Self-coherence restoring signal extraction and estimation of signal direction of arrival

• US 5,299,148 A
• Filed: 05/22/1990
• Issued: 03/29/1994
• Est. Priority Date: 10/28/1988
• Status: Expired due to Fees

• Current Assignee: Regents of the University of California (University of California)
• Original Assignee: Regents of the University of California (University of California)
• Inventors: Schell, Stephan V., Gardner, William A., Agee, Brian G.
• Primary Examiner(s): Black, Thomas G.
• Assistant Examiner(s): ZANELLI, MICHAEL J
• Application Number:
  US07/526,840
• Time in Patent Office: 1,407 Days
• Field of Search: 364/574, 364/554, 364/715, 364/724.08, 364/724.09, 364/572, 364/581, 364/724.19, 455/307, 455/315, 455/303, 455/305, 455/306, 375/99, 375/102, 375/103, 375/1, 375/115, 342/378
• US Class Current: 702/196
• CPC Class Codes: H04B 7/0854 using error minimizing algorithms, e.g. minimum mean squared error [MMSE], "cross-correlation" or matrix inversion

Abstract

A processor and method for extracting or estimating directions of arrival of signals from a received data vector x(t) which has been corrupted by interfering signals and noise is described. The processor extracts signals by forming the scalar product of x(t) and a weight vector which is chosen such that the spectral self-coherence or conjugate spectral self-coherence of the processor output is maximized. The processor estimates the directions of arrival of signals by spectral self-coherence-selective performance surfaces for maxima.

Claims

1. A processor adapting an array of antennas upon which one or more signals impinges and extracting a signal of interest s(t) therefrom, comprising:

(a) means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals, said signal of interest s(t) having a measure of complex-valued self-coherence;

(b) reference signal means, coupled to an output of said means for receiving, for generating a reference signal vector r(t) from said signal input vector x(t);

(c) weight means for providing and updating a weight vector w having M components from said signal input vector x(t), said weight means having a first input coupled to an output of said means for receiving and a second input coupled to an output of said reference signal means, said weight means including means for preserving phase information of the complex-valued self-coherence of the signal of interest s(t) when generating an output signal y(t), said means for preserving phase information having a first input coupled to an output of said reference signal means and a second input coupled to an output of said weight means; and

(d) summing means for generating an output signal y(t) having a measure of self-coherence, said summing means having a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(e) wherein said weight means provides and updates said weight vector w to maximize self-coherence in said output signal y(t).

2. The processor of claim 1, wherein said reference signal means includes:

filtering means for filtering each component of said x(t) through a predetermined filter, and shifting means for frequency shifting each component of x(t) by a frequency α

; and

wherein said weight means includes;

first correlator means for generating and updating an autocorrelation matrix of x(t), denoted R_xx ;

second correlator means for generating and updating a correlation matrix of x(t) and r(t), denoted R_xr ; and

generalized eigenvector means for generating and updating said weight vector w according to the equation

space="preserve" listing-type="equation">λ

R.sub.XX w=R.sub.XI w

wherein λ

is non-negligible.

3. The processor of claim 2, wherein each component of x(t) has an associated phase such that a set of said M phases jointly contains direction of arrival information for all signals presented to the processor, and further including:

at least one sensor coupled to an input of said means for receiving;

means for generating a matrix E_N including eigenvectors having eigenvalues, where

space="preserve" listing-type="equation">E.sub.N =[w.sub.d+1 w.sub.d+2 . . . w.sub.M ],

and the following equation holds

space="preserve" listing-type="equation">λ

.sub.i R.sub.xx w.sub.i =R.sub.xr w.sub.i,

where M is the number of sensors i=1, . . . , M and w_i is the ith eigenvector, and eigenvalues λ

_d+1, . . . , λ

_M are negligibly small compared with λ

₁, . . . , λ

_d, d being determined from such partitioning of the eigenvalues;

means for generating a measure of orthogonality P₁ (Θ

) containing at least one peak, where

space="preserve" listing-type="equation">P.sub.1 (Θ

)=||(E.sub.N)a(Θ

)||.sup.-2

and where ( ) denotes a Hermitian or conjugate transpose operation, Θ

is a direction of arrival estimation parameter, and a(Θ

) is a corresponding direction vector; and

means for locating peaks in said measure of orthogonality, said peaks corresponding to estimated directions of arrival for s(t).

7. The processor of claims 2 or 5 wherein said processor extracts s(t) from a wideband signal input vector x(t) having a narrow band interference.

8. The processor of claims 2 or 5, wherein x(t) is a wideband signal, and further comprising:

means for decomposing the signal x(t) into two disjoint frequency bands x₁ (t) and x₂ (t) having center frequencies separated by a cycle frequency α

, where each of x₁ (t) and x₂ (t) satisfies a narrowband condition;

means for generating a reference vector r₁ (t) equal to x₂ (t) and for generating a reference vector r₂ (t) equal to x₁ (t);

means for obtaining w(1) from x₁ (t) and r₁ (t) and for obtaining w(2) from x₂ (t) and r₂ (t); and

means for reconstructing the wideband desired signal by adding the scalar products

space="preserve" listing-type="equation">y(t)=w(1)x.sub.1 (t)+w(2)x.sub.2 (t).

9. The processor of claims 2 or 5 wherein x(t) is a wideband signal input vector, further comprising filter means for jointly restoring spectral coherence of the processor output signal.

10. The processor of claim 9 wherein said filter means is a tapped delay line of length K and tap spacing τ

_o added to each said antenna for receiving said x(t) according to the equation

space="preserve" listing-type="equation">x(t)=[x(t),x(t-τ

.sub.o), . . . x(t-(k-1)τ

.sub.o)].sup.T

where [ ]^T denotes a transpose.

4. A processor for extracting a signal of interest s(t) from a plurality of signals impinging upon an array of antennas, comprising:

(a) means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a conjugate self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals, said signal of interest s(t) having a measure of complex-valued conjugate self-coherence;

(b) reference signal means, coupled to an output of said means for receiving, for generating a reference signal vector r(t) from said signal input vector x(t);

(c) weight means for providing and updating a weight vector w having M components from said signal input vector x(t), said weight means having a first input coupled to an output of said means for receiving and a second input coupled to an output of said reference signal means, said weight means including means for preserving phase information of the complex-valued conjugate self-coherence of the signal of interest s(t) when generating an output signal y(t), said means for preserving phase information having a first input coupled to an output of said reference signal means and a second input coupled to an output of said weight means; and

(d) summing means for generating an output signal y(t) having a measure of conjugate self-coherence, said summing means having a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(e) wherein said weight means provides and updates said weight vector w to maximize conjugate self-coherence in said output signal y(t).

5. The processor of claim 4, wherein:

said reference signal means includes;

filtering means for filtering each component of said x(t) through a predetermined filter;

means for replacing each filtered component by the complex conjugate thereof; and

means for frequency shifting each component of x(t) by a frequency α

; and

wherein said weight means includes;

first correlator means for generating and updating an autocorrelation matrix of x(t), denoted R_xx ;

second correlator means for generating and updating a correlation matrix of x(t) and r(t), denoted R_xr ; and

generalized eigenvector means for generating and updating said weight vector w according to the equation

space="preserve" listing-type="equation">λ

R.sub.xx w=R.sub.xr w

wherein λ

is non-negligible.

6. The processor of claim 5, wherein each component of x(t) has an associated phase such that a set of said M phases jointly contains direction of arrival information for all signals presented to the processor, and further including:

means for generating a matrix E_N including eigenvectors having eigenvalues, where

space="preserve" listing-type="equation">E.sub.N [w.sub.d+1 w.sub.d+2 . . . w.sub.M ],

and the following equation holds

space="preserve" listing-type="equation">λ

.sub.i R.sub.xx w.sub.i =R.sub.xr w.sub.i,

where M is the number of antennas i=1, . . . , M and w_i is the ith eigenvector, and eigenvalues λ

_d+1, . . . , λ

_M are negligibly small compared with λ

₁, . . . , λ

_d, d being determined from such partitioning of the eigenvalues;

means for generating a measure of orthogonality P₁ (Θ

) containing at least one peak, where

space="preserve" listing-type="equation">P.sub.1 (Θ

)=||(E.sub.N).sup.T a(Θ

)||.sup.-2

and where ( )^T denotes a transpose operation, Θ

is a direction of arrival estimation parameter, and a(Θ

) is a corresponding direction vector; and

means for locating peaks in said measure of orthogonality, said peaks corresponding to estimated directions of arrival for s(t).

11. A processor for extracting a signal of interest s(t) from a signal input vector x(t) having M components in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) receiving means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a self-coherent signal of interest s(t) together with interference from noise and/or other signals;

(b) reference signal means, coupled to said receiving means, for generating a reference signal vector r(t) from said signal input vector x(t), said reference signal means including an adaptive line canceler means for filtering;

(c) means for computing the inverse of an autocorrelation matrix of said signal input vector x(t), denoted R^-1_xx ;

(d) means for computing a correlation matrix of said signal input vector x(t) and said reference signal vector r(t), denoted R_xr ;

(e) weight means for providing and updating a weight vector w having an equal number of components as said signal input vector x(t) by forming the product R^-1_xx R_xr c, where c is a vector having an equal number of components as said signal input vector x(t); and

(f) summing means for generating an output signal y(t) having a measure of self-coherence, wherein said summing means has a first input coupled to said receiving means and a second input coupled to an output of said weight means;

(g) wherein said weight means provides and updates said weight vector w to substantially maximize self-coherence in said output signal y(t) at frequency α and

delay τ

for predetermined values of α and

τ

.

12. The processor of claim 11, wherein said means for filtering comprises means for delaying each component of x(t) by a time equal to τ

.

13. The processor of claim 11 wherein said means for generating y(t) further comprises:

means for computing the correlation matrix of r(t) and x(t), R_rx ;

means for computing the autocorrelation matrices R_rr and R_xx ;

means for computing the inverse of the autocorrelation matrix of r(t), R_rr ; and

means for finding the values of λ

, w and c that solve the system of equations

space="preserve" listing-type="equation">λ

R.sub.xx w=R.sub.xr R.sup.-1.sub.rr R.sub.rx w

14. The processor of claim 13 wherein said filtering means comprises means for delaying each component of x(t) by a time equal to τ

.

15. The processor of claim 13 wherein said means for generating y(t) further comprises:

means for computing the correlation matrix of r(t) and x(t), R_rx ;

means for computing the autocorrelation matrices R_rr and R_xx ;

means for computing the inverse of the autocorrelation matrix of r(t), R^-1_rr ; and

means for finding the values of λ

, w and c that solve the system of equations

space="preserve" listing-type="equation">λ

R.sub.xx w=R.sub.xr R.sup.-1.sub.rr R.sub.rx w

space="preserve" listing-type="equation">λ

R.sub.rr c.sup.8 =R.sub.rx R.sup.-1.sub.xx R.sub.xr c.sup.*

16. An apparatus for extracting a signal of interest s(t) from a signal input vector x(t) having components in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) receiving means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a conjugate self-coherent signal of interest s(t) together with interference from noise and/or other signals;

(b) means for generating a reference signal vector r(t) from said signal input vector x(t) by using an adaptive line canceler;

means for replacing each component in said reference signal vector r(t) by the complex conjugate thereof; and

means for frequency shifting each component of said signal input vector x(t) by frequency α

;

(c) means for computing an inverse of the autocorrelation matrix of said signal input vector x(t), denoted R^-1_xx ;

(d) means for computing a correlation matrix of said signal input vector x(t) and said reference signal vector r(t), denoted R_xr ;

(e) weight means for providing and updating a weight vector w having an equal number of components as said signal input vector x(t) by forming the product R^-1_xx R_xr c^*, where c is a vector having an equal number of components as said signal input vector x(t); and

(f) summing means for generating an output signal y(t) having a measure of conjugate self-coherence, said summing means having a first input coupled to said receiving means and a second input coupled to an output of said weight means;

(g) wherein said weight means provides and updates said weight vector w to substantially maximize conjugate self-coherence in said output signal y(t) at frequency α and

delay τ

for predetermined values of α and

τ

.

17. A processor for extracting a signal of interest s(t) from a signal input vector x(t) having M components in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a self-coherent signal of interest s(t) together with interference from noise and/or other signals;

(b) weight means for obtaining and updating a weight vector w having M components from said signal input vector x(t), said weight means having an input coupled to an output of said means for receiving;

(c) summing means for generating and updating an output signal y(t) having a measure of self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(d) wherein said weight means obtains and updates said weight vector w to maximize self-coherence in said output signal y(t); and

(e) wherein said processor extracts a signal of interest s(t) from a wideband signal input vector x(t) having a narrow band interference.

18. The processor of claim 17, further including:

reference signal means for generating a reference vector r(t) from said x(t), coupled to an output of said means for receiving, including means for filtering each component of said x(t) through a predetermined filter, and means for frequency shifting each component of said x(t) by a frequency α

;

first correlator means for generating an inverse of an autocorrelation matrix of said x(t), denoted R^-1_xx ;

second correlator means for generating a correlation matrix of said x(t) and said reference vector r(t), denoted R_xr ;

means for obtaining and updating a vector c having M components; and

means for generating a product of gR_xx^-1 R_xr c to provide said weight vector w, where g is an arbitrary scaler gain variable.

19. A processor for extracting a signal of interest s(t) from a signal input vector x(t) having M components in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) haivng M components in which each component comprises an electrical signal representing a complex measurement of a conjugate self-coherent signal of interest s(t) together with interference from noise and/or other signals;

(b) weight means for obtaining and updating a weight vector w having M components from said signal input vector x(t), said weight means having an input coupled to an output of said means for receiving;

(c) summing means for generating an output signal y(t) having a measure of conjugate self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(d) wherein said weight means obtains and updates said weight vector w to maximize conjugate self-coherence in said output signal y(t); and

(e) wherein said processor extracts a signal of interest s(t) from a wideband signal input vector x(t) having a narrow band interference.

20. The processor of claim 19, further including:

reference signal means, coupled to an output of said receiving means for generating a reference vector r(t) from said x(t), said reference signal means including means for filtering each component of said x(t) through a predetermined filter, means for replacing each said filtered each component by the complex conjugate thereof, and further including means for frequency shifting each component of said x(t) by a frequency α

;

first correlator means for generating an inverse of an autocorrelation matrix of said x(t), denoted R_xx^-1 ;

second correlator means for generating a correlation matrix of said x(t) and said reference vector r(t), denoted R_xr ;

means for obtaining and updating a vector c^* having M components, wherein c^* isa conjugate of c; and

means for generating a product of gR_xx^-1 R_xx c^* to provide said weight vector w, where g is an arbitrary scalar gain variable.

21. A processor for extracting a signal of interest s(t) from a signal input vector x(t) having M components in which each component comprises a complex measurement of s(t) togehter with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a self-coherent signal of interest s(t) together with interference from noise and/or other signals;

(b) means for decomposing said signal input vector x(t) into two disjoint frequency bands x₁ (t) and x₂ (t) having center frequencies separated by a cycle frequency α

, where each of x₁ (t) and x₂ (t) satisfies a narrowband condition, wherein said means for decomposing has an input coupled to an output of said means for receiving;

(c) reference means for generating a reference vector r₁ (t) equal to x₂ (t) and for generating a reference vector r₂ (t) equal to x₁ (t), wherein said reference means has an input coupled to an output of said means for decomposing;

(d) weight means for obtaining and updating a weight vector w(1) from said x₁ (t) and said r₁ (t), and for obtaining and updating a weight vector w(2) from said x₂ (t) and said r₂ (t) where both said weight vectors w(1) and w(2) have M components, wherein said weight means has an input coupled to an output of said reference means;

(e) summing means, having a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means, for reconstructing a wideband desired signal y(t) having a measure of self-coherence by adding the outputs

space="preserve" listing-type="equation">y(t)=w(1)x.sub.1 (t)+w(2)x.sub.2 (t)

and wherein said weight means obtains and updates said weight vectors w(1) and w(2) to maximize self-coherence in said output signal y(t).

22. A processor for extracting a signal of interest s(t) from a signal input vector x(t) having M components in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a conjugate self-coherent signal of interest s(t) together with interference from noise and/or other signals;

(b) means for decomposing said signal input vector x(t) into two disjoint frequency bands x₁ (t) and x₂ (t) having center frequencies separated by a cycle frequency α

, where each of said x₁ (t) and said x₂ (t) satisfies a narrowband condition, wherein said means for decomposing has an input coupled to an output of said means for receiving;

(c) reference means for generating a reference vector r₁ (t) equal to said x₂ (t) and for generating a reference vector r₂ (t) equal to said x₁ (t), wherein said reference means has an input coupled to an output of said means for decomposing;

(d) weight means for obtaining and updating a weight vector w(1) from said x₁ (t) and said r₁ (t) and for obtaining and updating a weight vector w(2) from said x₂ (t) and said r₂ (t), where both said weight vectors w(1) and w(2) have M components, wherein said weight means has an input coupled to an output of said reference means; and

(e) summing means for reconstructing a wideband desired signal y(t) having a measure of conjugate self-coherence by adding the outputs

space="preserve" listing-type="equation">y(t)=w(1)x.sub.1 (t)+w(2)x.sub.2 (t)

and wherein said weight means obtains and updates said weight vectors w(1) and w(2) to maximize conjugate self-coherence in said output signal y(t).

23. A processor for extracting a signal of interest s(t) from a wide band signal input vector x(t) having M components in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a self-coherent signal of interest s(t) together with interference from noise and/or other signals;

(b) weight means for obtaining and updating a weight vector w having M components from said signal input vector x(t), said weight means having an input coupled to an output of said means for receiving;

(c) summing means for generating an output signal y(t) having a measure of self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(d) wherein said weight means obtains and updates said weight vector w to maximize self-coherence in said output signal y(t); and

(e) filter means for jointly restoring spectral coherence of said output signal y(t).

24. The processor of claim 23 wherein said filter means is a tapped delay line of length K and tap spacing Υ

_o added to each antenna for receiving said x(t) according to the equation

space="preserve" listing-type="equation">x(t)=[x(t),x(t-τ

.sub.o), . . . x(t-(k-1)τ

.sub.o)].sup.T

where [ ]^T denotes a transpose.

25. The processor of claim 24, further including:

reference signal means, coupled to an output of said means for receiving, for generating a reference vector r(t) from said x(t), said reference signal means including means for filtering each component of said x(t) through a predetermined filter, and means for frequency shifting each component of said x(t) by a frequency α

;

first correlator means for generating an inverse of an autocorrelation matrix of said x(t), denoted R_xx^-1 ;

second correlator means for generating a correlation matrix of said x(t) and said reference vector r(t), denoted R_xr ;

means for obtaining and updating a vector c having M components; and

means for generating a product of gR_xx^-1 R_xr c to provide said weight vector w, where g is an arbitrary scalar gain variable.

26. A processor for extracting a signal of interest s(t) from a wideband signal input vector x(t) having M components in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a conjugate self-coherent signal of interest s(t) together with interference from noise and/or other signals;

(b) weight means for obtaining and updating a weight vector w having M components from said x(t), wherein said weight means has an input coupled to an output of said means for receiving;

(c) summing means for generating an output signal y(t) having a measure of conjugate self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(d) wherein said weight means obtains and updates said weight vector w to maximize conjugate self-coherence in said output signal y(t); and

(e) filter means for jointly restoring spectral coherence of said output signal y(t).

27. The processor of claim 26 wherein said filter means is a tapped delay line of length K and tap spacing τ

_o added to each antenna for receiving said x(t) according to the equation

space="preserve" listing-type="equation">x(t)=[x(t),x(t-τ

.sub.o), . . . x(t-(K-1)τ

.sub.o)].sup.T

where [ ]^T denotes a transpose.

28. The processor of claim 27, further including:

reference signal means for generating a reference vector r(t) from said x(t), said reference signal means being coupled to an output of said means for receiving, and including means for filtering each component of said x(t) through a predetermined filter, means for replacing each said filtered each component by the complex conjugate thereof, and further including means for frequency shifting each component of said x(t) by a frequency α

;

first correlator means for generating an inverse of an autocorrelation matrix of said x(t), denoted R_xx^-1 ;

second correlator means for generating a correlation matrix of said x(t) and said reference vector r(t), denoted R_xr ;

means for obtaining and updating a vector c^* having M components, wherein c^* is a conjugate of c; and

means for generating a product of gR_xx^-1 R_xr c^* to provide said weight vector w, where g is an arbitrary scalar gain variable.

29. A processor for extracting at least one signal of interest s(t) from a signal input vector x(t) in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) receiving means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals;

(b) reference signal means, having an input coupled to an output of said receiving means, for generating and updating a reference signal vector r(t) from said signal input vector x(t), said reference signal means including means for filtering each component of said signal input vector x(t) through a predetermined filter, said reference signal means further including means for frequency shifting each component of said signal input vector x(t) by frequency α

;

(c) first correlator means, having an input coupled to an output of said reference signal means, for computing and updating an r(t) inverse autocorrelation matrix, denoted R_rr^-1 ;

(d) second correlator means, having a first input coupled to an output of said reference signal means, and a second input coupled to receive said x(t), for computing and updating a correlation matrix of x(t) and r(t), denoted R_xr ;

(e) means for computing a matrix F, having a first input coupled to an output of said first correlator means and a second input coupled to an output of said second correlator means, where

space="preserve" listing-type="equation">F=(A A).sup.-1 AR.sub.xr R.sub.rr.sup.-1 and

where A contains direction vectors corresponding to a given set of direction of arrival estimates associated with said signal s(t) and A=[a(Θ

₁) . . . a(Θ

_d)];

(f) means for generating a signal s(t), having a first input coupled to said means for computing, and a second input coupled to an output of said reference signal means, by computing a vector product of F and r(t) such that the following expression is minimized

space="preserve" listing-type="equation">min <

||x(t)-[a(Θ

.sub.1) . . . a(Θ

.sub.d)]s(t)||.sup.2 >

Θ

.sub.1, . . . , Θ

.sub.d,s(t)

where d is the number of transmitted signals being received by the processor; and

(g) output means for generating an output signal y(t) by computing a vector product of F and said signal input vector x(t), said output means having a first input coupled to an output of said means for computing and a second input coupled to said receiving means.

31. The processor of claims 29 or 30, further comprising:

means for computing a projection matrix denoted P_A where

space="preserve" listing-type="equation">P.sub.a =A (A A).sup.-1 A;

means for computing R.sub.α

where

space="preserve" listing-type="equation">R.sub.α

=R.sub.xr R.sup.-1.sub.rr R.sub.rx ;

and

means for performing a multidimensional search over Θ

₁, . . . , Θ

_d for maximization of ##EQU16## where tr{ } is a trace operator.

32. The processor of claim 31, further including means for estimating d, comprising:

means for obtaining a maximum value of tr{P_a R_a } assuming that d=1;

means for obtaining said maximum value under a sequence of assumptions d=2, d=3, . . . , until a maximum value obtained for some value of d is approximately equal to the maximum value obtained for d+1, at which point said assumed value of d is taken to be the true value of d.

33. The processor of claims 29 or 30, further comprising:

means for computing a projection matrix denoted P_A where

space="preserve" listing-type="equation">P.sub.A =A (A A).sup.-1 A

and means for performing a multidimensional search over Θ

₁, . . . , Θ

_d for maximization of ##EQU17## where tr{ } is a trace operator.

34. The processor of claim 33, further including means for estimating d, comprising:

means for obtaining a maximum value of tr{P_A R_a } assuming that d=1;

means for obtaining said maximum value under a sequence of assumptions d=2, d=3, . . . , until a maximum value obtained for some value of d is approximately equal to the maximum value obtained for d+1, at which point said assumed value of d is taken to be the true value of d.

35. The processor of claim 29 or 30, further including means for estimating d, comprising:

means for obtaining a maximum value of tr{P_A R_a } assuming that d=1; and

means for obtaining said maximum value under a sequence of assumptions d=2, d=3 . . . , until the maximum value obtained for some value of d is approximately equal to the maximum value obtained for d+1, at which point said assumed value of d is taken to be the true value of d.

30. A processor for extracting at least one signal of interest s(t) from a signal input vector x(t) in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) receiving means for receiving on an array of antennas upon which one or more signals impinges, a plurality of input signals represented by a signal input ector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a conjugate self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals;

(b) reference signal means, having an input coupled to receiving means, for generating and updating a reference signal vector r(t) from said signal input vector x(t), said reference signal means including means for filtering each component of said signal input vector x(t) through a predetermined filter, said reference signal means further including means for replacing each said filtered component by a complex conjugate thereof and means for frequency shifting each component of x(t) by frequency α

;

(c) first correlator means, having an input coupled to an output of said reference signal means, for computing and updating an r(t) inverse autocorrelation matrix, denoted R_rr^-1 ;

(d) second correlator means, having a first input coupled to an output of said reference signal means and a second input coupled to receive said receiving means, for computing and updating a correlation matrix of x(t) and r(t), denoted R_xr ;

(e) means for computing a matrix F, having a first input coupled to an output of said first correlator means and a second input coupled to an output of said second correlator means, where

space="preserve" listing-type="equation">F=(A A).sup.-1 AR.sub.xr R.sub.rr.sup.-1

and A contains direction vectors corresponding to a given set of direction of arrival estimates associated with said signal of interest s(t), and

space="preserve" listing-type="equation">A=[a(Θ

.sub.1) . . . a(Θ

.sub.d)];

(f) means for generating a signal s(t), having a first input coupled to said means for computing and a second input coupled to an output of said reference signal means, by computing a vector product of F and r(t) such that the following expression is minimized

space="preserve" listing-type="equation">min <

||s(t)-[a(Θ

.sub.1) . . . a(Θ

.sub.d)]s(t).sup.* ||.sup.2 >

Θ

.sub.1, . . . , Θ

.sub.d,s(t)

where d is the number of transmitted signals being received by the processor; and

(g) output means for generating an output signal y(t) by computing a vector product of F and signal input vector x(t), said output means having a first input coupled to an output of said means for computing and a second input coupled to said receiving means.

36. An apparatus for extracting a signal of interest s(t) from a signal input vector x(t) having M components, each component having an associated phase such that a set of said M phases jointly contains direction of arrival information for all signals presented to the apparatus, and in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of sensors upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals and in which each component has an associated phase such that a set of said M phases jointly contains direction of arrival information for all said signals;

(b) reference signal means, coupled to an output of said means for receiving, for generating a reference signal vector r(t) from said signal input vector x(t), said reference signal means including means for filtering each component of said signal input vector x(t) through a predetermined filter and means for frequency shifting each component of said x(t) by a frequency α

;

(c) first correlator means, coupled to said reference signal means, for generating and updating a correlation matrix of said signal input vector x(t) and said reference signal vector r(t), denoted R_xr ;

(d) weight means, having an input coupled to an output of said first correlator means, for providing and updating a weight vector w having M components from said signal input vector x(t) according to the equation

space="preserve" listing-type="equation">λ

w=R.sub.xr w,

where λ

is non-negligible;

(e) summing means for generating an output signal y(t) having a measure of self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(f) wherein said weight means obtains and updates said weight vector w to maximize self-coherence in said output signal y(t);

(g) means for generating a matrix E_N including eigenvectors having eigenvalues, where

space="preserve" listing-type="equation">E.sub.N [w.sub.d+1 w.sub.d+2 . . . w.sub.M ],

and the following equation holds

space="preserve" listing-type="equation">λ

.sub.i w.sub.i =R.sub.xr w.sub.i

where M is the number of sensors, i=1, 2, . . . , M and w_i is an ith eigenvector, and eigenvalues λ

_d+1, . . . , λ

_M are negligibly small compared with λ

₁, . . . , λ

_d, d being defined from such partitioning of the eigenvalues;

(h) means for generating a measure of orthogonality P₁ (Θ

) containing at least one peak, where

space="preserve" listing-type="equation">P.sub.1 (Θ

)=||(E.sub.N)a(Θ

)||.sup.-2

and where ( ) denotes a Hermitian transpose operation, Θ

is a direction of arrival estimation parameter, and a(Θ

) is a corresponding direction vector; and

(i) means for locating peaks in said measure of orthogonality, said peaks corresponding to estimated directions of arrival for said signal of interest s(t).

37. An apparatus for extracting a signal of interest s(t) from a signal input vector x(t) having M components, each component having an associated phase such that a set of said M phases jointly contains direction of arrival information for all signals presented to the apparatus, and in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of sensors upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a conjugate self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals and in which each component has an associated phase such that a set of said M phases jointly contains direction of arrival information for all said signals;

(b) reference signal means, coupled to an output of said means for receiving, for generating a reference signal vector r(t) from said signal input vector x(t), said reference signal means including means for filtering each component of said x(t) through a predetermined filter, said reference signal means further including means for replacing each said filtered component by the complex conjugate thereof and means for frequency shifting each component of said signal input vector x(t) by a frequency α

;

(c) first correlator means, coupled to said reference signal means for generating and updating a correlation matrix of said signal input vector x(t) and said reference signal vector r(t), denoted R_xr ;

(d) weight means, having an input coupled to an output of said first correlator means, for providing and updating a weight vector w having M components from signal input vector x(t) according to the equation

space="preserve" listing-type="equation">λ

w=R.sub.xr w,

where λ

is non-negligible;

(e) summing means for generating an output signal y(t) having a measure of conjugate self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(f) wherein said weight means obtains and updates said weight vector w to maximize conjugate self-coherence in said output signal y(t);

(g) means for generating a matrix E_N including eigenvectors having eigenvalues, where

space="preserve" listing-type="equation">E.sub.N =[w.sub.d+1 w.sub.d+2 . . . w.sub.M ],

and the following equation holds

space="preserve" listing-type="equation">λ

.sub.i w.sub.i =R.sub.xr w.sub.i

where M is the number of sensors, i=1, 2, . . . , M and w_i is an ith eigenvector, and eigenvalues λ

_d+1, . . . , λ

_M are negligibly small compared with λ

₁, . . . , λ

_d, d being defined from such partitioning of the eigenvalues;

(h) means for generating a measure of orthogonality P₁ (Θ

) containing at least one peak where

space="preserve" listing-type="equation">P.sub.1 (Θ

)=||(E.sub.N).sup.T a(Θ

)||.sup.-2

and where ( )^T denotes a transpose operation, Θ

is a direction of arrival estimation parameter, and a(Θ

) is a corresponding direction vector; and

(i) means for locating peaks in said measure of orthogonality, said peaks corresponding to estimated directions of arrival for said signal of interest s(t).

38. An apparatus for extracting a signal of interest s(t) from a signal input vector x(t) having M components, each component having an associated phase such that a set of said M phases jointly contains direction of arrival information for all signals presented to the apparatus, and in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of sensors upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals and in which each component has an associated phase such that a set of said M phases jointly contains direction of arrival information for all said signals;

(b) weight means for obtaining and updating a weight vector w having M components from said signal input vector x(t), said weight means having an input coupled to an output of said means for receiving;

(c) summing means for generating an output signal y(t) having a measure of self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(d) wherein said weight means obtains and updates said weight vector w to maximize self-coherence in said output signal y(t);

(e) means for decomposing said signal input vector x(t), wherein said signal input vector x(t) is a wideband signal input vector, into x₁ (t) and x₂ (t) to form two disjoint frequency bands;

(f) first correlator means for generating a correlation matrix of R_xr according to the equation

space="preserve" listing-type="equation">R.sub.xr R.sub.x.sbsb.1.spsb.x.sbsb.2 (τ

);

(g) means for generation λ

where

space="preserve" listing-type="equation">λ

w=R.sub.xr w;

(h) means for generating a matrix E_N including eigenvectors having eigenvalues where

space="preserve" listing-type="equation">E.sub.N =[w.sub.d+1 w.sub.d+2 . . . w.sub.M ]

and the following equation holds

space="preserve" listing-type="equation">λ

.sub.i w.sub.i =R.sub.xr w.sub.i

where M is a number of sensors, w_i is an ith eigenvector and eigenvalues λ

_d+1, . . . , λ

_M are negligibly small compared with λ

₁, . . . , λ

_d, d being defined from such partitioning of the eigenvalues;

(i) means for generating a measure of orthogonality P₁ (Θ

) containing at least one peak, where

space="preserve" listing-type="equation">P.sub.1 (Θ

)=||(E.sub.N)a(Θ

)||.sup.-2

and where ( ) denotes a Hermitian transpose operation, Θ

is a direction of arrival estimation parameter, and a (Θ

) is a corresponding direction vector for a frequency band corresponding to x₂ (t); and

(j) means for locating peaks in said measure of orthogonality, said peaks corresponding to estimated directions of arrival for said signal of interest s(t).

39. An apparatus for extracting a signal of interest s(t) from a signal input vector x(t) having M components, each component having an associated phase such that a set of said M phases jointly contains direction of arrival information for all signals presented to the apparatus, and in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of sensors upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) haing M components in which each component comprises an electrical signal representing a complex measurement of a conjugate self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals and in which each component has an associated phase such that a set of said M phases jointly contains direction of arrival information for all said signals;

(b) weight means for obtaining and updating a weight vector w having M components from said signal input vector x(t), said weight means having an input coupled to an output of said means for receiving;

(c) summing means for generating an output signal y(t) having a measure of conjugate self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(d) wherein said weight means obtains and updates said weight vector w to maximize self-coherence in said output signal y(t);

(e) means for decomposing said signal input vector x(t), wherein said signal input vector x(t) is a wideband signal input vector, into x₁ (t) and x₂ (t) to form two disjoint frequency bands;

(f) first correlator means for generating a correlation matrix of R_xr according to the equation

space="preserve" listing-type="equation">R.sub.xr =R.sub.x.sbsb.1.spsb.x.sbsb.2 (τ

);

(g) means for generating λ

where

space="preserve" listing-type="equation">λ

w=R.sub.xr w;

(h) means for generating a matrix E_N inclujding eigenvectors having eigenvalues where

space="preserve" listing-type="equation">E.sub.N =[w.sub.d+1 w.sub.d+2 . . . w.sub.M ]

and the following equation holds

space="preserve" listing-type="equation">λ

.sub.i w.sub.i =R.sub.xr w.sub.i

where M is the number of sensors, w_i is an ith eigenvector and eigenvalues λ

_d+1, . . . , λ

_M are negligibly small compared with λ

₁, . . . , λ

_d, d being defined from such partitioning of the eigenvalues;

(i) means for generating a measure of orthogonality P₁ (Θ

) containing at least one peak, where

space="preserve" listing-type="equation">P.sub.1 (Θ

)=||(E.sub.N).sup.T a(Θ

)||.sup.-2

and where ( )^T denotes a transpose operation, Θ

is a direction of arrival estimation parameter, and a(Θ

) is a corresponding direction vector for a frequency band corresponding to x₂ (t); and

(j) means for locating peaks in said measure of orthogonality, said peaks corresponding to estimated directions of arrival for said signal of interest s(t).

40. An apparatus for extracting a signal of interest s(t) from a signal input vector x(t) having M components, each component having an associated phase such that a set of said M phases jointly contains direction of arrival information for all signals presented to the processor, and in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of sensors upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals and in which each component has an associated phase such that a set of said M phases jointly contains direction of arrival information for all said signals;

(b) weight means for obtaining and updating a weight vector w having M components from said signal input vector x(t), said weight means having an input coupled to an output of said means for receiving;

(c) summing means for generating an output signal y(t) having a measure of self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(d) wherein said weight means obtains and updates said weight vector w to maximize self-coherence in said output signal y(t);

(e) means for decomposing said signal input vector x(t), wherein signal input vector x(t) is a wideband signal input vector, into K+k narrow frequency bands;

(f) means for computing correlation matrices of ##EQU18## (g) means for computing λ

w=R_x.sbsb.j+k.spsb.x.sbsb.j w;

(b) means for generating matrices E_N (1), . . . , E_N (k) including eigenvectors having eigenvalues where

space="preserve" listing-type="equation">E.sub.N (j)=[w.sub.d+1 (j)w.sub.d+2 (j) . . . w.sub.M (j)]

an dwhere j=1, . . . , K and the following equation holds for i=1, . . . , M, M being the number of sensors,

space="preserve" listing-type="equation">λ

.sub.i (j)w.sub.i (j)=R.sub.x.sbsb.j+k.spsb.x.sbsb.j w.sub.i (j)

where w_i (j) is an ith eigenvector of R_x.sbsb.j+k.spsb.x.sbsb.j, eigenvalues λ

_d+1 (j), . . . , λ

_M (j) being negligibly small compared with λ

₁ (j), . . . , λ

_d (j), and d is defined by such partitioning of the eigenvalues;

(i) means for generating a measure of orthogonality P(Θ

, j) containing at least one peak, where

space="preserve" listing-type="equation">P(Θ

, j)=||(E.sub.N (j))a(f.sub.j,Θ

)||.sup.-2

and where j=1, . . . , K and ( ) denotes a Hermitian transpose operation, Θ

is a direction of arrival estimation parameter, and a(f_j,Θ

) is a corresponding direction vector for a jth frequency band which has center frequency f_j ; and

(j) means for locating peaks in said measure of orthogonality, said peaks corresponding to estimated directions of arrival for said signal of interest s(t).

41. An apparatus for extracting a signal of interest s(t) from a signal input vector x(t) having M components, each component having an associated phase such that a set of said M phases jointly contains direction of arrival information for all signals presented to the processor, and in which each component comprises a complex measurement of s(t) together with interference from noise and/or other signals, comprising:

(a) means for receiving on an array of sensors upon which one or more signals impinges, a plurality of input signals represented by a signal input vector x(t) having M components in which each component comprises an electrical signal representing a complex measurement of a conjugate self-coherent signal of interest s(t) contained in said input signals together with interference from noise and/or other signals and in which each component has an associated phase such that a set of said M phases jointly contains direction of arrival information for all said signals;

(b) weight means for obtaining and updating a weight vector w having M components from said signal input vector x(t), said weight means having an input coupled to an output of said means for receiving;

(c) summing means for generating an output signal y(t) having a measure of self-coherence, wherein said summing means has a first input coupled to an output of said means for receiving and a second input coupled to an output of said weight means;

(d) wherein said weight means obtains and updates said weight vector w to maximize self-coherence in said output signal y(t);

(e) means for decomposing said signal input vector x(t), wherein said signal input vector x(t) is a wideband signal input vector, into K+k narrow frequency bands;

(f) means for computing correlation matrices of ##EQU19## (g) means for computing λ

w=R_x.sbsb.j+k.spsb.x.sbsb.j w;

(h) means for generating matrices E_N (1), . . . , E_N (k) including eigenvectors having eigenvalues where

space="preserve" listing-type="equation">E.sub.N (j)=[w.sub.d+1 (j)w.sub.d+2 (j) . . . w.sub.M (j)]

and where j=1, . . . , K and the following equation holds for i=1, . . . , M, M being the number of sensors,

space="preserve" listing-type="equation">λ

.sub.i (j)w.sub.i (j)=R.sub.x.sbsb.j+k.spsb.x.sbsb.j w.sub.i (j)

where w_i (j) is an ith eigenvector of R_x.sbsb.j+k.spsb.x.sbsb.j, eigenvalues λ

_d+1 (j), . . . , λ

_M (j) being negligibly small compared with λ

₁ (j), . . . , λ

_d (j), and d is defined by such partitioning of the eigenvalues;

(i) means for generating a measure of orthogonality P(Θ

,j) containing at least one peak, where

space="preserve" listing-type="equation">P(Θ

,j)=||(E.sub.N (j)).sup.T a(f.sub.j,Θ

)||.sup.-2

and where j=1, . . . , K and ( )^T denotes a transpose operation, Θ

is a direction of arrival estimation parameter, and a(f_j,Θ

) is a corresponding direction vector for a jth frequency band which has center frequency f_j ; and

(j) means for locating peaks in said measure of orthogonality, said peaks corresponding to estimated directions of arrival for said signal of interest s(t).