Design method of high degree of freedom low mutual coupling sparse array based on fourth-order cumulant

Abstract

This invention discloses a high-degree-of-freedom, low-coupling sparse array design method based on fourth-order cumulants, comprising: A: constructing a non-Gaussian signal receiving model and constructing a fourth-order differential array of the non-Gaussian signal using fourth-order cumulants; B: constructing a coprime displacement array composed of two coprime displacement subarrays and determining the array parameters; C: constructing an expanded nested array composed of two nested subarrays and determining the array parameters; D: constructing an expanded nested coprime displacement array based on the coprime displacement array and the expanded nested array and determining the expansion factor, ultimately obtaining a high-degree-of-freedom, low-coupling sparse array based on fourth-order cumulants. This invention can achieve stronger anti-coupling capability while maintaining a degree of freedom comparable to existing sparse arrays, and can significantly improve the signal estimation accuracy and direction-of-arrival resolution.

Description

Technical Field

[0001] This invention relates to the field of array signal processing, and in particular to a high-degree-of-freedom, low-coupling sparse array design method based on fourth-order cumulants. Background Technology

[0002] Direction of Arrival (DOA) estimation, a crucial component of array signal processing, is widely applied in radar, sonar, and wireless communication. Traditional uniform linear arrays with M elements can estimate the DOA of at most M-1 sources using multiple signal classification or rotation-invariant algorithms. This means that the more sources there are, the more physical array elements are required. Furthermore, uniform linear arrays require element spacing no greater than half a wavelength; small element spacing leads to severe mutual coupling effects, degrading DOA estimation performance. Sparse arrays, on the other hand, have become a research focus in array signal processing in recent years due to their ability to offer higher degrees of freedom in estimation and larger element spacing.

[0003] Most existing sparse arrays are designed for conventional ideal Gaussian signals based on second-order statistics such as covariance or augmented covariance matrices. However, signals received in actual communication systems are generally non-Gaussian. This necessitates extracting the features of non-Gaussian signals and designing arrays that efficiently receive them based on these features. Fourth-order cumulants can extract the features of non-Gaussian signals, compensating for the information loss caused by second-order statistics in extracting such signals. Therefore, compared to arrays based on second-order statistics, arrays designed based on fourth-order cumulants have more virtual array elements, larger virtual apertures, and higher signal estimation accuracy and resolution, leading to greater design complexity.

[0004] Therefore, there is an urgent need for a high degree of freedom, low mutual coupling sparse array and design method based on fourth-order cumulants, which can achieve stronger anti-mutual coupling capability while having a degree of freedom comparable to existing sparse arrays. Summary of the Invention

[0005] The purpose of this invention is to provide a high degree of freedom and low mutual coupling sparse array design method based on fourth-order cumulants, which can achieve stronger anti-mutual coupling capability while having a degree of freedom comparable to existing sparse arrays.

[0006] The present invention adopts the following technical solution:

[0007] A design method for high-degree-of-freedom, low-coupling sparse arrays based on fourth-order cumulants includes the following steps:

[0008] A: Construct a non-Gaussian signal reception model Combined with fourth-order cumulants Constructing a fourth-order difference array for non-Gaussian signals and physical array Decomposed into the first physical subarray Second physical subarray ;

[0009] Among them, the fourth-order difference array For the first physical subarray The difference set is based on the second physical subarray Translation of the positions of each virtual array element in the difference set;

[0010] B: Construct a subarray consisting of two coprime shift subarrays and Coprime displacement array Coprime displacement array As the first physical subarray The preferred array is determined, and the number of array elements, the array element spacing, and the inter-array spacing between two coprime displacement subarrays are determined.

[0011] C: Construct a system consisting of two nested subarrays and Constructed expanding nested array ,Will As the second physical subarray The preferred array is determined, and the number of array elements, the array element spacing, and the inter-array spacing between two nested subarrays are determined;

[0012] D: Based on coprime displacement array and expanding nested arrays An expanded nested coprime displacement array is constructed, and the expansion factor is determined, ultimately resulting in a high degree of freedom, low mutual coupling sparse array based on fourth-order cumulants.

[0013] Step A includes the following steps:

[0014] A1: Constructing a non-Gaussian signal reception model ;

[0015] A2: Based on a non-Gaussian signal reception model Fourth-order cumulants Constructing a fourth-order difference array for non-Gaussian signals ;

[0016] A3: Utilizing a non-Gaussian signal reception model The characteristics of the fourth-order cumulants are used for array design, and the physical array is used for array design. Decomposed into the first physical subarray Second physical subarray ; the first physical subarray The difference set is based on the second physical subarray The translation of the positions of each virtual array element in the difference set is considered as a fourth-order difference array. .

[0017] Coprime displacement array Composed of two coprime shift subarrays and Composition, wherein the first coprime shift subarray The number of array elements is And the array element interval is Second coprime shift subarray The number of array elements is And the array element interval is First coprime shift subarray With the second coprime shift subarray The inter-array interval is , .

[0018] Expanding nested arrays Composed of two nested subarrays and Composition, first nested subarray The number of array elements is And the array element interval is set to Second nested subarray The number of array elements is And the array element interval is set to First nested subarray Second nested subarray The inter-array interval is set to , This is the undetermined expansion factor.

[0019] High-degree-of-freedom, low-coupling sparse arrays are composed of coprime shift subarrays. and and nested subarrays and It consists of four subarrays, with the following number of antennas in each subarray: , , and The array element intervals are respectively , , and Inflation factor Inter-array spacing of coprime displacement array The total number of antennas is .

[0020] Based on the mathematical principle of fourth-order differential coarrays, this invention proposes a high-degree-of-freedom, low-coupling sparse array design method based on fourth-order cumulants. By combining a coprime displacement array with strong anti-coupling capability and a nested array with high degree of freedom, the discontinuous virtual array elements and their holes in the virtual array complement each other. This not only makes full use of the information of the discontinuous virtual array elements and improves the degree of freedom, but also expands the array element spacing by expanding the nested array, thereby enhancing the array's anti-coupling capability. This effectively improves the signal estimation accuracy and resolution, achieving stronger anti-coupling capability while maintaining a degree of freedom comparable to existing sparse arrays. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the process of the present invention;

[0022] Figure 2 This is a diagram of the coprime displacement array topology in this invention;

[0023] Figure 3 This is a diagram of the topology of the expanded nested array in this invention;

[0024] Figure 4 This is a topological diagram of the expanded nested coprime displacement array in this invention;

[0025] Figure 5 The array pattern is shown for the six array types in this invention;

[0026] Figure 6 This is a curve comparing the degrees of freedom of the five sparse arrays in this invention;

[0027] Figure 7 This is a comparison curve of mutual coupling leakage of five sparse arrays in this invention;

[0028] Figure 8 This is a graph showing the variation of the minimum mean square error of the five sparse arrays in this invention with the mutual coupling strength coefficient. Detailed Implementation

[0029] The array designed in this invention will be described in detail below with reference to the accompanying drawings and examples:

[0030] like Figure 1 As shown, the high-degree-of-freedom, low-coupling sparse array design method based on fourth-order cumulants described in this invention includes the following steps:

[0031] A: Construct a non-Gaussian signal reception model And combined with fourth-order cumulants Constructing a fourth-order difference array for non-Gaussian signals and physical array Decomposed into the first physical subarray Second physical subarray ;

[0032] Among them, the fourth-order difference array For the first physical subarray The difference set is based on the second physical subarray Translation of the positions of each virtual array element in the difference set;

[0033] In this invention, step A includes the following specific steps:

[0034] A1: Constructing a non-Gaussian signal reception model ;

[0035] Define time t A far-field narrowband, uncorrelated non-Gaussian signal From any angle Incident on a physical array normalized to half wavelength Then the physical array The received signal model is the non-Gaussian signal receiving model. for:

[0036] (1)

[0037] Where t represents the signal reception time. T represents the total signal reception time. Let K be the set of K non-Gaussian signals at time t. This represents the k-th non-Gaussian signal at time t, with the superscript T indicating transpose. This represents the k-th incident angle, where each non-Gaussian signal corresponds to one incident angle. Represents physical array The m-th element in the array, where M represents the total number of elements; Indicates the corresponding angle The steering vector, j represents the imaginary unit, and the noise vector. Each element has a mean of 0 and a variance of . Independent of non-Gaussian signals Additive white Gaussian noise, array manifold matrix ;

[0038] A2: Based on a non-Gaussian signal reception model Fourth-order cumulants Constructing a fourth-order difference array for non-Gaussian signals ;

[0039] Non-Gaussian signal receiving model Fourth-order cumulative for:

[0040] (2)

[0041] in, , , and Representing physical arrays The m-th, n-th, u-th, and v-th elements in the array. ,Signal For the fourth-order cumulant of the incident non-Gaussian signal, Indicates cumulative operations; This represents the k-th non-Gaussian signal at time t. express The conjugate transpose of;

[0042] From equation (2), we can see that the fourth-order cumulant It can be regarded as a signal Incident on virtual array element From the received signals, it can be deduced that the virtual array composed of virtual array elements corresponding to all received non-Gaussian signals can be represented as a set. That is, a fourth-order difference array :

[0043] (3)

[0044] A3: Utilizing a non-Gaussian signal reception model The characteristics of the fourth-order cumulants are used for array design, and the physical array is used for array design. Decomposed into the first physical subarray Second physical subarray ;

[0045] In this embodiment, the physical array Decomposed into the first physical subarray Second physical subarray Rewrite equation (3) as follows

[0046] (4)

[0047] From equation (4), it can be seen that the fourth-order difference array can be and The difference set of the physical array elements of the two physical subarrays is obtained by addition, and equation (4) can be rewritten as follows:

[0048] (5)

[0049] in, and Representing sets and set Elements in a set and set Representing the first physical subarray The difference array and the second physical subarray The difference matrix, Represents the union, Representative set The i-th element in the 4th-order difference array It can be viewed as a set Translation .

[0050] Therefore, a fourth-order difference array can be used. Considered as the first physical subarray The difference set is based on the second physical subarray The translation of the positions of each virtual array element in the difference set.

[0051] B: Construct a subarray consisting of two coprime shift subarrays and The constructed coprime displacement array has strong anti-coupling capability Coprime displacement array As the first physical subarray The preferred array is determined, and the number of array elements, the array element spacing, and the inter-array spacing between two coprime displacement subarrays are determined.

[0052] Coprime displacement array Structure such as Figure 2 As shown; where, coprime displacement array Composed of two coprime shift subarrays and The coprime displacement array, after normalizing the element positions by the basic element spacing, is composed of:

[0053] (6)

[0054] Among them, the first coprime shift subarray on the left The number of array elements is And the array element interval is The second coprime shift subarray on the right The number of array elements is And the array element interval is First coprime shift subarray With the second coprime shift subarray The inter-array interval is To accommodate coprime displacement arrays Due to the high degree of freedom and low mutual coupling requirements, the inter-array spacing is selected in this invention. , Half wavelength;

[0055] C: Construct a system consisting of two nested subarrays and Constructed high-degree-of-freedom expanding nested array ,Will As the second physical subarray The preferred array is determined, and the number of array elements, the array element spacing, and the inter-array spacing between two nested subarrays are determined;

[0056] Expanding nested arrays The structure to be expanded, such as Figure 3 As shown, its normalized set of array element positions is:

[0057] (7)

[0058] Expanding nested arrays Composed of two nested subarrays and Composition, the first nested subarray on the left The number of array elements is And the array element interval is set to The second nested subarray on the right The number of array elements is And the array element interval is set to First nested subarray Second nested subarray The inter-array interval is set to , This is the undetermined expansion factor.

[0059] It is readily apparent that, compared to coprime displacement arrays, nested arrays have the advantage of higher degrees of freedom. While the second-order virtual array of a nested array is holeless, the presence of dense subarrays with element spacing of 1 results in strong mutual coupling between elements. In contrast, coprime displacement arrays have larger element spacing and no element pairs with a spacing of 1, thus exhibiting strong anti-coupling capabilities. However, the holes present in their differential arrays disrupt the long continuity of the virtual elements, reducing the degrees of freedom.

[0060] D: Coprime displacement array obtained from steps B and C and expanding nested arrays An expanded nested coprime shift (DNA-ECADiS) array was constructed, and the expansion factor was determined, ultimately resulting in a high degree of freedom, low mutual coupling sparse array based on fourth-order cumulants.

[0061] The antenna position of the expanded nested coprime shift (DNA-ECADiS) array is expressed as: (normalized to half the wavelength of the received non-Gaussian signal)

[0062] (8)

[0063] like Figure 4 As shown, this high-degree-of-freedom, low-coupling sparse array based on fourth-order cumulants consists of antennas (i.e., array elements) with the following numbers: , , and It consists of four subarrays, with the element intervals of each subarray being as follows: , , and To ensure low mutual coupling and high degrees of freedom, an expansion factor is selected in this invention. Inter-array spacing of coprime displacement array .because and Since they share the first antenna, the total number of antennas in the array is: .

[0064] This invention fully utilizes the advantages of nested arrays and coprime displacement arrays to construct an expanded nested coprime displacement array based on a fourth-order differential comatrix design. This results in the constructed expanded nested coprime displacement array based on a fourth-order differential comatrix design having both high degrees of freedom and strong anti-coupling capability.

[0065] In this invention, the obtained dilated nested coprime shift (DNA-ECADiS) array has the following properties:

[0066] (1) Degrees of freedom of the dilatational nested coprime shift (DNA-ECADiS):

[0067] The set of positions of consecutive virtual elements in a fourth-order virtual array of dilated nested coprime shift (DNA-ECADiS) for:

[0068] ;

[0069] in, ;

[0070] (2) Weighting function for dilated nested coprime shifts (DNA-ECADiS):

[0071] The mutual coupling effect of sparse arrays can be controlled by the weighting function, i.e., the number of element pairs. Assessment, in which The element spacing is denoted as . The smaller the element spacing, the greater the introduced mutual coupling effect. Therefore, this invention focuses on analyzing the weighting functions for element spacings of 1, 2, and 3, i.e. The impact on array mutual coupling performance. The weighting function mentioned above is a conventional technique in this field and will not be elaborated upon here.

[0072] When both conditions are met: , and and coprime and When the element spacing is 1, 2, and 3, the weight function is: ;

[0073] When both conditions are met: , and and coprime and When the element spacing is 1, 2, and 3, the weight function is: ;

[0074] When both conditions are met: , and and coprime and When the element spacing is 1, 2, and 3, the weight function is: ;

[0075] When both conditions are met: , and and coprime and When the element spacing is 1, 2, and 3, the weight function is: .

[0076] As can be seen from the weighting function, the expanded nested coprime shift (DNA-ECADiS) array designed in this invention does not have a dense subarray with a weighting function value of 1 under any parameter configuration, especially... When the first three weights of the weight function are zero, there are no small-pitch array element pairs. Therefore, it can be proven from theoretical analysis that the array has a strong anti-coupling capability.

[0077] In this invention, to verify the performance of the expanded nested coprime shift (DNA-ECADiS) array, especially its strong anti-coupling capability, four-level nested arrays (FLNA), extended translation nested array (EASNA), enhanced four-level nested array (EFLNA), and compressed nested array (CNA) based on fourth-order differential coarray design from recent literature were selected as comparative arrays.

[0078] (1) Comparison of radiation patterns:

[0079] from Figure 5 The array pattern shows that:

[0080] (a) Among the six arrays, the uniform array ( Figure 5 The peak value of the grating lobe in the ULA is lower than that of all sparse arrays, reaching as low as -12.9287 dB. This is because the element spacing of the sparse array is greater than that of the uniform array.

[0081] (b) Among the five sparse arrays, the expanded nested coprime shift (DNA-ECADiS) designed in this invention ( Figure 5 The proposed array and the compressed nested array had the lowest grating lobe peak values, as low as -2.5dB, indicating that both arrays have strong grating lobe suppression capabilities.

[0082] (c) The main lobe width of a sparse array is much narrower than that of a uniform array with the same number of array elements. This is because the sparse array has a larger array aperture than the uniform array.

[0083] (2) Comparison of array degrees of freedom:

[0084] Comparative analysis Figure 6 From the changes in the curves, we can see that:

[0085] (a) The degrees of freedom of the five sparse arrays increase with the number of antennas.

[0086] (b) The degrees of freedom of the expanded nested coprime shift (DNA-ECADiS) array designed in this invention are comparable to those of the EASNA and EFLNA arrays, but as the number of array elements increases, the degrees of freedom are higher than those of the FLNA and CNA arrays and the advantages become greater and greater.

[0087] (3) Comparison of array mutual coupling leakage:

[0088] Figure 7 Comparative curves of mutual coupling leakage with the number of antennas for five different array types are presented, where the parameters related to the mutual coupling simulation are set as follows: , , , Comparative analysis Figure 7 The changes in each curve show that:

[0089] (a) The mutual coupling leakage curves of arrays FLNA, EASNA, EFLNA, and CNA are relatively high. This is because these four arrays are based on nested array design, and there are relatively dense subarrays in the array structure, resulting in a large number of array element pairs with smaller weight values.

[0090] (b) The mutual coupling leakage curve of the DNA-ECADiS array designed in this invention is much lower than that of the other four arrays. The reason is that the designed array sparsifies the dense subarrays in the nested array through equal expansion, which greatly reduces the weight function value with small element spacing, reduces the mutual coupling effect between antennas, and achieves stronger anti-mutual coupling capability.

[0091] (4) Experiment on the root mean square error of the array when the mutual coupling strength coefficient changes:

[0092] Figure 8 The five arrays are displayed as a function of mutual coupling strength. Add a curve showing the change in the root mean square error (RMSE). Set the Monte Carlo simulation count to 2000 and the signal-to-noise ratio... Quick shot number Assume there is A signal from angle Incident array. Comparative analysis. Figure 8 The changes in each curve show that:

[0093] (a) With increasing mutual coupling strength With the increase of [value], the RMSE curves of the five arrays showed an upward trend.

[0094] (b) The RMSE curve of the DNA-ECADiS array designed in this invention is... The accuracy is slightly higher than that of the two sparse arrays EASNA and EFLNA. The main reason is that when the mutual coupling is low, the estimation accuracy is greatly affected by the array's degrees of freedom but very little affected by the change in mutual coupling strength. When the five arrays have nine elements, the degrees of freedom of the array designed in this invention are slightly lower than those of EASNA and EFLNA.

[0095] (c) As the mutual coupling strength increases, the RSME curve of the DNA-ECADiS array is lower than that of the other four sparse arrays, indicating that the DNA-ECADiS array, compared with the other four arrays, has a degree of freedom comparable to that of the EASNA and EFLNA sparse arrays, but with a relatively sparse array structure. Therefore, in the interval... Minimum internal error results in optimal performance.

[0096] In summary, most existing sparse arrays are designed for conventional ideal Gaussian signals based on second-order statistics such as covariance or augmented covariance matrices. However, the signals received in actual communication systems are often non-Gaussian. Fourth-order cumulants can extract the features of non-Gaussian signals, compensating for the information loss caused by second-order statistics in extracting non-Gaussian signals. Therefore, it is necessary to design arrays for receiving non-Gaussian signals based on fourth-order cumulants.

[0097] It should be understood that this disclosure is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this disclosure is limited only by the appended claims.

Claims

1. A design method for high-degree-of-freedom, low-coupling sparse arrays based on fourth-order cumulants, comprising the following steps: A: Construct a non-Gaussian signal reception model And combined with fourth-order cumulants Constructing a fourth-order difference array for non-Gaussian signals Physical array Decomposed into the first physical subarray Second physical subarray ; Among them, the fourth-order difference array For the first physical subarray The difference set is based on the second physical subarray Translation of the positions of each virtual array element in the difference set; B: Construct a subarray consisting of two coprime shift subarrays and Coprime displacement array Coprime displacement array As the first physical subarray The preferred array is determined, and the number of array elements, the array element spacing, and the inter-array spacing between two coprime displacement subarrays are determined. C: Construct a system consisting of two nested subarrays and Constructed expanding nested array Expand nested array As the second physical subarray The preferred array is determined, and the number of array elements, the array element spacing, and the inter-array spacing between two nested subarrays are determined; D: Based on coprime displacement array and expanding nested arrays An expanded nested coprime displacement array is constructed, and the expansion factor is determined, ultimately resulting in a high degree of freedom, low mutual coupling sparse array based on fourth-order cumulants.

2. The high-degree-of-freedom, low-coupling sparse array design method based on fourth-order cumulants according to claim 1, characterized in that, Step A includes the following steps: A1: Constructing a non-Gaussian signal reception model ; A2: Based on a non-Gaussian signal reception model Fourth-order cumulative Constructing a fourth-order difference array for non-Gaussian signals ; A3: Utilizing a non-Gaussian signal reception model The characteristics of the fourth-order cumulants are used for array design, and the physical array is used for array design. Decomposed into the first physical subarray Second physical subarray ; the first physical subarray The difference set is based on the second physical subarray The translation of the positions of each virtual array element in the difference set is considered as a fourth-order difference array. .

3. The high-degree-of-freedom, low-coupling sparse array design method based on fourth-order cumulants according to claim 1, characterized in that: Coprime displacement array Composed of two coprime shift subarrays and Composition, wherein the first coprime shift subarray The number of array elements is And the array element interval is Second coprime shift subarray The number of array elements is And the array element interval is First coprime shift subarray With the second coprime shift subarray The inter-array interval is , .

4. The high-degree-of-freedom, low-coupling sparse array design method based on fourth-order cumulants according to claim 1, characterized in that: Expanding nested arrays Composed of two nested subarrays and Composition, first nested subarray The number of array elements is And the array element interval is set to Second nested subarray The number of array elements is And the array element interval is set to First nested subarray Second nested subarray The inter-array interval is set to , This is the undetermined expansion factor.

5. The high-degree-of-freedom, low-coupling sparse array design method based on fourth-order cumulants according to claim 1, characterized in that: High-degree-of-freedom, low-coupling sparse arrays are composed of coprime shift subarrays. and and nested subarrays and It consists of four subarrays, with the following number of antennas in each subarray: , , and The array element intervals are respectively , , and ; Inflation factor Inter-array spacing of coprime displacement array The total number of antennas is .

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