CN114384502A - Sparse array-based coherent gain processing method - Google Patents

Abstract

The invention provides a coherent gain processing method based on a sparse array, which is characterized in that a proper sparse array is selected to carry out sparse representation on an equidistant half-wavelength linear array aiming at a given number of detection array elements and design requirements; the method comprises the steps of optimally designing a sparse array by selecting subarray array elements to obtain the optimal sparse array performance under the same array element number; carrying out conjugate product processing on the beam pattern expressions of the two sub-arrays of the sparse array; and performing coherent processing on the outputs of the two sub-arrays to obtain a final output beam pattern. The invention effectively reduces the number of detection array elements by using the sparse characteristic of the sparse array; screening array element combinations of the sparse array to optimize the performance of the sparse array; the main lobe width of the sparse array beam pattern is close to that of the uniform linear array, so that better detection resolution is ensured; when the target detection is carried out, the same array gain as that of a uniform linear array under the same aperture can be realized, and the constant output signal-to-noise ratio can be met under different noise environments.

Description

Sparse array-based coherent gain processing method

Technical Field

The invention belongs to the technical field of underwater sonar array signal processing, and particularly relates to a coherent gain processing method based on a sparse array.

Background

When the hydrophone array is used for collecting underwater acoustic data, array element distribution is usually equal in spacing, and in order to avoid beam forming fuzziness, the spacing between the array elements is required to be smaller than or equal to half of the wavelength of a single-frequency signal. In array signal processing, the larger the aperture of the array, the higher the spatial resolution. Therefore, under the condition of a certain array element spacing, in order to obtain high resolution capability to the target, an array aperture as large as possible is required, and a large number of array elements are correspondingly required, which not only increases the hardware cost, but also increases the computational complexity. Therefore, it is a hot point of current research to realize a beam pattern similar to a uniform linear array with fewer array elements, i.e. to obtain similar spatial resolution and ensure the same array gain as the uniform linear array.

According to a certain signal-to-noise ratio, a proper sub-array is selected from the uniform linear array, a sparse array with similar aperture is designed and is processed by a multiplication processor, so that the performance of a beam pattern is ensured under the condition that the number of array elements is far lower than that of the traditional uniform linear array, and meanwhile, the cost of the transducer array is effectively reduced.

Disclosure of Invention

The invention aims to provide a coherent gain processing method based on a sparse array.

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

step 1: selecting a co-prime array or a nested array to carry out sparse representation on the uniform linear array;

the distance between the array elements of the uniform linear array is d ═ lambda/2, and lambda is the wavelength of the received signal; the co-prime matrix comprises two sub-matrices, namely a sub-matrix A and a sub-matrix B; the subarray A is formed by a uniform linear array with the array element number of M and the spacing of Nd; the subarray B is formed by a uniform linear array with an array element number of N and an interval of Md; the nested array comprises two sub-arrays, namely an inner sub-array and an outer sub-array; the internal subarray consists of a uniform linear array with array elements Q and a spacing d; the external subarray is composed of a uniform linear array with array element number P and spacing Qd; if no common factor exists between the numerical values M and N or between P and Q of the two types of array element intervals, the method is suitable for the co-prime array; if the numerical values M and N or P and Q of the spacing between the two types of array elements are in a multiple relation, the method is suitable for nested arrays;

step 2: the method comprises the following steps of obtaining an optimal design scheme of a sparse array by screening array element distribution of a subarray by taking the array element number as few as possible, the maximum sidelobe level of a beam pattern as low as possible and the main lobe width of the beam pattern as narrow as possible as screening standards; respectively processing the two sub-arrays by using a conventional beam former to obtain beam patterns, and then performing conjugate multiplication on the beam pattern expressions of the two sub-arrays of the sparse array by using a multiplication processor;

and step 3: determining two subarray signal acquisition models on the basis of the optimal design scheme;

the received signal vector x for a certain sub-array of the sparse array may be represented as:

x＝Aexp(-jωt)s+n

wherein a is signal strength; j is an imaginary unit, j²-1; ω is the signal frequency; s is a matrix response vector of a plane wave signal in a certain direction in the array; n is spatially isotropic white gaussian noise;

and 4, step 4: and performing coherent processing on the outputs of the two sub-arrays, namely performing conjugate multiplication on the beam output signals of the two sub-arrays, performing statistical averaging on the multiplication results under a plurality of snapshot data to keep phase correlation, and finally performing modulus value on the results to obtain a final output beam pattern.

Further, in the step 2, coherent gain processing is performed on the nested array, and u is set_T＝-j(2π/λ)sinθ_TJ is an imaginary unit, θ_TIs the incoming wave direction of the received signal, the desired signal is in the matrix response vector s of the internal sub-matrix A of the sparse matrix_AThe matrix response vector s of the outer subarray B_BExpressed as:

s_A＝exp(u_Td_A)

s_B＝exp(u_Td_B)

wherein d is_AAn array structure vector representation of the internal sub-array A; d_BAn array structure vector representation of the outer subarray B;

let u ═ j (2 pi/λ) sin θ, θ ∈ [ -90 °,90 ° ] denote the angle of arrival of the signal incident in different directions of the array, then the array manifold vector of the two sub-arrays of the sparse array is expressed as:

w_A＝exp(ud_A)

w_B＝exp(ud_B)

the beam pattern of the array may be represented as the product of the conjugate transpose of the array manifold vector and the corresponding desired signal base response vector; the beam pattern B of the two sub-arrays A, B of the sparse array after processing by a conventional beam processor_A(θ)、B_B(θ) can be represented by the following formula, where the denominator i_A、i_BFor normalizing the beam pattern;

and performing conjugate multiplication on the beam pattern expression formulas obtained by performing conventional beam forming on the two sub-arrays to obtain a beam pattern B (theta) of the sparse array, wherein the beam pattern B (theta) is as follows:

further, the final output beam pattern in step 4 is:

the array gain of the sparse array under coherent processing is as follows:

wherein s is_NAMatrix response vector, s, representing signal in sparse matrix_NA＝exp(u_Td_NA)；d_NAThe array structure vector of the sparse array is formed by combining all array elements of two sub-arrays, wherein the first array element is shared.

The invention has the beneficial effects that:

the invention utilizes the sparse characteristic of the sparse array, and effectively reduces the number of the detection array elements relative to the uniform linear array with the same aperture. According to the method, the sparse array performance is optimized by screening the array element combination of the sparse array; the main lobe width of the sparse array beam pattern is close to that of the uniform linear array, so that better detection resolution is ensured; when the target detection is carried out, the same array gain as that of a uniform linear array under the same aperture can be realized, and the constant output signal-to-noise ratio can be met under different noise environments.

Drawings

FIG. 1 is a flow chart of the present invention.

FIG. 2 shows the co-prime array beam pattern obtained by the multiplication processor under different parameters.

Fig. 3 is a nested array beam pattern obtained by using a multiplication processor under different parameters.

Fig. 4 is a schematic diagram of a sparse array (nested array) designed for a 42-element uniform linear array with an array element spacing d.

FIG. 5 is a flow diagram of a multiplication processor processing a sub-array.

Fig. 6 is a sparse array with (P, Q) ═ 6,7 and its subarray beam pattern.

Fig. 7 is a graph of simulation results of array gain under gaussian white noise for a sparse array with array parameters (P, Q) ═ 6,7 and a corresponding 42-ary uniform linear array.

Fig. 8 is a graph of simulation results of array gain under color noise for a sparse array with array parameters (P, Q) ═ 6,7 and a corresponding 42-ary uniform linear array.

Fig. 9 is a graph of simulation results of array gain under impulse noise for a sparse array with array parameters (P, Q) ═ 6,7 and a corresponding 42-ary uniform linear array.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

The invention aims to provide a coherent gain processing method based on a sparse array. The invention belongs to the field of sonar array signal processing. The invention specifically realizes the following steps: (1) selecting a proper sparse array to carry out sparse representation on an equidistant half-wavelength linear array aiming at a given number of detection array elements and design requirements; (2) the method comprises the steps of optimally designing a sparse array by selecting subarray array elements to obtain the optimal sparse array performance under the same array element number; (3) carrying out conjugate product processing on the beam pattern expressions of the two sub-arrays of the sparse array; (4) the output of the two sub-arrays is processed coherently, the output signal-to-noise ratio of the sparse array is improved, and the sparse array can be used in various noise environments. Compared with the traditional uniform linear array, the method has the advantages that (1) the number of detection array elements is effectively reduced, and the calculated amount is less; (2) better detection resolution is ensured; (3) the constant output signal-to-noise ratio can be met, and the method is suitable for various noise environments and has high engineering practical value.

The invention aims to provide a novel coherent gain processing method of a sparse array, which enables the array gain of the sparse array to be the same as that of a uniform linear array under the condition of Gaussian white noise through the combined optimization of optimal array element selection and coherent processing, can keep the array gain under various noise environments, and improves the spatial resolution capability of an array beam pattern.

The method comprises the following concrete implementation steps:

step 1: and designing a sparse array structure, and carrying out sparse representation on the uniform linear array, wherein the sparse array structure comprises two sub-arrays. The spacing between the array elements of the uniform linear array is represented as d lambda/2, where lambda is the wavelength of the received signal. A co-prime or nested array is selected for different design requirements. Two sub-arrays of the co-prime array are respectively a sub-array A and a sub-array B, wherein the sub-array A is composed of uniform linear arrays with the array element number of M and the spacing of Nd, and the sub-array B is composed of uniform linear arrays with the array element number of N and the spacing of Md; the two sub-arrays of the nested array are respectively an inner sub-array and an outer sub-array, the inner sub-array is composed of uniform linear arrays with array elements Q and an interval of d, and the outer sub-array is composed of P array elements and uniform linear arrays with an interval of Qd.

Considering that when the uniform linear array is divided into two sub-arrays, no matter the uniform linear array is a co-prime array or a nested array, the two sub-arrays are respectively uniform linear arrays with different intervals, and if no common factor exists between the numerical values of the intervals of the two types of array elements, the method is suitable for the co-prime array; if the numerical value of the spacing between the two types of array elements is in a multiple relation, the method is suitable for the nested array.

Step 2: the co-prime array and the nested array are both composed of two sub-arrays, and the beam patterns obtained by different combination forms of the two sparse array sub-arrays also have different performances. The method is characterized in that the array element number is as few as possible, the maximum sidelobe level of a beam pattern is as low as possible, and the main lobe width of the beam pattern is as narrow as possible as a screening standard, and the optimal design scheme of the sparse array is obtained by screening the array element distribution of the subarrays. Respectively processing the two sub-arrays by using a conventional beam former to obtain beam patterns, and then performing conjugate multiplication on the beam pattern expressions of the two sub-arrays of the sparse array by using a multiplication processor;

and step 3: determining two subarray signal acquisition models on the basis of the optimal design scheme;

and 4, step 4: and performing coherent processing on the outputs of the two sub-arrays, namely averaging a plurality of snapshots of the received signals, and then taking a module value of the result to obtain a final output beam pattern.

The invention provides a coherent gain processing method based on a sparse array. The invention utilizes the sparse characteristic of the sparse array, and effectively reduces the number of the detection array elements relative to the uniform linear array with the same aperture. According to the method, the sparse array performance is optimized by screening the array element combination of the sparse array; the main lobe width of the sparse array beam pattern is close to that of the uniform linear array, so that better detection resolution is ensured; when the target detection is carried out, the same array gain as that of a uniform linear array under the same aperture can be realized, and the constant output signal-to-noise ratio can be met under different noise environments.

The invention has the following characteristics:

(1) compared with the original uniform linear array, the array element number is reduced, and the calculated amount and the hardware cost are reduced; (2) in all sparse array designs corresponding to the same uniform linear array, a subarray array element combination is selected to enable sparse array performance to be optimal; (3) the main lobe width of the sparse array beam pattern is close to that of the original uniform linear array, so that better detection resolution performance is ensured; (4) under the condition of the same input signal-to-noise ratio, the output signal-to-noise ratio of the sparse array is the same as the output signal-to-noise ratio of the original uniform linear array; (5) the method can be used in various noise environments, and the output signal-to-noise ratio is stable; (6) under the condition that the array aperture is not changed, a proper sparse array (a co-prime array or a nested array) is selected according to given design requirements, the sparse array with less array elements is obtained by carrying out sparse representation on the uniform linear array, and the corresponding calculated amount and hardware cost are reduced. (7) And selecting the optimal subarray combination by designing different subarray element arrangement modes to obtain the optimal sparse array beam pattern performance. (8) The part can be used for sparse array underwater target detection and azimuth estimation, and good detection resolution performance is guaranteed under the condition of few array elements.

Under the condition of Gaussian white noise, when the input signal-to-noise ratio is the same, the output signal-to-noise ratio of the uniform linear array formed by the invention and the conventional wave beam is the same, namely the gain of the two arrays is the same; under the environment of color noise, impulse noise and the like, the sparse array can still keep a constant output signal-to-noise ratio.

Example 1:

the invention relates to a coherent gain processing method based on a sparse array, which comprises a sparse array design algorithm and a beam forming part by utilizing the sparse array, wherein a specific algorithm flow chart is shown in figure 1.

Step 1: a uniform linear array with an array element number of 42 is illustrated, where the array element spacing d is λ/2, λ being the received signal wavelength, and is sparsely represented. Two sub-arrays of the co-prime array are respectively a sub-array A and a sub-array B, wherein the sub-array A is composed of uniform linear arrays with the array element number of M and the spacing of Nd, and the sub-array B is composed of uniform linear arrays with the array element number of N and the spacing of Md; the nested array comprises two sub-arrays, namely an inner sub-array and an outer sub-array, wherein the inner sub-array is formed by uniform linear arrays with array elements Q and spacing d; the external subarrays are composed of uniform linear arrays with array elements P and spacing Qd. The numerical values M and N or P and Q of the two types of array element intervals do not have common factors, so that the method is suitable for a co-prime array; if the values M and N or P and Q of the spacing between the two types of array elements are in a multiple relation, the method is suitable for nested arrays.

Step 2: and carrying out conjugate product processing on the two sub-array beam pattern expressions of the sparse array by using a multiplication processor, and screening by comparing the sparse array beam patterns to obtain an optimal design scheme. The sparse array beam patterns obtained by different array element parameters are different, a sparse array is designed for a uniform linear array with the array element number of 42 and the spacing of d, the array element number is as small as possible, the maximum side lobe level is as low as possible, and the main lobe width is as narrow as possible as a screening standard, and the beam patterns of a co-prime array and a nested array obtained by arranging different sub-array elements are respectively shown in fig. 2 and fig. 3. It can be seen from the comparison of the beam patterns that the overall performance of the nested array is superior to that of the co-prime array, and when the number of array elements Q of the internal sub-array of the nested array is 7, the interval of the array elements is d, the number of array elements P of the external sub-array is 6, and the interval of the array elements is 7d, the beam pattern similar to other designs can be obtained with the least number of array elements, and at this time, the number of the array elements is 12, which is 30% of the represented uniform linear array.

Taking the nested array with the above parameters (P, Q) ═ 6,7 as an example, coherent gain processing is performed on it. Let u_T＝-j(2π/λ)sinθ_TWhere j is an imaginary unit, j²＝-1，θ_TWhen the direction of the incoming wave of the received signal is the direction of the desired signal, the matrix response vector s of the two sub-arrays A (inner sub-array) and B (outer sub-array) of the sparse array_A、s_BCan be expressed by the formulas (1) and (2).

s_A＝exp(u_Td_A). (1)

s_B＝exp(u_Td_B). (2)

Wherein the internal subarray structure vector is denoted as d_A＝[0,1,2,3,4,5,6,0₃₅]d, length 42, indicates that the inner subarray is made up of seven array elements with spacing d, 0₃₅The subscript 35 of (a) indicates the length of the 0 vector, i.e., the number of 0 elements. Compared with the uniform linear array, the internal subarray has no array elements at 35 continuous positions, and is marked as 0₃₅. The array structure vector of the outer subarray is denoted as d_B＝[0,0₆,7,0₆,14,0₆,21,0₆,28,0₆,35,0₆]d, length 42, indicates that the outer subarray is formed by six array elements with spacing of 7dCompared with a uniform linear array, the external subarray has 6 positions without array elements between every two array elements and is marked as 0₆。

Let u ═ j (2 π/λ) sin θ, where j is an imaginary unit, j²＝-1，θ∈[-90°,90°]And representing the arrival angles of the signals incident to the array in different directions, the array manifold vectors of the two sub-arrays of the sparse array are shown as formulas (3) and (4).

w_A＝exp(ud_A). (3)

w_B＝exp(ud_B). (4)

The beam pattern of the array may be represented as the product of the conjugate transpose of the array manifold vector and the corresponding desired signal base response vector. The beam patterns B of the two sub-arrays A, B of the sparse array are processed by a conventional beam processor_A(θ)、B_B(θ) may be represented by equations (5), (6), where the denominator is used to normalize the beam pattern.

The processing flow of the multiplication processor is as shown in fig. 5, and the processing flow of the multiplication processor is a flow chart of the multiplication processor for processing the sub-arrays by conjugate multiplying the beam pattern expressions of the two sub-arrays of the sparse array. Ideally, the input signals of the sub-arrays do not contain noise, the input signals can be directly represented by the array response vectors of the expected signals in the array, and the beam pattern expression formula (7) of the sparse array can be obtained by performing conjugate multiplication on the beam patterns obtained by performing conventional beam forming processing on the two sub-arrays.

The beam patterns of the two subarrays under an ideal condition and the beam picture of the sparse array are in the same image, as shown in fig. 4, for the sparse array (nested array) designed by a 42-element uniform linear array with an array element spacing of d, the array element number Q of the internal subarray is 7, the array element spacing is d, the array element number P of the external subarray is 6, the array element spacing is 7d, and the zero point of the beam pattern of the internal subarray is just located at the angle of the grating lobe of the external subarray, so that the grating lobe can be well suppressed. Compared with other design schemes, the sparse array design parameters meet the screening standards of the array element number as less as possible, the maximum side lobe level as low as possible and the main lobe width as narrow as possible.

And step 3: and determining two subarray acquisition signal models on the basis of the optimal design scheme. The received signal vector x of a certain sub-array of the sparse array can be expressed as formula (8):

x＝Aexp(-jωt)s+n, (8)

where A is the signal strength, j is the unit of an imaginary number, j²Where ω is the signal frequency, s is the matrix response vector of the plane wave signal in a certain direction in the array, and n is spatially isotropic white gaussian noise.

And 4, step 4: and performing coherent processing on the outputs of the two sub-arrays, namely performing conjugate multiplication on the beam output signals of the two sub-arrays, performing statistical averaging on the product results under a plurality of snapshot data to keep phase correlation, and finally taking a module value from the result to obtain the beam output result as shown in the formula (9).

The array gain of the sparse array under coherent processing can be obtained by equation (10),

wherein s is_NAExpressing the matrix response vector of the signal in the sparse matrix, wherein the expression is shown as the formula (11), and the array structure vector d of the sparse matrix_NA＝[0,1,2,3,4,5,6,7,0₆,14,0₆,21,0₆,28,0₆,35,0₆]d, a length of 42,all array elements of the two sub-arrays are combined to form the array, and the first array element is shared.

s_NA＝exp(u_Td_NA). (11)

For any sparse array with P, Q array element parameters, in the formula (10)

Can be expressed as the formulas (12) and (13),

when the sparse array parameter is (P, Q) ═ 6,7, the array manifold vector

And

the length is 42, and can be expressed as formulas (14) and (15),

wherein

And

the vector has and only the first element is not 0, so

When the array beam steering coincides with the incoming signal direction,

and

respectively with s_AAnd s_BCorrespondingly equal, the gain of the array obtained is:

it can be seen that the sparse array with the array element number P + Q-1 ═ 12 corresponds to the same array gain as the uniform linear array with the array element number PQ ═ 42. The sparse array with the array parameters of (P, Q) ═ 6,7 and the uniform linear array with the array element number of 42 are simulated and verified by the algorithm, and the result is shown in fig. 5, and it can be seen that the gains of the two arrays are basically consistent, and the size is 10log42 ≈ 16.2 dB.

Fig. 6 shows a sparse array with (P, Q) ═ 6,7 and its subarray beam pattern, and it can be seen that the null of the inner subarray beam pattern is located at the angle where the grating lobe of the outer subarray beam pattern is located, so that the grating lobe is suppressed. Fig. 7 shows the simulation result of the array gain under gaussian white noise of the sparse array with (P, Q) ═ 6,7) array parameters and the corresponding 42-element uniform linear array, where the abscissa is the input signal-to-noise ratio and the ordinate is the output signal-to-noise ratio, and the difference between the two is the array gain of the array, and it can be seen that the sparse array is very close to the array gain of the corresponding uniform linear array after the coherent product processing, and the magnitude is 10log42 ≈ 16.2 dB. Fig. 8 shows the simulation results of the array gain under color noise for a sparse array with (P, Q) ═ 6,7 and a corresponding 42-element uniform linear array. Fig. 9 shows simulation results of array gain under impulse noise for a sparse array with array parameters (P, Q) ═ 6,7 and a corresponding 42-element uniform linear array. The two arrays under the environment of excellent noise have the same array gain performance as that under the environment of white Gaussian noise, the sparse array under the environment of impulse noise still can keep the array gain of about 16.2dB, the gain of the array of the uniform linear array is about 6dB, and the performance is greatly reduced.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A coherent gain processing method based on sparse array is characterized by comprising the following steps:

step 1: selecting a co-prime array or a nested array to carry out sparse representation on the uniform linear array;

the distance between the array elements of the uniform linear array is d ═ lambda/2, and lambda is the wavelength of the received signal; the co-prime matrix comprises two sub-matrices, namely a sub-matrix A and a sub-matrix B; the subarray A is formed by a uniform linear array with the array element number of M and the spacing of Nd; the subarray B is formed by a uniform linear array with an array element number of N and an interval of Md; the nested array comprises two sub-arrays, namely an inner sub-array and an outer sub-array; the internal subarray consists of a uniform linear array with array elements Q and a spacing d; the external subarray is composed of a uniform linear array with array element number P and spacing Qd; if no common factor exists between the numerical values M and N or between P and Q of the two types of array element intervals, the method is suitable for the co-prime array; if the numerical values M and N or P and Q of the spacing between the two types of array elements are in a multiple relation, the method is suitable for nested arrays;

step 2: the method comprises the following steps of obtaining an optimal design scheme of a sparse array by screening array element distribution of a subarray by taking the array element number as few as possible, the maximum sidelobe level of a beam pattern as low as possible and the main lobe width of the beam pattern as narrow as possible as screening standards; respectively processing the two sub-arrays by using a conventional beam former to obtain beam patterns, and then performing conjugate multiplication on the beam pattern expressions of the two sub-arrays of the sparse array by using a multiplication processor;

and step 3: determining two subarray signal acquisition models on the basis of the optimal design scheme;

the received signal vector x for a certain sub-array of the sparse array may be represented as:

x＝A exp(-jωt)s+n

wherein a is signal strength; j is an imaginary unit, j²-1; ω is the signal frequency; s is a matrix response vector of a plane wave signal in a certain direction in the array; n is spatially isotropic white gaussian noise;

and 4, step 4: and performing coherent processing on the outputs of the two sub-arrays, namely performing conjugate multiplication on the beam output signals of the two sub-arrays, performing statistical averaging on the multiplication results under a plurality of snapshot data to keep phase correlation, and finally performing modulus value on the results to obtain a final output beam pattern.

2. The sparse array based coherent gain processing method of claim 1, wherein: in the step 2, coherent gain processing is carried out on the nested array, and u is set_T＝-j(2π/λ)sinθ_TJ is an imaginary unit, θ_TIs the incoming wave direction of the received signal, the desired signal is in the matrix response vector s of the internal sub-matrix A of the sparse matrix_AThe matrix response vector s of the outer subarray B_BExpressed as:

s_A＝exp(u_Td_A)

s_B＝exp(u_Td_B)

wherein d is_AAn array structure vector representation of the internal sub-array A; d_BAn array structure vector representation of the outer subarray B;

let u ═ j (2 pi/λ) sin θ, θ ∈ [ -90 °,90 ° ] denote the angle of arrival of the signal incident in different directions of the array, then the array manifold vector of the two sub-arrays of the sparse array is expressed as:

w_A＝exp(ud_A)

w_B＝exp(ud_B)

the beam pattern of the array may be represented as the product of the conjugate transpose of the array manifold vector and the corresponding desired signal base response vector; the beam pattern B of the two sub-arrays A, B of the sparse array after processing by a conventional beam processor_A(θ)、B_B(θ) can be represented by the following formula, where the denominator i_A、i_BFor wave-alignmentNormalizing the beam pattern;

and performing conjugate multiplication on the beam pattern expression formulas obtained by performing conventional beam forming on the two sub-arrays to obtain a beam pattern B (theta) of the sparse array, wherein the beam pattern B (theta) is as follows:

3. the sparse array-based coherent gain processing method of claim 2, wherein: the final output beam pattern in step 4 is:

the array gain of the sparse array under coherent processing is as follows:

wherein s is_NAMatrix response vector, s, representing signal in sparse matrix_NA＝exp(u_Td_NA)；d_NAThe array structure vector of the sparse array is formed by combining all array elements of two sub-arrays, wherein the first array element is shared.

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