant.
4. Beam forming capability, timed array.
5. Advanced parallel processing capability.
The limiting factors in time domain radar performance depend on:
(i) The total energy interacting with the target which is determined by: (a)
the total energy in the pulse duration, .DELTA.t, which, itself is limited by
the smallest resolvable, possible or desired, elementary scatterer on the
target, i.e., high energy individual WP signals emitters; (b) arrays of WP
emitters; (c) WP signals emitted as trains of pulses; (4) combinations of
(1)-(3); and (5) signal averaging.
(ii) The ratio, K, of the target's largest dimension, a, to the elementary
scatterer, a.sub.min, aforementioned.
(iii) The receiver gain, .xi., which must be less than or equal to K, and is a
function of the receiver sampling rate. These relations are shown in FIG. 29.
Practical example of a time domain radar system and analysis.
Below is listed a very general schematic for a practical WP radar system (FIG.
31). The component parts of any design will, of course, be chosen with the
specific intended mission in mind.
In some embodiments, the choice of source technologies includes:
(1) Diode laser array or other laser.
(2) Light-activated semiconductor switches (LASS), with or without compressed
pulse amplifications. These switches are generally silicon based.
(3) Commutative nonlinear magnetic switches.
(4) Vacuum triodes.
(5) Avalanche semiconductor diodes.
(6) Laser diodes.
(7) Spark gap generators.
For launch technologies, the choice includes:
(1) Timed array: Rotman lens, Lunneberg lens.
(2) Antennas: large current antennas: loop or magnetic coil; wideband TEM mode
horn; instantaneous wideband antennas; nonresonant antennas.
(3) Beam forming control: optical electronic.
(4) T/R switching.
For receiver technologies, the choice includes:
(1) Sample-and-hold oscilloscopes.
(2) Electronic sample-and-hold sliding correlators.
(3) Opto-electronic acquisition and a-d conversion.
(4) Optical continuous acquisition and correlation.
(5) Josephson junction technology receivers.
In the case of processing, the choice is among a variety of analog parallel
processors. One of the major advantages of WP radars is their ability to obtain
a large amount of target data, some of which will be aspect dependent. This
means that handling this large data input and assigning aspect-dependent
responses, as well as optical, resonance and late-time responses, to a single
target will require considerable computational capabilities.
Referring to FIG. 38, a transmit antenna array 100 is coupled by Roetman lens
101 to beam steering circuit 102, which is controlled by beam steering computer
control circuit 103. Wave (WP) packet transmission repetition rates are
controlled by computer repetition rate control circuit 105 via diode array 106
and Pockel's cell 107, which also receives a wave shape control signal input
from the computer wave shape control circuit 108. The Pockel's cell circuit
outputs signals via compressor 109 to control light activated switch 111. The
emitted time-frequency wave packets can be crafted to match the medium in which
the wave packet is launched, and the target. The initial search wave packets
can be matched loosely to one or more designated classes of media-target.
Return echoes are received by antenna 110, amplified in amplifier 111,
converted to digital in A to D converter 112 for processing by autocorrelator
113 and supplied to wavelet transform circuit 114. A first wavelet filter 115
outputs its signal to track and estimator range circuits 116, which provide
fire control signal to fire control circuit 117 to launch a rocket, for
example, as well as a steering signal to beam steering computer control to
thereby control beam steering computer control 102.
A second wavelet filter circuit 118 outputs the signal to a neural net 119,
which outputs a signal to the computer wave shape control circuit 109 to cause
transmission of time-frequency wave packets which are the complex conjugate of
the impulse response of the combined media and the target. The neural net 119
provides signals for the target imaging display 120 and decision control
circuit 121.
______________________________________
TABLE OF COMPONENTS
Subcomponent
Possible Choice
______________________________________
Pulse Power Source With
Light-Activated Semiconductor
Pulse Train Capability.
Switches; E-Beam-Activated
Semiconductor Switches; Semi-
conductor Switches; Spark-Gap/
Airbreakdown/Plasma Switch;
Compressed Pulse; Free Electron
Laser; Commutative Magnetic
Switch; Vacuum Triode; Vacuum
Electronic Device; Vacuum
Tube Devices; Laser Diodes;
Semiconductor Diodes; Relativis-
tic Devices; High Current
Accelerators; Cyclotron
Resonance Masers; Relativistic
Magnetrons; Relativistic
Klystrons; Energy-Resonator-
Accumulators; Non-Relativistic
Magnetron; Non-Relativistic
Klystron; Non-Relativistic
M-Type Devices; Non-
Relativistic O-Type Devices;
Multiresonator Klystrons;
Traveling Wave Tubes;
Backward Wave Tubes; Silcon-
Controlled Rectifiers;
Magnetic Pulse Compressors; etc.
Power Supplies.
Solid-State Batteries; Liquid-
State Batteries; etc.
Pulse Power Source Drivers.
Laser; Diode Laser; Diode Laser
Strip Array; etc.
Modulators. Pockels
Cell; Photorefractive
Device; Piezoelectric
Device; etc.
Compressors. Optical
Fiber; Optical Grating;
Magnetic Compressors; etc.
Computer Controls.
Digital; Analog; etc.
Antennas. TEM
Horn; Inverse Conformal
Bicone; End-Loaded Bicone;
Baseline-Folded Dipole; E-Plane
Sectional Horn; Nonresonant
Antennas; etc.
Transmit/Receive Switches
Electronic; Opto-electronic; etc.
Receivers.
Homodyne; Electronic; Electro-
optical; Optical; Superconduct-
ing; RF Electrodes; Channeled
Waveguides; Track and Range
Estimators; etc.
Beam Forming Capability.
Lunneberg Lens; Roetman Lens;
Time
Array; Fiber-Optic Cross-
Bar Switch; Electro-Optical
Array; etc.
A-D Converters.
Electro-optical; Optical; Optical
Fiber; Josephson Junction;
Superconducting; Flash A-D
Converters; Sample-And-Hold
Oscilloscope Devices; etc.
Correlators.
Optical; Electro-Optical; Analog;
Digital; Sliding Correlators;
Surface-Acoustic-Wave Devices;
Bragg Devices, etc.
Advanced Parallel Processing
Neural Net; Cellular Automata;
Capabilities.
Parallel Processor; Associative
Processor; Digital; Analog; etc.
______________________________________
While preferred embodiments of the invention have been shown and described, it
will be appreciated that numerous further embodiments, adaptations and
modifications of the invention will be apparent to those skilled in the art.
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