A method for direction of arrival estimation based on a virtual array of co-prime circular arrays
By constructing a weighted overcomplete dictionary and a sparse reconstruction algorithm, the problems of beam space transformation dependence and insufficient dictionary matching of coprime circular arrays are solved, achieving high-precision and high-resolution DOA estimation and breaking through the limitation of the number of physical array elements.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XIDIAN UNIV
- Filing Date
- 2026-03-16
- Publication Date
- 2026-07-07
AI Technical Summary
Existing methods for estimating the direction of arrival (DOA) of coprime circular arrays rely on beam space transformation, which is complex and suffers from severe information loss. These methods cannot fully utilize the high degree of freedom of the virtual array, and traditional overcomplete dictionaries cannot accurately match the manifold of the virtual array, resulting in insufficient accuracy and stability.
By constructing a compressed sensing model containing a weighted overcomplete dictionary, and combining it with a sparse reconstruction algorithm, the covariance matrix of the coprime circular array is used to analyze the corner positions and radii of the virtual array elements. A sparse reconstruction method adapted to the virtual uniform circular array is designed to achieve high-precision DOA estimation.
It significantly improves the array degrees of freedom and DOA estimation accuracy of coprime circular arrays, solves the problem of insufficient accuracy in existing technologies, and is suitable for high-resolution DOA estimation in complex scenarios.
Smart Images
Figure CN122345844A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of array signal processing technology, specifically relating to a direction-of-arrival estimation method based on a coprime circular array virtual array. Background Technology
[0002] In the field of array signal processing, Direction of Arrival (DOA) estimation, as one of the core supporting technologies, is widely used in radar, sonar, wireless communication, electronic reconnaissance, smart antennas, BeiDou navigation, and voice enhancement. Its estimation accuracy, resolution, and real-time performance directly determine the core performance and application effectiveness of the entire system. Among these, DOA estimation is an important research topic in array signal processing, aiming to estimate the spatial direction information of the incident signal using the signal data received by the array antenna.
[0003] Coprime arrays are a typical type of sparse array structure, composed of subarrays with coprime spacing between their elements. Since the element spacing of the two subarrays satisfies the coprime relationship, a difference coarray can be formed through differential operations between the element positions, thus obtaining more virtual element degrees of freedom than the actual number of elements. Therefore, coprime arrays can achieve high array aperture and strong signal resolution with a relatively small number of elements, attracting widespread attention in the field of array signal processing. Traditional coprime arrays often employ linear array structures. In this structure, a virtual array structure approximating a uniform linear array can be obtained by constructing a difference coarray, allowing direct use of existing high-resolution DOA estimation algorithms for signal direction estimation. However, in many practical applications, such as target localization, sound source localization, and wireless communication systems, omnidirectional signal perception is often required. Linear array structures have certain limitations in terms of azimuth coverage; therefore, researchers have extended coprime array structures to two-dimensional array structures, with a representative example being the coprime circular array. Coprime circular arrays typically consist of two uniform circular arrays with different numbers of elements, the number of which satisfies a coprime relationship. This structural design allows for a larger array aperture while maintaining a smaller number of physical elements, while also providing omnidirectional detection capability. Therefore, coprime circular arrays have significant application value in radar detection, sonar positioning, and wireless communication. Existing coprime circular array constructions mainly fall into two categories. The first type involves two subarrays with the same radius and a pair of coprime elements, arranged on the same circle. The second type involves two subarrays with different radii and a pair of coprime elements, arranged in concentric circles. The processing method for the first type of coprime circular array is similar to that for uniform circular arrays. Beamspace transformation is used to convert the circular array from the beam domain to the modal domain. In the modal domain, the array manifold resembles the Vandermonde matrix form of a linear array. Then, traditional high-resolution direction-of-arrival (DOA) estimation algorithms are used for signal direction estimation. For the second type of coprime circular array, there are also methods that utilize beam space transformation. A more novel approach is to achieve direction-of-arrival estimation by using differential co-matrix combined with sparse Bayesian learning (SBL).
[0004] Although some research results have been achieved in the application of coprime circular arrays, the following shortcomings still exist in practical signal processing: Existing methods often rely on beam space transformation, resulting in complex algorithm structures. These methods not only increase algorithm complexity but may also introduce information loss during beam space transformation, while failing to fully utilize the high degrees of freedom of coprime arrays.
[0005] After the virtual array is constructed, the virtual array will have inconsistent element radii, and the traditional compressed sensing dictionary cannot accurately match the virtual array manifold. Summary of the Invention
[0006] To address the aforementioned problems in the existing technology, this invention provides a direction-of-arrival estimation method based on a coprime circular array virtual array. In a first aspect, the present invention provides a direction-of-arrival estimation method based on a coprime circular array virtual array, the method comprising: Through pre-built inclusion The coprime circular array of each element confirms the array received signal corresponding to the incident signal. The covariance matrix is determined based on the received array signal. The covariance matrix is then vectorized to obtain a covariance matrix vector. The sum-to-product transformation of the covariance matrix vector yields the angular positions and virtual radii of each virtual array element on the circumference. Geometric analysis is performed on the angular positions of the virtual array elements in the coprime circular array corresponding to the covariance matrix vector. Combined with the corollary of Bézout's theorem in the integer field, a result containing 2... NM A virtual uniform circular array of elements; Division in angular space G A weighted overcomplete dictionary is constructed using discrete angle grids; each discrete angle grid corresponds to a column of guiding vectors, and each column of guiding vectors introduces the virtual radius and angular position corresponding to all virtual elements in the virtual uniform circular array; The compressed sensing model is confirmed using a weighted overcomplete dictionary; the compressed sensing model is solved using a sparse reconstruction algorithm to reconstruct sparse vectors; and the DOA estimation results are obtained based on the sparse vectors.
[0007] In one embodiment of the present invention, the coprime circular array includes: The first uniform circular array and the second uniform circular array; wherein... The first uniform circular array contains N array elements, and the second uniform circular array contains M array elements. The first uniform circular array and the second uniform circular array share the first array element. In the coprime circular array, the angular positions of all array elements as follows: .
[0008] In one embodiment of the present invention, the expression for the array received signal is as follows: ; in, This indicates that the array receives signals. The array steering matrix is composed of the steering vector components of all incoming wave signals received by each array element and the angular position of each element. Represents the incident signal vector. This represents the noise vector.
[0009] In one embodiment of the present invention, the expression for the covariance matrix is as follows: ; in, Represents the covariance matrix. The matrix representing the received signal of the array. This represents the conjugate transpose of the matrix corresponding to the array's received signal. Represents the array steering matrix. This represents the matrix corresponding to the incident signal vector. This represents the conjugate transpose of the matrix corresponding to the incident signal vector. This represents the conjugate transpose of the array guiding matrix. , Indicates the first K The power of a far-field narrowband signal, Represents a unit array.
[0010] In one embodiment of the present invention, the expression for the covariance matrix vector is as follows: ; in, Represents the covariance matrix vector. Vectorization is represented. Represents the covariance matrix. The adjoint matrix represents the array steering matrix. This represents the equivalent array manifold of the virtual array. Represents the array steering matrix. This represents a vector composed of the power of all incoming wave signals in the incident signal. This represents the noise covariance matrix.
[0011] In one embodiment of the present invention, the expression for the angular position of each virtual array element on the circumference is as follows: ; in, This indicates the angular position of the virtual array element on the circumference. This represents the number of elements in the first uniform circular array of coprime circular arrays. This represents the number of elements in the second uniform circular array within a coprime circular array. , , , .
[0012] In one embodiment of the present invention, the expression for the virtual radius of each virtual array element is as follows: ; in, The virtual radius represents the virtual array element. Denotes the first uniform circular array in a coprime circular array as the first circular array. i The corner positions of each array element Denotes the second uniform circular array in a coprime circular array. j The corner positions of each array element This represents the element radius of a coprime circular array.
[0013] In one embodiment of the present invention, the expression for the weighted overcomplete dictionary is as follows: ; in, , Indicates the first G The guide vector corresponding to each discrete angle grid. Indicates the first G Spatial angles corresponding to discrete angle grids Indicates the wavelength of the incoming signal. Represents the first in a virtual uniform circular array The virtual radius corresponding to each virtual array element. Represents the first in a virtual uniform circular array The corner positions corresponding to each virtual array element.
[0014] In a second aspect, the present invention provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; The memory is used to store computer programs; When the processor executes the program stored in the memory, it implements the steps of the direction-of-arrival estimation method based on a coprime circular array virtual array provided in the first aspect of the present invention.
[0015] Thirdly, the present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, it implements the steps of the direction-of-arrival estimation method based on a coprime circular array virtual array provided in the first aspect of the present invention.
[0016] The beneficial effects of this invention are: The solution provided by this invention constructs a virtual uniform circular array, which can obtain a far greater number of virtual array elements than physical array elements under the structure of a coprime circular array. This effectively breaks through the limitation of the number of physical array elements on the degree of freedom, significantly improves the array's degree of freedom, and can better adapt to complex scenarios with multiple signal sources coexisting, laying the foundation for high-resolution DOA estimation. The designed weighted overcomplete dictionary can accurately adapt to the irregular structure of the virtual uniform circular array with inconsistent radii, effectively reducing the modeling error between the traditional dictionary and the real manifold of the virtual array, significantly improving the accuracy and stability of direction estimation, and solving the problem of insufficient accuracy of existing sparse reconstruction methods in coprime circular array applications. This invention proposes a novel processing method for coprime circular arrays, breaking through the limitation of existing technologies where coprime circular arrays rely heavily on beam space conversion, providing a new approach to performance mining of coprime circular arrays, and enriching the application modes of coprime circular arrays in the field of DOA estimation. Attached Figure Description
[0017] Figure 1 This is a schematic diagram illustrating the steps of a direction-of-arrival estimation method based on a coprime circular array virtual array provided in an embodiment of the present invention. Figure 2 This is a flowchart illustrating a direction-of-arrival estimation method based on a coprime circular array virtual array provided in an embodiment of the present invention. Figure 3 This is a schematic diagram of the structure of a coprime circular array in a direction-of-arrival estimation method based on a coprime circular array provided in an embodiment of the present invention. Figure 4 This is a schematic diagram of the structure of a virtual uniform circular array in a direction-of-arrival estimation method based on a coprime circular array provided in an embodiment of the present invention. Figure 5 This is a schematic diagram of the structure of a weighted overcomplete dictionary in a direction-of-arrival estimation method based on a coprime circular array virtual array provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation
[0018] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.
[0019] Traditional DOA estimation algorithms largely rely on regularly structured uniform arrays. Among them, uniform linear arrays (ULAs) have long been the two most widely used array configurations due to their simple array manifold, easy algorithm implementation, and strong engineering scalability. Based on these uniform arrays, researchers have proposed a series of classic subspace-based estimation algorithms, such as the Multiple Signal Classification (MUSIC) algorithm and the Rotation Invariant Technique for Estimating Signal Parameters (ESPRIT) algorithm. These algorithms have been widely used in ideal scenarios with low to medium signal source density and high signal-to-noise ratio due to their high estimation resolution and stable performance. However, traditional uniform arrays have an inherent core limitation—the array's degree of freedom (DOF) is strictly limited by the number of physical array elements. When the number of signal sources to be estimated approaches or even exceeds the number of physical array elements, the estimation performance of subspace-based algorithms will significantly decrease, and they may even be unable to effectively estimate the signal direction. This makes it difficult to meet the practical application requirements of multiple signal sources, low signal-to-noise ratio, and high-density signals coexisting in complex electromagnetic environments, becoming a key bottleneck restricting the development of DOA estimation technology towards high performance.
[0020] To effectively enhance the degrees of freedom of arrays and overcome the performance bottlenecks of traditional uniform arrays within the constraint of a limited number of physical array elements, while simultaneously reducing system hardware costs and complexity, researchers have gradually shifted their focus to the design and application of sparse array structures. Sparse arrays, by deliberately reducing the number of physical array elements and optimizing their spatial arrangement, lower hardware deployment costs and system power consumption. Furthermore, they can construct virtual arrays through differential operations between elements, thereby indirectly expanding the array's degrees of freedom and achieving higher-resolution DOA estimation. Among various sparse array configurations, coprime arrays, with their unique structural advantages and performance potential, have become a research hotspot in the field of array signal processing in recent years. Coprime arrays are typically composed of two subarrays working together, with the element spacing between the two subarrays satisfying a coprime relationship. By differentially processing the received signals from the two subarrays, a virtual uniform array with a scale much larger than the physical array can be formed, namely a differential coarray. This significantly improves the array's degrees of freedom and DOA estimation performance, especially in complex scenarios with multiple signal sources, low signal-to-noise ratio, and a limited number of array elements. It exhibits unique advantages over traditional uniform arrays and other sparse arrays, providing an effective approach to solving the DOA estimation problem for multiple signal sources with a limited number of array elements.
[0021] With the rapid development of signal processing technology and the continuous expansion of DOA estimation application scenarios, traditional one-dimensional DOA estimation can no longer meet the application requirements of practical systems. In practical scenarios such as radar detection, electronic reconnaissance, and wireless communication, signals usually come from any direction in space, requiring the simultaneous acquisition of two-dimensional angle information of the signal's azimuth and elevation angles. Therefore, two-dimensional DOA estimation has gradually become an important research direction for scholars both domestically and internationally. At the same time, to adapt to the needs of two-dimensional DOA estimation, sparse arrays have gradually expanded from one-dimensional linear arrays to two-dimensional area arrays. The combination of coprime arrays and area array structures (such as coprime circular arrays and coprime rectangular arrays) has further expanded the application range of sparse arrays, providing new array configuration options for two-dimensional high-resolution DOA estimation. Among them, coprime circular arrays, with their advantages of unambiguous azimuth estimation and good omnidirectionality, show broad application prospects in the field of two-dimensional DOA estimation.
[0022] On the other hand, with the continuous improvement and development of compressed sensing (CS) theory, DOA estimation methods based on sparse reconstruction have gradually become a research hotspot, breaking the strict restrictions on array degrees of freedom imposed by traditional subspace algorithms. The core idea of this type of method is to utilize the sparsity of signals in the spatial domain—that is, the number of signal sources in space is much smaller than the number of divisions of the entire spatial angle range—to construct an overcomplete dictionary matrix covering the entire angle domain of interest. This transforms the DOA estimation problem into a sparse vector reconstruction problem, thereby achieving high-resolution angle estimation. Even in scenarios where the number of signal sources exceeds the number of physical array elements, it can still achieve good estimation performance. However, the construction of traditional overcomplete dictionary matrices is mostly based on ideal uniform array models, which assume uniform element spacing and regular array structure, and cannot adapt to the actual characteristics of coprime circular virtual arrays. When traditional overcomplete dictionaries are directly applied to virtual arrays of coprime circular arrays, the inconsistent radius distribution and non-uniform spacing of the virtual array elements in the coprime circular array lead to a large deviation between the array manifold described by the dictionary model and the actual array manifold of the virtual array. This severely affects the accuracy and stability of sparse reconstruction and restricts the application of DOA estimation methods based on sparse reconstruction in virtual arrays of coprime circular arrays.
[0023] Based on the aforementioned research background and existing problems, how to construct an ultracomplete dictionary model that can accurately describe the virtual array manifold and adapt to the distribution characteristics of virtual array elements on the basis of a coprime circular array virtual array structure, effectively eliminate the deviation between the dictionary model and the actual array manifold, and thus achieve high-precision, high-resolution two-dimensional DOA estimation, has become an important scientific problem and engineering challenge that urgently needs to be solved in the field of array signal processing. It has important theoretical significance and practical value for promoting the application of DOA estimation technology in complex scenarios.
[0024] Currently, research on the application of coprime circular arrays in the field of direction-of-arrival (DOA) estimation has made some progress. However, most existing methods are limited to combining with beamspace conversion technology and have not fully utilized virtual array construction, an effective means of improving array performance. This results in the array freedom advantage of coprime circular arrays not being fully utilized, making it difficult to meet the actual needs of high-precision, high-resolution DOA estimation in complex scenarios. Based on this, this invention focuses on the virtual array construction technology of coprime circular arrays. Addressing the problems of irregular virtual array structure, inconsistent array radius, and insufficient matching degree between subsequent dictionary construction and array manifold that arise after applying virtual array construction to coprime circular arrays, this invention proposes a DOA estimation method based on a virtual array of coprime circular arrays.
[0025] Therefore, the embodiments of the present invention address the above problems from two core aspects: on the one hand, they break through the limitations of existing coprime circular arrays with multiple combined beam space conversions and carry out research on the virtual array construction of coprime circular arrays; on the other hand, for the irregular structure with inconsistent radii generated after the virtual array construction, a weighted overcomplete dictionary adapted to its real manifold is designed, and finally a novel DOA estimation method is proposed, which aims to fully release the performance potential of coprime circular arrays and significantly improve the angle estimation accuracy and resolution of coprime circular arrays.
[0026] The following is a description of a method provided by an embodiment of the present invention.
[0027] The present invention provides a direction-of-arrival estimation method based on a coprime circular array virtual array, such as... Figure 1 and Figure 2 As shown, it may include the following steps: S1, through pre-built inclusion The coprime circular array of each element confirms the array received signal corresponding to the incident signal.
[0028] Coprime circular arrays, such as Figure 3 As shown, it may include: The first uniform circular array and the second uniform circular array; wherein... The first uniform circular array includes N Each array element, the second uniform circular array contains M There are several array elements; the first uniform circular array and the second uniform circular array share the first array element; the radius of each array element is... R ,and .
[0029] In a coprime circular array, such as Figure 3 As shown, with the center of the circular array as the reference point, the angular positions of all array elements are... as follows: .
[0030] For example, whenn When =1, the corner position of the corresponding array element is: ;when m When =1, the corner position of the corresponding array element is: By comparison and The size of the angular position can determine the positional relationship between the two array elements.
[0031] Assumption K The far-field narrowband signals are used as the incoming wave signals, and their azimuth angles are respectively The pitch angles are all Then the first l Each array element receives the first k The steering vector component of a far-field narrowband signal can be expressed as: ; in, Indicates the first l Each array element receives the first k The steering vector component of a far-field narrowband signal. Indicates the wavelength of the incoming signal. This represents the element radius of a coprime circular array. Indicates the first k The azimuth angle corresponding to a far-field narrowband signal Indicates the first l The corner positions corresponding to each array element.
[0032] The expression for the array-received signal is as follows: ; in, This indicates that the array receives signals. The array steering matrix is composed of the steering vector components of all incoming wave signals received by each array element and the angular position of each element. Represents the incident signal vector. This represents the noise vector.
[0033] S2, based on the received array signal, confirm the covariance matrix, vectorize the covariance matrix to obtain the covariance matrix vector; perform sum-to-product transformation on the covariance matrix vector to obtain the angular positions and virtual radii of each virtual array element on the circumference; perform geometric analysis on the angular positions of the virtual array elements in the virtual array of the coprime circular array corresponding to the covariance matrix vector, and combine the corollary of Bézout's theorem in the integer field to obtain the... 2NM A virtual uniform circular array with individual array elements.
[0034] The covariance matrix is determined based on the received signal from the array. The expression for the covariance matrix is as follows: ; in, Represents the covariance matrix. The matrix representing the received signal of the array. This represents the conjugate transpose of the matrix corresponding to the array's received signal. Represents the array steering matrix. This represents the matrix corresponding to the incident signal vector. This represents the conjugate transpose of the matrix corresponding to the incident signal vector. This represents the conjugate transpose of the array guiding matrix. , Indicates the first K The power of a far-field narrowband signal, Represents a unit array.
[0035] Vectorizing the covariance matrix, the resulting covariance matrix vector is expressed as follows: ; in, Represents the covariance matrix vector. Vectorization is represented. Represents the covariance matrix. The adjoint matrix represents the array steering matrix. This represents the equivalent array manifold of the virtual array. Represents the array steering matrix. This represents a vector composed of the power of all incoming wave signals in the incident signal. This represents the noise covariance matrix.
[0036] Its characteristics are similar to a single-snapshot receiver vector of a virtual array with extended degrees of freedom. For the equivalent array manifold of the virtual array, and .
[0037] Understandably, in a coprime linear array, vectorizing the covariance matrix reveals the positions of each element. The difference terms are used to obtain the positions of the virtual array elements. However, in coprime circular arrays, due to the special structure of circular arrays, the difference terms for the array element positions do not appear directly. Instead, they are in the form of the subtraction of two trigonometric functions, which can be obtained through the sum-to-product transformation: ; in, Indicates the first k The azimuth angle corresponding to a far-field narrowband signal Denotes the first uniform circular array in a coprime circular array as the first circular array. i The corner positions of each array element Denotes the second uniform circular array in a coprime circular array. jThe corner positions of each array element.
[0038] Virtual array element receiving the first k The virtual steering vector of a far-field narrowband signal is based on and The size relationship can be written as: ; in, Indicates the first k A virtual steering vector for a far-field narrowband signal. Indicates the first k The azimuth angle corresponding to a far-field narrowband signal This represents the element radius of a coprime circular array. Indicates the wavelength of the incoming signal. Denotes the first uniform circular array in a coprime circular array as the first circular array. i The corner positions of each array element Denotes the second uniform circular array in a coprime circular array. j The corner positions of each array element.
[0039] The positions of virtual array elements can be inferred from the virtual guide vector. N =2、 M Taking a coprime circular array with a density of 3 as an example, the virtual array is as follows: Figure 4 As shown, the azimuth angle of each virtual element on the circumference can be derived from the expression of the virtual steering vector: ; in, This indicates the angular position of the virtual array element on the circumference. Denotes the first uniform circular array in a coprime circular array as the first circular array. i The corner positions of each array element Denotes the second uniform circular array in a coprime circular array. j The corner positions of each array element.
[0040] The expression for the virtual radius of each virtual array element is as follows: ; in, The virtual radius represents the virtual array element. Denotes the first uniform circular array in a coprime circular array as the first circular array. i The corner positions of each array element Denotes the second uniform circular array in a coprime circular array. j The corner positions of each array element This represents the element radius of a coprime circular array.
[0041] By performing geometric analysis on the angular positions of the array elements in a virtual array of coprime circular arrays, and considering only the difference terms formed between two subarrays, the angular positions of the virtual array elements in a virtual uniform circular array are as follows: ; in, , .
[0042] For example, when n =2、 m When =3, the corner position of the corresponding virtual array element is: ;when n =3、 m When =2, the corner position of the corresponding virtual array element is: By comparing the angular positions of two virtual array elements, the positional relationship between their angular positions can be confirmed.
[0043] because N and M They are a pair of coprime numbers. According to Bézout's theorem in the integer field, they are linear combinations. exist n and m When iterating through each of its custom intervals, the values must include one of length 1. NM A continuous set. Take the modulo of this continuous set. NM Therefore, the expressions for the angular positions of each virtual array element on the circumference are as follows: ; in, This indicates the angular position of the virtual array element on the circumference. This represents the number of elements in the first uniform circular array of coprime circular arrays. This represents the number of elements in the second uniform circular array within a coprime circular array. , , , From the above equation, it can be concluded that there must exist a set of elements in the virtual array consisting of 2... NM A virtual uniform circular array composed of virtual array elements, wherein the corner positions of the virtual array elements are at... Uniformly distributed within.
[0044] S3, in angular space division G A weighted overcomplete dictionary is constructed using discrete angle grids; each discrete angle grid corresponds to a column of guiding vectors, and each column of guiding vectors introduces the virtual radius and angular position corresponding to all virtual elements in the virtual uniform circular array.
[0045] Assume the virtual uniform circular array has 2 NM Each virtual array element has a corresponding virtual radius of 1. Divide the angular space at equal intervals G A weighted overcomplete dictionary is constructed using discrete angle grids; the expression for the weighted overcomplete dictionary is as follows: ; in, , Indicates the first G The guide vector corresponding to each discrete angle grid. Indicates the first G Spatial angles corresponding to discrete angle grids Indicates the wavelength of the incoming signal. Represents the first in a virtual uniform circular array The virtual radius corresponding to each virtual array element. Represents the first in a virtual uniform circular array The corner positions corresponding to each virtual array element.
[0046] A structural diagram of a weighted overcomplete dictionary, as shown below. Figure 5 As shown, it can be seen that from arrive of G Each weight is divided at equal intervals in the angular space. G Each discrete angle grid corresponds to a specific element. Each column of guide vectors incorporates the virtual radius information of the virtual array element, achieving accurate modeling of the array's true manifold.
[0047] This invention addresses the array manifold mismatch problem caused by inconsistent equivalent radii of virtual array elements in a virtual array by proposing a weighted overcomplete dictionary construction method. By introducing weight factors into the guiding vectors corresponding to different virtual array elements in the dictionary matrix, the dictionary model can accurately match the virtual array manifold structure.
[0048] S4. The compressed sensing model is confirmed using a weighted overcomplete dictionary; the compressed sensing model is solved using a sparse reconstruction algorithm to reconstruct sparse vectors; and the DOA estimation result is obtained based on the sparse vectors.
[0049] Specifically, the expression for the compressed sensing model is as follows: ; in, This indicates a weighted overcomplete dictionary. This represents a sparse signal vector, where non-zero positions correspond to the signal incident direction. This represents noise in the compressed sensing model.
[0050] The sparse reconstruction algorithm is as follows: ; in, Let be the objective function. As constraints, This indicates the preset reconstruction threshold.
[0051] Solving using the sparse reconstruction algorithm, we obtain... K Sparse vectors , among them K The angle corresponding to the larger value is the DOA estimation result.
[0052] It is understood that, compared with the prior art, the embodiments of the present invention have the following advantages: A novel processing method for coprime circular arrays is proposed, which breaks through the limitation of existing technologies that rely heavily on beam space transformation for coprime circular arrays. This provides a new approach to performance mining of coprime circular arrays and enriches the application modes of coprime circular arrays in the field of DOA estimation.
[0053] Significantly enhances array degrees of freedom: By using the differential co-array construction method, a far greater number of virtual array elements than physical array elements can be obtained under the coprime circular array structure. This effectively breaks through the limitation of the number of physical array elements on the degrees of freedom, and can better adapt to complex scenarios with multiple signal sources coexisting, laying the foundation for high-resolution DOA estimation.
[0054] Significantly improves DOA estimation accuracy: The weighted overcomplete dictionary designed in this invention can accurately adapt to the irregular structure of virtual arrays with inconsistent radii of coprime circular arrays, effectively reducing the modeling error between traditional dictionaries and the real manifold of the virtual array, significantly improving the accuracy and stability of direction estimation, and solving the problem of insufficient accuracy of existing sparse reconstruction methods in coprime circular array applications.
[0055] The embodiments of the present invention are applicable to array signal processing fields such as radar, sonar, wireless communication, and electronic reconnaissance.
[0056] Secondly, embodiments of the present invention also provide an electronic device, such as... Figure 6 As shown, it includes a processor 001, a communication interface 002, a memory 003, and a communication bus 004, wherein the processor 001, the communication interface 002, and the memory 003 communicate with each other through the communication bus 004. The memory is used to store computer programs; When the processor executes the program stored in the memory, it implements the steps of any of the direction-of-arrival estimation methods based on coprime circular array virtual arrays provided in the first aspect of the present invention.
[0057] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.
[0058] The communication interface is used for communication between the aforementioned electronic devices and other devices.
[0059] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.
[0060] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.
[0061] The method provided in this invention can be applied to electronic devices. Specifically, the electronic device can be a desktop computer, a portable computer, a smart mobile terminal, a server, etc. No limitation is made herein; any electronic device that can implement this invention falls within the protection scope of this invention.
[0062] Thirdly, corresponding to the method provided in the first aspect, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the wave direction estimation methods based on coprime circular array virtual arrays provided in the first aspect of the present invention.
[0063] For the electronic device / storage medium embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and relevant details can be found in the description of the method embodiments.
[0064] It should be noted that the electronic device and storage medium in the embodiments of the present invention are respectively electronic devices and storage media that apply the above-mentioned direction of arrival estimation method based on coprime circular array virtual array. Therefore, all embodiments of the above-mentioned direction of arrival estimation method based on coprime circular array virtual array are applicable to the electronic device and storage medium, and can achieve the same or similar beneficial effects.
[0065] It should be noted that, in the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.
[0066] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.
Claims
1. A method for estimating direction of arrival (DOA) based on a coprime circular array virtual array, characterized in that, include: Through pre-built inclusion The coprime circular array of each element confirms the array received signal corresponding to the incident signal. The covariance matrix is determined based on the received array signal. The covariance matrix is then vectorized to obtain a covariance matrix vector. The sum-to-product transformation of the covariance matrix vector yields the angular positions and virtual radii of each virtual array element on the circumference. Geometric analysis is performed on the angular positions of the virtual array elements in the coprime circular array corresponding to the covariance matrix vector. Combined with the corollary of Bézout's theorem in the integer field, a result containing 2... NM A virtual uniform circular array of elements; Division in angular space G A weighted overcomplete dictionary is constructed using discrete angle grids; where each discrete angle grid corresponds to a column of guiding vectors, and each column of guiding vectors introduces the virtual radius and angular position corresponding to all virtual elements in the virtual uniform circular array; The compressed sensing model is confirmed using a weighted overcomplete dictionary; the compressed sensing model is solved using a sparse reconstruction algorithm to reconstruct sparse vectors. The DOA estimation result is obtained from the sparse vector.
2. The direction-of-arrival estimation method based on a coprime circular array virtual array according to claim 1, characterized in that, The coprime circular array includes: The first uniform circular array and the second uniform circular array; wherein... The first uniform circular array contains N array elements, and the second uniform circular array contains M array elements. The first uniform circular array and the second uniform circular array share the first array element. In the coprime circular array, the angular positions of all array elements as follows: 。 3. The direction-of-arrival estimation method based on a coprime circular array virtual array according to claim 1, characterized in that, The expression for the array receiving the signal is as follows: ； in, This indicates that the array receives signals. The array steering matrix is composed of the steering vector components of all incoming wave signals received by each array element and the angular position of each element. Represents the incident signal vector. This represents the noise vector.
4. The direction-of-arrival estimation method based on a coprime circular array virtual array according to claim 1, characterized in that, The expression for the covariance matrix is as follows: ； in, Represents the covariance matrix. The matrix representing the received signal of the array. This represents the conjugate transpose of the matrix corresponding to the array's received signal. Represents the array steering matrix. This represents the matrix corresponding to the incident signal vector. This represents the conjugate transpose of the matrix corresponding to the incident signal vector. This represents the conjugate transpose of the array guiding matrix. , Indicates the first K The power of a far-field narrowband signal, Represents a unit array.
5. The direction-of-arrival estimation method based on a coprime circular array virtual array according to claim 1, characterized in that, The expression for the covariance matrix vector is as follows: ； in, Represents the covariance matrix vector. Vectorization is represented. Represents the covariance matrix. The adjoint matrix represents the array steering matrix. This represents the equivalent array manifold of the virtual array. Represents the array steering matrix. This represents a vector composed of the power of all incoming wave signals in the incident signal. This represents the noise covariance matrix.
6. The direction-of-arrival estimation method based on a coprime circular array virtual array according to claim 1, characterized in that, The expressions for the angular positions of each virtual array element on the circumference are as follows: ； in, This indicates the angular position of the virtual array element on the circumference. This represents the number of elements in the first uniform circular array of coprime circular arrays. This represents the number of elements in the second uniform circular array within a coprime circular array. , , , .
7. The direction-of-arrival estimation method based on a coprime circular array virtual array according to claim 1, characterized in that, The expression for the virtual radius of each virtual array element is as follows: ； in, The virtual radius represents the virtual array element. Denotes the first uniform circular array in a coprime circular array as the first circular array. i The corner positions of each array element Describes the second uniform circular array in a coprime circular array. j The corner positions of each array element This represents the element radius of a coprime circular array.
8. The direction-of-arrival estimation method based on a coprime circular array virtual array according to claim 1, characterized in that, The expression for the weighted overcomplete dictionary is as follows: ； in, , Indicates the first G The guide vector corresponding to each discrete angle grid. Indicates the first G Spatial angles corresponding to discrete angle grids Indicates the wavelength of the incoming signal. Represents the first in a virtual uniform circular array The virtual radius corresponding to each virtual array element. Represents the first in a virtual uniform circular array The corner positions corresponding to each virtual array element.
9. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; The memory is used to store computer programs; When the processor executes the program stored in the memory, it implements the steps of the direction-of-arrival estimation method based on a coprime circular array virtual array as described in any one of claims 1-8.
10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the direction-of-arrival estimation method based on a coprime circular array virtual array as described in any one of claims 1-8.