A Phase Shift Keying Signal Localization Method Based on Coprime Sum Difference Coma Array Compensation
By repositioning and co-translating redundant sensors in the augmented coprime array to form a transformed augmented coprime array structure, the problem of ineffective utilization of redundant sensors is solved, and a wider range and higher accuracy of direction of arrival estimation is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- GUANGDONG UNIV OF TECH
- Filing Date
- 2025-12-15
- Publication Date
- 2026-07-17
AI Technical Summary
In the prior art, augmented coprime arrays fail to effectively utilize redundant sensors in direction-of-arrival estimation, resulting in limited estimation range and accuracy.
By repositioning redundant sensors in the augmented coprime array and moving them to the negative axis, and combining this with a cooperative translation strategy, a transformed augmented coprime array structure is formed. This utilizes redundant sensor resources to compensate for the gaps in the difference covariance matrix, enabling the calculation of the full-rank covariance matrix. The MUSIC algorithm is then used for direction-of-arrival estimation.
It improves the range and accuracy of direction-of-arrival estimation, especially demonstrating excellent positioning performance in complex environments, enhances the continuous degrees of freedom of virtual sensors, and supports the detection of more signal sources.
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Figure CN121633976B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of radar sonar positioning technology, and in particular to a phase shift keying signal positioning method based on coprime and differential coarray compensation. Background Technology
[0002] Non-circular signals are common in modern communication systems. Numerous processing techniques for non-circular signals (such as binary phase-shift keying signals) have emerged, and one of the key tasks is accurately determining the direction of arrival (DOA). Therefore, DOA estimation is a focal point in array signal processing, focusing on how to utilize the characteristics of non-circular signals to improve estimation performance. The most classic algorithm in DOA estimation is the MUSIC algorithm, which achieves direction estimation through spatial spectrum analysis: first, the received signal is spatially filtered and a covariance matrix is constructed; then, the matrix is decomposed into a signal subspace and a noise subspace, and the orthogonality of these two subspaces is used to construct a spatial spectrum, with the spectral peak position corresponding to the DOA. However, traditional uniform linear arrays are limited by the number of elements, and can only resolve a maximum of L-1 targets. To overcome this limitation, augmented coprime arrays (ACA) are often used, where the element positions are determined by coprime integers M and N. By differentially synthesizing a longer virtual continuous aperture, a virtual array element count far exceeding the physical element count is effectively obtained, thus estimating more targets without increasing hardware. The specific process can be broken down as follows: After receiving signals from multiple sources, the coprime array calculates the covariance matrix to reflect the correlation between signals; eigenvalue decomposition is performed on the covariance matrix, dividing it into signal and noise subspaces according to the magnitude of the eigenvalues; a virtual continuous array is constructed based on the differential positions, and its covariance matrix is estimated again; to eliminate the influence of coherent sources, the virtual covariance matrix is spatially smoothed by dividing the virtual array into several overlapping subarrays, calculating the covariance matrices of each subarray, and averaging them to obtain a smoothed matrix, resulting in a full-rank matrix; eigenvalue decomposition is performed again on this matrix to obtain the signal and noise subspaces; finally, the orthogonality between the noise subspace and the steering vector is used to construct the MUSIC spectral function, searching for spectral peaks in all possible directions, with the peak position representing the direction of the signal source. Through these steps, the MUSIC algorithm for coprime arrays achieves high-resolution direction-of-arrival estimation for more targets with fewer physical array elements.
[0003] A search of existing technical literature revealed a patent application (application number 202110467852.1) entitled "A Method for Estimating DOA of Non-Circular Signals under Coprime Array Pulse Environment." This patent uses a conjugate augmented coprime array to receive signal information. Based on the received signal information, it calculates the corresponding phase fraction low-order moment estimation covariance matrix. The obtained estimated covariance matrix is vectorized, rearranged, and truncated with continuous array elements of the sum and difference matrices in the virtual array to obtain the received signal information of a virtual uniform linear array. After redundancy removal, it includes one difference matrix and two sum matrices. Spatial smoothing matrices are constructed for the difference and sum matrices respectively. Then, the smoothed sum and difference matrices are concatenated to form a larger virtual array information, and the corresponding covariance matrix is constructed again. The accurate DOA estimate is obtained using a dimensionality reduction MUSIC method. However, this patent has a problem: it does not utilize the functional repositioning of redundant sensors. Summary of the Invention
[0004] Therefore, it is necessary to provide a phase shift keying signal localization method based on coprime and difference co-array compensation to address the above-mentioned technical problems, so as to achieve a wide estimation range and high estimation accuracy for direction of arrival estimation.
[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:
[0006] This invention provides a phase shift keying signal localization method based on coprime sum and difference co-array compensation, the method comprising:
[0007] S1: After receiving a non-circular signal through an array antenna with an augmented coprime array structure, the non-circular signal is digitized to obtain a digital signal. The augmented coprime array includes an array of array elements. The first subarray and the number of elements are 2 The second subarray, wherein the first and second subarrays are located on the positive axis and their elements coincide at the origin, and the first and second subarrays are uniform linear arrays with element spacings of [missing information]. and , For a non-circular signal, half the wavelength. and They are coprime numbers;
[0008] S2: Calculate the covariance matrix of the digitized signal and vectorize the covariance matrix to obtain the difference covariance matrix and the sum covariance matrix. The difference covariance matrix is the set of differences between any two array element positions in the augmented coprime array, and the sum covariance matrix is the set of sums between any two array element positions in the augmented coprime array.
[0009] S3: Based on the fact that removing the array elements in the augmented coprime array does not affect the structure of the differential coprime array, it is determined that there are redundant array elements in the second subarray. The redundant array elements are repositioned to obtain the third subarray and the fourth subarray, which are located on the negative axis.
[0010] S4: Shift the first subarray and the second subarray (with redundant elements removed) to the positive axis by the optimal shift distance, and shift the third subarray and the fourth subarray to the negative axis by the optimal shift distance to obtain the transformation augmented coprime array structure;
[0011] S5: Based on the transformed augmented coprime array structure, a new covariance matrix is recalculated. The new covariance matrix is processed using a preset algorithm to obtain a full-rank covariance matrix. Based on the full-rank covariance matrix, the MUSIC algorithm is used to estimate the direction of arrival to obtain the direction of arrival.
[0012] Preferably, the optimal array is calculated based on the total number of array elements in the augmented coprime array. and The calculation expression is as follows:
[0013]
[0014]
[0015] in, This represents the total number of elements in the augmented coprime array. If the calculated... It is a fraction, and the nearest integer to that fraction is . .
[0016] Preferably, the digitization process includes processing the non-circular signal. and its conjugate The covariance matrix is merged. The calculation expression is as follows:
[0017]
[0018]
[0019] in, Expressing expectations, Represents digital signals, Indicates transpose. This indicates the conjugate transpose.
[0020] Preferably, the redundant array element is located in the middle of the second subarray, and the number of elements in the redundant array element is [number missing]. ,like The nearest integer to this fraction is the number of redundant array elements.
[0021] Preferably, the number of elements in the third subarray is The expression for calculating the position of the third subarray is as follows:
[0022]
[0023] in, This indicates the position of the third subarray.
[0024] Preferably, the fourth subarray has 1 element, and the position calculation expression for the fourth subarray is as follows:
[0025]
[0026] in, This indicates the position of the fourth subarray.
[0027] Preferably, the expression for calculating the optimal shift distance is as follows:
[0028]
[0029] in, This indicates the optimal shift distance.
[0030] Preferably, the preset algorithm is a spatial smoothing algorithm.
[0031] Preferably, the direction of arrival (DOA) is estimated using the MUSIC algorithm based on the full-rank covariance matrix, including:
[0032] The full-rank covariance matrix is decomposed into eigenvalues, and the signal subspace and noise subspace are distinguished based on the eigenvalues obtained from the decomposition.
[0033] A MUSIC spectrum function is constructed based on the signal subspace and the noise subspace. The direction of arrival is estimated based on the MUSIC spectrum function to obtain the direction of arrival.
[0034] Preferably, the peak position of the spectral peak in the MUSIC spectral function is the direction of the non-circular signal.
[0035] Compared with the prior art, the beneficial effects of the present invention are:
[0036] This invention provides a phase shift keying signal localization method based on coprime and difference coarray compensation. By removing redundant sensors from their original positions in the augmented coprime array structure and repositioning them to specific positions on the negative axis, the redundant physical sensor resources in the original augmented coprime array are effectively utilized. All subarrays in the repositioned augmented coprime array are collaboratively shifted. The precise optimal shift distance ensures that the voids in the difference coarray in the augmented coprime array can be accurately compensated by the virtual sensor elements after the sum coarray transformation. The sum coarray can achieve a high degree of continuous freedom to support the detection of more signal sources. The transformed augmented coprime array exhibits excellent accuracy in direction-of-arrival estimation in complex real-world environments with moderate to strong mutual coupling. Attached Figure Description
[0037] Figure 1 This is a schematic flowchart of a phase shift keying signal localization method based on coprime sum and difference co-array compensation in one embodiment;
[0038] Figure 2 This is a schematic diagram of the redundant sensor relocation process in a phase shift keying signal positioning method based on coprime sum and difference co-array compensation in one embodiment;
[0039] Figure 3 This is a schematic diagram of a phase shift keying signal localization method based on coprime sum difference co-array compensation and a co-array precise compensation difference co-array in one embodiment;
[0040] Figure 4 This is a schematic diagram of a traditional augmented coprime array structure for a phase shift keying signal localization method based on coprime and difference coarray compensation in one embodiment. Detailed Implementation
[0041] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0042] Example 1
[0043] like Figure 1 As shown, this embodiment proposes a phase shift keying signal localization method based on coprime sum-difference co-array compensation, the method comprising:
[0044] S1: After receiving a non-circular signal through an array antenna with an augmented coprime array structure, the non-circular signal is digitized to obtain a digital signal. The augmented coprime array includes an array of array elements. The first subarray and the number of elements are 2 The second subarray, wherein the first and second subarrays are located on the positive axis and their elements coincide at the origin, and the first and second subarrays are uniform linear arrays with element spacings of [missing information]. and , For a non-circular signal, half the wavelength. and They are coprime numbers;
[0045] The specific implementation of this step is as follows: In some communication systems, the phase or amplitude of the signal may not be an ideal circular track (i.e., there is no uniform distribution on the complex plane). This may occur during the modulation process of the signal, especially when processing certain complex signals. In this case, "non-circular signal" may refer to this "imperfect" or non-ideal characteristic of the signal. In this embodiment, the signal used is a BPSK (Binary Phase Shift Keying) modulated signal, which is a type of non-circular signal. K A non-circular field uncorrelated source is incident on by P On a traditional augmented coprime array composed of physical sensors, the structure of the traditional augmented coprime array is as follows: Figure 4 As shown, assuming Indicates the physical sensor location. It is a unit spacing, typically half the wavelength of a non-circular signal, and the received non-circular signal vector. It can be written as:
[0046]
[0047] in, It is an array manifold signal matrix. It is the set of vectors of received non-circular signals. It is a Gaussian white noise vector. The received signal is first acquired and digitized to convert the analog signal into a digital signal. .
[0048] S2: Calculate the covariance matrix of the digitized signal and vectorize the covariance matrix to obtain the difference covariance matrix and the sum covariance matrix. The difference covariance matrix is the set of differences between any two array element positions in the augmented coprime array, and the sum covariance matrix is the set of sums between any two array element positions in the augmented coprime array.
[0049] In this specific implementation, the digitized signal is then subjected to covariance matrix calculation, and the covariance matrix is output. Vectorize the matrix , For inclusion covariance matrix Peace and Harmony Formation Virtual signals of information, differential covariance matrix With the peace formation Together they form a sum-difference comatrix , That is, the sum and difference comatrix The signal received at a certain moment.
[0050] S3: Based on the fact that removing the array elements in the augmented coprime array does not affect the structure of the differential coprime array, it is determined that there are redundant array elements in the second subarray. The redundant array elements are repositioned to obtain the third subarray and the fourth subarray, which are located on the negative axis.
[0051] The specific implementation of this step is as follows. For physical sensors, it has been found in practical use that some sensors do not change the structure of the differential array, such as... Figure 2 As shown, in this embodiment, these redundant sensors are repositioned to the negative axis to form the third and fourth subarrays. This repositioning strategy allows the virtual elements generated by these redundant sensors to fill the gaps in the previous differential array, making full use of these redundant sensors while expanding and arraying, without wasting physical resources.
[0052] S4: Shift the first subarray and the second subarray (with redundant elements removed) to the positive axis by the optimal shift distance, and shift the third subarray and the fourth subarray to the negative axis by the optimal shift distance to obtain the transformation augmented coprime array structure;
[0053] The specific implementation of this step is as follows: After repositioning the redundant sensors, in order to maximize the continuous degrees of freedom, the translation used in this embodiment is not a simple translation of the entire array, but a cooperative translation strategy, which translates the first subarray and the second subarray with the redundant elements removed towards the positive axis. Distance, shift the third and fourth subarrays towards the negative axis. distance, To obtain the optimal shift distance, the transformed position of the virtual sensor in the cosine array is overlapped with the position of the void in the difference cosine array to fill the void, while the continuous degrees of freedom are increased to support the detection of more signal sources.
[0054] like Figure 3 As shown, the number of physical array elements =12, coprime numbers =4, When = 5, (a) represents the arrangement of the difference comatrix after translation, (b) represents the arrangement of the sum comatrix after translation, and (c) represents the arrangement of the sum and difference comatrix (after compensation). It is clear that the sum comatrix perfectly compensates for the difference comatrix, filling in some gaps. After achieving accurate compensation, the continuous degrees of freedom of the sum and difference comatrix are greatly improved. The improvement in continuous degrees of freedom means that more signal sources can be estimated, and the continuous degrees of freedom can reach 5. .
[0055] S5: Based on the transformed augmented coprime array structure, a new covariance matrix is recalculated. The new covariance matrix is processed using a preset algorithm to obtain a full-rank covariance matrix. Based on the full-rank covariance matrix, the MUSIC algorithm is used to estimate the direction of arrival to obtain the direction of arrival.
[0056] Example 2
[0057] This embodiment further explains the phase shift keying signal localization method based on coprime sum and difference co-array compensation proposed in Embodiment 1.
[0058] The optimal array is calculated based on the total number of elements in the augmented coprime array. and The calculation expression is as follows:
[0059]
[0060]
[0061] in, This represents the total number of elements in the augmented coprime array. If the calculated... It is a fraction, and the nearest integer to that fraction is . .
[0062] The specific implementation of this step is as follows: the maximum degree of freedom that can be achieved is... and The decision, made after calculation and inference, is based on a given total number of physical sensors. At that time, and When the above formula is satisfied, the maximum number of continuous degrees of freedom can be achieved, that is, the total number of sensors. It is certain, but the optimal solution is not known. Is it odd or even? Assume it's optimal. It is an even number. Substituting into the above formula, if we get If it is indeed an even number, then use this. Otherwise, assume It is an odd number. Substituting into the above formula, if we assume Neither even nor odd is correct; find the answer. If it is a fraction, choose the one closest to the integer. .
[0063] The digital processing includes processing the non-circular signal. and its conjugate The covariance matrix is merged. The calculation expression is as follows:
[0064]
[0065]
[0066] in, Expressing expectations, Represents digital signals, Indicates transpose. This indicates the conjugate transpose.
[0067] The redundant array element is located in the middle of the second subarray, and the number of elements in the redundant array element is [number missing]. ,like The nearest integer to this fraction is the number of redundant array elements.
[0068] The number of elements in the third subarray is The expression for calculating the position of the third subarray is as follows:
[0069]
[0070] in, This indicates the position of the third subarray.
[0071] The fourth subarray has 1 element, and its position is calculated as follows:
[0072]
[0073] in, This indicates the position of the fourth subarray.
[0074] The expression for calculating the optimal shift distance is as follows:
[0075]
[0076] in, This indicates the optimal shift distance.
[0077] The specific implementation of this step is as follows: through analytical derivation, the voids appearing in the difference comatrix are located at specific positions. , and It is an integer greater than or equal to 0. To ensure that the position after the transformation of the comatrix falls precisely at the hole location, when the translation distance is... When the above formula is satisfied, the set of virtual elements in the harmonic matrix is:
[0078]
[0079] Will Bring into It can be found that the set of virtual sensors in the harmonic co-co-matrix is exactly the same as the set of voids in the difference co-co-matrix. This allows for precise compensation, and the discontinuities that originally existed in the difference co-co-matrix are eliminated to a certain extent.
[0080] Example 3
[0081] This embodiment further explains the phase shift keying signal localization method based on coprime sum and difference co-array compensation proposed in Embodiment 1.
[0082] Since the new covariance matrix will have a rank deficit, spatial smoothing is required to obtain a full-rank covariance matrix. The preset algorithm used is the spatial smoothing algorithm.
[0083] Based on the full-rank covariance matrix, the MUSIC algorithm is used to estimate the direction of arrival, including:
[0084] The full-rank covariance matrix is decomposed into eigenvalues, and the signal subspace and noise subspace are distinguished based on the eigenvalues obtained from the decomposition.
[0085] A MUSIC spectrum function is constructed based on the signal subspace and the noise subspace. The peak position of the spectral peak in the MUSIC spectrum function is the direction of the non-circular signal. The direction of arrival is estimated based on the MUSIC spectrum function to obtain the direction of arrival.
Claims
1. A phase shift keying signal localization method based on coprime sum and difference co-array compensation, characterized in that, include: S1: After receiving a non-circular signal through an array antenna with an augmented coprime array structure, the non-circular signal is digitized to obtain a digital signal. The augmented coprime array includes an array of array elements. The first subarray and the number of elements are 2 The second subarray, wherein the first and second subarrays are located on the positive axis and their elements coincide at the origin, and the first and second subarrays are uniform linear arrays with element spacings of [missing information]. and , For a non-circular signal, half the wavelength. and They are coprime numbers; S2: Calculate the covariance matrix of the digitized signal and vectorize the covariance matrix to obtain the difference covariance matrix and the sum covariance matrix. The difference covariance matrix is the set of differences between any two array element positions in the augmented coprime array, and the sum covariance matrix is the set of sums between any two array element positions in the augmented coprime array. S3: Based on the fact that removing the array elements in the augmented coprime array does not affect the structure of the differential coprime array, it is determined that there are redundant array elements in the second subarray. The redundant array elements are repositioned to obtain the third subarray and the fourth subarray, which are located on the negative axis. S4: Shift the first subarray and the second subarray (with redundant elements removed) to the positive axis by the optimal shift distance, and shift the third subarray and the fourth subarray to the negative axis by the optimal shift distance to obtain the transformation augmented coprime array structure; S5: Based on the transformed augmented coprime array structure, a new covariance matrix is recalculated. The new covariance matrix is processed using a preset algorithm to obtain a full-rank covariance matrix. Based on the full-rank covariance matrix, the MUSIC algorithm is used to estimate the direction of arrival to obtain the direction of arrival.
2. The phase shift keying signal localization method based on coprime sum and difference co-array compensation according to claim 1, characterized in that, The optimal array is calculated based on the total number of elements in the augmented coprime array. and The calculation expression is as follows: in, This represents the total number of elements in the augmented coprime array. If the calculated... It is a fraction, and the nearest integer to that fraction is . .
3. The phase shift keying signal localization method based on coprime sum and difference co-array compensation according to claim 1, characterized in that, The digital processing includes processing the non-circular signal. and its conjugate The covariance matrix is merged. The calculation expression is as follows: in, Expressing expectations, Represents digital signals, Indicates transpose. This indicates the conjugate transpose.
4. The phase shift keying signal localization method based on coprime sum and difference co-array compensation according to claim 1, characterized in that, The redundant array element is located in the middle of the second subarray, and the number of elements in the redundant array element is [number missing]. ,like The nearest integer to this fraction is the number of redundant array elements.
5. The phase shift keying signal localization method based on coprime sum and difference co-array compensation according to claim 4, characterized in that, The number of elements in the third subarray is The expression for calculating the position of the third subarray is as follows: in, This indicates the position of the third subarray.
6. The phase shift keying signal localization method based on coprime sum and difference co-array compensation according to claim 5, characterized in that, The fourth subarray has 1 element, and its position is calculated as follows: in, This indicates the position of the fourth subarray.
7. The phase shift keying signal localization method based on coprime sum and difference co-array compensation according to claim 1, characterized in that, The expression for calculating the optimal shift distance is as follows: in, This indicates the optimal shift distance.
8. The phase shift keying signal localization method based on coprime sum and difference co-array compensation according to claim 1, characterized in that, The preset algorithm is a spatial smoothing algorithm.
9. The phase shift keying signal localization method based on coprime sum and difference co-array compensation according to claim 1, characterized in that, Based on the full-rank covariance matrix, the MUSIC algorithm is used to estimate the direction of arrival, including: The full-rank covariance matrix is decomposed into eigenvalues, and the signal subspace and noise subspace are distinguished based on the eigenvalues obtained from the decomposition. A MUSIC spectrum function is constructed based on the signal subspace and the noise subspace. The direction of arrival is estimated based on the MUSIC spectrum function to obtain the direction of arrival.
10. The phase shift keying signal localization method based on coprime sum and difference co-array compensation according to claim 9, characterized in that, The peak position of the spectral peak in the MUSIC spectral function is the direction of the non-circular signal.