Arc-shaped array non-nulling modal beamforming method and system
By eliminating characteristic beam nulls through Fourier series expansion and transformation relationships of a uniform arc array, the performance degradation problem of modal domain beamformers is solved, achieving robustness and bandwidth extension, and is applicable to fields such as underwater acoustics and marine monitoring.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF ACOUSTICS CHINESE ACAD OF SCI
- Filing Date
- 2025-01-14
- Publication Date
- 2026-07-14
AI Technical Summary
In existing modal domain beamforming methods, the characteristic beams of uniform circular arrays suffer performance degradation due to the zeros of the Bessel function, resulting in weakened beamformer robustness, distorted azimuth estimation, and increased array structure complexity and cost.
By employing a uniform arc array, the sound pressure is expressed in polar coordinates and expanded using Fourier series. By changing the integration interval, the transformation relationship between the arc array and the arc harmonic domain is constructed, eliminating nulls in the characteristic beams and achieving null-free mode beamforming.
It eliminates characteristic beam nulls, improves the robustness of mode beamformers, expands the operating bandwidth, and reduces array complexity and cost, making it suitable for underwater acoustic detection, marine environmental monitoring, and underwater acoustic communication.
Smart Images
Figure CN122392479A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of acoustic array signal processing, specifically relating to a method and system for forming arc array zero-dip mode beamforming. Background Technology
[0002] Array beamforming plays a crucial role in target localization, direction of arrival (DOA) estimation, and noise suppression. In circular arrays, beamforming techniques can be categorized into element-domain methods and modal-domain methods. Modal-domain methods, based on the theory of sound wave propagation and scattering, decompose the sound field into spatial harmonics and combine the resulting characteristic beams to form frequency-independent modes. Benefiting from the decoupling of characteristic beam combinations from frequency, modal-domain methods maintain high directivity even at low frequencies.
[0003] However, when designing broadband modal domain beamformers using a uniform circular array (UCA), the forms of the characteristic beams obtained by decomposing the received sound pressure from the UCA are the same as those of the Bessel function. The zeros of the Bessel function cause nulls in the characteristic beams at certain frequencies, leading to a degraded beamformer performance, specifically decreased robustness, weakened directivity, and distorted azimuth estimation. Mounting the UCA on a rigid sphere can mitigate the effects of characteristic beam nulls. Wang Yong et al. studied a circular array mounted near the surface of a finite-length rigid cylinder, successfully eliminating the influence of characteristic beam nulls and proposing a robust, high-gain beamforming method directly applicable to the modal domain. The basic principle is that the sound pressure scattered by the baffle disrupts the rotational symmetry of the received sound pressure; therefore, a UCA with a baffle can avoid the Bessel null problem to some extent. However, this method has certain requirements on the length of the cylindrical baffle, which makes the system structure more complex and limits its application in small platforms. Because at larger elevation angles, a cylinder of finite dimensions naturally differs from a theoretically infinitely long cylinder, leading to discrepancies between simulations and measurements. Yan systematically studied UCA in the Circular Harmonic Domain (CHD), theoretically proving that the Minimum Variance Distortionless Response (MVDR) in CHD is equivalent to the Phase-mode (PM) beamformer in a planar isotropic noise field. He also used a second-order cone programming method to constrain white noise gain to combat performance degradation caused by characteristic beam nulls. However, this method requires strict constraint selection; with numerous constraints, computational complexity increases significantly, and a solution may not be found. Chan et al. combined two single-ring arrays without common Bessel zeros using concentric circular arrays, solving the null problem at low frequencies. Han Xinyu et al. optimized the arrangement distance between multiple circular arrays, but the concentric circular array method is not suitable for high frequencies with densely packed Bessel zeros. Furthermore, it requires a larger number of array elements, increasing the array's cost and complexity. Zhao et al. used an acoustic information neural network to predict a set of virtual concentric ring arrays based on the sound pressure received by the actual array elements, thereby eliminating Bessel nulls. This method cannot process received data in real time, and its effective operating bandwidth remains relatively narrow, failing to suppress the effects of mode aliasing.
[0004] Existing modal beamforming methods are all based on ring arrays. However, the acoustic field characteristic beam function derived from the ring array has the same form as the Bessel function. This leads to a large number of nulls on the characteristic beams of existing methods. At the frequency points where nulls appear, the performance of existing broadband modal beamforming methods degrades. Specifically, the robustness of the beamformer decreases, the directivity weakens, and the azimuth estimation becomes distorted, which is not conducive to the engineering implementation of modal beamformers.
[0005] Existing solutions require a greater number of array elements or structural baffles, which makes the array structure more complex, hinders the installation of the array on various platforms, and increases the cost of the array. Summary of the Invention
[0006] The purpose of this application is to eliminate the performance degradation of mode beamformers at nulls by utilizing algorithmic improvements. This requires technically addressing the problem of nulls appearing in the characteristic beams. Based on this, the present invention proposes using an arc array to decompose and obtain the characteristic beams, thereby eliminating nulls on the characteristic beams and solving the null interference of existing mode beamformers in a low-cost manner.
[0007] To achieve the above objectives, this application proposes a method for arc-shaped array zero-dip mode beamforming, comprising:
[0008] A uniform circular arc array is used to receive sound wave signals;
[0009] The sound pressure received by the uniform arc array is expressed in polar coordinates. The sound pressure received by the uniform arc array is expanded into a Fourier series. The integral interval when extracting the feature beam is changed by using the uniform circular arc array to obtain the sound field feature beam without null.
[0010] Based on the coordinate information of each array element, a uniform circular arc array transformation matrix containing basis vectors of different orders is constructed. The transformation relationship between the received sound field of the arc array in the uniform circular arc array element domain and the arc harmonic domain is obtained. The estimated value of the uniform circular arc beam response is obtained using this transformation relationship.
[0011] As an improvement to the above method, obtaining the acoustic field characteristic beam without nulls includes:
[0012] Step 1: Express the acoustic pressure received by the arc array in polar coordinates.
[0013]
[0014] in, The imaginary unit is represented by k; k = ω / c represents the wave number, c represents the speed of sound, and ω represents the angular frequency. represents the opening angle of the arc array; r represents the radius of the annulus containing the arc array, and the center of this annulus is the origin of the rectangular coordinate system in the xy plane; the incident direction of the plane wave is... θ represents the azimuth angle. s θ represents the pitch angle. s =π / 2; φ represents the range of azimuth angles;
[0015] Step 2: Expression for sound pressure level of the arc-shaped aperture Performing a Fourier series expansion, we obtain:
[0016]
[0017] in, For the arc characteristic beam, the expression is:
[0018]
[0019] in, And there are:
[0020]
[0021] As an improvement to the above method, obtaining the estimated value of the uniform circular arc beam response includes:
[0022] The transformation relationship between the acoustic field received by the arc array in the arc harmonic domain and the array element domain is as follows:
[0023]
[0024] in, For the arc harmonic domain sound pressure response; denoted as , where M is the number of array elements; n is the order of the coefficients; (·) H Indicates conjugate transpose; (·) T Indicates vector transpose;
[0025] The transformation relationship between the sound field received by the arc array in the uniform arc array element domain and the arc harmonic domain is expressed as follows:
[0026]
[0027] Where N represents the maximum modal truncation order; T represents the Fourier transform matrix of the circular arc array; For estimating the ideal steering vector in the arc harmonic domain;
[0028] The final estimated uniform arc array beam response is:
[0029]
[0030] in, This represents an estimate of the response of a uniform arc array beam; w h =[W -N(kr),···,W -n (kr),···,W0(kr),···,W n (kr),···,W N (kr)] T W is the modal domain guiding vector. n (kr) represents the Fourier coefficients of the element-domain weighted function of the circular aperture array.
[0031] This application also provides an arc-shaped array zero-depression mode beamforming system, implemented based on the above method, the system comprising:
[0032] The sound field feature beam acquisition module is used to express the sound pressure received by the uniform arc array in polar coordinates. The sound pressure received by the uniform arc array is expanded into a Fourier series. The integral interval when extracting the feature beam is changed by using the uniform arc array to obtain the sound field feature beam without nulls.
[0033] The module for estimating the uniform circular arc beam response is used to construct a uniform circular arc array transformation matrix containing basis vectors of different orders based on the coordinate information of each array element. This allows for the acquisition of the transformation relationship between the received sound field of the arc array in the uniform circular arc array element domain and the arc harmonic domain. The estimated value of the uniform circular arc beam response is then obtained using this transformation relationship.
[0034] Compared with existing technologies, the advantages of this application are:
[0035] 1. After the uniform arc array breaks the rotational symmetry between the received sound pressures, the zeros on the characteristic beam are completely eliminated, resulting in an arc array mode domain beamformer with strong robustness.
[0036] 2. It overcomes the limitation on applicable bandwidth caused by the maximum stage order of the circular array mode beamformer. Compared with the traditional uniform circular array mode beamforming method, the working bandwidth of the uniform arc array mode beamformer is extended.
[0037] 3. This method has high innovation and engineering applicability, and can be widely used in underwater acoustic detection, marine environmental monitoring and underwater acoustic communication. Attached Figure Description
[0038] Figure 1 The diagram shown is a schematic of a continuous arc-shaped aperture.
[0039] Figure 2(a) shows a schematic diagram of the modal amplitude response of a circular array.
[0040] Figure 2(b) shows a schematic diagram of the modal amplitude response of the arc array.
[0041] Figure 2(c) shows a schematic diagram of the modal amplitude response of the arc array.
[0042] Figure 2(d) shows a schematic diagram of the modal amplitude response of the arc array.
[0043] Figure 3(a) shows the opening angle. UAA beam diagram;
[0044] Figure 3(b) shows the opening angle. UAA beam diagram;
[0045] Figure 3(c) shows the opening angle. UAA beam diagram;
[0046] Figure 3(d) shows the opening angle. UAA beam diagram;
[0047] Figure 4(a) shows the WNG and DI curves (white noise gain) of UAA array phase mode beamformers with different opening angles;
[0048] Figure 4(b) shows the WNG and DI curves (directivity index) of beamformers with different opening angles in the UAA array phase mode;
[0049] Figure 5 The diagram shows the flowchart of the method for forming a zero-dip mode beamformation for an arc array. Detailed Implementation
[0050] The technical solution of this application will be described in detail below with reference to the accompanying drawings.
[0051] This invention utilizes a uniform arc array (UAA) to establish an arc harmonic domain (AHD) and provides mathematical support for the arc characteristic beams to form a complete set of bases in the acoustic field. By relying on the arc array structure, the rotational symmetry of the received sound pressure is broken, eliminating the performance degradation caused by nulls in the characteristic beams. After breaking the rotational symmetry between received sound pressures, the uniform arc array completely eliminates nulls on the characteristic beams, thereby extending the operating bandwidth of the arc array mode beamformer and overcoming the bandwidth limitation imposed by the maximum truncation order of the ring array mode beamformer. Compared with traditional UCA, the operating bandwidth of the uniform arc array PM beamformer is significantly extended. This method possesses high innovation and engineering practicality and can be widely applied in underwater acoustic detection, marine environmental monitoring, and underwater acoustic communication.
[0052] like Figure 1 As shown, with the opening angle as Taking an arc as an example, suppose the radius of the ring containing the arc is r, and the center of the ring is the origin of the rectangular coordinate system in the xy plane. A plane wave with an amplitude of 1 is incident on this arc-shaped aperture, and its incident direction is... θ represents the azimuth angle. s Denotes the pitch angle, where θ s =π / 2, and the frequency is f. Therefore, the sound pressure observed at point (r, φ) on the arc-shaped aperture can be expressed in polar coordinates as:
[0053]
[0054] Wherein, the wave number k = 2πf / c = ω / c, where c represents the speed of sound and ω represents the angular frequency. It is the imaginary unit; φ represents the range of azimuth angles. For the sake of simplicity, e is omitted in equation (1). -iωt .
[0055] The sound pressure expression for an arc aperture Performing a Fourier series expansion, we obtain:
[0056]
[0057] Among them, the subscript (·) arc,n Indicates the opening angle of the arc as The coefficient order is n. In studies of circular arrays, this series coefficient is often referred to as the characteristic beam (Eigenbeam). In this study, an arc-shaped aperture is used to decompose the sound field, therefore P... arc,n This is called an Arc Eigenbeam (AEB), which has the following forms:
[0058]
[0059] in, And there are:
[0060]
[0061] In equation (4), for J arc,n The definition of (kr) is similar to that of the first kind of Bessel function, except that its integration interval is over the arc-shaped aperture.
[0062] Figures 2(a)-2(d) Given At that time, the normalized characteristic beam amplitude response of the circular array and the arc array from order 0 to 7 is 20lg|P n (kr)|and 20lg|P arc,n The curve showing the variation of (kr)|. It can be seen that the circular characteristic beam P in Figure 2(a)... nNulls appear when kr takes certain values, and the nulls in the characteristic beam become more densely packed as kr increases. This means that in the high-frequency range, circular array modal domain beamformers are more susceptible to performance losses caused by characteristic beam nulls, resulting in beamformer distortion. In contrast, the arc characteristic beam curves in Figures 2(b), 2(c), and 2(d) do not exhibit nulls as kr changes. This indicates that in modal domain beamforming methods, using an arc array to disrupt the rotational symmetry of the received acoustic pressure signal effectively avoids null interference in the extracted arc characteristic beam. Furthermore, in the high-frequency region where kr is large, the arc characteristic beam also exhibits null-free characteristics. Therefore, this characteristic of the arc array can be used to create a modal beamformer that is not limited by nulls, while overcoming the limitation of high-frequency failure in traditional circular array modal beamformers.
[0063] definition The beam response of the arc-shaped aperture array characterizes the beam response of the arc-shaped aperture to an incident angle of 0°. The response capability of incoming waves. Define weighting coefficients. Then in the array element domain It can be represented as:
[0064]
[0065] in,(·) * Indicates complex conjugation.
[0066] Substituting equation (2) into equation (6), and utilizing the orthogonality of Fourier series:
[0067]
[0068] We can obtain:
[0069]
[0070] in Weighting function for circular aperture Fourier coefficients.
[0071] In practical engineering, it is necessary to select a reasonable number of array elements for sampling continuous aperture arrays. Assume that M array elements are used with an opening angle of... Sampling is performed on an arc-shaped array, and the coordinates of the m-th element on the arc aperture can be represented as... in:
[0072]
[0073] After sampling, equations (2) and (3) can be written as:
[0074]
[0075] in, This is an estimate of the modal response under ideal conditions, where N is the truncation order. When the number of sampling elements M ≥ 2N, the sampling error can be ignored. In this case, the beam response of the UAA in the element domain can be written as:
[0076]
[0077] in,(·) H This indicates the conjugate transpose, (·) e Represents the array element field. and Let be the steering vector and weighting vector of the uniform arc array, respectively. Substituting equation (11) into equation (13) yields the expression for the modal domain beam response of the uniform arc array:
[0078]
[0079] Among them, the subscript (·) h Represents the harmonic domain. Composed of arc-shaped characteristic beams, w h =[W -N (kr),···,W -n (kr),···,W0(kr),···,W n (kr),···,W N (kr)] T It is the modal domain steering vector; N represents the maximum modal cutoff order; W n (kr) represents the Fourier coefficients of the element-domain weighted function of the circular aperture array.
[0080] 3.1.3 Transformation relationship between the element domain and the arc harmonic domain
[0081] Define vector Equation (12) can be rewritten as:
[0082]
[0083] Further define the Fourier transform matrix of the circular arc array:
[0084]
[0085] Therefore, the transformation relationship between the received sound field of the arc array in the UAA element domain and the arc harmonic domain can be expressed as follows:
[0086]
[0087] in, This is an estimate of the ideal steering vector in the arc harmonic domain. Substituting equation (17) into equation (14), the UAA beam response value can be estimated as:
[0088]
[0089] like Figure 5 As shown, the arc array zero-dip mode beamforming method proposed in this application includes:
[0090] By utilizing a non-circular array to change the integration interval when extracting feature beams, a sound field feature beam without nulls can be obtained. This includes: expressing the received sound pressure of the arc array in polar coordinates, performing a Fourier series expansion on the received sound pressure of the arc array, and then using a non-circular array to change the integration interval when extracting feature beams to obtain a sound field feature beam without nulls. Specifically, this includes:
[0091] Step 1: Express the acoustic pressure received by the arc array in polar coordinates:
[0092]
[0093] Among them, the opening angle of the arc array is Assume the radius of the annulus it is in is r, and the center of the annulus is the origin of the rectangular coordinate system in the xy plane, such as Figure 1 As shown. A plane wave with an amplitude of 1 is incident on this arc-shaped aperture, and its incident direction is... Where θ s =π / 2, with a frequency of f.
[0094] Step 2: Expression for sound pressure level of the arc-shaped aperture Performing a Fourier series expansion, we obtain:
[0095]
[0096] Among them, P arc,n This is called an Arc Eigenbeam (AEB), which has the following forms:
[0097]
[0098] in, And there are:
[0099]
[0100] The transformation process of the received sound field of the arc array between the element domain and the arc harmonic domain is based on a defined complex vector, which is composed of the coordinate information of each element in the array. Then, by constructing a circular arc array transformation matrix containing basis vectors of different orders, the transformation of the received sound field of the arc array between the uniform circular arc array element domain and the arc harmonic domain is achieved. Finally, the estimated value of the uniform circular arc beam response is obtained using this transformation matrix, specifically including:
[0101] Define vector The transformation relationship between the arc harmonic domain and the array element domain is as follows:
[0102]
[0103] in, For the arc harmonic domain sound pressure response, p e This represents the sound pressure response in the element domain. Further, the Fourier transform matrix of the circular arc array is defined as follows:
[0104]
[0105] Therefore, the transformation relationship between the uniform arc array element domain and the arc harmonic domain can be expressed as follows:
[0106]
[0107] in, This is an estimate of the ideal steering vector in the arc harmonic domain. The final uniform arc array beam response can be estimated as:
[0108]
[0109] This application also proposes an arc-shaped array zero-depression mode beamforming system, implemented based on the above method, the system comprising:
[0110] The sound field feature beam acquisition module is used to express the sound pressure received by the uniform arc array in polar coordinates. The sound pressure received by the uniform arc array is expanded into a Fourier series. The integral interval when extracting the feature beam is changed by using the uniform arc array to obtain the sound field feature beam without nulls.
[0111] The module for estimating the uniform circular arc beam response is used to construct a uniform circular arc array transformation matrix containing basis vectors of different orders based on the coordinate information of each array element. This allows for the acquisition of the transformation relationship between the received sound field of the arc array in the uniform circular arc array element domain and the arc harmonic domain. The estimated value of the uniform circular arc beam response is then obtained using this transformation relationship.
[0112] Figures 3(a)-3(d) The above four opening angles are shown. The beamformer's performance within the simulated frequency band is shown in Figure 3(a). It can be seen that the beamformer of the UCA array exhibits significant distortion in the mid-to-high frequency band in Figure 3(a), because the UCA method is inevitably affected by the nulls of the characteristic beams, resulting in performance loss. From Figures 3(b), 3(c), and 3(d), it can be observed that as the UCA opening angle decreases, the distortion of the beamformer decreases. Especially when the opening angle... At that time, the PM beamformer of UAA showed no distortion, thanks to the disruption of the rotational symmetry of the array's received sound pressure by UAA. In the low-frequency region, the main lobe of Figure 3(d) is wider than that of Figures 3(a), 3(b), and 3(c). This is because the array opening angle of Figure 3(d) is the smallest, which limits the array aperture and thus widens the main lobe. In the high-frequency region, the beam patterns shown in Figures 3(c) and 3(d) gradually show submaxima in the 180° (-180°) direction. This is because higher-order characteristic beams account for a larger proportion in the high-frequency region, and the order used in the simulation is limited. However, it is easy to see that the effective operating bandwidth of the PM beamformer obtained by applying UAA is significantly greater than that of the UCAPM beamformer. This indicates that the UAA array effectively overcomes the limitation of high-frequency failure of the PM beamformer, although its operating bandwidth is still limited by the modal order.
[0113] Four types of opening angles were calculated. The WNG and DI curves of the UAA array are shown in Figures 4(a) and 4(b). When When using UCA (Unified Bezier Amplifier), nulls appear near the same frequency point for both WNG and DI, especially at higher frequencies where the nulls are more concentrated. Because traditional UCA array PM beamformers cannot avoid the losses caused by Bezier nulls, they can only operate within the kr range where no nulls appear, thus severely limiting their operating bandwidth.
[0114] At the same time, the application of UAA (i.e. When using π and π / 2) arrays, no nulls appear on the WNG and DI curves, which proves that the method proposed in this application can effectively solve the problem of characteristic beam null interference in traditional UCAPM beamformers.
[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application, and should all be covered within the scope of the claims of this application.
Claims
1. A method for forming a null-free mode beamformer with an arc array, comprising: A uniform circular arc array is used to receive sound wave signals; The sound pressure received by the uniform arc array is expressed in polar coordinates. The sound pressure received by the uniform arc array is expanded into a Fourier series. The integral interval when extracting the feature beam is changed by using the uniform circular arc array to obtain the sound field feature beam without null. Based on the coordinate information of each array element, a uniform circular arc array transformation matrix containing basis vectors of different orders is constructed. The transformation relationship between the received sound field of the arc array in the uniform circular arc array element domain and the arc harmonic domain is obtained. The estimated value of the uniform circular arc beam response is obtained using this transformation relationship.
2. The method for forming arc-shaped array zero-dip mode beamforming according to claim 1, characterized in that, The process of obtaining a sound field characteristic beam without nulls includes: Step 1: Express the acoustic pressure received by the arc array in polar coordinates. in, The imaginary unit is represented by k; k = ω / c represents the wave number, c represents the speed of sound, and ω represents the angular frequency. represents the opening angle of the arc array; r represents the radius of the annulus containing the arc array, and the center of this annulus is the origin of the rectangular coordinate system in the xy plane; the incident direction of the plane wave is... θ represents the azimuth angle. s θ represents the pitch angle. s =π / 2; φ represents the range of azimuth angles; Step 2: Expression for sound pressure level of the arc-shaped aperture Performing a Fourier series expansion, we obtain: in, For the arc characteristic beam, the expression is: in, And there are:
3. The method for forming arc-shaped array zero-dip mode beamforming according to claim 2, characterized in that, The estimated value of the uniform circular arc beam response is obtained, including: The transformation relationship of the acoustic field received by the arc array between the arc harmonic domain and the array element domain is as follows: in, The acoustic pressure response in the arc harmonic domain; denoted as , where M is the number of array elements; n is the order of the coefficients; (·) H Indicates conjugate transpose; (·) T Indicates vector transpose; The transformation relationship between the sound field received by the arc array in the uniform arc array element domain and the arc harmonic domain is expressed as follows: Where N represents the maximum modal truncation order; T represents the Fourier transform matrix of the circular arc array; For estimating the ideal steering vector in the arc harmonic domain; The final estimated uniform arc array beam response is: in, This represents an estimate of the response of a uniform arc array beam; w h =[W -N (kr),···,W -n (kr),···,W0(kr),···,W n (kr),···,W N (kr)] T W is the modal domain guiding vector. n (kr) represents the Fourier coefficients of the element-domain weighted function of the circular aperture array.
4. An arc-shaped array zero-dip mode beamforming system, implemented based on the method described in any one of claims 1-3, characterized in that, The system includes: A sound field feature beam acquisition module is used to express the sound pressure received by a uniform arc array in polar coordinates. The sound pressure received by the uniform arc array is expanded into a Fourier series. By changing the integration interval when extracting the feature beam using the uniform circular arc array, a sound field feature beam without nulls is obtained. The module for estimating the uniform circular arc beam response is used to construct a uniform circular arc array transformation matrix containing basis vectors of different orders based on the coordinate information of each array element. This allows for the acquisition of the transformation relationship between the received sound field of the arc array in the uniform circular arc array element domain and the arc harmonic domain. The estimated value of the uniform circular arc beam response is then obtained using this transformation relationship.