A coherent gain processing method based on sparse array

Abstract

The present invention provides a coherent gain processing method based on a sparse array. For a given number of detection array elements and design requirements, a suitable sparse array is selected to sparsely represent an equally spaced half-wavelength linear array; the sparse array is optimized by selecting sub-array elements to obtain the optimal sparse array performance under the same number of array elements; the beam pattern expressions of the two sub-arrays of the sparse array are processed by conjugate product; the outputs of the two sub-arrays are coherently processed to obtain the final output beam pattern. The present invention utilizes the sparse characteristics of the sparse array to effectively reduce the number of detection array elements; the sparse array performance is optimized by screening the combination of sparse array sub-array elements; the main lobe width of the sparse array beam pattern is similar to that of a uniform linear array, ensuring good detection resolution; when performing target detection, it can achieve the same array gain as a uniform linear array under the same aperture, and can meet a constant output signal-to-noise ratio under different noise environments.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater sonar array signal processing, and in particular relates to a coherent gain processing method based on a sparse array. Background Art

[0002] When using a hydrophone array to collect water acoustic data, the array elements are usually equally spaced. In order to avoid beamforming ambiguity, the array element spacing is required to be less than or equal to half the wavelength of the single-frequency signal. In array signal processing, the larger the array aperture, the higher the spatial resolution. Therefore, under the condition of a certain array element spacing, in order to obtain high resolution of the target, the array aperture needs to be as large as possible, and a large number of array elements are required, which not only increases the hardware cost, but also increases the computational complexity. Therefore, being able to use fewer array elements to achieve a beam pattern similar to that of a uniform linear array, that is, to obtain similar spatial resolution while ensuring the same array gain as that of a uniform linear array, is a hot topic of current research.

[0003] According to a certain signal-to-noise ratio, an appropriate subarray is selected from the uniform linear array, and a sparse array with similar aperture is designed and processed using a multiplication processor. In this way, the performance of the beam pattern is guaranteed with a number of array elements far lower than that of a traditional uniform linear array, while effectively reducing the cost of the transducer array. Summary of the invention

[0004] The object of the present invention is to provide a coherent gain processing method based on a sparse array.

[0005] A coherent gain processing method based on a sparse array comprises the following steps:

[0006] Step 1: Select coprime arrays or nested arrays to perform sparse representation on uniform linear arrays;

[0007] The spacing between uniform linear array elements is d=λ / 2, where λ is the wavelength of the received signal; the coprime array includes two subarrays, namely subarray A and subarray B; subarray A is composed of a uniform linear array with M elements and Nd spacing; subarray B is composed of a uniform linear array with N elements and Md spacing; the nested array includes two subarrays, namely an inner subarray and an outer subarray; the inner subarray is composed of a uniform linear array with Q elements and d spacing; the outer subarray is composed of a uniform linear array with P elements and Qd spacing; if there is no common factor between the values ​​of the spacing between two types of elements M and N or between P and Q, then the coprime array is applicable; if the values ​​of the spacing between two types of elements M and N or between P and Q are multiples, then the nested array is applicable;

[0008] Step 2: Take the number of array elements as small as possible, the maximum sidelobe level of the beam pattern as low as possible, and the main lobe width of the beam pattern as narrow as possible as the screening criteria, and obtain the optimal design scheme of the sparse array by screening the array element distribution of the sub-array; use the conventional beamformer to process the two sub-arrays respectively to obtain the beam pattern, and then use the multiplication processor to conjugate multiply the beam pattern expressions of the two sub-arrays of the sparse array;

[0009] Step 3: Based on the optimal design solution, determine the signal acquisition models of the two sub-arrays;

[0010] The received signal vector x of a sub-array of the sparse array can be expressed as:

[0011] x=Aexp(-jωt)s+n

[0012] Where A is the signal strength; j is the imaginary unit, j 2 =-1; ω is the signal frequency; s is the base array response vector of a plane wave signal in a certain direction in the array; n is the spatially isotropic Gaussian white noise;

[0013] Step 4: Coherently process the outputs of the two sub-arrays. First, conjugate the beam output signals of the two sub-arrays and multiply them. Then, statistically average the product results under multiple snapshot data to retain the phase correlation. Finally, modulus the result to obtain the final output beam diagram.

[0014] Furthermore, in step 2, the nested array is subjected to coherent gain processing, and u T =-j(2π / λ)sinθ T , j is the imaginary unit, θ T is the incoming direction of the received signal, then the base array response vector s of the expected signal in the internal subarray A of the sparse array is A , the matrix response vector s of the external sub-array B B It is expressed as:

[0015] s A =exp(u T d A )

[0016] s B =exp(u T d B )

[0017] Among them, d A is the array structure vector representation of the internal sub-matrix A; d B is the array structure vector representation of the external sub-matrix B;

[0018] Assume u = -j(2π / λ)sinθ, θ∈[-90°,90°] represents the arrival angle of the signal incident on the array in different directions, then the array manifold vector of the two sub-arrays of the sparse array is expressed as:

[0019] w A =exp(ud A )

[0020] w B =exp(ud B )

[0021] The beam pattern of the array can be expressed as the product of the conjugate transpose of the array manifold vector and the corresponding expected signal base array response vector; after being processed by a conventional beam processor, the beam pattern B of the two subarrays A and B of the sparse array is A (θ), B B (θ) can be expressed by the following formula, where the denominator i A 、i B Used to normalize the beam pattern;

[0022]

[0023]

[0024] The beam pattern expressions of the two sub-arrays obtained by conventional beamforming are conjugate multiplied to obtain the beam pattern B(θ) of the sparse array:

[0025]

[0026] Furthermore, the final output beam pattern in step 4 is:

[0027]

[0028] The array gain of the sparse array under coherent processing is:

[0029]

[0030] Among them, s NA Represents the matrix response vector of the signal in the sparse matrix, s NA =exp(u T d NA );d NA is the array structure vector of the sparse array, which is composed of all array elements of the two sub-arrays, of which the first array element is shared.

[0031] The beneficial effects of the present invention are:

[0032] The present invention utilizes the sparse characteristics of the sparse array to effectively reduce the number of detection array elements relative to the uniform linear array of the same aperture. The present invention optimizes the sparse array performance by screening the sparse array sub-array element combination; the main lobe width of the sparse array beam pattern is similar to that of the uniform linear array, ensuring better detection resolution; when performing target detection, it can achieve the same array gain as the uniform linear array under the same aperture, and can meet a constant output signal-to-noise ratio under different noise environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of the present invention.

[0034] Figure 2 The coprime array beam patterns obtained using the multiplication processor under different parameters.

[0035] Figure 3 The nested array beam patterns obtained using the multiplication processor under different parameters.

[0036] Figure 4 Schematic diagram of a sparse array (nested array) designed for a 42-element uniform linear array with an element spacing of d.

[0037] Figure 5 Flowchart of a multiplication processor for processing subarrays.

[0038] Figure 6 It is a sparse array with array parameters (P,Q)=(6,7) and its sub-array beam pattern.

[0039] Figure 7 The figure shows the array gain simulation results of a sparse array with array parameters (P, Q) = (6, 7) and a corresponding 42-element uniform linear array under Gaussian white noise.

[0040] Figure 8 The figure shows the simulation results of array gain under colored noise for a sparse array with array parameters (P,Q)=(6,7) and the corresponding 42-element uniform linear array.

[0041] Fig. 9 The figure shows the simulation results of array gain under impulse noise for a sparse array with array parameters (P,Q)=(6,7) and the corresponding 42-element uniform linear array. DETAILED DESCRIPTION

[0042] The present invention will be further described below in conjunction with the accompanying drawings.

[0043] The purpose of the present invention is to provide a coherent gain processing method based on a sparse array. The present invention belongs to the field of sonar array signal processing. The specific implementation steps of the present invention are as follows: (1) for a given number of detection array elements and design requirements, select a suitable sparse array to sparsely represent the equally spaced half-wavelength linear array; (2) optimize the design of the sparse array by selecting sub-array elements to obtain the optimal sparse array performance under the same number of array elements; (3) perform conjugate product processing on the beam pattern expressions of the two sub-arrays of the sparse array; (4) perform coherent processing on the outputs of the two sub-arrays to improve the output signal-to-noise ratio of the sparse array, which can be used in a variety of noise environments. Compared with traditional uniform linear arrays, the advantages of the present invention are (1) effectively reducing the number of detection array elements and reducing the amount of calculation; (2) ensuring better detection resolution; (3) being able to meet a constant output signal-to-noise ratio, and being suitable for a variety of noise environments, and having strong engineering practical value.

[0044] The purpose of the present invention is to provide a new coherent gain processing method for a sparse array. By jointly optimizing the optimal array element selection and coherent processing, the array gain of the sparse array under Gaussian white noise conditions is made the same as that of a uniform linear array, and such array gain can be maintained under a variety of noise environments, thereby improving the spatial resolution capability of the array beam pattern.

[0045] The specific implementation steps of the present invention are as follows:

[0046] Step 1: Design a sparse array structure, and perform a sparse representation of the uniform linear array, which includes two subarrays. The spacing between the elements of the represented uniform linear array is d=λ / 2, where λ is the wavelength of the received signal. Select a coprime array or a nested array according to different design requirements. The two subarrays of the coprime array are subarray A and subarray B. Subarray A consists of a uniform linear array with M elements and Nd spacing, and subarray B consists of a uniform linear array with N elements and Md spacing. The two subarrays of the nested array are the inner subarray and the outer subarray. The inner subarray consists of a uniform linear array with Q elements and d spacing, and the outer subarray consists of a uniform linear array with P elements and Qd spacing.

[0047] Considering that when a uniform linear array is divided into two sub-arrays, whether it is a coprime array or a nested array, the two sub-arrays are uniform linear arrays with different spacings. If there is no common factor between the values ​​of the spacings between the two types of array elements, it is applicable to coprime arrays; if the values ​​of the spacings between the two types of array elements are in a multiple relationship, it is applicable to nested arrays.

[0048] Step 2: Both the coprime array and the nested array are composed of two sub-arrays. The beam pattern performance obtained by different combinations of the sub-array elements of these two sparse arrays is also different. The optimal design of the sparse array is obtained by screening the distribution of sub-array elements with the minimum number of array elements, the minimum maximum sidelobe level of the beam pattern, and the narrowest main lobe width of the beam pattern as the screening criteria. Use a conventional beamformer to process the two sub-arrays separately to obtain the beam pattern, and then use a multiplication processor to conjugate and multiply the beam pattern expressions of the two sub-arrays of the sparse array;

[0049] Step 3: Based on the optimal design solution, determine the signal acquisition models of the two sub-arrays;

[0050] Step 4: Coherently process the outputs of the two sub-arrays, that is, first average multiple snapshots of the received signal, then take the modulus value of the result to obtain the final output beam pattern.

[0051] The present invention proposes a coherent gain processing method based on a sparse array. The present invention utilizes the sparse characteristics of the sparse array to effectively reduce the number of detection array elements relative to a uniform linear array of the same aperture. The present invention optimizes the performance of the sparse array by screening the combination of sparse array sub-array elements; the main lobe width of the sparse array beam pattern is similar to that of a uniform linear array, ensuring better detection resolution; when performing target detection, it can achieve the same array gain as a uniform linear array under the same aperture, and can meet a constant output signal-to-noise ratio under different noise environments.

[0052] The characteristics of the present invention are as follows:

[0053] (1) Compared with the original uniform linear array, the number of array elements is reduced, which reduces the amount of calculation and hardware cost; (2) In all sparse array designs corresponding to the same uniform linear array, the sub-array element combination is selected to optimize the sparse array performance; (3) The main lobe width of the sparse array beam pattern is similar to that of the original uniform linear array, ensuring good detection resolution performance; (4) Under the same input signal-to-noise ratio, the output signal-to-noise ratio of the sparse array is the same as that of the original uniform linear array; (5) It can be used in a variety of noise environments, and the output signal-to-noise ratio is relatively stable; (6) Under the condition that the array aperture remains unchanged, a suitable sparse array (coprime array or nested array) is selected for a given design requirement. By sparsely representing the uniform linear array, a sparse array with fewer array elements is obtained, and the corresponding amount of calculation and hardware cost are reduced. (7) By designing different sub-array element arrangements and selecting the optimal sub-array combination, the optimal sparse array beam pattern performance is obtained. (8) The above-mentioned part can be used for underwater target detection and azimuth estimation in a sparse array, ensuring good detection and resolution performance with fewer array elements.

[0054] Under Gaussian white noise conditions, when the input signal-to-noise ratio is the same, the output signal-to-noise ratio of the uniform linear array formed by the present invention is the same as that of the conventional beamforming, that is, the array gains of the two are equal; in environments such as color noise and impulse noise, the sparse array can still maintain a constant output signal-to-noise ratio.

[0055] Embodiment 1:

[0056] The present invention is a coherent gain processing method based on a sparse array, including a sparse array design algorithm and beamforming using the sparse array. The specific algorithm flow chart is as follows: Figure 1 shown.

[0057] Step 1: Take a uniform linear array with 42 array elements as an example, where the array element spacing d = λ / 2, λ is the wavelength of the received signal, and sparsely represent the uniform linear array. The two subarrays of the coprime array are subarray A and subarray B, where subarray A consists of a uniform linear array with M array elements and Nd spacing, and subarray B consists of a uniform linear array with N array elements and Md spacing; the nested array contains two subarrays, namely the inner subarray and the outer subarray, where the inner subarray consists of a uniform linear array with Q array elements and d spacing; the outer subarray consists of a uniform linear array with P array elements and Qd spacing. If there is no common factor between the values ​​of the two types of array element spacings M and N or P and Q, then it is applicable to coprime arrays; if the values ​​of the two types of array element spacings M and N or P and Q are multiples, then it is applicable to nested arrays.

[0058] Step 2: Use the multiplication processor to perform conjugate product processing on the two sub-array beam pattern expressions of the sparse array, and select the optimal design solution by comparing the sparse array beam patterns. The sparse array beam patterns obtained by different array element parameters are also different. For a uniform linear array with 42 array elements and a spacing of d, a sparse array is designed. The selection criteria are as few array elements as possible, the maximum sidelobe level as low as possible, and the main lobe width as narrow as possible. The beam patterns of the coprime array and the nested array obtained by different sub-array element arrangements are as follows: Figure 2 and Figure 3 By comparing the beam patterns, it can be seen that the overall performance of the nested array is better than that of the coprime array, and when the number of elements in the inner sub-array of the nested array is Q = 7, the element spacing is d, and the number of elements in the outer sub-array is P = 6, and the element spacing is 7d, a beam pattern similar to other designs can be obtained with the least number of elements. At this time, the number of elements is 12, which is 30% of the uniform linear array represented.

[0059] Take the nested array with the parameters (P, Q) = (6, 7) as an example, and perform coherent gain processing on it. T =-j(2π / λ)sinθ T , where j is the imaginary unit, j 2 =-1,θ Tis the direction of the received signal, then the base array response vector s of the expected signal in the two sub-arrays A (inner sub-array) and B (outer sub-array) of the sparse array is A 、s B It can be expressed as formula (1) and (2).

[0060] s A =exp(u T d A ). (1)

[0061] s B =exp(u T d B ). (2)

[0062] The internal sub-array structure vector is represented by d A =[0,1,2,3,4,5,6,0 35 ]d, the length is 42, indicating that the internal sub-array is composed of seven array elements with an interval of d, 0 35 The subscript 35 indicates the length of the 0 vector, that is, the number of 0 elements. Compared with a uniform linear array, the inner subarray has no elements at 35 consecutive positions, marked as 0. 35 The array structure vector of the external sub-array is represented by d B =[0,06,7,06,14,06,21,06,28,06,35,06]d, with a length of 42, indicating that the outer subarray is composed of six array elements with an interval of 7d. Compared with the uniform linear array, there are 6 positions without array elements between every two array elements in the outer subarray, marked as 06.

[0063] Let u = -j(2π / λ)sinθ, where j is the imaginary unit, j 2 = -1, θ∈[-90°,90°] represents the arrival angle of the signal incident on the array in different directions, then the array manifold vectors of the two sub-arrays of the sparse array are shown in equations (3) and (4).

[0064] w A =exp(ud A ). (3)

[0065] w B =exp(ud B ). (4)

[0066] The beam pattern of the array can be expressed as the product of the conjugate transpose of the array manifold vector and the corresponding desired signal base array response vector. After being processed by a conventional beam processor, the beam pattern B of the two subarrays A and B of this sparse array is A (θ), B B (θ) can be expressed by equations (5) and (6), where the denominator is used to normalize the beam pattern.

[0067]

[0068]

[0069] The processing flow of the multiplication processor is as follows Figure 5 As shown in FIG. 1 , the multiplication processor flowchart for processing the subarray is to conjugate multiply the beam pattern expressions of the two subarrays of the sparse array. Ideally, the input signal of the subarray does not contain noise and can be directly represented by the base array response vector of the desired signal in the array. The beam pattern expressions of the two subarrays obtained by conventional beamforming processing are conjugate multiplied to obtain the beam pattern of the sparse array as equation (7).

[0070]

[0071] The ideal beam diagrams of the two sub-arrays and the beam diagram of the sparse array are plotted in the same figure, as shown in Figure 4 As shown in the figure, for a sparse array (nested array) designed for a 42-element uniform linear array with an element spacing of d, the number of elements in the internal subarray is Q=7, the element spacing is d, the number of external subarrays is P=6, the element spacing is 7d, and the zero point of the internal subarray beam pattern is exactly located at the angle where the grating lobe of the external subarray is located, so the grating lobe can be well suppressed. Compared with other design schemes, the design parameters of the sparse array meet the screening criteria of as few elements as possible, as low a maximum sidelobe level as possible, and as narrow a main lobe width as possible.

[0072] Step 3: Based on the optimal design solution, determine the signal acquisition model of the two sub-arrays. The received signal vector x of a sub-array of the sparse array can be expressed as formula (8):

[0073] x=Aexp(-jωt)s+n, (8)

[0074] Where A is the signal strength, j is the imaginary unit, j 2 =-1, ω is the signal frequency, s is the base array response vector of a plane wave signal in a certain direction in the array, and n is the spatially isotropic Gaussian white noise.

[0075] Step 4: Coherently process the outputs of the two sub-arrays. First, conjugate the beam output signals of the two sub-arrays and multiply them. Then, statistically average the product results under multiple snapshot data to retain the phase correlation. Finally, modulus the result to obtain the beam output result as shown in formula (9).

[0076]

[0077] The array gain of the sparse array under coherent processing can be obtained by formula (10):

[0078]

[0079] where s NA represents the base array response vector of the signal in the sparse array, and the expression is shown in equation (11). The array structure vector d of the sparse array NA =[0,1,2,3,4,5,6,7,06,14,06,21,06,28,06,35,06]d, with a length of 42. It is composed of all the array elements of the two sub-arrays, of which the first array element is shared.

[0080] s NA =exp(u T d NA ). (11)

[0081] For any sparse matrix with element parameters P and Q, the It can be expressed as formula (12) and (13),

[0082]

[0083]

[0084] When the sparse array parameters are (P,Q) = (6,7), the array manifold vector and The length is 42, which can be expressed as formula (14) and (15).

[0085]

[0086]

[0087] in and The first and only element of a vector is not 0, so

[0088] When the array beam is oriented in the same direction as the signal wave, and Respectively with s A and B Correspondingly, the array gain can be obtained as:

[0089]

[0090] It can be seen that the array gain corresponding to the sparse array with the number of array elements P+Q-1=12 is equal to the array gain of the uniform linear array with the number of array elements PQ=42. The above algorithm is used to simulate and verify the sparse array with array parameters (P,Q)=(6,7) and the uniform linear array with the number of array elements 42. The results are as follows Figure 5 As shown, it can be seen that the array gains of the two are basically the same, which is 10log42≈16.2dB.

[0091] Figure 6 The sparse array with array parameters (P, Q) = (6, 7) and its sub-array beam pattern. It can be seen that the zero point of the inner sub-array beam pattern is exactly located at the angle where the grating lobe of the outer sub-array beam pattern is located, so the grating lobe is suppressed. Figure 7 The following are the simulation results of the array gain of a sparse array with array parameters (P, Q) = (6, 7) and the corresponding 42-element uniform linear array under Gaussian white noise. The horizontal axis is the input signal-to-noise ratio and the vertical axis is the output signal-to-noise ratio. The difference between the two is the array gain of the array. It can be seen that the array gain of the sparse array after coherent product processing is very close to that of the corresponding uniform linear array, which is 10log42≈16.2dB. Figure 8 The array gain simulation results of a sparse array with array parameters (P, Q) = (6, 7) and a corresponding 42-element uniform linear array under colored noise. Fig. 9 The simulation results of the array gain of the sparse array with array parameters (P, Q) = (6, 7) and the corresponding 42-element uniform linear array under impulse noise are shown in Figure 2. It can be seen that the array gain performance of the two arrays under colored noise environment is the same as that under Gaussian white noise environment. In the impulse noise environment, the sparse array can still maintain an array gain of about 16.2dB, while the uniform linear array gain is about 6dB, and the performance has dropped significantly.

[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A coherent gain processing method based on a sparse array, characterized in that: The following steps are involved: Step 1: Select coprime arrays to perform sparse representation on uniform linear arrays; The spacing between uniform linear array elements is d=λ / 2, where λ is the wavelength of the received signal; the coprime array includes two subarrays, namely subarray A and subarray B; subarray A is composed of a uniform linear array with M array elements and Nd spacing; subarray B is composed of a uniform linear array with N array elements and Md spacing; and there is no common factor between M and N; Step 2: Take the number of array elements as small as possible, the maximum sidelobe level of the beam pattern as low as possible, and the main lobe width of the beam pattern as narrow as possible as the screening criteria, and obtain the optimal design scheme of the sparse array by screening the array element distribution of the sub-array; use the conventional beamformer to process the two sub-arrays respectively to obtain the beam pattern, and then use the multiplication processor to conjugate multiply the beam pattern expressions of the two sub-arrays of the sparse array; Step 3: Based on the optimal design solution, determine the signal acquisition models of the two sub-arrays; The received signal vector x of a sub-array of the sparse array can be expressed as: x=Aexp(-jωt)s+n Where A is the signal strength; j is the imaginary unit, j 2 =-1; ω is the signal frequency; s is the base array response vector of a plane wave signal in a certain direction in the array; n is the spatially isotropic Gaussian white noise; Step 4: Coherently process the outputs of the two sub-arrays. First, conjugate the beam output signals of the two sub-arrays and multiply them. Then, statistically average the product results under multiple snapshot data to retain the phase correlation. Finally, modulus the result to obtain the final output beam diagram.

2. The coherent gain processing method based on a sparse array according to claim 1, characterized in that: The final output beam pattern in step 4 is: The array gain of the sparse array under coherent processing is: Among them, s NA Represents the matrix response vector of the signal in the sparse matrix, s NA =exp(u T d NA );d NA is the array structure vector of the sparse array, which is composed of all array elements of the two sub-arrays, of which the first array element is shared.

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