Jammer counting using cholesky factor diagonal elements

Details Jammer counting using cholesky factor diagonal elements Jammer counting using cholesky factor diagonal elements

2000-10-05

2002-11-12

Sotomayor, John B. (Department: 3662)

Communications: directive radio wave systems and devices (e.g.,

Radar ew

C342S016000, C342S017000, C342S159000, C342S162000, C342S194000, C342S195000

Reexamination Certificate

active

06480139

ABSTRACT:

BACKGROUND OF THE INVENTION
This invention generally relates to radar electronic counter measure applications, and more specifically, to a method and system for counting the number of interfering signals, or jammers, in a received radar signal from an antenna array.
In radar ECCM applications, it is often of interest to count the number of jammers in the source distribution. This problem consists of estimating the number of self-luminous point sources using a passive array, and well-known methods exist for forming the estimate. These methods require knowledge (or an estimate) of the eigenvalues of the spatial covariance matrix. A test function is formed using these eigenvalues which attempts to locate a knee in the eigenvalue profile, the location of which gives an indication of the signal subspace dimension. One such test function which is widely used is the AIC test function.
Obtaining the eigenvalues of a sample covariance matrix requires a great deal of computation, both in the creation of the sample covariance matrix and in its eigendata decomposition. Since these operations are not typically performed in a radar, jammer counting can represent a considerable additional cost in the construction of the radar.
If adaptive beamforming is being performed in the radar system to counter the jamming threat, then it is possible that the ECCM processor has at its disposal an estimate of the Cholesky factor decomposition of the covariance matrix, which is used, for example, to solve for sidelobe canceller weights. The Cholesky factorization of the covariance matrix has the form
R
x
=LL
H
where the Cholesky factor L is lower triangular and the superscript “H” represents the operation of Hermetian transposition. Since this matrix is available, significant processing time can be saved if the number of jammers can be determined, or reliably estimated, using the Cholesky factor.
There are several well-known ways of producing or estimating a triangular factorization of the sample covariance matrix such as that given above. One of these, described in “Algorithm and systoloc architecture for solving Gram-Schmidt orthogonalization (GSO) systems,” S. M. Yien,
Intl. Journal Mini and Microcomputers,
vol. 7 1985, is the so-called Gram-Schmidt (GS) processor. This processor estimates, from measurements of the wavefield received by the antenna array, the triangular matrix of weights required to transform the input data vector into a vector with uncorrelated components. Thus the GS processor produces a matrix U such that
y=Ux,
where x is an antenna array observation and y is a vector, the covariance matrix of which is diagonal:
R
y
=D=E{yy
H
}=E{Uxx
H
U
H
}=UR
x
U
H
,
where D is a diagonal matrix which is also computed by the GS processor. From the above, it can be seen that the Cholesky factor is given by
L=U
−1
sqrt
(
D
),
where sqrt(D) is a diagonal matrix whose main diagonal elements are the square roots of those on the main diagonal of D.
Another method of obtaining the Cholesky factor is to perform the Cholesky decomposition algorithm on the sample covariance matrix, which is first estimated from the array observations. This method is described in
Numerical Recipies in C,
3d Ed., W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Cambridge University Press, 1992. This method requires substantial computations.
Yet another well-known approach is that of operating directly on the matrix of array observations to estimate the factor L without first estimating a sample covariance matrix. This approach is described in “Matrix triangularization by systolic arrays,” W. M. Gentleman and H. T. Kung,
Proc. SPIE,
vol. 298, Real Time Signal Processing IV, pp. 298-303, 1981. If the covariance matrix estimate is written
R
x
=X
H
X,
where X is a rectangular array of measured data, and if the array X is factored into a Q-R form given by
X=QL
H
where Q is an orthonormal matrix and L is lower triangular, then L is the required triangular factor. The Q-R factorization can be performed by either the Givens rotation or Householder reflection methods.
All of the methods discussed above can be implemented in software or in special-purpose hardware.
SUMMARY OF THE INVENTION
An object of this invention is to count the number of jammers in a radar signal in a manner that avoids the necessity of computing a separate eigen-decomposition of the sample covariance matrix to be used for jammer counting.
Another object of the present invention is to provide a computationally attractive technique that makes use of the structure of the Cholesky factor to count the number of jammers in a radar signal.
These and other objectives are attained with a method and system for estimating the number of interfering signals in a received signal from a radar antenna array. The method comprises the steps of estimating the Cholesky factor decomposition of the covariance matrix from the received signal, and using that estimate of the Cholesky factor to obtain a count of the number of interfering signals in the radar signal.
The Cholesky factor has diagonal elements and these elements are its eigenvalues; and, preferably, the using step includes the step of using those diagonal elements of the Cholesky factor to obtain the count of the number of interfering signals in the radar signal. Also, preferably, the Cholesky factor is estimated by estimating a triangular Cholesky factor of the covariance matrix directly from the received radar signal.
It is well known that the covariance eigenvalues are the squares of the singular values of L. The singular value decomposition (SVD) of a square matrix A can be written as
A=V&Sgr;U
H
where V and U are unitary (complex orthonormal) matrices (which have the property VV
H
=I), and &Sgr; is a diagonal matrix whose non-zero elements are the square roots of the eigenvalues of the matrix AA
H
. If we write the SVD of the N-by-N Cholesky factor L as
L=V&Sgr;U
H
then the covariance matrix can be written
R=LL
H
=V&Sgr;U
H
U&Sgr;V
H
=V&Sgr;
2
V
H
which is an eigendata decomposition of R
x
, since V is unitary and therefore biorthogonal.
Considering the above, the most reliable way of counting jammers, starting from the Cholesky factor, is to compute the singular value decomposition of L, using a standard method such as the Golub-Reinsch algorithm, and using the singular values in the AIC test function. The Golub-Reinsch algorithm is computationally intensive, requiring as many as 12N
3
operations when applied to a square matrix of dimension N; however, it may be noted that parallel and systolic versions of the SVD exist in the literature.
The Cholesky factor singular value method has the advantage that it avoids computations of the sample covariance matrix and starts with the existing Cholesky factor estimate. However, the computation required to get the covariance eigenvalues is quite substantial, and it may be desirable to find a method of jammer counting based on the Cholesky factor estimate which requires less computation.
Although the singular values and eigenvalues of a square matrix are not identical (in general), they are related. In fact, signal and noise subspace dimensions which are clear in the singular values must also be present to some degree in the eigenvalues.
In view of this, the present invention preferably uses the eigenvalues of L in the AIC test function, in place of its singular values. This can be done without any further processing of the matrix, simply by using the diagonal entries of the Cholesky factor (which are its eigenvalues) in the AIC test function, and so it is computationally very attractive.
Further benefits and advantages of the invention will become apparent from a consideration of the following detailed description, given with reference to the accompanying drawings, which specify and show preferred embodiments of the invention.


REFERENCES:
patent: 5617099 (1997-04-01), Warren et al.
patent: 5798942 (1998-08-01), Danchick et

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