A linear array line spectrum coherent accumulation detection method in a multipath environment

Abstract

The present application relates to a kind of linear array line spectrum coherent accumulation detection method under multi-path environment, comprising the following steps: collecting the received signal of each array element in the N array elements of uniform linear array, the received signal is carried out sliding FFT processing, and the narrowband line spectrum signal of time dimension is extracted;The narrowband line spectrum signal output by each array element is autocorrelated, and the time autocorrelation matrix of each frequency point output signal is obtained;Eigen decomposition is carried out to time correlation matrix, and the difference between the maximum eigenvalue of autocorrelation matrix and the average of remaining eigenvalues can be used as the estimation of signal power.The algorithm of the present application can carry out phase compensation to the output of different array elements, realize the in-phase addition of array element output, and simulation results show that the algorithm has higher processing gain than non-coherent accumulation, and is consistent with the processing gain of conventional beam forming under plane wave condition.

Description

Technical Field

[0001] This invention belongs to the technical field of underwater acoustic signal processing methods, specifically relating to a method for detecting the coherent accumulation of linear array spectrum in a multipath environment. Background Technology

[0002] LOFAR line spectrum analysis is one of the main passive submarine detection methods for sonar, used to detect narrowband noise signals radiated by underwater and surface targets such as submarines, ships, and torpedoes. The LOFAR line spectrum represents the distribution of acoustic energy in both time and frequency dimensions, and can generally be extracted using algorithms such as Short-Time Fourier Transform (STFT) and adaptive line enhancement. Linear array sonar is currently the main form of hull-mounted sonar and towed sonar, generally using horizontal arrays, and is widely used in submarine detection sonar worldwide. Vertical linear array sonar has also been widely used in recent years in underwater acoustic measurement and airborne sonar buoys. Due to the non-uniformity of the ocean propagation channel and reflections from the sea surface and seabed, linear array sonar faces severe multipath interference during use, which is particularly significant for vertical linear arrays. Due to the influence of multipath environment, the phase relationship between the elements of the linear array cannot be assumed according to the far-field plane wave, making it difficult to achieve spatial processing gain based on conventional beamforming. Therefore, phase information is usually ignored and amplitude accumulation is used to achieve incoherent accumulation between array elements. However, the processing gain of incoherent accumulation is not high and is significantly different from the processing gain of conventional beamforming under plane wave conditions, which cannot meet the signal processing requirements. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention proposes a coherent accumulation algorithm for line array spectrum extraction under multipath conditions. This algorithm performs phase compensation on the outputs of different array elements, achieving in-phase addition of the array element outputs. This results in a higher processing gain than incoherent accumulation and an effect consistent with the processing gain of conventional beamforming under plane wave conditions.

[0004] To achieve the above objectives, the technical solution provided by the present invention is as follows:

[0005] A method for detecting coherent accumulation of linear array spectrum under multipath conditions includes the following steps:

[0006] The received signal of each of the N elements of a uniform linear array is collected, and the received signal is processed by sliding FFT to extract the narrowband line spectrum signal in the time dimension.

[0007] Autocorrelation is performed on the narrowband line spectrum signals output by each array element to obtain the time autocorrelation matrix of the output signals at each frequency point;

[0008] The signal power can be estimated by performing eigenvalue decomposition on the time-correlation matrix and taking the difference between the largest eigenvalue and the average of the remaining eigenvalues.

[0009] Furthermore, each of the N elements of the uniform linear array undergoes a sliding FFT process to extract the narrowband line spectrum in the time dimension.

[0010] include

[0011] The received signal of each of the N elements of a uniform linear array is collected, and the received signal is processed by sliding FFT to extract the narrowband line spectrum signal in the time dimension.

[0012] A uniform linear array consisting of N omnidirectional elements, where the received signal after sampling of each element is x. i (n)(i=1,2…N), where the subscript i represents the i-th element. To extract the LOFAR line spectrum, as shown... Figure 1 As shown, firstly, a sliding FFT is performed on the array element outputs. Let the output of each array element at each frequency after the sliding FFT be... but

[0013]

[0014] Where the superscript m denotes the m-th frequency point, m represents different frequency points, n represents different times, and K represents the number of data samples processed by the FFT, which is also the number of samples in the frequency domain. Clearly, if x i (n) has a frequency of When the line spectrum signal is obtained, the calculation process of equation (1) performs phase compensation on each data sample to achieve in-phase addition, that is, completes the coherent accumulation processing in the time dimension, and its processing gain is K times.

[0015] Furthermore, the autocorrelation of the narrowband line spectrum signals output by each array element is performed to obtain an estimate of the time autocorrelation matrix of the output signal at each frequency point.

[0016] include

[0017] If the same frequency is output from different array elements Represented in vector form, without loss of generality, omitting the superscript m, it can be expressed as:

[0018]

[0019] v1(n), θ i y(n) represents the signal envelope and phase of each array element, respectively, and n(n) is the noise vector. The autocorrelation matrix R of y(n) can be estimated through a time correlation process.

[0020]

[0021] L is the number of relevant samples. Since equation (3) is a correlation accumulation process, let's analyze its processing gain. for The matrix elements, then

[0022]

[0023] Where s i (n+l) represents the spectral line signal output by the FFT.

[0024]

[0025] but The signal-to-noise ratio can be expressed as

[0026]

[0027] Assuming that the spectral lines of different array elements have the same amplitude and that the signal and noise are uncorrelated, then equation (6) can be expressed as follows:

[0028]

[0029] SNR y For the output y of FFT i The signal-to-noise ratio of (n).

[0030] Furthermore, the autocorrelation matrix Eigenvalue decomposition is performed, and the difference between the largest eigenvalue and the average of the remaining eigenvalues ​​can be used as an estimate of the signal power, including...

[0031] Assuming that the noise of different array elements is uncorrelated, and the signal and noise are uncorrelated, then the autocorrelation matrix R of y(n) is:

[0032] R = E[y(n)y H [(n)]=|v1(n)| 2 μ(n)μ H (n)+σ 2 I (8)

[0033] Where H is the conjugate transpose operation, v1(n) is the signal envelope of array element 1, and vector μ(n) represents the phase relationship between the line spectrum output signal of each array element and the line spectrum signal of array element 1:

[0034]

[0035] σ 2 Let I be the noise power, and I be the identity matrix.

[0036] Rμ(n)=λμ(n) (10)

[0037]

[0038] λ is the eigenvalue of the autocorrelation matrix, and μ(n) is its corresponding eigenvector.

[0039]

[0040] E|d(n)| 2 =λ (13)

[0041] θ1(n) is the signal phase of array element 1;

[0042] From equation (12), we know that from vector μ H (n) Phase compensation was performed on the outputs of different array elements to achieve in-phase addition of the array element outputs, i.e., coherent accumulation. From the form of equation (11), we know that the eigenvalue λ is actually the sum of the signal power and noise power after coherent accumulation. When |μ i (n)|=1, which means that the amplitudes of the output signals of all array elements are consistent.

[0043] λ=N|v1(n)| 2 +σ 2 (14)

[0044] It is easy to see that it has achieved a processing gain of N times, which is consistent with the processing gain of conventional beamforming under plane wave conditions;

[0045] Therefore, by performing eigenvalue decomposition on the autocorrelation matrix R of y(n), the largest eigenvalue obtained is the coherent accumulated output signal power and noise power σ. 2 The sum of these values, and the noise power, can be estimated by averaging the smaller eigenvalues. Therefore, the power of the spectral line signal can be estimated as follows:

[0046]

[0047] Where λ max λ is the largest eigenvalue. i For eigenvalues ​​other than the largest eigenvalue, the processing gain is N, where N is the number of array elements.

[0048] Since the autocorrelation matrix R is actually unknown, the eigenvalue decomposition needs to be performed on the aforementioned estimation of the autocorrelation matrix. On;

[0049] Taking into account the FFT, autocorrelation, and eigenvalue decomposition processes, the processed signal-to-noise ratio can be expressed as:

[0050]

[0051] Where SNR0 is the array element received signal x i The signal-to-noise ratio of (n).

[0052] Furthermore, by applying the above calculation process to the narrowband line spectrum signals of each frequency output by each array element over a continuous time period, a LOFAR spectrum that is continuous in both the time and frequency domains can be obtained.

[0053] On the other hand, the present invention also provides a computer-readable storage medium comprising a stored program, wherein the program, when executed, performs the aforementioned method for detecting coherent accumulation of linear array line spectra in a multipath environment.

[0054] Furthermore, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor is configured to execute the aforementioned multipath environment linear array coherent accumulation detection method via the computer program.

[0055] Compared with the prior art, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0056] A coherent accumulation algorithm for line spectrum extraction of linear arrays under multipath conditions is proposed. First, each array element undergoes sliding FFT processing to extract narrowband line spectra in the time dimension. Then, the narrowband signals output by each element are autocorrelated. The difference between the maximum eigenvalue and the average of the remaining eigenvalues ​​of the autocorrelation matrix is ​​the signal power estimate, and the corresponding eigenvector is used as the weighting vector for the array element outputs. This algorithm can perform phase compensation on the outputs of different array elements, achieving in-phase addition of the element outputs. Simulation results show that the algorithm has a higher processing gain than incoherent accumulation, consistent with the processing gain of conventional beamforming under plane wave conditions. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the line spectrum processing flow using the method of the present invention;

[0058] Figure 2 is a schematic diagram comparing the theoretical gain value (indicated in the figure) of the line spectrum processed by the method of the present invention and the gain value (indicated in the figure) of the line spectrum processed by Monte Carlo simulation. Figure 2(a) is the gain diagram of SNR0 = -2.9dB and Figure 2(b) is the gain diagram of N = 16.

[0059] Figures 3(a) and 3(b) are schematic diagrams comparing the theoretical gain value of the line spectrum processed by the method of the present invention and the gain value of the line spectrum processed by the incoherent accumulation method. Figure 3(a) is the line spectrum processed by incoherent accumulation, and Figure 3(b) is the line spectrum processed by coherent accumulation. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Embodiments of the present invention provide a method for detecting coherent accumulation of linear array spectrum in a multipath environment, comprising the following steps:

[0062] Step S001: Collect the received signal of each of the N array elements of the uniform linear array, perform sliding FFT processing on the received signal, and extract the narrowband line spectrum signal in the time dimension.

[0063] A uniform linear array consisting of N omnidirectional elements, where the received signal after sampling of each element is x. i (n)(i=1,2…N), where the subscript i represents the i-th element. To extract the LOFAR line spectrum, as shown... Figure 1 As shown, firstly, a sliding FFT is performed on the array element outputs. Let the output of each array element at each frequency after the sliding FFT be... but

[0064]

[0065] Where the superscript m denotes the m-th frequency point, m represents different frequency points, n represents different times, and K represents the number of data samples processed by the FFT, which is also the number of samples in the frequency domain. Clearly, if x i (n) has a frequency of When the line spectrum signal is obtained, the calculation process of equation (1) performs phase compensation on each data sample to achieve in-phase addition, that is, completes the coherent accumulation processing in the time dimension, and its processing gain is K times.

[0066] The FFT processing results are analyzed as follows:

[0067] Since sliding FFT processing is actually a narrowband processing procedure, its output... It is a narrowband signal. Due to the multipath effect of signal transmission, the target radiated signal is incident on the receiving array from multiple directions. Taking array element 1 as the reference array element, then... It can be represented as

[0068]

[0069] Where ω m M is the signal frequency. i This represents the number of target radiation signals received by the i-th array element under multipath effects. For the signal envelope, The signal phase represents the amplitude and phase fluctuations of the signal, respectively. It is the output after sliding FFT processing and can be considered as a slowly varying narrowband low-pass signal. For noise signals, since the summation formula in equation (1-1) represents M... i The sum of vectors can be set as follows:

[0070]

[0071] but

[0072]

[0073] As shown in equation (1-3), in a multipath environment, the array element output after sliding FFT processing is still a narrowband line spectrum signal, but due to the... and In reality, it is the result of summing multiple vectors as shown in equation (1-2), with the amplitude determined by multipath transmission. and phase angle Since neither of these parameters can be obtained, the amplitude and phase in equation (1-2) are unknown, and the amplitude and phase relationships between different array elements are also unknown. Therefore, in a multipath environment, the amplitude and phase between array element outputs after sliding FFT processing do not satisfy the far-field parallel wave condition, making it impossible to use conventional beamforming methods to perform phase compensation on the array element outputs and achieve coherent accumulation in the spatial dimension. Therefore, incoherent accumulation is usually used, i.e., firstly, detection processing is performed to extract... The amplitude information is ignored, while the phase information is ignored.

[0074]

[0075] Where * represents the conjugate operation, and then the gain is processed through amplitude accumulation:

[0076]

[0077] If we assume that the signal and noise are uncorrelated, then the last two terms in equation (1-4) can be ignored after accumulation in equation (1-5):

[0078]

[0079] Where N is the number of array elements and L is the time accumulation quantity. As can be seen from equation (1-6), the output of incoherent accumulation includes the average signal power and the noise power. Since the noise follows a Rayleigh distribution after detection, the difference from coherent accumulation is that, since the mean of the Rayleigh distribution is not zero, it cannot achieve a signal-to-noise ratio gain of NL times after accumulation, but will tend to the ratio of signal power to Rayleigh mean.

[0080] Therefore, the multipath environment linear array coherent accumulation detection method of the present invention is needed to achieve spatial coherent accumulation under multipath conditions.

[0081] Step S002: Perform time-averaged autocorrelation (i.e., time correlation of multiple frequencies of the same array element) on the narrowband line spectrum signal output by each array element after sliding FFT processing to obtain an estimate of the autocorrelation matrix of the output signal at each frequency point, including...

[0082] If the same frequency is output from different array elements Represented in vector form

[0083]

[0084] Where T is the transpose operation and n(n) is the noise vector. Therefore... For narrowband line spectrum signals, the envelope v i (n) and phase θ i (n) is a slowly varying narrowband 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 relationship between the same-frequency line spectrum signals of each array element is a fixed value, still constituting a coherent signal. Therefore, without loss of generality, the superscript of m is omitted, and y m (n) can be represented as

[0085]

[0086] v1(n), θ i Let y(n) represent the signal envelope and phase of each array element, respectively. Consider the autocorrelation matrix of y(n):

[0087] R = E[y(n)y H (n)] (2-1)

[0088] Based on v i (n) and θ i (n) Given a slowly varying condition, R can be estimated through a time-dependent process, i.e., estimated as

[0089]

[0090] Or it can be expressed as (without omitting the superscript m):

[0091]

[0092] Where L represents the number of relevant samples, the superscript m represents the m-th frequency point, m represents different frequency points, n represents different times, and K represents the number of data samples processed by FFT, which is also the number of samples in the frequency domain. Equations (3) and (3-1) have the same effect, both calculating for each specific m-th frequency point. L represents the number of relevant samples; the more relevant samples, the longer the correlation duration.

[0093] Since equation (3) is a process of correlation accumulation, let's analyze its processing gain. for The matrix elements, then

[0094]

[0095] Where s i (n+l) represents the spectral line signal in the FFT output.

[0096]

[0097] but The signal-to-noise ratio can be expressed as

[0098]

[0099] Assuming that the spectral lines of different array elements have the same amplitude and that the signal and noise are uncorrelated, then equation (6) can be expressed as follows:

[0100]

[0101] SNR y For the output y of FFT i The signal-to-noise ratio of (n).

[0102] Step 003: Perform eigenvalue decomposition on the autocorrelation matrix. The difference between the largest eigenvalue and the average of the remaining eigenvalues ​​can be used as an estimate of the signal power. The corresponding eigenvector is used as the weighting vector of the array element outputs. Phase compensation is performed on the outputs of different array elements to achieve in-phase addition of the outputs of each array element, i.e., spatial coherence accumulation.

[0103] Assuming that the noise of different array elements is uncorrelated, and the signal and noise are uncorrelated, then the autocorrelation matrix R of y(n) is:

[0104] R = E[y(n)y H [(n)]=|v1(n)| 2 μ(n)μ H (n)+σ 2 I (8)

[0105] Where H is the conjugate transpose operation, v1(n) is the signal envelope of array element 1, and vector μ(n) represents the phase relationship between the line spectrum output signal of each array element and the line spectrum signal of array element 1:

[0106]

[0107] σ 2 Let I be the noise power, and I be the identity matrix.

[0108] Rμ(n)=λμ(n) (10)

[0109]

[0110] λ is the eigenvalue of the autocorrelation matrix, and μ(n) is its corresponding eigenvector.

[0111]

[0112] E|d(n)| 2 =λ (13)

[0113] θ1(n) is the signal phase of array element 1.

[0114] From equation (13), we know that from vector μ H (n) Phase compensation was performed on the outputs of different array elements to achieve in-phase addition of the array element outputs, i.e., coherent accumulation. From the form of equation (12), we know that the eigenvalue λ is actually the sum of the signal power and noise power after coherent accumulation. When |μ i (n)|=1, which means that the amplitudes of the output signals of all array elements are consistent.

[0115] λ=N|v1(n)| 2 +σ 2 (14)

[0116] It is easy to see that it achieved a processing gain of N times, which is consistent with the processing gain of conventional beamforming under plane wave conditions.

[0117] If we express y(n) as

[0118]

[0119] in

[0120] μ(n) = [1μ2(n)...μ N (n)] T (9-1-1)

[0121]

[0122] but

[0123] y i (n)=μ i (n)y1(n)+n i (n) (9-2)

[0124] y i (n) is the i-th element of y(n).

[0125] Due to the envelope v i (n) and phase θ i (n) is a slowly varying narrowband low-pass signal. When the number of signal samples is small, it can be approximated that v in a single sample... i (n) and θi If (n) is a constant, then μ i (n) can also be approximated as a constant within a single sample, meaning that under multipath conditions, the outputs of different array elements are still coherent signals. However, due to the influence of multipath conditions, the amplitude and phase relationship between the outputs of different array elements represented by equation (7) is unknown. To achieve coherent accumulation, corresponding phase compensation needs to be performed on the outputs of each array element before addition to achieve in-phase addition. Therefore, assuming that the noise of different array elements is uncorrelated and the signal is uncorrelated with the noise, the autocorrelation matrix of y(n) is:

[0126] R = E[y(n)y H (n)|=|v1(n)| 2 μ(n)μ H (n)+σ 2 I (17)

[0127] Where H is the conjugate transpose operation, σ 2 Let I be the noise power, and I be the identity matrix.

[0128] Rμ(n)=λμ(n) (18)

[0129]

[0130] Clearly, λ is the eigenvalue of the autocorrelation matrix, and μ(n) is its corresponding eigenvector, and

[0131]

[0132] E|d(n)| 2 =λ (21)

[0133] From equation (20), we know that from vector μ H (n) Perform phase compensation on the outputs of different array elements to achieve in-phase addition of the array element outputs, i.e., coherent accumulation.

[0134] From the form of equation (19), we know that the eigenvalue λ is actually the sum of the signal power and noise power after coherent accumulation. When |μ i (n)|=1, which means that the amplitudes of the output signals of all array elements are consistent.

[0135] λ=N|v1(n)| 2 +σ 2 (twenty two)

[0136] It achieved a processing gain of N times, consistent with the processing gain of conventional beamforming under plane wave conditions. Therefore, by performing eigenvalue decomposition on the autocorrelation matrix R of y(n), the largest eigenvalue obtained is the coherent accumulated output power and noise power σ. 2The sum of these values ​​is given by the sum of the values ​​of the array elements, and the corresponding eigenvector is the weighted vector of the array element output. Noise power can be estimated by averaging the smaller eigenvalues, thus the power of the spectral line signal can be estimated as follows:

[0137]

[0138] Where λ max λ is the largest eigenvalue. i For eigenvalues ​​other than the largest eigenvalue, the processing gain is N, where N is the number of array elements.

[0139] Or it can be expressed as (without omitting the superscript m):

[0140]

[0141] in The largest eigenvalue, These are the eigenvalues ​​other than the largest eigenvalue. Equations (15) and (15-1) have the same effect, both calculating for each specific m-th frequency point.

[0142] Since the autocorrelation matrix R is actually unknown, the eigenvalue decomposition needs to be performed on the estimation of the autocorrelation matrix. If the above calculation process is applied to the narrowband line spectrum signals of each frequency output by each array element over a continuous time period, a spectrum that is continuous in both the time and frequency domains can be obtained.

[0143] Taking into account the FFT, autocorrelation, and eigenvalue decomposition processes, the processed signal-to-noise ratio can be expressed as:

[0144]

[0145] Where SNR0 is the array element received signal x i The signal-to-noise ratio of (n).

[0146] Step 004: Apply the above calculation process to the narrowband line spectrum signals of each frequency output by each array element over a continuous time period to obtain a spectrum that is continuous in both the time and frequency domains.

[0147] In summary, the coherent accumulation process of the linear array spectrum under multipath conditions is as follows:

[0148] The pairwise output is processed by a sliding FFT with a processing gain of K times, where K is the FFT processing length.

[0149] Calculate the time correlation matrix of the output signal at each frequency point after FFT processing. Processing gain;

[0150] Time-related array Perform eigenvalue decomposition to obtain its eigenvalues;

[0151] The eigenvalues ​​are processed, and the difference between the largest eigenvalue and the average of the remaining eigenvalues ​​is taken as the signal power estimate for each frequency point. The processing gain is N, where N is the number of array elements.

[0152] The verification results of the multipath environment linear array coherent accumulation detection method of the present invention are as follows:

[0153] The Monte Carlo simulation test method was used to verify the performance in two aspects.

[0154] Experiment 1 verifies the theoretical gain value of the method of the present invention for processing line spectrum under different signal-to-noise ratios and different numbers of array elements, and compares the performance with the gain value of line spectrum processed by Monte Carlo simulation.

[0155] Experiment 2 verifies the algorithm's performance when amplitude and phase fluctuate. Verification is performed using incoherent accumulation.

[0156] Experiment 1: Assuming a signal sampling rate of 1 kHz and an FFT processing time of 1 second, the number of data samples processed by the FFT is K = 1000; the sliding FFT overlap rate is 0; the correlation accumulation time is 60 seconds, so the number of correlated samples is L = 60; the simulation duration is 100 minutes. The target radiation signal is a 300 Hz single-tone signal with Gaussian white noise. Figure 2(a) shows the processing gain under different array element numbers when the signal-to-noise ratio is -2.9 dB. Figure 2(b) shows the processing gain under different signal-to-noise ratios when the number of array elements is 16. As shown in Figure 2, Monte Carlo simulation analysis shows that the theoretical gain value and the simulated value of the coherent accumulation algorithm of the present invention for processing line spectra are basically consistent.

[0157] Experiment 2: To simulate amplitude and phase fluctuations, a 200th-order rectangular window filter was used to smooth Gaussian white noise, and then multiplied with a 300 Hz single-tone signal to modulate the low-pass signal to 300 Hz as the target radiation signal. The signal-to-noise ratio was set to 1 dB, the number of array elements was 64, and the incoherent accumulation of Equation (6) was used as a comparison. Other conditions were the same as in Experiment 1. Figure 3 shows the LOFAR spectrum analysis results. As shown in Figure 3, under the condition of amplitude and phase fluctuations, the coherent accumulation algorithm of the present invention also has a significantly higher signal-to-noise ratio in processing the line spectrum, reflecting its higher processing gain. That is, Figure 3(b) shows a higher processing gain compared to the incoherent accumulation method for processing the line spectrum (Figure 3(a)).

[0158] On the other hand, this embodiment also provides a computer-readable storage medium, which includes a stored program, wherein the program executes the aforementioned multipath environment linear array line spectrum coherent accumulation detection method when it runs.

[0159] Furthermore, this embodiment also provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor is configured to execute the aforementioned multipath environment linear array coherent accumulation detection method through the computer program.

Claims

1. A method for detecting coherent accumulation of linear array spectrum under multipath conditions, characterized in that... Includes the following steps: The received signal of each of the N elements of a uniform linear array is collected, and the received signal is processed by sliding FFT to extract the narrowband line spectrum signal in the time dimension. Autocorrelation is performed on the narrowband line spectrum signals output by each array element to obtain the time autocorrelation matrix of the output signals at each frequency point; Eigenvalue decomposition of the autocorrelation matrix, with the difference between the largest eigenvalue and the average of the remaining eigenvalues, can be used as an estimate of the signal power, including... Assuming that the noise of different array elements is uncorrelated, and the signal and noise are uncorrelated, then the autocorrelation matrix R of y(n) is: (8) Among them, if the same frequency is output from different array elements Represented in vector form, Indicates the first There are n array elements, where n represents different times, and the superscript m represents the m-th frequency point. Without loss of generality, the superscript m is omitted and denoted as . H represents the conjugate transpose operation. The signal envelope of array element 1, vector This indicates the phase relationship between the line spectrum output signal of each array element and the line spectrum signal of array element 1: (9) For noise level, Let I be the noise power, and I be the identity matrix. R =λ (10) (11) where is the eigenvalue of the autocorrelation matrix, and Let it be its corresponding feature vector, and (12) (13) The signal phase of array element 1; From equation (12), we know that from the vector Phase compensation was performed on the outputs of different array elements to achieve in-phase addition of the array element outputs, i.e., coherent accumulation; and as shown in the form of equation (11), the eigenvalue λ is actually the sum of the signal power and noise power after coherent accumulation, when That is, when the output signal amplitudes of all array elements are consistent (14) It is easy to see that it has achieved a processing gain of N times, which is consistent with the processing gain of conventional beamforming under plane wave conditions; Therefore, by performing eigenvalue decomposition on the autocorrelation matrix R of y(n), the largest eigenvalue obtained is the coherently accumulated output signal power and noise power. The sum of these values, and the noise power, can be estimated by averaging the smaller eigenvalues. Therefore, the power of the spectral line signal can be estimated as follows: (15) in The largest eigenvalue, For eigenvalues ​​other than the largest eigenvalue, the processing gain is N, where N is the number of array elements; Since the autocorrelation matrix R is actually unknown, the eigenvalue decomposition needs to be performed on the aforementioned estimation of the autocorrelation matrix. On; Taking into account the FFT, autocorrelation, and eigenvalue decomposition processes, the processed signal-to-noise ratio can be expressed as: (16) Where SNRO is the array element received signal x i The signal-to-noise ratio of (n), where L is the number of relevant samples and K represents the number of data samples processed by FFT.

2. The method for detecting coherent accumulation of linear array spectrum under multipath environment according to claim 1, characterized in that... Each of the N elements of the uniform linear array is subjected to sliding FFT processing to extract the narrowband line spectrum in the time dimension. include Assume the received signal after sampling of each array element (i=1,2…N), where the subscript i represents the i-th array element, and n represents different times; let the output of each array element at each frequency after sliding FFT processing be... ,but (1) Where the superscript m represents the m-th frequency point, and K represents the number of data samples processed by the FFT, which is also the number of samples in the frequency domain; if The frequency of existence is When the line spectrum signal is obtained, the calculation process of equation (1) performs phase compensation on each data sample to achieve in-phase addition, that is, completes the coherent accumulation processing in the time dimension, and its processing gain is K times.

3. The method for detecting coherent accumulation of linear array spectrum under multipath environment according to claim 2, characterized in that... The method involves performing autocorrelation on the narrowband line spectrum signals output by each array element to obtain an estimate of the time autocorrelation matrix of the output signal at each frequency point. include If the same frequency is output from different array elements Represented in vector form, without loss of generality, omitting the superscript m, it can be expressed as: (2) , Let be the signal envelope and phase of each array element, respectively, and n(n) be the noise vector. The autocorrelation matrix R of y(n) can be estimated through a time correlation process. (3) L is the number of relevant samples. Since equation (3) is a correlation accumulation process, let's analyze its processing gain. for The matrix elements, then (4) in: Represents the spectral line signal output by the FFT. (5) but The signal-to-noise ratio can be expressed as (6) Assuming that the spectral lines of different array elements have the same amplitude and that the signal and noise are uncorrelated, then equation (6) can be expressed as follows: (7) SNR y y is the output of the FFT i The signal-to-noise ratio of (n).

4. The method for detecting coherent accumulation of linear array spectrum under multipath environment according to claim 1, characterized in that... By applying the above calculation process to the narrowband line spectrum signals of each frequency output by each array element over a continuous time period, a LOFAR spectrum that is continuous in both the time and frequency domains can be obtained.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein the program, when executed, performs the multipath environment linear array line spectrum coherent accumulation detection method as described in any one of claims 1 to 4.

6. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to execute the multipath environment linear array line spectrum coherent accumulation detection method as described in any one of claims 1 to 4 through the computer program.

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