CN113189570A - Array signal processing method and system based on complex domain compressed sensing - Google Patents

Array signal processing method and system based on complex domain compressed sensing Download PDF

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CN113189570A
CN113189570A CN202110442884.6A CN202110442884A CN113189570A CN 113189570 A CN113189570 A CN 113189570A CN 202110442884 A CN202110442884 A CN 202110442884A CN 113189570 A CN113189570 A CN 113189570A
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CN113189570B (en
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郑恩明
陈新华
李嶷
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Institute of Acoustics CAS
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Abstract

The invention relates to the field of sonar signal processing, in particular to an array signal processing method and system based on complex domain compressed sensing. The method comprises the following steps: carrying out complex analytic transformation on array signals received by the sonar array to obtain complex analytic data of each array element, carrying out time delay compensation, correlation and accumulation processing on the complex analytic data of each array element in a complex domain according to the estimated orientation, constructing an observation sequence and a complex domain perception matrix, and realizing array signal processing by adopting a complex domain compressed sensing method. Compared with a frequency domain compressed sensing method, the method provided by the invention has the advantages that the minimum requirement on the input signal-to-noise ratio is reduced by nearly 10lgMdB (M is the number of channels) under the same detection probability, and the detection capability of a weak target is improved.

Description

Array signal processing method and system based on complex domain compressed sensing
Technical Field
The invention relates to the field of sonar signal processing, in particular to an array signal processing method and system based on complex domain compressed sensing.
Background
In array signal processing, in order to realize an efficient and high-performance spatial spectrum synthesis technology, researchers have conducted intensive research on space from the aspects of beam forming, subspace decomposition, compressed sensing and the like, and have obtained certain research results. However, as a matter of concern for researchers: background level, spatial resolution, requirements on input signal-to-noise ratio and the like in the spatial spectrum synthesis technology are not well solved. Although the requirement on the input signal-to-noise ratio is the lowest, the space spectrum synthesis technology based on beam forming is limited by array element number and Rayleigh limit, the problems of serious space spectrum leakage and wide main lobe are always not solved well, and the multi-target azimuth estimation effect needs to be improved; although the subspace decomposition-based spatial spectrum synthesis technology breaks through the Rayleigh limit and realizes high-resolution spatial spectrum synthesis, the subspace decomposition-based spatial spectrum synthesis technology is greatly influenced by the requirement of an input signal-to-noise ratio, cannot realize effective synthesis on a spatial spectrum under a lower signal-to-noise ratio and has a poor estimation effect on a weak target azimuth.
Compressed sensing has been widely applied to the relevant research field as an emerging theory that changes the "nyquist" sampling theory. In the target orientation estimation, on the basis of compressed sensing space target airspace sparsity, synthesizing a space spectrum by constructing a corresponding sensing matrix and a measured value, and then estimating the target orientation by the space spectrum; in subsequent combination with practical application, researchers have proposed some methods for improving the performance of compressed sensing in target orientation estimation. In general, the existing target orientation estimation methods based on compressed sensing are all realized in a frequency domain, and have certain performance degradation problems under the condition of low signal-to-noise ratio.
Disclosure of Invention
The invention aims to solve the problem of performance degradation of an array signal processing method based on frequency domain compressed sensing under the condition of low signal-to-noise ratio, and provides an array signal processing method and system based on complex domain compressed sensing.
In order to achieve the above object, the present invention provides an array signal processing method based on complex domain compressed sensing, including:
carrying out complex analytic transformation on array signals received by the sonar array to obtain complex analytic data of each array element, carrying out time delay compensation, correlation and accumulation processing on the complex analytic data of each array element in a complex domain according to the estimated orientation, constructing an observation sequence and a complex domain perception matrix, and realizing array signal processing by adopting a complex domain compressed sensing method.
As an improvement of the above method, the method specifically comprises:
step 1) carrying out complex analytic transformation on array signals received by the sonar array by adopting complex analytic wavelet transformation, and constructing complex analytic data of each array element and complex analytic data of the m-th array element in a complex domain
Figure BDA0003035621820000021
Comprises the following steps:
Figure BDA0003035621820000022
wherein, M is 1,2, … M, M is array element number of sonar array, xm(t) and
Figure BDA0003035621820000023
respectively real part data and imaginary part data, j is an imaginary part symbol, and t represents a time domain;
step 2) at the nth scanning angle thetanThe complex analysis data of the m-th array element
Figure BDA0003035621820000024
Push button
Figure BDA0003035621820000025
Performing time delay compensation to obtain the complex analysis data of the mth array element after the time delay compensation
Figure BDA0003035621820000026
Comprises the following steps:
Figure BDA0003035621820000027
wherein d is array element spacing of the sonar array, c is sound velocity, N is 1,2, … N, and N is the number of scanning angles;
step 3) constructing a covariance matrix after time delay compensation in a complex domain
Figure BDA0003035621820000028
To pair
Figure BDA0003035621820000029
Zeroing the main diagonal elements and aligning the zeroed covariance matrix
Figure BDA00030356218200000210
Performing accumulation processing to obtain corresponding spatial spectrum P (theta)n) Comprises the following steps:
Figure BDA00030356218200000211
wherein the content of the first and second substances,
Figure BDA00030356218200000212
I＝[1,1,…,1]implementation of
Figure BDA00030356218200000213
Performing medium element accumulation treatment;
step 4) according to P (theta) ═ P (theta)1),P(θ2),…,P(θN)]T，[·]TFor matrix transposition, let I be the observation sequence, for the corresponding spatial spectrum P (θ)n) Performing transformation processing, expressing in the form of observation sequence and complex domain perception matrix, and constructing complex domain perception matrix
Figure BDA00030356218200000214
Wherein, A (theta)n) Satisfies the following formula:
Figure BDA0003035621820000031
step 5), obtaining a space signal sparse coefficient S (t) by solving the following convex optimization problem:
min||S(t)||1
Figure BDA0003035621820000032
step 6) processing the space signal sparse coefficient S (t) to obtain a synthetic space spectrum P (theta) which is as follows:
P(θ)＝|S(t)|2
the peak position of the synthesized spatial spectrum P (θ) is searched for target detection.
A complex domain compressed sensing based array signal processing system, the system comprising: the method comprises the following steps: the device comprises a complex analysis transformation module, a time delay compensation and correlation accumulation module, a complex domain observation sequence and perception matrix construction module and a complex domain compressed perception processing module; wherein the content of the first and second substances,
the complex analytic transformation module is used for carrying out complex analytic transformation on array signals received by the sonar array to obtain complex analytic data of each array element;
the time delay compensation and correlation accumulation module is used for carrying out time delay compensation, correlation and accumulation processing on the complex analysis data of each array element in the complex domain according to the estimated azimuth;
the complex domain observation sequence and sensing matrix construction module is used for constructing an observation sequence and a complex domain sensing matrix;
the complex domain compressed sensing processing module is used for realizing array signal processing by adopting a complex domain compressed sensing method.
As an improvement of the above system, the specific processing procedure of the complex analytic transformation module includes:
carrying out complex analytic transformation on array signals received by the sonar array by adopting complex analytic wavelet transformation, and constructing complex analytic data of each array element and complex analytic data of the m-th array element in a complex domain
Figure BDA0003035621820000033
Comprises the following steps:
Figure BDA0003035621820000034
wherein, M is 1,2, … M, M is array element number of sonar array, xm(t) and
Figure BDA0003035621820000035
real and imaginary data, respectively, j is the imaginary symbol, and t represents the time domain.
As an improvement of the above system, the specific processing procedure of the delay compensation and correlation accumulation module includes:
at the nth scan angle thetanThe complex analysis data of the m-th array element
Figure BDA0003035621820000036
Push button
Figure BDA0003035621820000037
Performing time delay compensation to obtain the complex analysis data of the mth array element after the time delay compensation
Figure BDA0003035621820000038
Comprises the following steps:
Figure BDA0003035621820000039
wherein d is array element spacing of the sonar array, c is sound velocity, N is 1,2, … N, and N is the number of scanning angles;
constructing a time-delay compensated covariance matrix in a complex domain
Figure BDA0003035621820000041
To pair
Figure BDA0003035621820000042
Zeroing the main diagonal elements and aligning the zeroed covariance matrix
Figure BDA0003035621820000043
Performing accumulation processing to obtain corresponding spatial spectrum P (theta)n) Comprises the following steps:
Figure BDA0003035621820000044
wherein the content of the first and second substances,
Figure BDA0003035621820000045
I＝[1,1,…,1]implementation of
Figure BDA0003035621820000046
And (5) performing medium element accumulation processing.
As an improvement of the above system, the specific processing procedure of the complex-domain observation sequence and perception matrix construction module includes:
according to P (theta) ═ P (theta)1),P(θ2),…,P(θN)]T，[·]TFor matrix transposition, let I be the observation sequence, for the corresponding spatial spectrum P (θ)n) Performing transformation processing, expressing in the form of observation sequence and complex domain perception matrix, and constructing complex domain perception matrix
Figure BDA0003035621820000047
Wherein, A (theta)n) Satisfies the following formula:
Figure BDA0003035621820000048
as an improvement of the above system, the specific processing procedure of the complex domain compressed sensing processing module includes:
obtaining the spatial signal sparsity coefficient s (t) by solving the following convex optimization problem:
min||S(t)||1
Figure BDA0003035621820000049
processing the space signal sparse coefficient S (t) to obtain a synthetic space spectrum P (theta) as follows:
P(θ)＝|S(t)|2
the peak position of the synthesized spatial spectrum P (θ) is searched for target detection.
Compared with the prior art, the invention has the advantages that:
1. according to the method, correlation and accumulation processing are carried out on array data in a complex domain, the signal-to-noise ratio contained in data at each position of a sensing matrix is improved, so that the data at each position of the sensing matrix has certain array gain, and compared with an observation sequence used in an array signal processing method based on frequency domain compressed sensing, the signal-to-noise ratio contained in the data at each position of the sensing matrix is improved, and further the minimum requirement of the frequency domain compressed sensing method on the input signal-to-noise ratio is improved;
2. compared with a frequency domain compressed sensing method, the method provided by the invention has the advantages that the minimum requirement on the input signal-to-noise ratio is reduced by nearly 10lgMdB (M is the number of channels) under the same detection probability, and the detection capability of a weak target is improved.
Drawings
Fig. 1 is a schematic view of a horizontal towed-line array sonar structure adopted in embodiment 1 of the present invention;
FIG. 2 is a flow chart of the array signal processing method based on complex domain compressed sensing of the present invention;
FIG. 3 is a graph showing the probability of detection of a target obtained by 200 independent statistics using the MVDR method, the MUSIC method, the FCS method and the CCS method of the present invention, respectively;
FIG. 4 shows the spatial spectra (SNR ═ 0dB) obtained by the MVDR method, the MUSIC method, the FCS method and the CCS method of the present invention, respectively;
FIG. 5 shows the spatial spectrum (SNR-10 dB) obtained by the MVDR method, the MUSIC method, the FCS method and the CCS method of the present invention, respectively;
FIG. 6 shows the spatial spectrum (SNR-15 dB) obtained by the MVDR method, the MUSIC method, the FCS method and the CCS method of the present invention, respectively;
FIG. 7 is an azimuth history graph output using the MVDR method;
FIG. 8 is a diagram of an azimuth history output using the MUSIC method;
FIG. 9 is a chart of azimuth history output using the FCS method;
FIG. 10 is a chart of azimuth history output using the CCS method of the present invention.
Detailed Description
Aiming at the problem of performance degradation of an array signal processing method based on frequency domain compressed sensing under the condition of low signal-to-noise ratio, the invention provides an array signal processing method based on complex domain compressed sensing according to the relation of phase shift and time delay in array signal processing. The method comprises the steps of carrying out complex analytic transformation on received signals of the linear array, carrying out time delay compensation, correlation and accumulation processing on each array element signal in a complex domain according to an estimated azimuth, constructing a complex domain sensing matrix and a measured value, and realizing array signal processing by adopting a complex domain compression sensing method. The numerical simulation and actual measurement data processing results show that compared with a frequency domain compressed sensing method, the method has the advantages that the minimum requirement on the input signal-to-noise ratio is reduced by nearly 10lgMdB (M is the number of channels) under the same detection probability, and the detection capability of a weak target is improved.
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and examples.
Example 1
Before describing the method of the present invention in detail, the horizontal drawing line array used in the method of the present invention will be described. Fig. 1 is a schematic structural view of a horizontal towed array sonar, which comprises 6 parts, a display control and signal processor 1, a deck cable 2, a winch 3, a cable guide frame 4, a towing cable 5 and a horizontal towed array 6. The horizontal towing line array 6 is connected with a deck cable 2 on a winch 3 through a towing cable 5, and the towing cable 5 is also arranged on a cable guide frame 4; and the signal received by the horizontal dragging linear array 6 is transmitted to the display control and signal processor 1. It should be noted that the method of the present invention is not limited to horizontal towed linear arrays, and may be sonar arrays with multiple array elements.
The process of the present invention is further illustrated below.
Frequency domain compressed sensing method
Order: the frequency domain expression of the M-element equidistant linear array receiving signals is as follows:
X(f)＝A(f,θ)S(f)+V(f) (1)
wherein X (f) ═ X1(f),X2(f),…,XM(f)]TIn the form of a frequency domain vector of the linear array of received signals, S (f) ([ S ]1(f),S2(f),…,SK(f)]TIn the form of a frequency domain vector of K target radiation signals in space, V (f) ═ V1(f),V2(f),…,VM(f)]TIn the form of a frequency domain vector of noise contained in the linear array of received signals,A(f,θ)＝[a(f,θ1),a(f,θ2),…,a(f,θK)]is a linear array manifold, thetak(K1, 2, … K) e theta is the orientation of the kth target relative to the linear array,
Figure BDA0003035621820000061
is a direction vector. Wherein [ ·]TAnd c represents the matrix transfer operator, c represents the speed, and d represents the distance between adjacent array elements.
If the entire space is divided into sufficiently small directional intervals
Figure BDA0003035621820000062
And assuming every possible direction
Figure BDA0003035621820000063
All corresponding to a potential target signal
Figure BDA0003035621820000064
Thus, N target signals are constructed
Figure BDA0003035621820000065
Complete array manifold constructed at this time
Figure BDA0003035621820000066
Wherein the content of the first and second substances,
Figure BDA0003035621820000067
the frequency domain wideband model shown in equation (1) can be expressed as:
Figure BDA0003035621820000068
where J is 1,2, …, and J is the band number.
It is clear that the following description of the preferred embodiments,
Figure BDA0003035621820000069
Sa(fj) Only the corresponding direction in (theta)1,θ2,…θNThe target energy on is large, while the other direction is a sufficiently small value, i.e. Sa(fj) Is a sparse representation of the frequency domain of the signal space. Comparing the compressed sensing models, if any
Figure BDA0003035621820000071
To be seen as a sequence of observations,
Figure BDA0003035621820000072
as a sensing matrix, Sa(fj) For the sparse coefficient component to be solved, Va(fj) To measure noise, the spatial signal sparsity coefficient S can be solved by solving the following convex-down optimization problema(fj)：
Figure BDA0003035621820000073
At this time, S calculated by equation (4)a(fj) I.e. the spatial spectrum estimation value of the j-th sub-band.
P(fj,θ)＝|Sa(fj)|2 (4)
Repeating the above process for all sub-bands and summing, so as to obtain a total space spectrum P (theta), and searching the peak position of the space spectrum P (theta) to realize target azimuth estimation.
Figure BDA0003035621820000074
The method is an array signal processing method based on frequency domain compressed sensing.
Complex domain compressed sensing method
Basic principle
According to the array signal processing method model based on frequency domain compressed sensing, when an observation sequence and a sensing matrix are constructed by using single frequency domain data, the signal-to-noise ratio contained in the array element domain data is enhanced only by using the self information of each array element and not by using the correlation difference characteristic between the signals and the noises of each array element. In contrast, the present invention provides a complex domain processing method, i.e., an array signal processing method based on complex domain compressed sensing, in which correlation and accumulation processing are performed on array data in a complex domain, so as to improve the signal-to-noise ratio of data at each position of a sensing matrix, as shown in fig. 2.
Firstly, complex analytic wavelet transform is adopted to carry out complex analytic transform on array data, and complex analytic data of each array element signal x (t) are constructed in a complex domain
Figure BDA0003035621820000075
Figure BDA0003035621820000076
Is x (t) the corresponding imaginary data.
Second, at a scan angle θnIn the above, the data is repeatedly analyzed for each array element
Figure BDA0003035621820000077
Push button
Figure BDA0003035621820000078
And carrying out time delay compensation to obtain data after time delay compensation.
Figure BDA0003035621820000079
In the formula, d is the array element spacing, c is the sound velocity, N is 1,2, … N, N is the number of scanning angles, M is 1,2, … M, and M is the number of array elements.
Constructing a time-delay compensated covariance matrix in a complex domain
Figure BDA00030356218200000710
To pair
Figure BDA00030356218200000711
Zeroing the main diagonal elements and aligning the zeroed sum-pair covariance matrices
Figure BDA00030356218200000712
And accumulating to obtain a corresponding spatial spectrum as follows:
Figure BDA0003035621820000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003035621820000082
I＝[1,1,…,1]implementation of
Figure BDA0003035621820000083
And (5) performing medium element accumulation processing.
Then, equation (7) is transformed and expressed in the form of an observation sequence or a perceptual matrix, that is, I is regarded as an observation sequence, and P (θ) ([ P (θ) ]1),P(θ2),…,P(θN)]T，[·]TFor matrix transposition, for sparse coefficient components to be solved, a complex domain sensing matrix is used
Figure BDA0003035621820000084
The design is as follows:
Figure BDA0003035621820000085
finally, the spatial signal sparsity coefficient s (t) is solved by solving the following convex optimization problem:
Figure BDA0003035621820000086
and (4) processing the S (t) to obtain a synthesized space spectrum P (theta) of the method, and searching the peak position of the space spectrum P (theta) to realize target detection.
P(θ)＝|S(t)|2 (10)
Method capability analysis of the invention
In the processing frequency band, the correlation between the space target signals and the correlation between the background noises are made to be zero, and the power spectrum of the background noises is made to be
Figure BDA0003035621820000087
Signal power of
Figure BDA0003035621820000088
Then
Figure BDA0003035621820000089
Each location data may be represented as:
Figure BDA0003035621820000091
in addition, the array signal processing method based on frequency domain compressed sensing is used for forming observation sequences, and the observation sequences
Figure BDA0003035621820000092
Each position data contains a signal-to-noise ratio of:
Figure BDA0003035621820000093
also, as can be seen from equation (11), after complex domain processing,
Figure BDA0003035621820000094
each position data contains a signal-to-noise ratio of:
Figure BDA0003035621820000095
comparing the equations (12) and (13), the array signal processing method based on complex domain compressed sensing makes each position data of the sensing matrix have a certain array gain by correlating and accumulating each array element data, and improves the signal-to-noise ratio of each position data of the sensing matrix compared with the observation sequence used by the array signal processing method based on frequency domain compressed sensing, thereby improving the minimum requirement of the array signal processing method based on frequency domain compressed sensing on the input signal-to-noise ratio.
Simulation example analysis 1
The effect of the process of the invention is compared below with reference to example 1.
In order to further verify that the method can effectively realize array signal processing under the condition of low signal-to-noise ratio, and realize detection on the target, the following numerical simulation analysis is carried out.
The following table is a numerical simulation parameter set.
TABLE 1
Figure BDA0003035621820000096
Figure BDA0003035621820000101
FIG. 3 shows the probability of target detection obtained by 200 independent statistics of the MVDR method, the MUSIC method, the array signal processing method based on frequency domain compressed sensing (referred to as FCS method in the present invention) and the method of the present invention (referred to as CCS method in the present invention) under the condition that the SNR is-24 dB-0 dB
As can be seen from the results in fig. 3, compared with the FCS method, the CCS method performs correlation and accumulation processing on each array element signal, so that effective target detection is achieved under the condition of low signal-to-noise ratio; compared with the FCS method, the CCS method reduces the minimum requirement on the input signal-to-noise ratio by 6 dB.
FIG. 4 shows the spatial spectra (SNR ═ 0dB) obtained by the MVDR method, the MUSIC method, the FCS method and the CCS method;
FIG. 5 shows the spatial spectra (SNR-10 dB) obtained by MVDR method, MUSIC method, FCS method, and CCS method;
fig. 6 shows the spatial spectra (SNR-15 dB) obtained by the MVDR method, the MUSIC method, the FCS method, and the CCS method.
From the simulation results, it can be obtained: compared with the MVDR method and the MUSIC method, the FCS method and the CCS method can realize high-resolution detection and resolution on adjacent targets; however, as the signal-to-noise ratio is reduced, the resolving power of the MVDR method and the MUSIC method is reduced more severely, under the condition that the signal-to-noise ratio is-10 dB, the MVDR method and the MUSIC method cannot achieve the resolution of two targets, and the FCS method and the CCS method also maintain the target resolving power under the condition of high signal-to-noise ratio, but compared with the condition of high signal-to-noise ratio, the spatial spectrum obtained by the FCS method is seriously polluted by noise, and effective detection of the two targets cannot be achieved under the condition of-15 dB.
Simulation example analysis 2
The effect of the process of the invention is compared below with reference to example 2.
A plurality of targets exist in the data processing time period, wherein the relative array orientations of 30 degrees, 60 degrees, 80 degrees, 100 degrees, 130 degrees and 140 degrees are ships with large tonnage, and the sound level is about 120 dB-130 dB @1 kHz.
The 4 methods were performed as described in example analysis 1. Fig. 7 to 10 are output time history charts of 4 methods. Specifically, the method comprises the following steps:
FIG. 7 is a diagram of an output azimuth history of the MVDR method;
FIG. 8 is a diagram of the output azimuth history of the MUSIC method;
FIG. 9 is a diagram of the output azimuth history of the FCS method;
FIG. 10 is a diagram of the CCS method output bearing history.
As can be seen from the results shown in fig. 7 to 10, the spatial spectrum obtained by the MUSIC method and the FCS method cannot effectively detect the 130 ° target within a time period of 0 to 180s, and the azimuth history chart formed by the spatial spectrum obtained by the CCS method can clearly show the target tracks (carrying platforms) of 30 °, 60 °, 80 °, 100 °, 130 °, 140 ° and 160 °, so that the target azimuth is clearly recognizable; although the MVDR method can effectively detect a plurality of targets in the time interval, the detection effect of the target azimuth at 20 degrees is inferior to that of the CCS method due to the unknown pulse target at 40 degrees, and the background level is much higher than that of the CCS method.
The data processing result verifies that the CCS method can effectively detect the target under the condition of low signal-to-noise ratio.
Example 2
Based on the above method, embodiment 2 of the present invention provides an array signal processing system based on complex domain compressed sensing, where the system includes: the method comprises the following steps: the device comprises a complex analysis transformation module, a time delay compensation and correlation accumulation module, a complex domain observation sequence and perception matrix construction module and a complex domain compressed perception processing module; wherein the content of the first and second substances,
the complex analytic transformation module is used for carrying out complex analytic transformation on array signals received by the sonar array to obtain complex analytic data of each array element;
the time delay compensation and correlation accumulation module is used for carrying out time delay compensation, correlation and accumulation processing on the complex analysis data of each array element in the complex domain according to the estimated azimuth;
the complex domain observation sequence and sensing matrix construction module is used for constructing an observation sequence and a complex domain sensing matrix;
the complex domain compressed sensing processing module is used for realizing array signal processing by adopting a complex domain compressed sensing method.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (7)

1. A method for array signal processing based on complex domain compressed sensing, the method comprising:
carrying out complex analytic transformation on array signals received by the sonar array to obtain complex analytic data of each array element, carrying out time delay compensation, correlation and accumulation processing on the complex analytic data of each array element in a complex domain according to the estimated orientation, constructing an observation sequence and a complex domain perception matrix, and realizing array signal processing by adopting a complex domain compressed sensing method.
2. The array signal processing method based on complex domain compressed sensing according to claim 1, wherein the method specifically comprises:
step 1) carrying out complex analytic transformation on array signals received by the sonar array by adopting complex analytic wavelet transformation, and constructing complex analytic data of each array element and complex analytic data of the m-th array element in a complex domain
Figure FDA0003035621810000011
Comprises the following steps:
Figure FDA0003035621810000012
wherein, M is 1,2, … M, M is array element number of sonar array, xm(t) and
Figure FDA0003035621810000013
respectively real part data and imaginary part data, j is an imaginary part symbol, and t represents a time domain;
step 2) at the nth scanning angle thetanThe complex analysis data of the m-th array element
Figure FDA0003035621810000014
Push button
Figure FDA0003035621810000015
Performing time delay compensation to obtain the complex analysis data of the mth array element after the time delay compensation
Figure FDA0003035621810000016
Comprises the following steps:
Figure FDA0003035621810000017
wherein d is array element spacing of the sonar array, c is sound velocity, N is 1,2, … N, and N is the number of scanning angles;
step 3) constructing a covariance matrix after time delay compensation in a complex domain
Figure FDA0003035621810000018
To pair
Figure FDA0003035621810000019
Zeroing the main diagonal elements and aligning the zeroed covariancesMatrix array
Figure FDA00030356218100000110
Performing accumulation processing to obtain corresponding spatial spectrum P (theta)n) Comprises the following steps:
Figure FDA00030356218100000111
wherein the content of the first and second substances,
Figure FDA0003035621810000021
I＝[1,1,…,1]implementation of
Figure FDA0003035621810000022
Performing medium element accumulation treatment;
step 4) according to P (theta) ═ P (theta)1),P(θ2),…,P(θN)]T，[·]TFor matrix transposition, let I be the observation sequence, for the corresponding spatial spectrum P (θ)n) Performing transformation processing, expressing in the form of observation sequence and complex domain perception matrix, and constructing complex domain perception matrix
Figure FDA0003035621810000025
Wherein, A (theta)n) Satisfies the following formula:
Figure FDA0003035621810000023
step 5), obtaining a space signal sparse coefficient S (t) by solving the following convex optimization problem:
min||S(t)||1
Figure FDA0003035621810000024
step 6) processing the space signal sparse coefficient S (t) to obtain a synthetic space spectrum P (theta) which is as follows:
P(θ)＝|S(t)|2
the peak position of the synthesized spatial spectrum P (θ) is searched for target detection.
3. An array signal processing system based on complex domain compressed sensing, the system comprising: the device comprises a complex analysis transformation module, a time delay compensation and correlation accumulation module, a complex domain observation sequence and perception matrix construction module and a complex domain compressed perception processing module; wherein the content of the first and second substances,
the complex analytic transformation module is used for carrying out complex analytic transformation on array signals received by the sonar array to obtain complex analytic data of each array element;
the time delay compensation and correlation accumulation module is used for carrying out time delay compensation, correlation and accumulation processing on the complex analysis data of each array element in the complex domain according to the estimated azimuth;
the complex domain observation sequence and sensing matrix construction module is used for constructing an observation sequence and a complex domain sensing matrix;
the complex domain compressed sensing processing module is used for realizing array signal processing by adopting a complex domain compressed sensing method.
4. The array signal processing system based on complex domain compressed sensing of claim 3, wherein the specific processing procedure of the complex analytic transformation module comprises:
carrying out complex analytic transformation on array signals received by the sonar array by adopting complex analytic wavelet transformation, and constructing complex analytic data of each array element and complex analytic data of the m-th array element in a complex domain
Figure FDA0003035621810000031
Comprises the following steps:
Figure FDA0003035621810000032
wherein, M is 1,2, … M, M is array element number of sonar array, xm(t) and
Figure FDA0003035621810000033
real and imaginary data, respectively, j is the imaginary symbol, and t represents the time domain.
5. The array signal processing system based on complex domain compressed sensing of claim 4, wherein the specific processing procedure of the delay compensation and correlation accumulation module comprises:
at the nth scan angle thetanThe complex analysis data of the m-th array element
Figure FDA0003035621810000034
Push button
Figure FDA0003035621810000035
Performing time delay compensation to obtain the complex analysis data of the mth array element after the time delay compensation
Figure FDA0003035621810000036
Comprises the following steps:
Figure FDA0003035621810000037
wherein d is array element spacing of the sonar array, c is sound velocity, N is 1,2, … N, and N is the number of scanning angles;
constructing a time-delay compensated covariance matrix in a complex domain
Figure FDA0003035621810000038
To pair
Figure FDA0003035621810000039
Zeroing the main diagonal elements and aligning the zeroed covariance matrix
Figure FDA00030356218100000310
Performing accumulation processing to obtain corresponding spatial spectrum P (theta)n) Comprises the following steps:
Figure FDA00030356218100000311
wherein the content of the first and second substances,
Figure FDA00030356218100000312
I＝[1,1,…,1]implementation of
Figure FDA00030356218100000313
And (5) performing medium element accumulation processing.
6. The array signal processing system based on complex domain compressed sensing of claim 5, wherein the specific processing procedure of the complex domain observation sequence and sensing matrix construction module comprises:
according to P (theta) ═ P (theta)1),P(θ2),…,P(θN)]T，[·]TFor matrix transposition, let I be the observation sequence, for the corresponding spatial spectrum P (θ)n) Performing transformation processing, expressing in the form of observation sequence and complex domain perception matrix, and constructing complex domain perception matrix
Figure FDA00030356218100000314
Wherein, A (theta)n) Satisfies the following formula:
Figure FDA0003035621810000041
7. the array signal processing system based on complex domain compressed sensing of claim 6, wherein the specific processing procedure of the complex domain compressed sensing processing module comprises:
obtaining the spatial signal sparsity coefficient s (t) by solving the following convex optimization problem:
min||S(t)||1
Figure FDA0003035621810000042
processing the space signal sparse coefficient S (t) to obtain a synthetic space spectrum P (theta) as follows:
P(θ)＝|S(t)|2
the peak position of the synthesized spatial spectrum P (θ) is searched for target detection.
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