AU2020356795B2

AU2020356795B2 - Method of array extension for linear arrays

Info

Publication number: AU2020356795B2
Application number: AU2020356795A
Authority: AU
Inventors: Jianrun CHEN; Weining Mao; Jin Qian
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2020-07-22
Filing date: 2020-12-21
Publication date: 2022-12-15
Anticipated expiration: 2040-12-21
Also published as: CN111736118A; AU2020356795A1; CN111736118B; WO2022016796A1

Abstract

The present invention belongs to the technical field of array beamforming and discloses a method of array extension for linear arrays. The method includes: 5 acquiring a received signal of a linear array; dividing the linear array into two sub-arrays according to odd and even array elements; calculating a covariance matrix of the received signals of the two sub-arrays composed of odd and even array elements; constructing an extended receiving array signal according to the covariance matrix of the received signals of the two sub-arrays composed of odd and even array 10 elements; and using conventional beamforming or minimum variance distortionless response beamforming method to perform beamforming and target detection. The present invention solves the problems in the existing linear array extension method of degraded performance and poor robustness at low signal-to-noise ratio, required non-circular symmetry for a source signal which has limitations in application, 15 complicated array extension process, and high computational complexity which are limitations in application.

Description

METHOD OF ARRAY EXTENSION FOR LINEAR ARRAYS BACKGROUND OF THE INVENTION

Field of the Invention The present invention relates to processing of array signals, and more particularly to a method of array extension for linear arrays.

Description of Related Art Array signal processing technology is widely used in many military and civilian fields such as radar, communications, sonar, etc., and it is a focus issue in these fields. Signal-to-noise ratio is a key factor affecting the performance of array signal processing. For a given array configuration, the number of physical array elements and the array aperture are determined. How to improve the detection performance of weak targets at low signal-to-noise ratio is a problem urgently need to be solved in engineering applications. It is an effective way to use the array extension technology to realize the extension of the array aperture and improve the detection performance of weak targets at low signal-to-noise ratio by virtually increasing the number of array elements. At present, the common array extension techniques mainly include: array extension methods based on high-order cumulant, based on array interpolation, based on data reconstruction according to source and received signal characteristics, and linear array extension methods based on delay characteristics of a linear array and non-circular symmetry of source signals, etc.

The high-order cumulant method has good and robust array extension characteristics, and according to the property that the high-order cumulant of the Gaussian white noise is zero, it can suppress the Gaussian noise in the system, so that it has a good parameters estimation performance in different Gaussian noise environments. However, this method has a huge amount of calculation and there is a lot of redundant information, which, when the number of array elements increases, may cause coupling between array elements. The array interpolation method realizes array extension by increasing the number of array elements, but the size of sub-regions and the step size of angles of this method are difficult to determine.

Keeping a balance between computational complexity and parameters estimation precise is a major difficulty of the array interpolation. The reconstruction data method based on source and received signal characteristics is proposed to solve the problems of "angle sensitivity", "interpolation step size sensitivity" and large amount of calculation in the array interpolation method, but it is mainly applied to special two-dimensional arrays such as L-shaped arrays. How to apply this method to one-dimensional linear array needs to be studied. One-dimensional linear array extension based on the delay characteristics of a linear array and based on the non-circular characteristics of a source signal are current common methods. The first can resolve coherent sources while extending the array, but the robustness is poor at low signal-to-noise ratio. The second requires an incident source signal to have non-circular symmetry, which has limitations in application.

Therefore, it is necessary to propose a new method of array extension for linear arrays.

SUMMARY OF THE INVENTION Object of the present invention: in order to overcome the shortcomings in the prior art, the present invention provides a method of array extension for linear arrays with good robustness at low signal-to-noise ratio and low computational complexity.

Technical solution: in order to achieve the objective mentioned above, the following technical solutions are adopted in the present invention:

A method of array extension of linear arrays, comprising the following steps:

(1) acquiring a received signal x(t) of a linear array, where x(t) is a 2Mx 1

-dimensional received signal vector:

x(t)=[x1 (t), x 2(,..., X 2M(t)]T,

2 M is the number of array elements of the linear array;

(2) dividing the linear array into two sub-arrays according to odd and even array

elements, to obtain received signals x 0(t) and x,(t) of the two sub-arrays,

respectively:

x. (t)=[x (t),X3 (0'''.,X2Mu-1(t)]T

X,(t)=[x2 (t),x 4 (t),-..,x2M(t)]

where x1 (t) is a received signal of the i th array element, x,(t) is a received

signal of the sub-array composed of odd array elements, X(t) is a received signal of

the sub-array composed of even array elements;

(3) calculating a covariance matrix R, of the received signals of the two

sub-arrays composed of odd and even array elements;

(4) constructing an extended receiving array signal Y according to the

covariance matrix Rx of the received signals of the two sub-arrays and the

rotational invariance of the linear array:

y yT T

where Y = R (:,1:M-1) , Y 2 =R.(:,2:M) , Rx(:,1: M -1) and

Rx(:,2:M) are matrices composed of a first M-1 columns and last M-1

columns, respectively, of the covariance matrix R., matrix Y3 is a conjugate and

flipud of matrix Y2 , and matrix Y4 is a conjugate and flipud of matrix Yi;

(5) calculating a covariance matrix Ry of the extended receiving array signal

Y: Ryy=E(YYH);

(6) according to the covariance matrix Ry of the extended receiving array

signal Y, performing beamforming and target detection on the extended array using the beamforming method.

Further, in the step (1), the receiving array is a uniform linear array, the number

of array elements is 2M, K far-field signal sources imping on the receiving array, and the received signal is denoted as:

x(t)= As(t)+n(t)

s(t) is a Kx1 -dimensional source signal vector and n(t) is a 2Mx1 -dimensional noise vector:

s(t)=[s 1(t),s2 (t), ,sK(t)] n(t)=[n,(t),n2 (t),-.- n""(t)

A is a 2Mx K -dimensional array manifold matrix:

A =[ a(O0), a(0 2 ),'',a(OK)]

j~rrd cos0 2rc(2M-1)d cos0k where a(Ok)= 1,e ,---,e 'd , A is a signal wavelength, d

is an element spacing, and 6k is an incident angle of the k th signal source,

k =1,2,- --,K, K is the number of uncorrelated far-field narrowband signal sources.

Further, in the step (2), the linear array is divided into two sub-arrays according to odd and even array elements, and the received signals of the two sub-arrays are respectively:

x(t)=[x 1 (t), x3(t),- .. , x2M-1(t)]

Xe(t)[X2 (t), x4 .. x 2 '(t)' (t)] T

where x,(t) is a received signal of the i th element, x(t) is a received signal

of the sub-array composed of odd array elements, and Xe(t) is a received signal of

the sub-array composed of even array elements.

Further, in the step (3), the covariance matrix of the received signals of the two sub-arrays composed of odd and even array elements is:

(t)I=ARA H R. = Et x,(t)- x H

where A, and A, are array manifold matrices of the two sub-arrays

composed of odd and even array elements, respectively, and derived from the array manifold matrix A, and R,, is a covariance matrix of source signals.

Further, in the step (4), the constructed extended receiving array signal is:

Y=[Y1 1,Y 2TY3 1,Y4] T

where Yi=R.(:,1:M-1) , Y 2 = R.(:,2: M) , R.(:,1: M -1) and

R,,(:,2:M) are matrices composed of a first M-1 columns and a last M-1 columns, respectively, of the covariance matrix R,, matrix Y3 is a conjugate and flipud of matrix Y2 , and matrix Y4 is a conjugate and flipud of matrix Y1

. Further, in the step (5), the covariance matrix of the extended receiving array signal is:

Ry7=E(YYH)

Still further, in the step (6), beamforming and target detection is performed on the extended array using conventional beamforming (CBF) or minimum variance distortionless response (MVDR) beamforming method, and the beam output powers of the CBF and MRDR beamforming are:

CBF W"Ryyw

1 PMVDR (0) H -w

where, w=[(a)T,(a,b-1)T,(ab)T,(a )T T , b=ej2c2dcos6/A , a. isasteering

vector of the sub-array composed of odd array elements,

a.= [1 e2.2dcosO/A... ej2 2 M-2 )dcosO/ 2I( , A is a signal wavelength, d is an array

element spacing, and 0 is a steering angle.

Beneficial effects: the present invention uses the uncorrelation of noise between array elements and the rotational invariance of a linear array to reconstruct the array signal to realize the extension of a one-dimensional linear array. Improving the detection performance of weak targets by array extension can greatly reduce the hardware cost of the detection system. Compared with the prior art, the present invention mitigates the effect of noise on weak sources detection while extending the array based on the uncorrelation of noise between elements, reduces the beam output side lobes, improves the detectability of weak sources and provides robustness at low signal-to-noise, and improves the practicability because of its low computational complexity and its effective enlarged array aperture without nonircularity symmetry of sources.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a flowchart of a method of array extension for linear arrays provided by an embodiment of the present invention;

FIG. 2 is a schematic curve of the change with angle of the beam output power of conventional beamforming for an extended array obtained according to the embodiment of the present invention;

FIG. 3 is a schematic curve of the change with angle of the beam output power of minimum variance distortionless response beamforming for the extended array obtained according to the embodiment of the present invention; and

FIG. 4 is a schematic curve of the change with signal-to-noise ratio of the detection probability of the extended array obtained according to the embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION The technical solutions of the present invention are further illustrated below with reference to the accompanying drawings.

With reference to FIG. 1, in an embodiment, an array extension method for a one-dimensional linear array includes the following steps:

step (1), acquiring a received signal of a linear array:

given that a source signal is a band limited noise with the frequency band 2000 Hz-2400 Hz, the sampling frequency is 16000 Hz, a uniform linear array with 6 array elements is used, the sound speed is 1500 m/s, the element spacing is half of the center frequency wavelength, the number of single snapshot is 1024, the number of source is 1, the incident angle of the source signal is 60 and the signal-to-noise ratio is -10 dB.

The array received signal is:

x(t)= As(t)+n(t) (1)

where x(t) isa 2Mx1-dimensional received signal vector:

x(t)=[x(t),x 2(X)2, Mtx2 ) (2) s(t)is a Kx1-dimensional signal vector (sent from the signal source) and n(t) is a 2Mx1-dimensional noise vector: s(t)=[s(0t),s 2 (t),...,SK (t)] (3) n(t)=[n,(t),n2 () - -, n2(t]T (4) the noise is Gaussian white noise with a mean of zero and a variance of U.2 , and A is a 2Mx K -dimensional array manifold matrix:

A =[a(0,),a(62),---, a(OK)] (5)

Fj2rdcos@k j2r(2M-l)dcos0 T where a(Ok)= 1,e c ,...,e , A is the signal wavelength,

d is the element spacing, and 6k is the incident angle of the kth signal source,

k =1,2,---,K; j represents a complex factor;

step (2), dividing the linear array into two sub-arrays according to odd and even array elements:

the received signals of the two sub-arrays composed of odd and even array elements are:

x,(t)= [X(t),x3(t), --, (t (6)

X,(t)=[x2(t),x 4 (t'),.. ,x 2M(t)1 (7)

where x,(t) is a received signal of the i th element, x,(t) is a received signal

the sub-array composed of even array elements.

step (3), calculating a covariance matrix of the received signals of the two sub-arrays composed of odd and even array elements:

Rx = E (,(t) -x H(t))=A.R.A," (8)

where A, and A, are array manifold matrices of the two sub-arrays composed

of odd and even array elements, respectively, which can be derived from the array manifold matrix A as described above. A is a 2Mx K -dimensional matrix , the odd rows in A xK dimension is extracted to get A,, the even rows in A xK dimension is extracted to get A, and R,, is a covariance matrix of source signals.

The superscript T indicates transpose, and the superscript H indicates conjugate. Since

the noise of each element is uncorrelated, the covariance matrix R, of the received

signals of the sub-arrays composed of odd and even array elements eliminates the influence of noise.

step (4), constructing an extended receiving array signal:

Y =[YJTyT yTyT]T (9)

where Yi=R.(:,1:M-1) , Y 2 = R.(:,2: M) , R.(:,1: M -1) and

R.(:,2:M) are a matrix composed of the first M-1 columns and last M-1

columns, respectively of the covariance matrix R,, the first M-1 columns referring

tol to M- columns, the last M-1 columns referring to 2 to M columns. Matrices Y,

and Y4 are derived by the rotational invariance of the linear array, and are

respectively conjugates and flipud of matrices Y 2 and Yi ; particularly, Y 3 is obtained by conjugation and then flipudof Y 2 , andY 4 isobtained by conjugation and

then flipud of Y1 .

step (5), calculating a covariance matrix of the extended receiving array signal:

R, = E(YY ") (10)

step (6), calculating beam output powers of the conventional beamforming (CBF) and the minimum variance distortionless response beamforming (MVDR):

PBF H RWrw (11)

PMVDR? ( H0-W (12)

where, w=[(a)T, ,b-)T,(ab)T,(a )T T , b=ej2e2dcoso/A, a. isasteering

vector of the sub-array composed of odd array elements,

a.=[1I e2 2 .. cosO/A... e 2If(2-2>cos/ , A is the signal wavelength, d is the

element spacing, and 0 is a steering angle.

Figure 2 shows the change with angle of the beam output power of the conventional beamforming for the extended linear array and the unextended linear array. Figure 3 is the change with angle of the beam output power of the MVDR beamforming for the extended linear array and the unextended linear array. It can be seen from Figure 2 and Figure 3 that the extended linear array has lower sidelobes, indicating that the ability to suppress noise is enhanced. Figure 4 is the changes with signal-to-noise ratio of the detection probability of the extended linear array and the unextended linear array, which are obtained from 100 Monte Carlo experiments. It can be seen from Figure 4 that the detection probability of the extended linear array is significantly higher than that of the unextended linear array at low signal-to-noise ratio, which is beneficial to the detection of weak targets.

The reference to any prior art in this specification is not, and should not be taken as,

an acknowledgement or any form of suggestion that such prior art forms part of the

common general knowledge.

It will be understood that the terms "comprise" and "include" and any of their

derivatives (e.g. comprises, comprising, includes, including) as used in this

specification, and the claims that follow, is to be taken to be inclusive of features to

which the term refers, and is not meant to exclude the presence of any additional

features unless otherwise stated or implied.

Claims

1. A method of array extension for linear arrays, comprising the following steps:

(1) acquiring a received signalx(t) of a linear array, where x(t) is a 2Mx1

-dimensional received signal vector:

x(t)=[x1 (t), x 2 ,''', X 2 A(t)]T

2M is the number of array elements of the linear array;

elements, to obtain received signals x,(t) and x'(t) of the two sub-arrays,

respectively:

x,(t)=[x1 (t),x3 (,..,x2M-1(t)]

Xe(t)=[x 2 (t),x 4 (t),-..,x2M(t)]

where x,(t) is a received signal of the i th array element, x0 (t) is a received signal

of the sub-array composed of odd array elements, x,(t) is a received signal of the

sub-array composed of even array elements;

(3) calculating a covariance matrix Rx of the received signals of the two sub-arrays

composed of odd and even array elements;

(4) constructing an extended receiving array signal Y according to the covariance

matrix R, of the received signals of the two sub-arrays and the rotational

invariance of the linear array:

Y = JT [Y2T 3T4] T

where Yi = R.(:,1:M-1) , Y2 = R. (:,2: M) , R.(:,1: M -1) and R,(:,2: M) are matrices composed of a first M-1 columns and last M-1 columns, respectively, of the covariance matrix R , matrix Y3 is a conjugate and flipud of

matrix Y 2 , and matrix Y4 is a conjugate and flipud of matrix Yi;

(5) calculating a covariance matrix Ryy of the extended receiving array signal Y:

Ry, = E(YY H);

(6) according to the covariance matrix Ry, of the extended receiving array signal

Y, performing beamforming and target detection on the extended array using the beamforming method.

2. The method of array extension for linear arrays according to claim 1, wherein in the step (1), the received signal of the linear array is:

x(t)= As(t)+n(t)

s(t) is a Kx1-dimensional source signal vector and n(t) is a 2Mx1-dimensional noise vector:

s(t)=[s(t),s2 (t), -,sK(t)]

n(t)=[n,(t),n2 (t), . - n2M(t)]T

A is a 2Mx K -dimensional array manifold matrix:

A =[a(Ol),a(02 ),---,a(OK)]

~j2cdcos9 j2rc(2M-)dcos90 where a(Ok)= 1,e ,--,e I, A is a signal wavelength, d is

0 an element spacing, k is a incident angle of the k th signal source, k =1,2,- -,K,

K is the number of uncorrelated far-field narrowband signal sources.

3. The method of array extension for linear arrays according to claim 1, wherein in the step (3), the covariance matrix of the received signals of the two sub-arrays composed of odd and even array elements is:

R. = Et x,(t) x'H (t)I=A.R.A H

where A, and A, are array manifold matrices of the two sub-arrays composed of odd and even array elements, respectively, and Rs, is a covariance matrix of source signals.

4. The method of array extension for linear arrays according to claim 1, wherein in the step (6), beamforming and target detection is performed on the extended array using conventional beamforming (CBF) or minimum variance distortionless response (MVDR) beamforming method, and the beam output powers of the CBF and MRDR beamforming are respectively:

PCBF HRyw

PMVDR() HR w

where, w=[(a.)T,(ab-1)T,(ab)T,(a )T ]T , b=e2, 2 dcs/ 2 , a. is a steering vector

of the sub-array composed of odd array elements,

a,= [1I e2 2 cosO/ 2 ... e 2 co I , A is a signal wavelength, d is an

element spacing, and 0 is a steering angle.