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Claims  |
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We claim:
1. A method for recovering at least one of a plurality I of source signals
{S.sub.i }, each said source signal S.sub.i arriving at a receiver from
one of a plurality J of directions {D.sub.i }, said receiver including a
plurality K of sensors each having a sensor output signal E.sub.k, wherein
i, j and k are non-zero positive integers and I, J and K are positive
integers greater than unity, said method comprising:
creating a plurality K of said sensor output signals {E.sub.k } responsive
to said plurality I of source signals {S.sub.i };
multiplying said sensor output signals {E.sub.k } by predetermined shading
factors {b.sub.k } to create a plurality K of shaded sensor output signals
{b.sub.k E.sub.k };
delaying said shaded sensor output signals {b.sub.k E.sub.k } by means of a
plurality J of phasing vectors [.beta..sub.k ] to produce a plurality
J.multidot.K of delayed shaded sensor output signals [b.sub.k E.sub.k
].sub.j and combining said delayed shaded sensor output signals to create
a plurality J of spatial beam signals {B.sub.j } such that
##EQU17##
wherein t is time and .lambda..sub.k is a predetermined constant; and
producing an estimated source signal Y.sub.i at an output such that
Y.sub.i =.epsilon.B.sub.j, wherein said estimated source signal Y.sub.i
corresponds to said at least one source signal S.sub.i, .epsilon. is a
predetermined constant, and said shaded sensor output signals {b.sub.k
E.sub.k } are filtered by means of a filter characteristic H.sub.k
(.omega.) substantially equivalent to
##EQU18##
wherein .alpha.(.omega.), .delta.(.omega.) and .gamma.(.omega.) are
predetermined functions of frequency .omega. selected such that each said
spatial beam signal B.sub.j is unchanging over a predetermined continuous
frequency band.
2. The method of claim 1 wherein said predetermined functions
.alpha.(.omega.), .delta.(.omega.) and .gamma.(.omega.) are selected such
that
##EQU19##
wherein .tau. is a steering angle time delay in the interval [0,
.tau..sub.o ], said interval including delays for said plurality J of
directions {D.sub.j }, .omega..sub.0 is a frequency within said
predetermined continuous frequency band, .alpha..sub.o
=.alpha.(.omega..sub.0), .alpha.=.alpha.(.omega.),
.delta.=.delta.(.omega.), and .gamma.=.gamma.(.omega.).
3. The method of claim 2 wherein said receiver comprises K=2M+1 sensor
elements uniformly spaced in a line, wherein M is a non-zero positive
integer.
4. The method of claim 1 wherein said producing step further incorporates
the step of:
updating a plurality of transform signals {c.sub.ij } by means of
successive approximation to create an adaptive transform matrix [C.sub.ij
] such that said estimated source signal Y.sub.i =.epsilon.[C.sub.ij
][B.sub.j ].
5. A method for recovering at least one of a plurality I of source signals
{S.sub.i } in a communications system, wherein each said source signal
S.sub.i arrives at a receiver from one of a plurality J of directions
{D.sub.j }, said receiver including a plurality K of sensors each having a
sensor output signal E.sub.k, where i, j and k are nonzero positive
integers and I, J and K are positive integers greater than unity, said
method comprising:
creating a plurality K of said sensor output signals {E.sub.k } in response
to said plurality I of source signals {S.sub.i };
creating a plurality J of spatial beam signals {B.sub.j } in response to
said sensor output signals {E.sub.k } such that
##EQU20##
wherein t is time and .beta..sub.kj, b.sub.k and .lambda..sub.k are
predetermined constants; and
producing one or more of said estimated source signals {Y.sub.i } in
response to said plurality a of spatial beam signals {B.sub.j } and a
plurality I.J of transform signals {c.sub.ji }, wherein each estimated
source signal Y.sub.i corresponds to one of said source signals {S.sub.i }
and said plurality I.J of transform signals {c.sub.ij } corresponds to a
transform matrix updated by successive approximation of a plurality I of
estimated source signals {Y.sub.i } and by successive addition to each
said transform signal c.sub.ji of an increment signal .DELTA.C.sub.ji
=(-.mu.)f(Y.sub.j)g(Y.sub.i), wherein [Y.sub.j ]=[II+C.sub.ji ].sup.-1
[B.sub.j ], [II] is the unit matrix, .mu. is a predetermined constant and
f(x) and g(x) are predetermined odd functions of x.
6. A method for recovering at least one of a plurality I of source signals
{S.sub.i }, each said source signal S.sub.i arriving at a receiver from
one of a plurality J of directions {D.sub.j }, said receiver including a
plurality K of sensors each having a sensor output signal E.sub.k, wherein
i, j and k are nonzero positive integers and I, J and K are positive
integers greater than unity, said method comprising:
creating a plurality K of said sensor output signals {E.sub.k } responsive
to said plurality I of source signals {S.sub.i };
multiplying said sensor output signals {E.sub.k } by predetermined shading
factors {b.sub.k } to create a plurality K of shaded sensor output signals
{b.sub.k E.sub.k };
delaying said shaded sensor output signals {b.sub.k E.sub.k } by means of a
plurality J of phasing vectors [.beta..sub.k ].sub.i to produce a
plurality J.multidot.K of delayed shaded sensor output signals [b.sub.k
E.sub.k ].sub.j and combining said delayed shaded sensor output signals to
create a plurality J of spatial beam signals {B.sub.j }; and
repeatedly performing the steps of
combining said spatial beam signals {B.sub.j } to create a plurality I of
estimated source signals {Y.sub.i } so that [Y.sub.i ]=[II+C.sub.ji
].sup.-1 [B.sub.j ], wherein [II] is the unit matrix and [C.sub.ji ] is an
adaptive transform matrix corresponding to a plurality J.multidot.K of
transform signals {c.sub.ji };
adjusting said transform signals {c.sub.ji } in response to said estimated
source signals {Y.sub.i } to correct said adaptive transform matrix
[C.sub.ji ]; and
producing at least one of said estimated source signals {Y.sub.i }, wherein
said produced estimated source signal corresponds to said at least one of
said source signals {S.sub.i }.
7. The method of claim 6 wherein:
said delaying step is performed such that said spatial beam signal
##EQU21##
wherein t is time and .lambda..sub.k is a predetermined constant; and said
adjusting step is performed such that each of said transform signals
{c.sub.ji } is adjusted by an increment signal .DELTA.C.sub.ji
=(.mu.)f(Y.sub.j)g(Y.sub.i), wherein .mu. is a predetermined constant and
f(x) and g(x) are predetermined odd functions of x, respectively.
8. The method of claim 7 further comprising:
filtering said shaded sensor output signals {b.sub.k E.sub.k } by means of
a filter characteristic H.sub.k (.omega.) substantially equivalent to
##EQU22##
wherein .alpha.(.omega.), .delta.(.omega.), and .gamma.(.omega.) are
predetermined functions of frequency .omega. selected such that each
spatial beam signal B.sub.j is unchanging over a predetermined continuous
frequency band.
9. The method of claim 8 wherein said predetermined functions
.alpha.(.omega.), .delta.(.omega.) and .gamma.(.omega.) are selected such
that
##EQU23##
wherein .tau. is a steering angle time delay in the interval [0,
.tau..sub.o ], said interval including delays for said plurality J of
directions {D.sub.j }, .omega..sub.0 is a frequency within said
predetermined continuous frequency band, .alpha..sub.o
=.alpha.(.omega..sub.0), .alpha.=.alpha.(.omega.),
.delta.=.delta.(.omega.), and .gamma.=.gamma.(.omega.).
10. The method of claim 6 wherein said receiver comprises K=2M+1 sensor
elements uniformly spaced in a line, wherein M is a nonzero positive
integer.
11. A system for separating a plurality I of source signals {S.sub.i },
each said source signal S.sub.i arriving from one of a plurality J of
directions {D.sub.j }, said system comprising:
sensor array means having a plurality K of sensors for receiving said
source signals {S.sub.i };
transducer means in each sensor for creating a sensor output signal E.sub.k
in response to plurality I of source signals {S.sub.i };
beamformer means coupled to said sensor array means for creating a
plurality J of spatial beam signals {B.sub.j } in response to said
plurality K of sensor output signals {E.sub.k };
broadband shading means coupled to said sensor array means for adjusting
said plurality K of sensor output signals {E.sub.k } over a predetermined
frequency band for equalizing the amplitude response of said sensor array
means over said predetermined frequency band; and
output means coupled to said beamformer means and said broadband shading
means for generating a plurality I of output signals {Y.sub.i }
corresponding to estimates of said source signals {S.sub.i }, wherein i, j
and k are nonzero positive integers and I, J and K are positive integers
greater than unity.
12. The system of claim 11 wherein said broadband shading means comprises a
plurality K of filter means having filter characteristics {H.sub.k
(.omega.)}, wherein
##EQU24##
wherein .alpha.(.omega.), .delta.(.omega.), and .gamma.(.omega.) are
predetermined functions of frequency .omega. selected such that each said
spatial beam signal B.sub.j is unchanging over said predetermined
continuous frequency band.
13. The system of claim 12 wherein said predetermined functions
.alpha.(.omega.), .delta.(.omega.) and .gamma.(.omega.) are selected such
that
##EQU25##
wherein .tau. is a steering angle time delay in the interval [0,
.tau..sub.o ], said interval including delays for said plurality J of
directions {D.sub.j }, .omega..sub.0 is a frequency within said
predetermined continuous frequency band, .alpha..sub.o
=.alpha.(.omega..sub.0), .alpha.=.alpha.(.omega.),
.delta.=.delta.(.omega.), and .gamma.=.gamma.(.omega.).
14. A system for separating a plurality I of source signals {S.sub.i },
each said source signal S.sub.i arriving from one of a plurality J of
directions {D.sub.j }, said system comprising:
sensor array means having a plurality K of sensors for receiving said
source signals {S.sub.i };
transducer means in each sensor for creating a sensor output signal E.sub.k
in response to said plurality I of source signals {S.sub.i };
beamformer means coupled to said sensor array means for creating a
plurality J of spatial beam signals {B.sub.j } in response to said
plurality K of sensor output signals {E.sub.k };
transform means coupled to said beamformer means for creating and storing a
plurality I.J of transform signals {c.sub.ji } corresponding to an
adaptive transform matrix [C.sub.ji ];
output means coupled to said beamformer means and said transform means for
generating a plurality I of output signals {Y.sub.i } corresponding to
estimates of said source signals {S.sub.i } such that [Y.sub.i
]=[II+C.sub.ji ].sup.- [B.sub.j ], wherein [II] is the unit matrix; and
adaptive transform means coupled to said output means and said transform
means for adjusting each of said plurality I.J of transform signals
{c.sub.ji } in response to an increment signal .DELTA.c.sub.ji
=(.mu.)f(Y.sub.j)g(Y.sub.i), wherein .mu. is a predetermined constant and
f(x) and g(x) are predetermined odd functions of x, wherein i, j and k are
nonzero positive integers and I, J and K are positive integers greater
than unity.
15. The system of claim 14 wherein said plurality K of sensors are disposed
on a plane and said beamformer means creates said plurality J of spatial
beam signals {B.sub.j } such that
##EQU26##
for said direction D.sub.j, wherein t is time and .beta..sub.kj,
.lambda..sub.k and b.sub.k are predetermined constants.
16. The system of claim 15 wherein said plurality K=2M+1, wherein M is a
nonzero positive integer.
17. The system of claim 14 further comprising:
broadband shading means coupled to said sensor array means for adjusting
said plurality K of sensor output signals {E.sub.k } over a predetermined
frequency band for equalizing the amplitude response of said sensor array
means over said predetermined frequency band.
18. The system of claim 17 wherein said broadband shading means comprises a
plurality of finite-impulse-response filters each coupled to at least one
of said plurality K of sensors.
19. The system of claim 14 wherein said plurality I of source signals
{S.sub.i } comprises acoustic signals and said sensor array means
comprises a plurality of acoustic transducers.
20. The system of claim 14 wherein said plurality I of source signals
{S.sub.i } comprises electromagnetic signals and said sensor array means
comprises a plurality of antenna elements.
21. A system for adaptive cancellation of one or more interferer signals
{S.sub.i } in a signal receiver having a sensor array with a plurality K
of sensors, said system comprising:
transducer means in each sensor for creating a sensor output signal E.sub.k
in response to a plurality 1 of said interferer signals {S.sub.i };
beamformer means coupled to said sensor array for creating a plurality J of
spatial beam signals {B.sub.j } in response to said plurality K of sensor
output signals {E.sub.k };
transform means coupled to said beamformer means for creating and storing a
plurality I.J of transform signals {c.sub.ji .sub. } corresponding to an
adaptive transform matrix [C.sub.ji ];
output means coupled to said beamformer means and said transform means for
signals {S.sub.i } such that [Y.sub.i ]=[II+C.sub.ji ].sup.-1 [B.sub.j ],
wherein [II] is the unit matrix; and
adaptive transform means coupled to said output means and said transform
means for adjusting each of said plurality I.J of transform signals
{c.sub.ji } in response to an increment signal .DELTA.c.sub.ji
=(.mu.)f(Y.sub.j)g(Y.sub.i), wherein f(x) and g(x) are predetermined odd
functions of x,.mu. is a predetermined constant, i, j and k are nonzero
positive integers and I, J and K are positive integers greater than unity.
22. The system of claim 21 wherein said plurality K of sensors are disposed
on a plane and said beamformer means creates said plurality J of spatial
beam signals {B.sub.j } such that
##EQU27##
for said direction D.sub.j, wherein t is time and .beta..sub.kj,
.lambda..sub.k and b.sub.k are predetermined constants.
23. The system of claim 22 wherein said plurality K=2M+1, wherein M is a
nonzero positive integer.
24. The system of claim 21 further comprising:
broadband shading means coupled to said sensor array means for adjusting
said plurality K of sensor output signals {E.sub.k } over a predetermined
frequency band to equalize the amplitude response of said sensor array
means over said predetermined frequency band.
25. The system of claim 24 wherein said broadband shading means comprises a
plurality of finite-impulse-response filters each coupled to at least one
of said plurality K of sensors.
26. A system for separating a plurality 1 of source signals {S.sub.i } in
an underwater acoustic communications system, each said source signal
S.sub.i arriving from one of a plurality J of directions {D.sub.j }, said
system comprising:
sensor array means having a plurality K of acoustic sensors for receiving
said plurality I of source signals {S.sub.i };
transducer means in each acoustic sensor for creating a sensor output
signal E.sub.k in response to said plurality I of source signals {S.sub.i
};
beamformer means coupled to said sensor array means for creating a
plurality J of spatial beam signals {B.sub.j } in response to said
plurality K of sensor output signals {E.sub.k };
transform means coupled to said beamformer means for creating and storing a
plurality I.J of transform signals {c.sub.ji } corresponding to an
adaptive transform matrix [C.sub.ji ];
output means coupled to said beamformer means and said transform means for
generating a plurality I of output signals {Y.sub.i } corresponding to
estimates of said source signals {S.sub.i } such that [Y.sub.i
]=[II+C.sub.ji ].sup.-1 [B.sub.j ], wherein [II] is the unit matrix; and
adaptive transform means coupled to said output means and said transform
means for adjusting each of said plurality I.J of transform signals
{c.sub.ji } in response to an increment signal .DELTA.C.sub.ji
=(.mu.)f(Y.sub.j)g(Y.sub.i), wherein f(x) and g(x) are predetermined odd
functions of x,.mu. is a predetermined constant, i, j and k are nonzero
positive integers and I, J and K are positive integers greater than unity.
27. A system for separating a plurality I of source signals {S.sub.i } in a
cellular telecommunication system, each said source signal S.sub.i
arriving from one of a plurality J of directions {D.sub.j }, said system
comprising:
sensor array means having a plurality K of antenna elements for receiving
said plurality I of source signals {S.sub.i };
transducer means in each antenna element for creating a sensor output
signal E.sub.k in response to said plurality I of source signals {S.sub.i
};
beamformer means coupled to said sensor array means for creating a
plurality J of spatial beam signals {B.sub.j } in response to said
plurality K of sensor output signals {E.sub.k };
transform means coupled to said beamformer means for creating and storing a
plurality I.J of transform signals {c.sub.ji } corresponding to an
adaptive transform matrix [C.sub.ji ];
output means coupled to said beamformer means and said transform means for
generating a plurality I of output signals {Y.sub.i } corresponding to
estimates of said source signals {S.sub.i } such that [Y.sub.i
]=[II+C.sub.ji ].sup.-1 [B.sub.j ], wherein [II] is the unit matrix; and
adaptive transform means coupled to said output means and said transform
means for adjusting each of said plurality I.J of transform signals
{c.sub.ji } in response to an increment signal .DELTA.c.sub.ji
=(.mu.)f(Y.sub.i)g(Y.sub.i), wherein f(x) and g(x) are predetermined odd
functions of x, .mu. is a predetermined constant, i, j and k are nonzero
positive integers and I, J and K are positive integers greater than unity. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to systems for discriminating among multiple signals
to recover information and, more specifically, to an adaptive system for
recovering a signal from among several signal sources in a channel having
reverberation.
2. Discussion of the Related Art
The separation of independent sources from an array of sensors is a classic
but difficult problem in signal processing. Generally, the signal sources
as well as their mixture characteristics are unknown. Without knowledge of
the signal sources other than the general assumption of source
independence, the signal processing problem is denominated "blind
separation of sources". The separation is "blind" because nothing is known
about the frequency or phase of the independent signals.
A concrete example of the blind separation of sources problem is where the
pure (source) signals are sounds generated in a room and the mixed
(sensor) signals are the outputs of several microphones (FIG. 1). Each of
the pure signals is delayed and attenuated in some manner during
transmission from source to microphone, where it is then mixed with other
delayed and attenuated source signals. Multipath signals ("ghosts" created
by reverberation) are delayed versions of the source signals arriving from
different directions. This is denominated the "cocktail party" problem,
where a person wishes to listen to a single sound source while filtering
out other interfering sources including those created by reverberation.
Practitioners in the signal processing arts have pursued solutions to the
blind source separation problem because of their broad application in many
fields. For instance, in underwater acoustic digital communication, a
receiver must eliminate multipath or reverberating versions of the
transmitted signal to avoid unacceptable levels of intersymbol
interference. The same multipath distortion problem is also well-known in
the cellular telecommunications art.
Because the human ear automatically performs blind source separation, some
practitioners have explored the neural network art for solutions to the
blind separation of sources problem. For instance, Christian Jutten, et al
("Space or Time Adaptive Signal Processing By Neural Network Models",
Neural Networks for Computing, Snowbird, UI, J. S. Denker, Ed., AIP
Conference Proceedings 151, pp. 207-211, 1986) first introduced a simple
neural network, herein denominated the Herault-Jutten (HJ) network, with
adaptive separation capability.
Since its introduction, the HJ network has been extensively studied by
practitioners in the art. For a detailed discussion of the HJ network,
reference is made to C. Jutten, et al, "Blind Separation of Sources, Part
I: An Adaptive Algorithm Based On A Neuromimetic Architecture", Signal
Processing 24(1), pp. 1-10 (1991). Jutten, et al show that their HJ
network can provide an exact solution to the blind source separation
problem provided that the signal mixtures are linear and that the number
of independent sensors is at least equal to the number of sources.
Unfortunately, it is not commonly possible to obtain N distinct linear
combinations of N signals without delays or phase shifts. This is
especially the case in channels with reverberation. To generate N
full-rank linear combinations of inputs for the HJ network, microphones
must be placed at N different locations for signal sources located at N
different places (FIG. 1). The propagating medium between the N sources
and the N sensors produces different weights on the different source
signal arrivals at each sensor and introduces significant signal delays
that cannot be accommodated by the conventional HJ network.
For a statistical explanation of the HJ network function and a discussion
of a non-adaptive version of the HJ network, reference is made to Pierre
Comon, et al "Blind Separation of Sources, Part II: Problem Statement",
Signal Processing 24(1), pp. 11-20 (1991). Comon, et al observe that the
HJ network actually functions by searching for common zeros of N
functionals through pipelined stochastic iterations. They show that it
relies on the assumed independence of sensor signals, which follows from
the assumption of independent source signals only if the sensor signals
are linear combinations of the source signals. They observe that any
introduction of non-linearity changes the problem to one requiring
solution of an overdetermined system of non-linear equations with several
variables; a class of very difficult problems.
For a discussion of the stability of the HJ network, reference is made to
E. Sorouchyari, "Blind Separation Sources, Part III: Stability Analysis",
Signal Processing 24(1), pp. 21-29 (1991). Sorouchyari shows that using
simple linear and cubic HJ network adaptation functions f(x) and g(x)
offers convergence and stability that cannot be improved through the use
of higher order non-linear adaptation functions.
For an extensive discussion of a monolithic circuit implementation of the
HJ network and a review of HJ network operation, reference is made to Marc
H. Cohen, et al, "Analog VLSI Implementation of An Auto-Adaptive Network
for Real Time Separation of Independent Signals", Advances in Neural
Information Processing Systems, Vol. 4, Morgan-Kaufmann, San Mateo, Calif.
(1992).
Because of the difficulty of ensuring linear combinations of source signals
at the sensor outputs, the problem of separating non-linear signal
combinations is of great interest. For instance, John G. Proakis
("Adaptive Equalization Techniques For Acoustic Telemetry Channels", IEEE
Journal of Oceanic Engineering, Vol. 16, No. 1, pp. 21-31, Jan. 1991)
provides a tutorial review of adaptive equalization techniques for
reducing intersymbol interference in high-speed digital communications
over time-dispersive channels. Also, Jeffrey H. Fischer, et al ("A High
Data Rate, Underwater Acoustic Data-Communications Transceiver", IEEE
Oceans 92, Vol. 2, pp. 571-576, 1992) describe an underwater high-speed
data communications transceiver that features direct-sequence
spread-spectrum encoding to mitigate intersymbol interference arising from
reverberation in shallow acoustic channels. Neither Proakis nor Fischer,
et al propose multichannel blind separation as a model for reducing
intersymbol interference. Both practitioners rely on frequency redundancy
in the signals; the classical adaptive techniques they advocate either
treat multipath signals as noise or rely on embedded training signals and
enormous computational complexity. Except for the nonlinearity rising from
time delays over the source-to-sensor path, the HJ network offers a
superior and simpler solution to the intersymbol interference problem.
Accordingly, John C. Platt, et al ("Networks For The Separation of Sources
That Are Superimposed and Delayed", Advances in Neural Information
Processing Systems, Vol. 4, Morgan-Kaufmann, San Mateo, Calif., 1992) have
proposed extending the HJ network to also estimate a matrix of time delays
while estimating the HJ network mixing matrix. Platt, et al have proposed
a new network to separate signals that are mixed either with time delays
or through filtering. They show that the Herault-Jutten learning rules
fulfill a minimum output power principle, which they then apply to their
extension. However, Platt, et al also note that their learning technique
has multiple stable states and they cannot predict convergence to a
solution except through experimentation.
Accordingly, a reliable and useful method for coping with unknown delays in
the blind separation of sources problem is a clearly-felt need in the art.
The related unresolved problems and deficiencies are clearly felt in the
art and are solved by this invention in the manner described below.
SUMMARY OF THE INVENTION
The system of this invention adds directionality to the sensor response as
a technique for coping with unknown source signal delays at the sensor. A
linear array of sensors is used to produce N fixed beam lobes without
phase shifts. Reverberation is thereby reduced (spatially filtered) so
that multipath signals may be treated as independent sources.
This is the equivalent of having N virtual directional sensors at a single
spatial location, with each oriented to a different direction. If N signal
sources are located such that each lies in a different direction from the
M.gtoreq.N collocated sensors, then M full-rank linear combinations of N
signals are formed as required for the HJ network. Each sensor output may
be filtered to equalize for variations in beamlobe response over a
predetermined frequency range.
It is an object of this invention to extend the HJ network to compensate
for nonlinearity in source signal combinations arising from source signal
propagation delays at the sensor. It is an advantage of the system of this
invention that adding linear array beamforming processing to the HJ
network eliminates intersymbol interference arising from unknown source
signal time delays.
It is another object of this invention to adaptively separate signals that
are unknown in location, frequency and time delay. It is an advantage of
this invention that HJ network adaptation procedure readily converges to a
stable solution to the blind separation of source problem once the
propagation medium time delays are removed through beamformer processing.
It is yet another advantage of the system of this invention that there is
no performance penalty for long impulse responses caused by long
propagation delays. It is a further advantage of the system of this
invention that no training signals are needed for equalization because the
HJ network is self-training.
The foregoing, together with other objects, features and advantages of our
invention, will become more apparent when referring to the following
specification, claims and the accompanying drawing.
BRIEF DESCRIPTION OF THE DRAWINGS
For a more complete understanding of our invention, we now refer to the
following detailed description of the embodiments as illustrated in the
accompanying drawing, wherein:
FIG. 1 illustrates the blind separation of sources problem from the prior
art;
FIG. 2 comprising FIGS. 2A-2D, shows several embodiments of the
Herault-Jutten network from the prior art;
FIG. 3 shows the problem of FIG. 1 recast in accordance with the system of
this invention;
FIG. 4 shows a linear sensor array from the prior art;
FIG. 5 shows an illustrative embodiment of the linear sensor array
beamforming network used in this invention;
FIG. 6, comprising FIGS. 6A and 6B, shows array beam power versus operating
frequency with simple Gaussian shading for sensor compensation;
FIG. 7, comprising FIGS. 7A and 7B, compares the effects of applying the
system of this invention to a first example problem;
FIG. 8 shows array beam power versus operating frequency with the sensor
frequency compensation of this invention;
FIG. 9 shows gain amplitude versus operating frequency for the plurality of
sensor compensation filters of this invention required in an illustrative
linear sensor array;
FIG. 10 shows the sensor array transfer function provided by the
illustrative FIR filter embodiment of FIG. 9;
FIG. 11 provides a functional block diagram of the system of this
invention;
FIG. 12 provides a simple flow chart illustrating the signal recovery
method of this invention; and
FIG. 13 shows an illustrative estimation matrix convergence pattern for a
2.times.2 HJ network.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The Blind Separation of Sources Problem
FIG. 1 shows an exemplary arrangement for the blind separation of signal
sources problem. Three independent Talkers are generating three
independent source signals. Three Microphones are positioned in three
different locations. Each Microphone produces a single electrical output
signal (not shown) corresponding to a linear combination of the three
signals from the Talkers. These three microphone signals are independent
because the three Microphones are located independently. Unfortunately, at
each Microphone, each Talker signal has a different time delay with
respect to its actual source signal. For instance, the signal from Talker
B at Microphone B has a different propagation delay than the signal from
Talker B at Microphone C. Since these delay differences are unknown in the
"blind" separation problem, the simple additive model of interference
assumed by the Herault-Jutten (HJ) network is then not adequate to recover
the original source signals.
FIG. 2A shows a functional representation of a N.times.N HJ network 20 from
the prior art. FIG. 2B shows a detailed functional diagram of the
N.times.N HJ network of FIG. 2A. FIG. 2C shows a simple functional diagram
of a 2.times.2 HJ network from the prior art. FIG. 2D shows an extended
version of the 2.times.2 HJ network of FIG. 2C first proposed by Platt, et
al in the above-cited reference for application to the blind source
separation problem with delays (FIG. 1).
HJ network 20 is an N by N network that can be used to solve a signal
processing problem described as follows: Given N observed data sequences
that are distinct linear combinations (full rank) of N physical
independent signals without time delays or phase shifts, network 20 can
adaptively recover the N physical signals without prior knowledge of the
linear mixing matrix relating the two groups of signals. This is expressed
in mathematical form as:
##EQU1##
where {E.sub.i (t)} are the known observed data, [A.sub.ij ] is an unknown
full rank matrix and {S.sub.j (t)} are the original source signals to be
recovered. HJ network 20 is a memoryless system, as may be appreciated by
examining Eqn. 1. Thus, at any given time t=t.sub.1, the output [E.sub.i
(t.sub.1)] depends only on [S.sub.j (t.sub.1)] and not on any other past
or future values of [S.sub.j (t.sub.1)]. Note also that E.sub.i (t) is a
linear combination of {S.sub.1 (t), . . . , S.sub.N (t)}, which are
presumed independent of one another, and the mixing matrix [A.sub.ij ] is
nonsingular. Herein, {E.sub.i } denominates an unordered set of elements
E.sub.i, and [E.sub.i ] denominates an ordered vector of elements,
E.sub.i.
HJ network 20 functions by defining a transform matrix [C.sub.ij ] as
follows:
##EQU2##
The outputs of HJ network 20 are the estimated source signals, {Y.sub.j
(t)}, which are equal to {S.sub.j (t)} when the transform matrix
coefficients stabilize at a solution to the blind source separation
problem. This estimation can be written as:
##EQU3##
where [II] is the identity matrix having "zero" off-diagonal terms and
"unity" diagonal terms. The transform matrix elements {c.sub.ji } are
adjusted over time in accordance with an adaptive rule expressed as:
##EQU4##
where f(E) and g(E) are different odd functions selected according to a
Heppian learning rule to provide rapid convergence to a solution. These
are odd adaptation functions because they must preserve the assumed zero
mean condition and their product must constitute a test for independence.
Several practitioners have suggested making f(E)=E.sup.3 and g(E)=E. The
value of .mu. sets the speed of adaptation over time. When the HJ network
learning approaches an equilibrium point, Y.sub.j (t) approaches S.sub.j
(t). At the solution point, [II+C] is equal to the mixing matrix [A]
multiplied by some diagonal gain matrix and some permutation matrix. Thus,
after convergence, each output of HJ network 20 is proportional to (or
equal to) only one initial source signal.
FIG. 2B shows a detailed functional embodiment of HJ network 20 from FIG.
2A. An exemplary transform estimator element 22 is shown in the inset
area. The i.sup.th estimated source signal S.sub.i is fed back as the
kernel of the adaptor function f(x). Similarly, the j.sup.th estimated
source signal S.sub.j is also fed back through the network as the kernel
the second adaptor function g(x). The product of these two adaptation
functions is then weighted and subtracted from the stored value of the
appropriate element c.sub.ij (Eqn. 4). The transform element c.sub.ij is
presented to a multiplier 24 where it is multiplied by the j.sup.th input
signal E.sub.i. The resulting product is then added to the bus 26, where
it is summed into a new value of the j.sup.th output signal S.sub.j. This
process can be appreciated with reference to Eqns. 3-4 and the above-cited
Cohen, et al reference.
FIG. 2C shows a 2.times.2 HJ network representation, where the dashed
arrows represent adaptation. In similar format, FIG. 2D shows another
embodiment of the HJ network adapted to separate signals mixed with single
delays. The dashed arrows represent adaptation and the source of the arrow
is the source of the error used by gradient descent. The adjustable delay
28 avoids the degeneracy in the learning rule arising when attempting to
solve the blind source separation problem shown in FIG. 1. This network
can handle some simple delayed interference problems, while the HJ
networks of FIG. 2B-2C cannot. The performance of this extended HJ network
can be understood with reference to the above-cited Platt, et al paper.
An Adaptive Network Extension Using Directional Separation
The system of this invention redefines the blind source separation problem
of FIG. 1 and casts it as shown in FIG. 3. The same three Talkers are
positioned as in FIG. 1 but the three Microphones are shown collocated
with directionality rather than distributed as in FIG. 1. Normally three
collocated Microphones cannot provide three independent linear
combinations of the signals from Talkers A-C. However, the system of this
invention introduces a beamformer to form multiple beamlobes using the
three microphone outputs. These multiple beams represent independent
signals that are propagated from different directions. Each such spatial
beam output signal is a distinct linear combination of S.sub.j (t), as is
required by the HJ network represented in Eqn. 1.
Because HJ network 20 cannot remove time delays or phase distortions, the
beamformer of this invention must not introduce phase changes in the
received signals. Moreover, this "zero phase" requirement must be
satisfied over the entire operating frequency range of interest. That is,
the beamformer of this invention must process each S.sub.j (t) over a
predetermined frequency range of interest without variation in signal
phase shift. This beamformer is now described below.
Referring to FIG. 4, a row of sensors, exemplified by sensor 30, are
uniformly spaced at distance d to form a sensor array 32. Because the
number of sensors is equal to 2M+1, where M is an integer, sensor array 32
is symmetrical about the center element 30. If the signal 34 from center
element 30 is defined as E.sub.0 (t), a spatial beam signal B.sub.j (t) is
formed by adding time delays .tau..sub.j to the output of each sensor and
adding them up such that:
##EQU5##
where B.sub.j (t) is the j.sup.th spatial beam signal oriented at angle
.theta..sub.j with respect to the array normal, E.sub.m (t) is the output
of the m.sup.th sensor counting from center element 30, and b.sub.m is the
m.sup.th shading multiplier used in forming the beam, exemplified by
multiplier 36 in FIG. 5. The relationship between the signal time delay
.tau..sub.j and the spatial beam stearing angle .theta..sub.j is:
##EQU6##
where .theta..sub.j is the main beamlobe angle with respect to the array
normal as shown in FIG. 4. FIG. 5 provides a functional block diagram of
the beamformer for the array of FIG. 4.
Assuming that a plane-wave source signal S.sub.i (t) is arriving from an
angle .theta..sub.i (FIG. 4), the output of the m.sup.th sensor is:
E.sub.m (t)=.eta..sub.m S.sub.i (t-m.tau..sub.i) (7)
where .eta..sub.m is a scalar transducer gain for the m.sup.th sensor and
.tau..sub.j (see Eqn. 6) is the time delay between neighboring sensors
arising from the finite wave propagation velocity c in the medium along
the path from the direction of the i.sup.th Source signal S.sub.i
(t.sub.). If Eqn. 7 is substituted into Eqn. 5, the resulting
relationship:
##EQU7##
shows the fraction of source signal S.sub.i that is received in the
j.sup.th spatial beam signal B.sub.j (t).
Eqn. 8 shows that the beam direction can be steered by changing
.tau..sub.j. If the sensor weights b.sub.m and .eta..sub.m are symmetric
with respect to center sensor signal 34, then b.sub.m -b.sub.-m and
.eta..sub.m =.eta..sub.-m. If b.sub.0 .eta..sub.0 =1, then the Fourier
transform of Eqn. 8 is:
##EQU8##
Because a.sub.ij (.omega.) in Eqn. 9 has no imaginary component, there are
no phase shifts or delays introduced in B.sub.j (.omega.) for any values
of .omega., .tau..sub.j or .tau..sub.i. Thus, the symmetry of the sensor
array 32 with respect to central sensor signal 34 eliminates the phase
shifts between the several spatial beam outputs B.sub.j. If exact delay
lines are used to form the beam, the phase shifts of the -m.sup.th and
+m.sup.th sensor outputs must cancel exactly.
For narrow-band signals centered at .omega..sub.0, {a.sub.ij (.omega..sub.0
0} from Eqn. 9 can be considered to be substantially constant over the
narrow bandwidth. For I incoming signals from different angles
.theta..sub.j, one may form N.gtoreq.I separate beams by selecting N sets
of delays .tau..sub.j for N different but fixed directions. These beam
signals represent N linear combinations of the I narrow-band source
signals without delays and these combinations may then usefully serve as
inputs to an adaptive network such as a HJ network. This arrangement is
equivalent to having N virtual directional microphones at single location
at central sensor 30, each aimed in a different direction. If all original
narrow-band source signals are located in different directions, N
full-rank linear combinations of I signals are formed as required for the
HJ network. In the time domain, Eqn. 9 has the same form as Eqn. 1, where
{a.sub.ij (.omega..sub.0)} are the elements of the mixing matrix [A.sub.ij
].
A conventional HJ network (FIG. 2A) uses amplitude differences to form the
different elements {c.sub.ij } of the transform matrix [C.sub.ij ]. The
system of this invention relies on differences in spatial beam signal
magnitudes representing linear combinations of signals arriving from
different directions. Passing I.ltoreq.N of the N beamformer outputs
{B.sub.j (t)} through an I by I HJ network recovers the I original signals
{S.sub.i (t)} when the HJ network stabilizes at an equilibrium.
Obtaining Broadband Distortion-Free Spatial Beam Signals
The separation of multiple broadband signal sources is not feasible with
the beamformer described above in connection with FIG. 5 because the
directional sensitivity of sensor array 32 varies with operating
frequency. In such case, each a.sub.ij (.omega.) in Eqn. 9 varies with
frequency and Eqn. 9 is no longer equivalent to Eqn. 1 for broadband
signals. However, the system of this invention corrects this problem by
adding a filter element to each of the weighting multipliers exemplified
by multiplier 36 in FIG. 5. With this approach, it should be possible to
construct a beamformer whose beamlobe width is frequency-invariant over a
predetermined frequency bandwidth. Substituting the necessary filter
characteristic h.sub.m (t) for the m.sup.th sensor element in Eqn. 8
yields:
##EQU9##
where * indicates convolution. In the frequency domain, Eqn. 10 adopts the
form:
##EQU10##
where the array symmetry assumption is extended to H.sub.m
(.omega.)=H.sub.-m (.omega.) and the expression in brackets is real as in
Eqn. 9.
FIG. 6A shows the family of curves representing the mainlobe beam pattern
from "zero frequency" (curve 38) to 8 kHz (curve 40) for an exemplary
25-element array (not shown) with Gaussian-window shading at a
single-frequency .omega..sub.o according to Eqn. 12 below. FIG. 6B shows
the same information displayed in three dimensions to better illustrate
the beam-narrowing effect of increased operating frequency. Frequency
dependence of transducer constants and related effects are ignored in this
illustration. The system of this invention adds filters {H.sub.m } to the
individual sensor elements as necessary to cancel the beamlobe
frequency-dependence shown in FIG. 6B, thereby obtaining the
frequency-invariant beam pattern exemplified by the three-dimensional
illustration in FIG. 8. Selecting the filter characteristics necessary to
perform this array equalization function should result in complete
cancellation of time and phase delays in the sensor array beam signals
{B.sub.j } over a predetermined operating frequency range. The beam signal
characteristic shown in FIG. 8 provides the linear combination of source
signals necessary for proper convergence of the HJ network (FIGS. 2A-C).
The filter transfer functions {H.sub.m (.omega.)} should be selected so
that {B.sub.j (.omega.)} (Eqn. 11) are independent of .omega. over the
predetermined signal bandwidth interval (.omega..sub.a
.ltoreq..omega..sub.b). There are many useful ways to parameterize H.sub.m
(.omega.). The method of this invention preferred for achieving this
objective is now described.
First, a frequency .omega..sub.0 is chosen such that | | |
