Broadband coherent signal positioning estimation method based on antenna array

Abstract

The invention discloses a broadband coherent signal positioning estimation method based on an antenna array, and belongs to the technical field of microwave antennae, the method comprises the following steps: respectively radiating P broadband information sources to an N-element uniform antenna array in different directions, n; the method comprises the steps of decomposing broadband signals generated by P broadband information sources into J narrowband components in a frequency domain, performing narrowband processing on each narrowband component, including performing characteristic decomposition on a spectral density matrix of the narrowband components to obtain a signal subspace and a noise subspace, and constructing a spatial spectrum according to orthogonality of the signal subspace and the noise subspace; and averaging the spatial spectrums of all the narrowband components to obtain spatial spectrum estimation of P broadband information sources. According to the method, a processing method combining a weighted multi-signal classification algorithm, spatial smoothing and broadband signal subspace division is adopted, the spatial resolution of the antenna array can be enhanced, separation of multi-source broadband coherent signals is achieved, and the positioning precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of microwave antenna and array signal processing, and more specifically, relates to a broadband coherent signal positioning estimation method based on an antenna array. Background Art

[0002] Most of the current signal positioning estimation methods are based on the premise that the measured signal is a narrowband signal, but in reality, there are a large number of signals that do not meet the narrowband requirements, such as broadband signals. If a narrowband signal model is used to process broadband signals, since the array element spacing is not always equal to half the wavelength of the signal frequency (the frequency of the signal is different), the array manifold will change with the change of frequency, so the resolution performance of positioning estimation is poor, and a broadband array signal processing model must be used for processing. The processing of broadband signals has always been a difficult problem in the field of array signal processing technology. With the development of communication, electronic countermeasures and other technologies, the application of broadband signals such as spread spectrum signals, linear frequency modulation signals, and frequency modulation signals is increasing. Therefore, the research on broadband signal positioning estimation algorithms has become increasingly important. Summary of the invention

[0003] To solve the above technical problems, the present invention provides a broadband coherent signal positioning estimation method based on an antenna array, which adopts a processing method that combines a weighted multi-signal classification algorithm, spatial smoothing and broadband signal subspace division to decompose broadband data into narrowband data on non-overlapping frequency bands, and then performs narrowband signal subspace processing on each frequency band to obtain an estimate of the initial angle, and then obtains the final result by averaging the estimates of these spatial spectra.

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

[0005] A broadband coherent signal positioning estimation method based on an antenna array comprises the following steps:

[0006] Step (1): radiate P broadband signal sources in different directions to an N-element uniform antenna array, where P <N;

[0007] Step (2), decomposing the broadband signals generated by the P broadband information sources into J narrowband components in the frequency domain, performing narrowband processing on each narrowband component, including eigendecomposing the spectral density matrix of the narrowband component to obtain a signal subspace and a noise subspace, and constructing a spatial spectrum according to the orthogonality of the signal subspace and the noise subspace;

[0008] Step (3): average the spatial spectra of all narrowband components to obtain spatial spectrum estimates of P broadband sources.

[0009] Furthermore, in step (1), the broadband array elements included in the antenna array are isotropic, and the array element spacing is half the wavelength corresponding to the signal center frequency; the broadband signal source is a stationary Gaussian random signal with zero mean, each broadband signal source has the same bandwidth and center frequency, and the additional broadband noise is independent of the source signal and has the same bandwidth as the broadband signal source.

[0010] Furthermore, the step (2) includes:

[0011] Step (2.1), divide the broadband signal generated by the broadband source collected during the observation time into K segments, and then perform DFT transformation on each segment of the signal to obtain J groups of mutually unrelated narrowband components in the frequency domain;

[0012] Step (2.2), perform eigenvalue decomposition on the spectral density matrix corresponding to J groups of mutually uncorrelated frequency domain narrowband components, wherein the eigenvectors corresponding to the columns in the eigenvalue matrix constitute the signal subspace, and the eigenvectors corresponding to the rows in the eigenvalue matrix constitute the noise subspace.

[0013] Furthermore, the step (2.1) includes dividing the broadband signal collected during the observation time into K segments, performing DFT on each segment of the signal to obtain J groups of mutually unrelated frequency domain narrowband components, i.e., J frequency domain snapshots, denoted as , k=1,2,…,K, j=1,2,…,J.

[0014] Furthermore, the step (2.2) includes: The corresponding spectral density matrix Perform eigenvalue decomposition:

[0015] ,

[0016] Among them, the eigenvalue The eigenvectors corresponding to (i=1,2,…,P) constitute the signal subspace , eigenvalue The eigenvectors corresponding to (i=P+1,…,N) constitute the noise subspace , the superscript H indicates the conjugate transpose, represents the noise spectral density, represents the feature vector;

[0017] Extract the covariance matrix of the j-th narrowband component to form the spatial spectrum:

[0018] ,

[0019] In the formula, the signal spectral density is , I is the unit matrix, E(·) represents the expectation operation, is the received signal vector of the N×1 antenna array, is the middle vector of the P×1 antenna array, representing the source signal The array output of the frequency band, N×P dimensional matrix A(f j ) is about the frequency band f j The narrowband directional cluster matrix of .

[0020] Furthermore, the spectral density matrix for:

[0021] ,

[0022] Among them, the forward and reverse covariance matrices , q is an integer between 2 and N, the number of sub-arrays M = N-q + 1, the initial spectral density matrix , Z is an N×N permutation matrix.

[0023] Furthermore, the spatial spectrum of the P broadband sources in step (3) is estimated as:

[0024] ,

[0025] Among them, the orthogonal projection on the noise subspace , the unit vector , direction vector , wave vector , the relative position vector of each array element , θ represents the azimuth angle of the signal, represents the position vector of the i-th array element, is the position vector of the initial array element.

[0026] The beneficial effects of the present invention are:

[0027] The present invention can enhance the spatial resolution of the antenna array, realize the separation of multi-source broadband coherent signals, improve the positioning accuracy, and provide a key solution to complex signal processing problems in various fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a flow chart of a method for positioning and estimating a broadband coherent signal based on an antenna array according to the present invention;

[0029] Figure 2 A schematic diagram of an antenna array provided in an embodiment of the present invention;

[0030] Figure 3 is a simulation result of a broadband signal spectrum used in an embodiment of the present invention;

[0031] Figure 4 This is the simulation result of broadband coherent signal positioning estimation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0032] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0033] As Figure 1 shown, it is a flowchart of a broadband coherent signal positioning and estimation method based on an antenna array according to the present invention. First, a broadband signal is decomposed into multiple narrowband components in the frequency domain, and then narrowband processing is directly performed on each sub-band, that is, eigenvalue decomposition is performed on the spectral density matrix of each sub-band. According to the orthogonality of the signal subspace and the noise subspace, a spatial spectrum is constructed, and the spatial spectra of all sub-bands are averaged. Finally, a broadband signal spatial spectrum estimation is obtained. In order to estimate the spectral density matrix of each narrowband, it is necessary to convert the time-domain observation signal to the frequency domain, perform eigenvalue decomposition on the spectral density matrix of each sub-band, combine the weighted multi-signal classification algorithm, the forward and backward covariance matrices with spatial smoothing, perform a decorrelation operation on the received data matrix, construct a spatial spectrum according to the orthogonality of the signal subspace and the noise subspace, and average the spatial spectra of all sub-bands, ultimately realizing the positioning and estimation of broadband coherent signals. Specifically, it includes:

[0034] (1) P broadband signal sources radiate to an N-element uniform linear array in different directions respectively, where P < N. The array consists of isotropic broadband array elements, and the element spacing is half the wavelength corresponding to the center frequency of the signal. The source signals are assumed to be zero-mean stationary Gaussian random signals, each signal has the same bandwidth and center frequency, the additional broadband noise is independent of the source signals and has the same bandwidth as the source signals;

[0035] (2) The broadband signal s(t) is decomposed into the superposition of J narrowband components in the frequency domain: , where is a narrowband signal with as the center frequency, and represents all the narrowband components after superposition;

[0036] The directions of arrival of the P broadband signal sources are θ1, θ2,..., θp respectively, then the frequency-domain representation of the antenna array output vector is:

[0037] ,

[0038] where:

[0039] ,

[0040] ,

[0041] ,

[0042] ,

[0043] In the formula, is the received signal vector of the N×1 antenna array, is the middle vector of the P×1 antenna array, representing the source signal Array output of frequency band, is the middle vector of the N×1 antenna array, indicating the additional noise of each array element Frequency band data, N×P dimensional matrix A(f j ) is about the frequency band f j The narrowband directional cluster matrix, a(·) represents the N×P dimensional matrix A(f j ), the superscript T indicates the transpose of the matrix.

[0044] Extract the covariance matrix of the j-th narrowband component to form the spatial spectrum:

[0045] ,

[0046] In the formula, , I is the identity matrix, is the noise spectral density.

[0047] (3) In order to estimate the spectral density matrix on each narrowband, the time domain observation signal is converted to the frequency domain. First, the signal collected during the observation time is divided into K segments, and then DFT is performed on each segment to obtain J groups of mutually unrelated narrowband frequency domain components. In broadband processing, J is called a frequency domain snapshot. Thus, J frequency domain snapshots can be obtained, which are recorded as , k=1,2,…,K, j=1,2,…,J.

[0048] (4) Frequency The corresponding spectral density matrix Perform eigenvalue decomposition:

[0049] ,

[0050] Among them, the eigenvalue The eigenvectors corresponding to (i=1,2,…,P) constitute the signal subspace , eigenvalue The eigenvectors corresponding to (i=P+1,…,N) constitute the noise subspace , the superscript H indicates the conjugate transpose, represents the noise spectral density, represents a feature vector.

[0051] Spectral density matrix The improved MUSIC algorithm is calculated by combining the weighted MUSIC algorithm, the forward and reverse covariance matrix and spatial smoothing:

[0052] ,

[0053] in, (q is an integer between 2 and N, M=N-q+1), the number of subarrays M=N-q+1, the initial spectral density matrix , J is an N×N permutation matrix (all elements except the anti-diagonal elements are 1 and all other elements are 0).

[0054] (5) The spatial spectrum of each sub-band signal is:

[0055] ,

[0056] Among them, the orthogonal projection on the noise subspace , the unit vector , direction vector , wave vector , the relative position vector of each array element , θ represents the azimuth angle of the signal, represents the position vector of the i-th array element, is the position vector of the initial array element. The spatial spectrum of all sub-bands is averaged to obtain the spatial spectrum estimation of the broadband signal.

[0057] Example

[0058] Take an equidistant array such as Figure 2As shown, the number of array elements N = 10, the array element spacing d = λ / 2, the number of signal sources P = 3, and the angular positions are -30°, 0° and -30° respectively. The two signal sources at -30° and 0° are coherent. The source signal is assumed to be a stationary Gaussian random signal with zero mean. Each source signal has the same center frequency f = 100Hz and a relative bandwidth of 40%. The noise is a zero-mean Gaussian process with the same bandwidth as the source signal. The sampling frequency is 80Hz, the total observation time is T1 = 51.2s, and the product of time × bandwidth is T × B = 2048. T1 is divided into K = 64 segments, each segment is 0. 8s. Through the unwindowed FFT, the array output is decomposed into 33 narrowband frequency components, the number of snapshots is 100, and the signal-to-noise ratio is 5dB. The number of array elements N is 10, and the array elements are divided into 5 sub-arrays. The number of array elements in each sub-array is 6, that is, there are 10 array elements, and each 6 elements form a sub-array, which is divided into 5 sub-arrays as follows: [1,2,3,4,5,6], [2,3,4,5,6,7], [3,4,5,6,7,8], [4,5,6,7,8,9], [4,5,6,7,8,9,10]. The MUSIC spectrum estimation method combining the spatial smoothing technology of the present invention with the forward and reverse covariance technology is adopted to obtain the simulation results of DOA estimation of broadband signals. Figure 3 shows the spectrum of a broadband signal, from Figure 4 It can be seen that the method proposed in the present invention can accurately locate and estimate the broadband coherent signal source. The peak of the spatial spectrum curve of the method of the present invention represented by the solid line shows that the three signal sources are accurately estimated to be located at -30°, 0° and -30° respectively, while the traditional MUSIC algorithm represented by the dotted line can only estimate the two signal sources at -30° and -30°.

[0059] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A broadband coherent signal positioning estimation method based on an antenna array, characterized in that: The following steps are involved: Step (1): radiate P broadband signal sources in different directions to an N-element uniform antenna array, where P <N; Step (2), decomposing the broadband signals generated by the P broadband information sources into J narrowband components in the frequency domain, performing narrowband processing on each narrowband component, including eigendecomposing the spectral density matrix of the narrowband component to obtain a signal subspace and a noise subspace, and constructing a spatial spectrum according to the orthogonality of the signal subspace and the noise subspace; Step (3): average the spatial spectra of all narrowband components to obtain spatial spectrum estimates of P broadband sources.

2. The method for positioning and estimating a broadband coherent signal based on an antenna array according to claim 1, characterized in that: In the step (1), the broadband array elements included in the antenna array are isotropic, and the array element spacing is half the wavelength corresponding to the signal center frequency; the broadband signal source is a stationary Gaussian random signal with zero mean, each broadband signal source has the same bandwidth and center frequency, and the additional broadband noise is independent of the source signal and has the same bandwidth as the broadband signal source.

3. The method for positioning and estimating a broadband coherent signal based on an antenna array according to claim 1, characterized in that: The step (2) comprises: Step (2.1), divide the broadband signal generated by the broadband source collected during the observation time into K segments, and then perform DFT transformation on each segment of the signal to obtain J groups of mutually unrelated narrowband components in the frequency domain; Step (2.2), perform eigenvalue decomposition on the spectral density matrix corresponding to J groups of mutually uncorrelated frequency domain narrowband components, wherein the eigenvectors corresponding to the columns in the eigenvalue matrix constitute the signal subspace, and the eigenvectors corresponding to the rows in the eigenvalue matrix constitute the noise subspace.

4. The method for positioning and estimating a broadband coherent signal based on an antenna array according to claim 1, characterized in that: The step (2.1) includes dividing the broadband signal collected during the observation time into K segments, performing DFT on each segment of the signal to obtain J groups of mutually unrelated frequency domain narrowband components, i.e., J frequency domain snapshots, denoted as , k=1,2,…,K, j=1,2,…,J.

5. The method for positioning and estimating a broadband coherent signal based on an antenna array according to claim 1, characterized in that: The step (2.2) includes: The corresponding spectral density matrix Perform eigenvalue decomposition: ， Among them, the eigenvalue The eigenvectors corresponding to (i=1,2,…,P) constitute the signal subspace , eigenvalue The eigenvectors corresponding to (i=P+1,…,N) constitute the noise subspace , the superscript H indicates the conjugate transpose, represents the noise spectral density, represents the feature vector; Extract the covariance matrix of the j-th narrowband component to form the spatial spectrum: ， In the formula, the signal spectral density is , I is the unit matrix, E(·) represents the expectation operation, is the received signal vector of the N×1 antenna array, is the middle vector of the P×1 antenna array, representing the source signal The array output of the frequency band, N×P dimensional matrix A(f j ) is about the frequency band f j The narrowband directional cluster matrix of .

6. The method for positioning and evaluating broadband coherent signals based on antenna array according to claim 5, characterized in that: The spectral density matrix for: ， Among them, the forward and reverse covariance matrices , q is an integer between 2 and N, the number of sub-arrays M = N-q + 1, the initial spectral density matrix , Z is an N×N permutation matrix.

7. The method for positioning and estimating a broadband coherent signal based on an antenna array according to claim 1, characterized in that: The spatial spectrum of the P broadband sources in step (3) is estimated as: ， Among them, the orthogonal projection on the noise subspace , the unit vector , direction vector , wave vector , the relative position vector of each array element , θ represents the azimuth angle of the signal, represents the position vector of the i-th array element, is the position vector of the initial array element.

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