CN116106879A - Linear array line spectrum coherent accumulation detection method in multi-path environment - Google Patents

Linear array line spectrum coherent accumulation detection method in multi-path environment Download PDF

Info

Publication number
CN116106879A
CN116106879A CN202310056371.0A CN202310056371A CN116106879A CN 116106879 A CN116106879 A CN 116106879A CN 202310056371 A CN202310056371 A CN 202310056371A CN 116106879 A CN116106879 A CN 116106879A
Authority
CN
China
Prior art keywords
array
signal
array element
autocorrelation
line spectrum
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202310056371.0A
Other languages
Chinese (zh)
Inventor
李涛
孙心毅
成建波
吕余海
刘坚强
张刚
侯旺
张丙飞
陈强强
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Unit 92728 Of Pla
Original Assignee
Unit 92728 Of Pla
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Unit 92728 Of Pla filed Critical Unit 92728 Of Pla
Priority to CN202310056371.0A priority Critical patent/CN116106879A/en
Publication of CN116106879A publication Critical patent/CN116106879A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
    • G01S7/539—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G06F17/142—Fast Fourier transforms, e.g. using a Cooley-Tukey type algorithm
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention relates to a line array line spectrum coherent accumulation detection method in a multi-path environment, which comprises the following steps: collecting a received signal of each array element in N array elements of a uniform linear array, performing sliding FFT processing on the received signal, and extracting a time-dimensional narrowband line spectrum signal; carrying out autocorrelation on the narrowband spectrum signals output by each array element to obtain a time autocorrelation array of the output signals of each frequency point; and performing characteristic decomposition on the time correlation array, and taking the difference between the maximum characteristic value of the autocorrelation array and the average value of the rest characteristic values as the estimation of the signal power. The algorithm of the invention can carry out phase compensation on different array element outputs, realizes in-phase addition of the array element outputs, and has higher processing gain compared with incoherent accumulation, and is consistent with the conventional beam forming processing gain under the plane wave condition.

Description

Linear array line spectrum coherent accumulation detection method in multi-path environment
Technical Field
The invention belongs to the technical field of underwater acoustic signal processing methods, and particularly relates to a linear array line spectrum coherent accumulation detection method in a multi-path environment.
Background
LOFAR line spectrum spectrogram analysis is one of the main passive sounding modes of sonar and is used for detecting narrow-band noise signals radiated by underwater and water targets such as submarines, ships, torpedoes and the like. The line spectrum of the LOFAR is the distribution of acoustic energy in both the time and frequency dimensions, and can be generally extracted by short-time fourier (STFT), adaptive spectral line enhancement, and other algorithms. The linear array sonar is a main form of the prior hull sonar, the towed sonar and the like, generally mainly adopts a horizontal array, and is widely applied to the world-wide nationwide submarine sonar. In recent years, vertical linear array sonar is widely applied to the fields of underwater sound measurement, aviation sonobuoys and the like. Due to the non-uniformity of ocean propagation channels and the reflection of sea surfaces and seafloors, linear array sonar is subjected to serious multi-path effect interference during use, which is particularly remarkable in vertical linear arrays. Because the influence of the multi-path environment makes the phase relation among the linear array elements unable to be processed based on the conventional wave beam forming mode according to the assumption of the far-field plane wave, so that the incoherent accumulation among the array elements is realized by generally adopting a mode of neglecting the phase information and adopting the amplitude accumulation, but the incoherent accumulation has low processing gain, has larger difference with the conventional wave beam forming processing gain under the plane wave condition, and cannot meet the signal processing requirement.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a coherent accumulation algorithm for extracting the linear array line spectrum under the multi-path condition, and carries out phase compensation on different array element outputs, so as to realize the in-phase addition of the array element outputs, and achieve the effects of higher processing gain than incoherent accumulation and consistent processing gain with the conventional beam forming under the plane wave condition.
In order to achieve the above purpose, the technical scheme provided by the invention is as follows:
a method for detecting line spectrum coherent accumulation of a linear array in a multi-path environment comprises the following steps:
collecting a received signal of each array element in N array elements of a uniform linear array, performing sliding FFT processing on the received signal, and extracting a time-dimensional narrowband line spectrum signal;
carrying out autocorrelation on the narrowband spectrum signals output by each array element to obtain a time autocorrelation array of the output signals of each frequency point;
and performing characteristic decomposition on the time correlation array, and taking the difference between the maximum characteristic value of the autocorrelation array and the average value of the rest characteristic values as the estimation of the signal power.
Further, each of the N array elements of the uniform linear array is subjected to sliding FFT processing to extract a narrowband line spectrum of a time dimension,
Included
collecting a received signal of each array element in N array elements of a uniform linear array, performing sliding FFT processing on the received signal, and extracting a time-dimensional narrowband line spectrum signal;
an even linear array composed of N omni-directional array elements is provided with x as the receiving signal after sampling each array element i (N) (i=1, 2 … N), and subscript i denotes the i-th element. In order to extract the LOFAR line spectrum, as shown in FIG. 1, the output of each array element is subjected to sliding FFT processing, and the output of each frequency after each array element is subjected to sliding FFT processing is set as
Figure BDA0004060606460000021
Then
Figure BDA0004060606460000022
Wherein the superscript m represents the mth frequency point, m represents different frequency points, n represents different times, and K represents the number of data samples processed by the FFT and is also the number of samples of the frequency domain. Obviously, if x i (n) the frequency of existence is
Figure BDA0004060606460000023
When the line spectrum signal of (1) is obtained, the calculation process of (1) performs phase compensation on each data sample to realize in-phase addition, that is, the coherent accumulation process of the time dimension is completed, and the processing gain is K times.
Further, the narrowband spectrum signals output by each array element are subjected to autocorrelation, and estimation of a time autocorrelation array of the output signals of each frequency point is obtained
Included
If the same frequency of different array elements is output
Figure BDA0004060606460000031
Expressed in vector form, without loss of generality, can be expressed as
Figure BDA0004060606460000032
v 1 (n)、θ i (n) is the signal envelope and phase of each array element, n (n) is the noise vector, and y (n) is estimated by time correlation process
Figure BDA0004060606460000033
L is the number of relevant samples, and since equation (3) is a relevant accumulation process, the processing gain is analyzed, and then
Figure BDA0004060606460000034
Is->
Figure BDA0004060606460000035
Matrix elements of (2)
Figure BDA0004060606460000036
Wherein s is i (n+l) represents the spectral line signal of the FFT output
Figure BDA0004060606460000037
Then
Figure BDA0004060606460000038
The signal-to-noise ratio of (2) can be expressed as +.>
Figure BDA0004060606460000041
Assuming that the spectral lines of different array elements have consistent signal amplitudes and are uncorrelated with noise, equation (6) can be expressed as
Figure BDA0004060606460000042
Wherein SNR is y Output y for FFT i (n) signal to noise ratio.
Further, the pair of autocorrelation arrays
Figure BDA0004060606460000043
Performing characteristic decomposition to obtain the difference between the maximum characteristic value and the average value of the rest characteristic values as the estimation of the signal power, including
Assuming that the noise of different array elements is uncorrelated, and the signal is uncorrelated with the noise, the autocorrelation array R of y (n) is
R＝E[y(n)y H (n)]＝|v 1 (n)| 2 μ(n)μ H (n)+σ 2 I
(8)
Wherein H isConjugate transpose operation, v 1 (n) is the signal envelope of the array element 1, and the vector μ (n) represents the phase relationship between the line spectrum output signal of each array element and the line spectrum signal of the array element 1:
Figure BDA0004060606460000044
σ 2 is the noise power, I is the identity matrix, then
Rμ(n)＝λμ(n)
(10)
Figure BDA0004060606460000051
Lambda is the eigenvalue of the autocorrelation matrix and mu (n) is its corresponding eigenvector
Figure BDA0004060606460000052
/>
E|d(n)| 2 ＝λ
(13)
θ 1 (n) is the signal phase of array element 1;
from equation (12), the vector μ H And (n) carrying out phase compensation on different array element outputs to realize in-phase addition, namely coherent accumulation, of the array element outputs. From the form of equation (11), the eigenvalue λ is actually the sum of the coherently accumulated signal power and noise power, when |μ i (n) |=1, i.e. when the output signal amplitudes of the array elements are identical
λ＝N|v1(n)| 2 +σ 2
(14)
It is easily known that it achieves N times the processing gain, which is consistent with conventional beamforming processing gain under plane wave conditions;
it follows that the maximum eigenvalue obtained by performing eigenvalue decomposition on the autocorrelation matrix R of y (n), namelyFor coherently accumulating the output signal power and the noise power sigma 2 And the noise power can be estimated by taking the average of small eigenvalues, the power of the spectral line signal can be estimated as
Figure BDA0004060606460000053
Figure BDA0004060606460000061
Wherein lambda is max Is the maximum eigenvalue, lambda i The processing gain is N, and N is the number of array elements;
since the autocorrelation matrix R is not known in practice, the feature decomposition is estimated in the autocorrelation matrix
Figure BDA0004060606460000062
Carrying out on the process;
considering the FFT, autocorrelation and eigen decomposition processes together, the processed signal-to-noise ratio can be expressed as
Figure BDA0004060606460000063
Wherein SNR0 is the array element received signal x i (n) signal to noise ratio.
Further, the above calculation process is applied to each frequency narrowband spectrum signal output by each array element in a continuous time period, so that a local spectrum with continuous time-frequency domain can be obtained.
In another aspect, the present invention further provides a computer readable storage medium, where the computer readable storage medium includes a stored program, where the program executes the above-mentioned method for detecting line-array spectral coherence accumulation in a multi-path environment when running.
Furthermore, the invention also provides an electronic device, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor is used for executing the method for detecting the line spectrum coherence accumulation of the linear array in the multi-path environment through the computer program.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
according to a coherent accumulation algorithm for extracting the linear array line spectrum under the multi-path condition, firstly, each array element is subjected to sliding FFT processing to realize narrow-band line spectrum extraction in a time dimension, then, the narrow-band signals output by each array element are subjected to autocorrelation, the difference between the maximum eigenvalue of the autocorrelation array and the average value of the rest eigenvalues is the signal power estimation, and the corresponding eigenvector is used as a weighting vector output by the array element. The algorithm can carry out phase compensation on different array element outputs, realizes in-phase addition of the array element outputs, and has higher processing gain compared with incoherent accumulation, and is consistent with the conventional beam forming processing gain under the plane wave condition.
Drawings
FIG. 1 is a schematic diagram of a line spectrum processing flow using the method of the present invention;
fig. 2 is a schematic diagram showing a comparison of a theoretical gain value (denoted as a theoretical value in the figure) of a line spectrum graph processed by the method of the present invention and a gain value (denoted as a simulation value in the figure) of a line spectrum graph simulated by the monte carlo method, fig. 2 (a) is a SNR 0= -2.9dB processing gain graph, and fig. 2 (b) is an n=16 processing gain graph;
fig. 3 (a) and 3 (b) are schematic diagrams showing comparison of theoretical gain values of a line spectrum processed by the method of the present invention and gain values of a line spectrum processed by an incoherent accumulation mode, fig. 3 (a) is a line spectrum processed by incoherent accumulation, and fig. 3 (b) is a line spectrum processed by coherent accumulation.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, are intended to fall within the scope of the present invention.
The embodiment of the invention provides a line array line spectrum coherent accumulation detection method in a multi-path environment, which comprises the following steps of:
step S001, collecting a received signal of each array element in N array elements of a uniform linear array, performing sliding FFT processing on the received signal, and extracting a time-dimensional narrowband line spectrum signal;
an even linear array composed of N omni-directional array elements is provided with x as the receiving signal after sampling each array element i (N) (i=1, 2 … N), and subscript i denotes the i-th element. In order to extract the LOFAR line spectrum, as shown in FIG. 1, the output of each array element is subjected to sliding FFT processing, and the output of each frequency after each array element is subjected to sliding FFT processing is set as
Figure BDA0004060606460000071
Then
Figure BDA0004060606460000072
Wherein the superscript m represents the mth frequency point, m represents different frequency points, n represents different times, and K represents the number of data samples processed by the FFT and is also the number of samples of the frequency domain. Obviously, if x i (n) the frequency of existence is
Figure BDA0004060606460000081
When the line spectrum signal of (1) is obtained, the calculation process of (1) performs phase compensation on each data sample to realize in-phase addition, that is, the coherent accumulation process of the time dimension is completed, and the processing gain is K times.
The FFT processing result is analyzed as follows:
since the sliding FFT processing is effectively a narrowband processing procedure, its output
Figure BDA0004060606460000082
Is a narrowband signal. The multi-path effect of signal transmission, the target radiation signal is respectively incident to the receiving array from multiple directions, and the array element 1 is used as the reference array element
Figure BDA0004060606460000083
Can be expressed as
Figure BDA0004060606460000084
Wherein omega m For signal frequency, M i And the number of target radiation signals received by the ith array element under the multipath effect is represented.
Figure BDA0004060606460000085
For signal envelope>
Figure BDA0004060606460000086
The amplitude and phase fluctuations of the signal, which are the output after the sliding FFT processing, are characterized for the signal phase, respectively, which can be considered as slow-varying narrowband low-pass, +.>
Figure BDA0004060606460000087
Is a noise signal. Since the sum formula in the formula (1-1) represents M i Sum of vectors can make
Figure BDA0004060606460000088
Then
Figure BDA0004060606460000089
As shown in the formulas (1-3), under the multi-path environment, the array element output is still a narrow-band line spectrum signal after the sliding FFT processing, but due to the formulas (1-3)
Figure BDA00040606064600000810
And->
Figure BDA00040606064600000811
In fact, the result of the summation of a plurality of vectors as shown in the formula (1-2), the amplitude determined by the multi-way transmission +.>
Figure BDA00040606064600000812
And phase angle>
Figure BDA00040606064600000813
Neither is it available, and therefore both the amplitude and phase in equation (1-2) are unknown, nor are the amplitude and phase relationships between the different elements. Therefore, in a multi-path environment, the amplitude and the phase between the array element outputs after the sliding FFT processing do not meet the far-field parallel wave condition, and the phase compensation can not be carried out on the array element outputs in a conventional wave beam forming mode, so that the coherent accumulation of the space dimension is realized. For this purpose, the treatment is usually carried out in the form of incoherent accumulation, i.e. by first extracting +.>
Figure BDA0004060606460000091
Amplitude information of (2), and ignoring phase information
Figure BDA0004060606460000092
Where is conjugate operation, then the processing gain is achieved by the form of amplitude accumulation:
Figure BDA0004060606460000093
if it is assumed that the signal and noise are uncorrelated, the last two terms in equation (1-4) are ignored after accumulation processing in equation (1-5):
Figure BDA0004060606460000094
wherein N is the number of array elements, and L is the time accumulation number. As can be seen from equations (1-6), the incoherent accumulation output includes the average signal power and the noise power, and since the noise is rayleigh distributed after detection, the difference between the incoherent accumulation output and the coherent accumulation output is that since the average value of the rayleigh distribution is not zero, the signal-to-noise ratio gain NL times can not be realized after accumulation, and the ratio of the signal power to the rayleigh average value tends to be the same.
Therefore, the method for detecting the line-array line spectrum coherent accumulation under the multi-path environment needs to realize the spatial coherent accumulation under the multi-path condition.
Step S002, performing time-average autocorrelation (i.e. time correlation of multiple frequencies of the same array element) on the narrowband spectrum signal output by each array element through sliding FFT processing to obtain an estimate of the autocorrelation array of each frequency point output signal, including
If the same frequency of different array elements is output
Figure BDA0004060606460000095
Expressed in vector form
Figure BDA0004060606460000096
Where T is the transpose operation and n (n) is the noise vector. Then due to
Figure BDA0004060606460000097
For narrow-band line spectrum signals, envelope v i (n) and phase θ i (n) is a slowly varying narrow band low pass signal, which can be approximated as v within a single array sample i (n) and θ i (n) is a constant, and the phase relation between the co-frequency line spectrum signals among the array elements is a fixed value and still is a coherent signal. Therefore, without losing generality, the m superscript is omitted, y m (n) can be expressed as
Figure BDA0004060606460000101
/>
v 1 (n)、θ i (n) is the signal envelope and phase of each array element, considering the autocorrelation matrix of y (n):
R＝E[y(n)y H (n)] (2-1)
based on v i (n) and θ i (n) the slowly varying condition, R, can be estimated by a time dependent process, i.eEstimated as
Figure BDA0004060606460000102
Or expressed (without omitting superscript m):
Figure BDA0004060606460000103
wherein L represents the number of related samples, the superscript m represents the mth frequency point, m represents different frequency points, n represents different times, K represents the number of data samples processed by FFT and is also the number of samples of the frequency domain. The use effects of the formulas (3) and (3-1) are the same, and are calculated for each specific mth frequency point. L represents the number of correlation samples, the longer the correlation sample number is the longer the correlation period is.
Since equation (3) is a correlation accumulation process, the processing gain is analyzed, and then
Figure BDA0004060606460000104
Is->
Figure BDA0004060606460000105
Matrix elements of (2)
Figure BDA0004060606460000106
Wherein s is i (n+l) represents the spectral line signal in the FFT output
Figure BDA0004060606460000107
Then
Figure BDA0004060606460000108
The signal to noise ratio of (2) can be expressed as
Figure BDA0004060606460000111
Assuming that the spectral lines of different array elements have consistent signal amplitudes and are uncorrelated with noise, equation (6) can be expressed as
Figure BDA0004060606460000112
/>
Wherein SNR is y Output y for FFT i (n) signal to noise ratio.
Step 003, performing characteristic decomposition on the autocorrelation array, taking the difference between the maximum characteristic value and the average value of the rest characteristic values of the autocorrelation array as an estimate of signal power, taking the corresponding characteristic vector as a weighting vector of the array element output, performing phase compensation on each different array element output, and realizing in-phase addition, namely spatial coherence accumulation, of each array element output, including
Assuming that the noise of different array elements is uncorrelated, and the signal is uncorrelated with the noise, the autocorrelation array R of y (n) is
R＝E[y(n)y H (n)]＝|v 1 (n)| 2 μ(n)μ H (n)+σ 2 I (8)
Wherein H is conjugate transpose operation, v 1 (n) is the signal envelope of the array element 1, and the vector μ (n) represents the phase relationship between the line spectrum output signal of each array element and the line spectrum signal of the array element 1:
Figure BDA0004060606460000113
σ 2 is the noise power, I is the identity matrix, then
Rμ(n)＝λμ(n) (10)
Figure BDA0004060606460000121
Lambda is the eigenvalue of the autocorrelation matrix and mu (n) is its corresponding eigenvector
Figure BDA0004060606460000122
E|d(n)| 2 ＝λ (13)
θ 1 And (n) is the signal phase of array element 1.
From equation (13), the vector μ H And (n) carrying out phase compensation on different array element outputs to realize in-phase addition, namely coherent accumulation, of the array element outputs. From the form of equation (12), the eigenvalue λ is effectively the sum of the coherently accumulated signal power and noise power, when |μ i (n) |=1, i.e. when the output signal amplitudes of the array elements are identical
λ＝N|v 1 (n)| 2 +σ 2 (14)
It is readily apparent that it achieves N times the processing gain, which is consistent with conventional beamforming processing gain under plane wave conditions.
If y (n) is expressed as
Figure BDA0004060606460000123
Wherein the method comprises the steps of
μ(n)＝[1μ 2 (n)…μ N (n)] T (9-1-1)
Figure BDA0004060606460000124
Then
y i (n)＝μ i (n)y 1 (n)+n i (n) (9-2)
y i (n) is the ith element of y (n).
Due to envelope v i (n) and phase θ i (n) is a slowly varying narrow band low y (n) communication, which can be approximately considered to be within a single sample v when the number of signal samples is small i (n) and θ i (n) is a constant, mu i (n) can also be considered approximately constant within a single sample, that is, under multipass conditionsThe outputs of different array elements are still coherent signals, but the amplitude and phase relation between the outputs of different array elements represented by the formula (7) is unknown due to the influence of multi-path conditions. The coherent accumulation process needs to perform corresponding phase compensation and addition on the output of each array element so as to realize in-phase addition. For this purpose, assuming that the noise of the different array elements is uncorrelated and the signal is uncorrelated with noise, then the autocorrelation array of y (n):
R＝E[y(n)y H (n)|＝|v 1 (n)| 2 μ(n)μ H (n)+σ 2 I (17)
wherein H is conjugate transpose operation, sigma 2 Is the noise power, I is the identity matrix, then
Rμ(n)＝λμ(n) (18)
Figure BDA0004060606460000131
Obviously, λ is the eigenvalue of the autocorrelation matrix, and μ (n) is its corresponding eigenvector, an
Figure BDA0004060606460000132
E|d(n)| 2 ＝λ (21)
From equation (20), the vector μ H And (n) carrying out phase compensation on different array element outputs to realize in-phase addition, namely coherent accumulation, of the array element outputs.
From the form of equation (19), the eigenvalue λ is actually the sum of the coherently accumulated signal power and noise power, when |μ i (n) |=1, i.e. when the output signal amplitudes of the array elements are identical
λ＝N|v 1 (n)| 2 +σ 2 (22)
It achieves a processing gain of N times, consistent with conventional beamforming processing gain under plane wave conditions. Thus, the maximum eigenvalue obtained by performing eigenvalue decomposition on the autocorrelation matrix R of y (n)Coherent accumulation of output power and noise power sigma 2 And the corresponding feature vector is the weighting vector of the array element output. The noise power can be estimated by taking the average of the small eigenvalues, and the power of the spectral line signal can be estimated as
Figure BDA0004060606460000141
Wherein lambda is max Is the maximum eigenvalue, lambda i The processing gain is N, and N is the number of array elements;
or expressed (without omitting superscript m):
Figure BDA0004060606460000142
wherein the method comprises the steps of
Figure BDA0004060606460000143
For maximum characteristic value, ++>
Figure BDA0004060606460000144
Is a feature value other than the maximum feature value. The use effects of the formulas (15) and (15-1) are the same, and are calculated for each specific mth frequency point.
Since the autocorrelation matrix R is not known in practice, the feature decomposition needs to be estimated in the autocorrelation matrix
Figure BDA0004060606460000145
If the above calculation process is performed on each frequency narrowband spectrum signal output by each array element over a continuous period of time, a spectrum with continuous time-frequency domains can be obtained.
Considering the FFT, autocorrelation and eigen decomposition processes together, the processed signal-to-noise ratio can be expressed as
Figure BDA0004060606460000146
Wherein SNR0 is the array element received signal x i (n) signal to noise ratio.
Step 004: and applying the calculation process to each frequency narrowband line spectrum signal output by each array element on a continuous time period to obtain a spectrogram with continuous time and frequency domains.
In summary, the linear array line spectrum coherent accumulation process in the multi-path environment is as follows:
performing sliding FFT processing on the array element output, wherein the processing gain is K times, and K is the FFT processing length;
calculating time correlation matrix of output signals of each frequency point after FFT processing
Figure BDA0004060606460000147
Processing the gain;
for time correlation matrix
Figure BDA0004060606460000148
Performing characteristic decomposition to obtain a characteristic value;
and processing the characteristic value, taking the difference between the maximum characteristic value and the average value of the rest characteristic values as the signal power estimation of each frequency point, wherein the processing gain is N, and N is the number of array elements.
The verification result of the application of the linear array line spectrum coherent accumulation detection method in the multi-path environment is as follows:
the performance of the two aspects is verified by using a Monte Carlo simulation test method.
The method provided by the invention is used for processing the theoretical gain value of the line spectrum spectrogram under the conditions of different signal to noise ratios and different array element numbers, and simulating the gain value contrast performance of the line spectrum spectrogram by using a Monte Carlo method;
and secondly, verifying the algorithm performance when the amplitude and the phase fluctuate. Are all verified by comparison with incoherent accumulation.
Test one: setting the signal sampling rate to be 1 khz, and setting the FFT processing time to be 1 second, wherein the data sample number K=1000 of the FFT processing; the sliding FFT overlap ratio is 0; the correlation accumulation period is 60 seconds, and the correlation sample number l=60; the simulation time was 100 minutes. The target radiation signal is 300 Hz single-tone signal, the noise is Gaussian white noise, and the processing gain under the condition of different array element numbers is given in the signal-to-noise ratio of-2.9 dB in the figure 2 (a). Fig. 2 (b) shows the processing gain at different signal-to-noise ratios for a number of array elements of 16. As shown in fig. 2, simulation analysis of the Monte Carlo method shows that the theoretical gain value and the simulation value of the line spectrum spectrogram processed by the coherent accumulation algorithm of the method are basically consistent.
And (2) testing II: for simulating amplitude and phase fluctuation signals, a 200-order rectangular window filter is adopted to carry out smooth filtering on Gaussian white noise, the Gaussian white noise is multiplied by a 300 Hz single-tone signal, the low-pass signal is modulated to 300 Hz as a target radiation signal, the signal to noise ratio is set to be 1dB, the array element number is 64, incoherent accumulation of the formula (6) is adopted for comparison, other conditions are the same as those of the experiment one, and a LOFAR spectrogram analysis result is shown in FIG. 3. As shown in FIG. 3, under the condition of amplitude and phase slow fluctuation signals, the result of the line spectrum spectrogram processed by the coherent accumulation algorithm of the method also has obviously higher signal-to-noise ratio, and reflects higher processing gain. That is, fig. 3 (b) reflects a higher processing gain than the result of processing the line spectrum in the incoherent accumulation mode (fig. 3 (a).
On the other hand, the embodiment also provides a computer readable storage medium, wherein the computer readable storage medium comprises a stored program, and the program executes the method for detecting the line spectrum coherence accumulation in the multi-path environment.
Furthermore, the present embodiment provides an electronic device, including a memory and a processor, where the memory stores a computer program, and the processor is configured to execute the above-mentioned method for detecting line-array spectral coherence accumulation in a multi-path environment by using the computer program.

Claims (7)

1. A method for detecting line spectrum coherent accumulation of a linear array in a multi-path environment is characterized by comprising the following steps:
collecting a received signal of each array element in N array elements of a uniform linear array, performing sliding FFT processing on the received signal, and extracting a time-dimensional narrowband line spectrum signal;
carrying out autocorrelation on the narrowband spectrum signals output by each array element to obtain a time autocorrelation array of the output signals of each frequency point;
and carrying out characteristic decomposition on the autocorrelation array, and taking the difference between the maximum characteristic value of the autocorrelation array and the average value of the rest characteristic values as the estimation of the signal power.
2. The method for detecting line spectrum coherence accumulation in a multi-path environment according to claim 1, wherein each of the N array elements of the uniform line array is subjected to sliding FFT processing to extract a time-dimensional narrowband line spectrum
Included
Let the sampled received signal of each array element be x i (N) (i=1, 2 … N), subscript i denotes the i-th element and N denotes a different time; let the output of each frequency after each array element is processed by sliding FFT be
Figure FDA0004060606450000011
Then
Figure FDA0004060606450000012
Wherein the superscript m represents the mth frequency point, K represents the number of data samples processed by FFT and is the number of samples of the frequency domain; if x i (n) the frequency of existence is
Figure FDA0004060606450000013
When the line spectrum signal of (1) is obtained, the calculation process of (1) performs phase compensation on each data sample to realize in-phase addition, that is, the coherent accumulation process of the time dimension is completed, and the processing gain is K times.
3. The method for detecting line spectrum coherence accumulation in a multi-path environment according to claim 2, wherein the method comprises performing autocorrelation on narrowband line spectrum signals output by each array element to obtain an estimate of a time autocorrelation array of output signals of each frequency point
Included
If it is toSame frequency output of different array elements
Figure FDA0004060606450000021
Expressed in vector form, without loss of generality, can be expressed as
Figure FDA0004060606450000022
v 1 (n)、θ i (n) is the signal envelope and phase of each array element, n (n) is the noise vector, and y (n) is estimated by time correlation process
Figure FDA0004060606450000023
L is the number of relevant samples, and since equation (3) is a relevant accumulation process, the processing gain is analyzed, and then
Figure FDA0004060606450000024
Is->
Figure FDA0004060606450000025
Matrix elements of->
Figure FDA0004060606450000026
Wherein s is i (n+l) represents the spectral line signal of the FFT output
Figure FDA0004060606450000027
Then
Figure FDA0004060606450000031
The signal to noise ratio of (2) can be expressed as
Figure FDA0004060606450000032
Assuming that the spectral lines of different array elements have consistent signal amplitudes and are uncorrelated with noise, equation (6) can be expressed as
Figure FDA0004060606450000033
Wherein SNR is y Output y for FFT i (n) signal to noise ratio.
4. The method for detecting line spectrum coherent accumulation in a multi-path environment according to claim 3, wherein said pair of autocorrelation arrays
Figure FDA0004060606450000034
Performing characteristic decomposition to obtain the difference between the maximum characteristic value and the average value of the rest characteristic values as the estimation of the signal power, including
Assuming that the noise of different array elements is uncorrelated, and the signal is uncorrelated with the noise, the autocorrelation array R of y (n) is
R＝E[y(n)y H (n)]＝|v 1 (n)| 2 μ(n)μ H (n)+σ 2 I
(8)
Wherein H is conjugate transpose operation, v 1 (n) is the signal envelope of the array element 1, and the vector μ (n) represents the phase relationship between the line spectrum output signal of each array element and the line spectrum signal of the array element 1:
Figure FDA0004060606450000041
σ 2 is the noise power, I is the identity matrix, then
Rμ(n)＝λμ(n)
(10)
Figure FDA0004060606450000042
Lambda is the eigenvalue of the autocorrelation matrix and mu (n) is its corresponding eigenvector
Figure FDA0004060606450000043
E|d(n)| 2 ＝λ
(13)
θ 1 (n) is the signal phase of array element 1;
from equation (12), the vector μ H (n) carrying out phase compensation on different array element outputs to realize in-phase addition, namely coherent accumulation, of the array element outputs; from the form of equation (11), the eigenvalue λ is actually the sum of the coherently accumulated signal power and noise power, when |μ i (n) |=1, i.e. when the output signal amplitudes of the array elements are identical
λ＝N|v 1 (n)| 2 +σ 2
(14)
It is easily known that it achieves N times the processing gain, which is consistent with conventional beamforming processing gain under plane wave conditions;
from this, the maximum eigenvalue obtained by performing eigenvalue decomposition on the autocorrelation matrix R of y (n) is the coherent accumulation output signal power and noise power sigma 2 And the noise power can be estimated by taking the average of small eigenvalues, the power of the spectral line signal can be estimated as
Figure FDA0004060606450000051
Wherein lambda is max Is the maximum eigenvalue, lambda i For other characteristic values than the maximum characteristic value, the process increasesN is beneficial to the number of array elements;
since the autocorrelation matrix R is not known in practice, the feature decomposition is estimated in the autocorrelation matrix
Figure FDA0004060606450000052
Carrying out on the process; />
Considering the FFT, autocorrelation and eigen decomposition processes together, the processed signal-to-noise ratio can be expressed as
Figure FDA0004060606450000053
Wherein SNR0 is the array element received signal x i (n) signal to noise ratio.
5. The method for detecting line-array line spectrum coherent accumulation in a multi-path environment according to claim 4, wherein the time-frequency domain continuous LOFAR spectrum can be obtained by applying the calculation process to each frequency narrowband line spectrum signal output by each array element in a continuous time period.
6. A computer-readable storage medium, characterized in that the computer-readable storage medium comprises a stored program, wherein the program, when run, performs the linear array line spectrum coherent accumulation detection method under the multi-path environment as set forth in any one of claims 1 to 5.
7. An electronic device comprising a memory and a processor, wherein the memory has stored therein a computer program, the processor being arranged to execute the method of linear array linear spectral coherence accumulation detection in a multi-pass environment as claimed in any one of claims 1 to 5 by means of the computer program.
CN202310056371.0A 2023-01-17 2023-01-17 Linear array line spectrum coherent accumulation detection method in multi-path environment Pending CN116106879A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202310056371.0A CN116106879A (en) 2023-01-17 2023-01-17 Linear array line spectrum coherent accumulation detection method in multi-path environment

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202310056371.0A CN116106879A (en) 2023-01-17 2023-01-17 Linear array line spectrum coherent accumulation detection method in multi-path environment

Publications (1)

Publication Number Publication Date
CN116106879A true CN116106879A (en) 2023-05-12

Family

ID=86265099

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202310056371.0A Pending CN116106879A (en) 2023-01-17 2023-01-17 Linear array line spectrum coherent accumulation detection method in multi-path environment

Country Status (1)

Country Link
CN (1) CN116106879A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117607876A (en) * 2024-01-24 2024-02-27 汉江国家实验室 Method and system for detecting passive sonar multi-beam narrowband signals

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117607876A (en) * 2024-01-24 2024-02-27 汉江国家实验室 Method and system for detecting passive sonar multi-beam narrowband signals
CN117607876B (en) * 2024-01-24 2024-04-19 汉江国家实验室 Method and system for detecting passive sonar multi-beam narrowband signals

Similar Documents

Publication Publication Date Title
CN108375763B (en) Frequency division positioning method applied to multi-sound-source environment
US20080043574A1 (en) Sonar system and method providing low probability of impact on marine mammals
JP2011158471A (en) Method for detecting target in time-space adaptive processing system
CN101876715A (en) Method for suppressing noises from towing ships by using towed acoustic array
CN108880586B (en) A kind of broadband weak signal enhancement method and apparatus
CN116106879A (en) Linear array line spectrum coherent accumulation detection method in multi-path environment
CN110763327A (en) Single-vector hydrophone signal detection method under condition of plane baffle
Foroozan et al. Direction finding algorithms for time reversal MIMO radars
Chi et al. Design of an adaptive noise canceller for improving performance of an autonomous underwater vehicle-towed linear array
CN110146854B (en) Robust anti-interference method for FDA-MIMO radar
CN115242583B (en) Channel impulse response passive estimation method based on horizontal linear array
US6590833B1 (en) Adaptive cross correlator
Kulhandjian et al. 2-D DOA estimation of coherent wideband signals with auxiliary-vector basis
CN113704685A (en) Deep sea blind deconvolution method based on vertical line array
CN109861770B (en) Broadband signal detection method based on beam forming output power combination
Zhang et al. Two-Stage Learning Model-Based Angle Diversity Method for Underwater Acoustic Array
Aktas et al. Acoustic direction finding in highly reverberant environment with single acoustic vector sensor
Talebpour et al. Time Delay Estimation in Underwater Environment using Cross-Correlation Based Techniques
Yu et al. Robust adaptive beamforming for multi-path environment based on domain weighted PCA
Hassanien et al. Single-snapshot beamforming using fast iterative adaptive techniques
CN112834623B (en) Acoustic covering layer echo reduction measurement method based on compressed sensing technology
Grall et al. Theoretical analysis of a new approach to order determination for a modified Prony method in swath mapping application
Ma et al. Further results on maximal ratio combining under correlated noise for multi-carrier underwater acoustic communication using vector sensors
Sun et al. Robust adaptive beamforming method for active sonar in single snapshot
Shang et al. The analysis of interference suppression capability of mvdr algorithm based on microphone array

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination