General codebook design method and system for near-field super-large scale arc array

Abstract

This invention belongs to the field of large-scale MIMO technology and discloses a general codebook design method and system for near-field ultra-large-scale arc arrays. The method includes: Step 1, establishing an arc antenna array model, including an arc ULA antenna model or an arc UPA antenna model; Step 2, performing Taylor expansion on the distance between the transmitting antenna and the receiving end to obtain an approximate distance formula, which is then substituted into the response vector to obtain the array response vector generated by the entire antenna array; Step 3, decomposing the phase part of the correlation function of any two antenna response vectors into two parts: one containing only angle and the other containing both angle and distance. Based on the objective of minimizing the correlation function, including angle domain design and distance domain design, the optimal sampling angle and sampling distance are found; Step 4, constructing codewords based on the optimal sampling angle and sampling distance to obtain the optimal three-dimensional codebook. This invention significantly reduces the overhead and latency of real-time beam training.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, specifically to a general codebook design method and system for near-field ultra-large-scale arc arrays, applicable to the application of arc antenna array structures in near-field communication. Background Technology

[0002] With the rapid development of 6G mobile communication technology, very large-scale antenna arrays (VMAs) have become a key enabling technology for improving system capacity and spectrum efficiency. By deploying large-scale antenna arrays at base stations, systems can significantly improve spectrum utilization using spatial division multiplexing technology to meet the ever-increasing demand for mobile data. However, the continuous expansion of antenna array size and the continuous increase in communication frequency have fundamentally changed the communication scenario.

[0003] According to antenna theory, the boundary between the far field and the near field is usually determined by the Rayleigh distance, which is expressed as: Where D is the array aperture, λ The wavelength is denoted by λ. In traditional communication systems, due to the relatively small array size and low operating frequency, the Rayleigh distance is typically within a few meters, and communication scenarios are mainly in the far field. At this time, electromagnetic waves can be approximated as plane waves, and beamforming only needs to consider angle information, i.e., achieving "beam steering." However, in 6G systems, the widespread application of millimeter-wave and terahertz bands, along with the significant increase in antenna array aperture, has led to a dramatic expansion of the Rayleigh distance. For example, a massive array operating in the 28 GHz band with a size of 2m × 3m can achieve a Rayleigh distance of up to 200 meters, far exceeding the radius of a traditional cell. This means that a large number of future communication scenarios will occur in the near field. In the near field, electromagnetic waves must be accurately modeled using a spherical wave model, and wavefront characteristics depend on both angle and distance information. This change renders traditional far-field beamforming techniques unsuitable, requiring a shift from "beam steering" to "beam focusing." Beam focusing technology can precisely concentrate electromagnetic energy to a specific point in space, providing a new dimension for achieving high-precision spatial multiplexing. However, effective beam focusing relies on accurate channel state information, which becomes particularly difficult in near-field scenarios. Near-field channel estimation requires simultaneous acquisition of angle and range information, and traditional channel estimation methods based on angle-domain sparsity are no longer applicable. Therefore, beam training schemes based on predefined codebooks have become a practical and efficient solution.

[0004] On the other hand, conformal antenna arrays, as an emerging array topology, have attracted widespread attention in order to achieve wider coverage and higher spatial degrees of freedom. Among them, curved antenna arrays have significant application value due to their unique geometric characteristics. Compared with traditional planar arrays, curved arrays have the following significant advantages: First, they can achieve 360° omnidirectional coverage in the horizontal plane, meeting the deployment requirements of 6G communication for large-scale non-cellular MIMO systems; second, they conform to the carrier surface, reducing the impact on the carrier's aerodynamic performance; third, they are easy to install and deploy, and can be attached to various object surfaces such as streetlights, pillars, and tree trunks.

[0005] However, near-field beam focusing and codebook design for arc arrays face unique challenges. First, the geometric non-uniformity of arc arrays makes the mathematical expression of the array response vector more complex than that of uniform linear or planar arrays. Second, the beam focusing characteristics (including main lobe width, side lobe structure, and effective focusing depth) are strongly dependent on the array's radius of curvature and bending angle. Finally, traditional codebook design methods based on uniform sampling cannot fully utilize the geometric characteristics of arc arrays, resulting in low codebook efficiency.

[0006] Currently, research on near-field codebook design mainly focuses on uniform linear arrays and uniform planar arrays. For example, existing technologies have proposed improved codebooks based on discrete Fourier transform and codebook design methods based on polynomial phase approximation. However, most of these methods assume that the array has a regular geometric structure and cannot be directly applied to curved arrays. Research on curved arrays mainly focuses on their structural design and far-field characteristic analysis, while research on near-field beam focusing and codebook design is still in its early stages. More specifically, existing three-dimensional codebook design methods face the following technical problems: First, they fail to fully consider the propagation characteristics of near-field spherical waves, resulting in a severe performance degradation in the near-field region; second, they do not fully utilize the rotational symmetry of curved arrays, resulting in an inefficient codebook structure; third, the sampling strategies in the angle and range domains are not jointly optimized, leading to oversampling or insufficient coverage. Therefore, there is an urgent need for a near-field three-dimensional codebook design method specifically for curved antenna arrays. This method should be able to: fully utilize the geometric characteristics of the curved array; adapt to the near-field spherical wave propagation model; achieve adaptive joint sampling in the angle and range domains; and minimize the codebook size while ensuring performance.

[0007] To address the aforementioned technical problems, this invention proposes a general three-dimensional codebook design method for arc-shaped ultra-large-scale antenna arrays. By introducing a polar coordinate angle grid and an adaptive distance sampling strategy based on effective Rayleigh distance, efficient three-dimensional spatial coverage is achieved, providing a feasible solution for the practical deployment of near-field arc-shaped large-scale MIMO systems.

[0008] The relevant reference CN120128224A discloses a general 3D codebook design method for ultra-large-scale MIMO, including S1, establishing a dual-layer antenna array model, including a dual-layer ULA antenna model or a dual-layer UPA antenna model; S2, performing a Taylor expansion on the distance between the transmitting antenna and the receiving end to obtain an approximate distance formula, which is then substituted into the response vector to obtain the array response vector generated by the entire antenna array as the codebook; S3, decomposing the phase part of the correlation function of any two antenna response vectors into two parts containing only angle and two parts containing both angle and distance, and finding the optimal sampling angle and sampling distance based on the objective of minimizing the correlation function; S4, constructing codewords based on the optimal sampling angle and sampling distance to obtain the optimal codebook. This method considers the interlayer spacing between different antenna array layers, fully utilizing the degrees of freedom provided by the additional space in the vertical dimension, thus significantly improving the performance of the codebook design, but it cannot reduce the codebook size. Summary of the Invention

[0009] The purpose of this invention is to address the shortcomings of existing technologies by proposing a near-field three-dimensional codebook design method for arc-shaped ultra-large-scale antenna arrays. This method solves the problems of existing codebook design methods failing to fully utilize the geometric characteristics of arc-shaped arrays, neglecting near-field spherical wave propagation effects, and failing to jointly optimize angular and range domain sampling.

[0010] This invention provides the following technical solution:

[0011] A general three-dimensional codebook design method for curved ultra-large-scale antenna arrays, the method comprising:

[0012] Step 1: Establish an arc-shaped antenna array model, including an arc-shaped ULA antenna model or an arc-shaped UPA antenna model;

[0013] Step 2: Perform Taylor expansion on the distance between the transmitting antenna and the receiving end to obtain an approximate formula for the distance. Substitute this formula into the response vector to obtain the array response vector generated by the entire antenna array.

[0014] Step 3: Decompose the phase part of the correlation function of any two antenna response vectors into two parts: one containing only angle and the other containing both angle and distance. Based on the goal of minimizing the correlation function, use a polar coordinate angle grid and an adaptive distance sampling strategy based on effective Rayleigh distance to find the optimal sampling angle and sampling distance.

[0015] The objectives based on minimizing the correlation function include:

[0016] Angle domain design: Polar coordinate grid is used, and polar coordinates are defined ( ρ、 Φ):

[0017] ;

[0018] Where θ represents the elevation angle of the user's position, and Φ represents the azimuth angle of the user's position. Therefore, the angle sampling interval is determined by the beamwidth.

[0019] ;

[0020] in, , Based on The first zero sampling point.

[0021] Distance domain design: based on effective Rayleigh distance for each angle Calculate the effective Rayleigh distance:

[0022] ;

[0023] use r and The region is divided into near-field and far-field areas, and sampling is performed in these areas.

[0024] Step 4: Construct codewords based on the optimal sampling angle and sampling distance to obtain the optimal three-dimensional codebook.

[0025] Furthermore, the arc-shaped antenna array model specifically includes:

[0026] Arc-shaped ULA antenna: Composed of N antenna elements, with a radius of R and a bending angle of θ. β The arcs are evenly arranged; the coordinates of the nth antenna element are:

[0027] ;

[0028] in, ;

[0029] Arc-shaped UPA antenna: Composed of M*N antenna elements, with M arc-shaped ULAs arranged along the X-axis, each arc-shaped ULA containing N antenna elements; the coordinates of the (m, n)th antenna element are:

[0030] ;

[0031] in, , The antenna spacing is in the X direction.

[0032] Furthermore, the Taylor expansion of the distance between the transmitting antenna and the receiving end specifically includes:

[0033] The distance of the arc-shaped ULA can be approximated as follows:

[0034] ;

[0035] in, This represents the precise distance between the user and the nth element;

[0036] The distance of the arc-shaped UPA can be approximated as follows:

[0037] ;

[0038] Where m represents the m-th arc-shaped ULA in the arc-shaped UPA array composed of M arc-shaped arrays. This represents the precise distance between the user and the nth element of the m-th arc array.

[0039] Furthermore, the correlation function of any two antenna response vectors specifically includes:

[0040] The relevant functions for curved ULA and curved UPA are denoted as:

[0041] ;

[0042] in, and This indicates the distance, elevation angle, and azimuth angle between the user and different antenna elements; It is the near-field beam focusing vector, used to compensate for the phase change of the spherical wave at the array aperture. H represents the conjugate transpose function.

[0043] Furthermore, the phase decomposition in the third step specifically includes:

[0044] For an arc-shaped ULA, the phase difference is decomposed into a phase containing only angular information as follows:

[0045] ;

[0046] λ Indicates wavelength;

[0047] The phase that contains both angle and distance information is:

[0048] ;

[0049] Where F is a function related to array geometry.

[0050] Furthermore, the specific operation steps of the angle sampling scheme include:

[0051] (1) Establish a polar coordinate angle grid and determine the maximum coverage angle. Calculate the radial spacing of the foundation Generate radial stratification .in, It is the maximum radial angle covered. .

[0052] (2) Generate circumferential sampling for each layer and calculate the circumferential resolution of that layer. :

[0053] ;

[0054] Therefore, the number of circumferential samples is determined as follows:

[0055] ;

[0056] (3) Convert to spherical coordinates, for each Calculate the corresponding spherical coordinates:

[0057] ;

[0058] Furthermore, the specific operational steps of the distance sampling scheme include:

[0059] (1) Calculate the effective Rayleigh distance for each angle. The effective Rayleigh distance in the horizontal direction is calculated as follows:

[0060] ;

[0061] The effective Rayleigh distance in the arc direction is:

[0062] ;

[0063] in, For gain descent tolerance,

[0064] .

[0065] (2) Definition ,exist Uniform sampling in the domain: Map back to the distance domain The number of sampling points is:

[0066] ;

[0067] Near-field and far-field sampling points are merged to remove duplicates. There may be overlaps at the boundaries. The points are sorted in ascending order of distance.

[0068] A system for implementing a general codebook design method for near-field ultra-large-scale arcuate arrays, comprising:

[0069] Antenna parameter acquisition unit: used to acquire the type, geometric parameters, and operating frequency of the antenna array;

[0070] Polar coordinate angle mesh generation unit: used to generate adaptive polar coordinate angle mesh, including: beamwidth calculation module, radial layering module, circumferential sampling module, and coordinate transformation module.

[0071] Effective Rayleigh distance calculation unit: used to calculate the effective Rayleigh distance for each angle, including: direction projection factor calculation module, near-field boundary determination module, and distance division module.

[0072] Adaptive distance sampling unit: used to generate distance sampling points, including: near-field $\tau$ domain sampling module, far-field logarithmic sampling module, and sampling point optimization module.

[0073] Codeword construction and optimization unit: used to construct codewords and optimize codebooks, including: array response vector calculation module, phase quantization module, redundancy removal module, and hierarchical codebook generation module.

[0074] Performance verification unit: used to verify codebook performance, including: coverage testing module, correlation analysis module, and training cost evaluation module.

[0075] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0076] 1. Fully utilize the geometric characteristics of the arc array: By introducing a polar coordinate angle grid, the rotational symmetry of the arc array is fully utilized, reducing the codebook size by 15-30% compared to the traditional rectangular grid, while maintaining higher coverage performance.

[0077] 2. Adaptive Near-Field-Far-Field Processing: An adaptive distance sampling strategy based on effective Rayleigh distance is employed in the near-field region. Uniform sampling in the field achieves natural density, while logarithmic uniform sampling in the far field achieves efficient coverage, reducing the number of sampling points by 20-40% compared to uniform distance sampling.

[0078] 3. Physically guided optimization design: The determination of the sampling interval is based on the closed expression of beamwidth and focusing depth, which has clear physical meaning and avoids the blindness of empirical parameter selection.

[0079] 4. High-performance beam focusing: The designed codebook can achieve precise beam focusing, with beamforming gain in the near field region improved by 3-5dB compared to traditional far-field codebooks, and inter-user interference reduced by 30-50%.

[0080] 5. High versatility: The method framework is applicable to both curved ULA and curved UPA array structures, and can be adapted to different coverage requirements and performance indicators through parameter adjustment.

[0081] 6. Scalability: The method framework is easily extended to other conformal array structures (such as spherical arrays, conical arrays) and more complex propagation environments (such as multipath, occlusion, etc.).

[0082] This invention provides a complete, efficient, and practical three-dimensional codebook design solution for near-field arc-shaped large-scale array systems, which significantly improves system performance, reduces implementation complexity, and has important theoretical value and engineering application prospects. Attached Figure Description

[0083] To more clearly illustrate the technical solutions of the embodiments of the present invention, color drawings are used:

[0084] Figure 1 This is a flowchart of the design of this invention;

[0085] Figure 2 This is a diagram of the arc-shaped ULA system of the present invention;

[0086] Figure 3 This is a schematic diagram of the sampling grid of the present invention;

[0087] Figure 4 This is a diagram of the arc-shaped UPA system of the present invention;

[0088] Figure 5 This is a simulation diagram of the arc-shaped ULA angular domain wave velocity gain of the present invention;

[0089] Figure 6 This is a simulation diagram of the arc-shaped ULA range domain wave velocity gain of the present invention;

[0090] Figure 7 This is a comparison chart of the effective Rayleigh distance between the arc-shaped array of this invention and a conventional ULA array;

[0091] Figure 8 This is a sampling density distribution diagram of the arc-shaped ULA angle domain of the present invention;

[0092] Figure 9 This is a simulation diagram of the wave velocity gain in the angular domain of the arc-shaped UPA of this invention;

[0093] Figure 10 This is a comparison chart of the normalized mean square error of the codebook of this invention with other codebooks;

[0094] Figure 11 This is a simulation diagram of the spectral efficiency of the arc-shaped ULA of the present invention;

[0095] Figure 12 This is a simulation diagram of the spectral efficiency of the arc-shaped UPA of the present invention. Detailed Implementation

[0096] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0097] This invention describes an example of a general codebook design method for near-field ultra-large-scale arc-shaped arrays. The disclosed codebook design method comprises two parts: angle-domain polar coordinate grid design and distance-domain adaptive sampling design. The disclosed codebook design method applies two models: the arc-shaped ULA model and the arc-shaped UPA model. Based on the objective of minimizing correlation, the design method obtains the optimal sampling scheme for angle and distance through polar coordinate transformation and a sampling strategy guided by effective Rayleigh distance, effectively limiting interference between users and improving the performance of the near-field communication system.

[0098] In this embodiment of the invention, the arc antenna array design includes: the array being an arc ULA composed of antenna array elements uniformly arranged along a circular arc or an arc UPA composed of multiple arc ULAs arranged in a horizontal direction.

[0099] In any of the above aspects / embodiments, the antenna elements are uniformly arranged on an arc.

[0100] In any of the above aspects / embodiments, the geometric parameters of the arc array include the radius of curvature R and the bending angle β.

[0101] In any of the above aspects / embodiments, electromagnetic coupling effects are not considered between the antenna array elements.

[0102] The codebook design method includes solving for the correlation between different array response vectors, wherein the array response vector is determined by the distance from each antenna element in the array to the user. The distance is approximated using a second-order Taylor expansion, taking into account both angle and distance information.

[0103] In the communication model of this invention embodiment, the user is located in the near-field region, and the antenna array response vector is derived from the spherical wave model. Since all antenna array responses have the same form, differing only in unknown angle and distance parameters, the codebook design method utilizes a unified correlation function form for minimization to obtain the pre-coded angle and distance intervals. Specifically, in the arc-shaped ULA model, a polar coordinate angle grid is first established, and the angle sampling interval is determined based on the beamwidth; then, the near-field and far-field regions are divided based on the effective Rayleigh distance, employing different distance sampling strategies. In the arc-shaped UPA model, the horizontal dimension is extended, and the conclusions are generalized according to the processing method in the arc-shaped ULA, considering the effective aperture in both the horizontal and arc dimensions.

[0104] In any of the above aspects / embodiments, the arc-shaped antenna array may have arbitrary radius of curvature and bending angle;

[0105] In any of the above aspects / embodiments, the arc-shaped antenna array can cover any angular range;

[0106] In any of the above aspects / embodiments, the codebook design algorithm can be applied to the arc-shaped ULA model;

[0107] In any of the above aspects / embodiments, the codebook design algorithm can be applied to the arc-shaped UPA model;

[0108] In any of the above aspects / embodiments, the codebook design algorithm can be applied to near-field communication scenarios;

[0109] In any of the above aspects / embodiments, the codebook design algorithm can be applied to far-field communication scenarios.

[0110] In this embodiment of the invention, the base station includes an arc-shaped antenna array for transmitting and receiving in wireless communication. The base station utilizes the codebook design scheme for precoding, optimizes signal spatial distribution, achieves near-field beam focusing, effectively reduces inter-user interference, and improves communication quality.

[0111] Specifically, the specific implementation steps of this invention in the arc-shaped ULA model are as follows:

[0112] First, modeling the arc-shaped ULA antenna array: (e.g.) Figure 1 As shown, this invention studies the codebook design scheme of an arc-shaped antenna model. The arc-shaped ULA consists of N antenna elements, uniformly arranged along an arc with radius R and bending angle β. The coordinates of the nth antenna element are: The central angle corresponding to the nth element is... , , .

[0113] Secondly, near-field distance approximation and array response derivation: the user is located in spherical coordinates. At this point, the distance from the nth antenna element to the user, after a second-order Taylor expansion, is approximately:

[0114] .

[0115] in, This represents the precise distance between the user and the nth element.

[0116] The correlation function for any two antenna response vectors specifically includes:

[0117] Related functions for curved ULA and curved UPA:

[0118]

[0119] in, and It indicates the distance, elevation angle, and azimuth angle between the user and different antenna elements. It is the near-field beam focusing vector, used to compensate for the phase change of the spherical wave at the array aperture. H represents the conjugate transpose function.

[0120] Beamforming gain analysis: two positions and The beamforming gain (correlation function) between them is: The array response vector generated by the entire antenna array is:

[0121] .

[0122] For an arc-shaped ULA, the phase difference is decomposed into a phase containing only angular information as follows:

[0123] .

[0124] λ This represents the wavelength. Therefore, the phase, which contains both angle and distance information, is:

[0125] .

[0126] Where F is a function related to array geometry.

[0127] Third, polar coordinate angle grid design: introducing polar coordinates :

[0128] .

[0129] In polar coordinates, the angle-domain beam gain can be approximated as:

[0130] .

[0131] in, Indicates through the Relative to 1 / r Perform a first-order Taylor expansion to obtain the far-field steering vector in polar coordinates. , , and .based on The zero point of the function, the angle sampling interval is:

[0132] .

[0133] in, It is a predetermined threshold. Based on The first zero sampling point, Therefore, the angle mesh generation algorithm is as follows:

[0134] (1) Calculate the average resolution: take ;

[0135] (2) Establish a polar coordinate angle grid and determine the maximum coverage angle. Calculate the basic radial spacing Δρ, and calculate the radial layering: , ;in, It is the maximum radial angle covered. .

[0136] Generate circumferential sampling for each layer and calculate the circumferential resolution of that layer.

[0137] .

[0138] (3) Calculate circumferential sampling: For each layer ,definition ,exist Uniform sampling in the domain:

[0139] .

[0140] Map back to the distance domain The number of sampling points is:

[0141] .

[0142] Near-field and far-field sampling points are merged to remove duplicates. There may be overlaps at the boundaries. The points are sorted in ascending order of distance.

[0143] (4) Convert to spherical coordinates: for each Calculate the corresponding spherical coordinates:

[0144] .

[0145] Fourth, the arc-shaped ULA is based on the distance sampling design of the effective Rayleigh distance: for each angle pair Calculate the effective Rayleigh distance:

[0146] ;

[0147] in, For gain descent tolerance, .

[0148] Distance sampling strategies are divided into:

[0149] (1) In the near field region ( ):definition ,exist Uniform sampling in the domain:

[0150] , ,in, .

[0151] (2) In the far field region ( Logarithmic uniform sampling is used.

[0152] ;

[0153] in, , It is a sparsity factor.

[0154] Fifth, three-dimensional codebook construction: for each sampling point First, convert to spherical coordinates: Then calculate the array response vector. Finally, normalization. .

[0155] The specific implementation steps of this invention in the arc-shaped UPA model are as follows:

[0156] First, modeling the arc-shaped UPA antenna array: (e.g.) Figure 2 As shown. The arc-shaped UPA consists of M*N antenna elements, with M arc-shaped ULAs arranged along the X-axis. Each arc-shaped ULA contains N antenna elements. The coordinates of the (m,n)th antenna element are: .in, , The antenna spacing is in the X direction. Defined as an arc-shaped ULA.

[0157] Secondly, the near-field distance approximation and array response derivation: The distance from the (m,n)th antenna element to the user is approximately:

[0158]

[0159] Where m represents the m-th arc-shaped ULA in the arc-shaped UPA array composed of M arc-shaped arrays. This represents the precise distance between the user and the nth element of the m-th arc array.

[0160] Third, the array response vector is .

[0161] Fourth, beam gain analysis and polar coordinate grid design: The beam gain of the arc-shaped UPA can be decomposed into the product of the X direction and the arc direction.

[0162] In angular domain sampling, the beam gain in polar coordinates is approximately:

[0163] .

[0164] in, It is the gain contribution from the dimension (yz plane) of the arc-shaped ULA array. This is the gain contribution of the planar array dimension (x-axis), expressed by the classical ULA formula. Therefore, the angular sampling interval considers the resolution in two dimensions: the resolution in the yz direction. and x-direction resolution The smaller of the two is used as the actual sampling interval.

[0165] Fifth, for curved UPAs, the distance sampling design based on the effective Rayleigh distance needs to consider two dimensions:

[0166] .

[0167] The effective Rayleigh distance in the horizontal direction is:

[0168] .

[0169] The effective Rayleigh distance in the arc direction is:

[0170] .

[0171] in, For gain descent tolerance,

[0172] .

[0173] The distance sampling strategy is similar to that of the arc-shaped ULA, but it needs to be based on... The value is adjusted. If At that time, the x-direction dominates, and the near-field region is relatively narrow; if At that time, the arc direction dominates, and the near-field area is relatively wide.

[0174] Sixth, the three-dimensional codebook construction is similar to that of the arc-shaped ULA, but the two-dimensional structure of the UPA needs to be considered: First, generate the angular mesh. Subsequently, for each angle pair, distance samples are generated. Finally, calculate each The array response vector.

[0175] Seventh, hierarchical codebook structure: To support efficient beam training, a hierarchical codebook is constructed.

[0176] (1) First-level codebook (coarse search): sparse angular grid, fixed distance;

[0177] (2) Second-level codebook (fine search): dense angle grid, complete distance sampling.

[0178] This invention proposes a codebook design suitable for near-field arc-shaped arrays. By analyzing the type and geometric parameters of the arc-shaped antenna array, the near-field spherical wave range approximation model for arc-shaped ULAs and arc-shaped UPAs is solved, laying the foundation for codebook design. Innovatively, a polar coordinate system is used to describe beam pointing, fully utilizing the rotational symmetry of the arc-shaped array to achieve efficient angle-domain sampling. Furthermore, the concept of direction-dependent effective Rayleigh distance is proposed, based on which an adaptive range sampling strategy for near-field and far-field operations is implemented. Finally, a codebook design framework for joint optimization in the angle and range domains is established, minimizing the codebook size while ensuring performance.

[0179] The codebook designed in this invention achieves high discrimination in both angle and distance dimensions. To demonstrate these two advantages, we conducted targeted simulation experiments. Given the crucial role of the radius of curvature and bending angle in the arc array, we specifically analyzed the specific impact of these parameters on codebook design and performance. Furthermore, we also conducted corresponding simulation experiments to verify the universality of the near-field codebook design. The functionality and effects of this invention are further illustrated through the following simulation experiments:

[0180] Simulation conditions: The antenna array operates at a frequency of 30 GHz (millimeter-wave band). The arc-shaped ULA consists of N=512 antenna elements, with a radius of curvature R=0.5 m and a bending angle β=60°. Coverage angle range: , When testing the codebook's performance in the angular domain, we fixed the user distance at r = 10m. Since this invention considers a near-field codebook design, to ensure the codebook's effectiveness, the user distance must be within the effective communication area defined by Rayleigh distance.

[0181] Figure 2 shows the distribution diagram of the arc-shaped ULA system of the present invention.

[0182] Figure 3 illustrates a schematic diagram of the sampling grid implementation in near-field communication.

[0183] Figure 4 shows the distribution diagram of the arc-shaped UPA system of the present invention.

[0184] Figures 5 and 6 clearly reveal the spatial distribution characteristics of beamforming gain in the near-field region of the arc-shaped uniform linear array.

[0185] Figure 5 shows different array curvature angles. β The impact on the beam pattern. Simulation results show that the curvature angle β It is a key parameter that determines the antenna's directivity and beamwidth. With β As the value increases (the array curvature becomes more pronounced), the main lobe width of the beam narrows accordingly, resulting in enhanced directivity. This phenomenon is consistent with the derived beamwidth formula. They match, among which Followβ The increase in size and decrease in width lead to a narrowing of the theoretical beamwidth. Furthermore, in the near-field spherical wave model, the beam pattern exhibits a complex spatial distribution, its shape significantly different from that in the far-field environment. The function describes a simple lobe structure. These unique spatial focusing features and beam deformations reveal the ability of flexible arrays in the millimeter-wave band to achieve high-precision beam control and fan-shaped coverage in the near-field region, providing important physical support for the design of reconfigurable smart surfaces and conformal antennas for 6G.

[0186] Figure 6 focuses on the characteristics of beamforming gain variation in the range dimension. To verify the accuracy of the derived closed-form expression for near-field beamforming gain, we fixed the focusing angle... Under the given conditions, the theoretical beamforming gain calculated based on Lemma 1 (blue curve) was compared with the precise numerical result obtained by directly calculating the inner product of the array response vectors (red curve). The simulation was performed with the focusing distance set. r=40m The results show that the two curves are highly consistent across the entire observation range, especially in the main lobe region and near the first null. The theoretical curve accurately captures the oscillating attenuation trend of the gain, fully validating the accuracy of the proposed approximation model. Furthermore, the 3 dB beamwidth boundary (i.e., the distance range where the gain drops to half its peak value), clearly marked in the figure, is basically consistent with the predicted value. This demonstrates the effectiveness of the Bessel function-based model. and effective Rayleigh distance The theoretical framework can effectively characterize the focusing performance of near-field beams and lays a solid theoretical foundation for subsequent range domain codebook sampling based on this model.

[0187] Figure 7 shows a comparison of the effective Rayleigh distance (ERD) distribution of different antenna structures in spherical space. It can be observed that the direction-dependent arcuate ULA exhibits the widest near-field range, with its ERD value varying with beam direction. Significant changes occur. This phenomenon indicates that in arc-shaped array systems, the array's geometric curvature and the beam's pointing direction jointly determine the boundary of the near-field region. In contrast, the ERD distribution of traditional uniform linear arrays (ULA) and uniform planar arrays (UPA) exhibits more symmetrical and uniform characteristics. This result not only provides a solid theoretical basis for adaptively dividing the near-field and far-field regions in complex geometric array systems, but more importantly, it reveals the significant changes in ERD distribution in different directions in three-dimensional space. The inherent directional asymmetry exists in the arc array. This asymmetry stems from the non-uniform aperture projection of the arc array, a characteristic not present in traditional rectangular arrays. Based on this key discovery, this invention proposes an adaptive angle codebook design method based on polar coordinate grids. The core idea of ​​this method is to systematically transform the spatial resolution requirements driven by ERD into adaptive sampling density in the angular domain. Specifically, in regions with smaller ERD values ​​(typically corresponding to narrower beams and higher angular resolution requirements), the codebook design employs denser angular sampling to obtain finer angular resolution, ensuring accurate beam pointing and effective suppression of inter-user interference. In regions with larger ERD values ​​(typically corresponding to wider beams and lower angular resolution requirements), the codebook achieves sufficient spatial coverage through sparser angular sampling, thereby avoiding unnecessary codeword redundancy and significantly reducing codebook size and beam training overhead.

[0188] Figure 8 This study demonstrates the non-uniform distribution of sampling density in the angular domain of an arc-shaped array, validating the theoretical basis of the polar coordinate sampling strategy. The color gradient from blue to red clearly reflects the design principle of "sparse at the center and dense at the edges": the sampling interval is largest at the lowest sampling density (dark blue region). This is because the beamwidth is wider in the array normal direction, requiring only sparse sampling for effective coverage. As the sampling density gradually increases (transitioning to the red region), the sampling interval decreases accordingly. At the array edges, the beam narrows significantly, requiring a higher density of sampling points to ensure the accuracy of beam training. Therefore, in scenarios with limited codebook storage, sampling points in key areas can be prioritized based on this density distribution; in time-sensitive beam training applications, a progressive search strategy from sparse to dense can be adopted to further improve training efficiency.

[0189] Figure 9 The beamforming gain of the arc-shaped UPA array was analyzed, and the results show that the arc-shaped UPA array achieves superior angular coverage performance and sidelobe suppression compared to the comparative scheme. This advantage mainly stems from the increased spatial degrees of freedom. From a system performance perspective, these improvements directly translate into more stable link quality, higher spectral efficiency, and stronger multi-user interference suppression, making it particularly suitable for future communication scenarios requiring dense deployment and high reliability, such as industrial IoT and millimeter-wave indoor coverage.

[0190] Figure 10 Showing different bending angles βThe curves showing the normalized mean square error (NMSE) versus signal-to-noise ratio (SNR) are presented. Simulation results show that as the SNR increases from -10dB to 20dB, the NMSE of all compared algorithms exhibits a monotonically decreasing trend. The proposed scheme with a β=30° bending angle demonstrates the best performance, maintaining the lowest estimation error across the entire SNR range. Notably, compared to the performance of the β=90° configuration within the approximately 10dB SNR range, the proposed scheme reduces NMSE by about 23%. The results verify a non-monotonic correlation between the bending angle $\beta$ and channel estimation accuracy: there exists an optimal β range for the bending UPA that minimizes NMSE, and a smaller bending angle does not necessarily lead to better system performance. Under the same β=60° configuration, the estimation errors of the traditional discrete Fourier transform (DFT) far-field scheme and the uniform three-dimensional codebook scheme are both higher than the proposed algorithm, failing to achieve equivalent performance.

[0191] Figure 11 and Figure 12 The spectral efficiency curves of the arc-shaped ULA array and arc-shaped UPA array under different SNRs are presented. The results show that the proposed hierarchical polar domain codebook simultaneously integrates angular domain far-field DFT sampling and near-field spherical wave phase modeling in the spherical domain distance dimension, which can accurately characterize the spatial phase evolution characteristics of the near-field channel and the geometric features of the flexible array. This scheme significantly outperforms all benchmark codebook schemes in terms of spectral efficiency.

[0192] Therefore, we can conclude that by accurately calculating and rationally utilizing the key parameter in near-field codebook design—the effective Rayleigh distance—this invention can adaptively distinguish between near-field and far-field regions and employ different sampling strategies. When the user distance is greater than or equal to the effective Rayleigh distance, the codebook designed in this invention can provide performance similar to that of a far-field beam; while when the user is in the near-field region, the codebook can achieve precise beam focusing, thereby effectively providing services to users across the entire range.

[0193] The above analysis results demonstrate that this invention possesses the following significant advantages: First, by employing a polar coordinate angle grid design, it fully leverages the rotational symmetry of the arc array to achieve high-precision angular resolution. Second, the adaptive range sampling strategy based on the effective Rayleigh distance enables dense sampling in the near-field region to ensure focusing accuracy, while sparse sampling in the far-field region improves efficiency. Finally, by jointly optimizing the sampling schemes in the angular and range domains, this invention not only provides beams with high angular and range resolution but also significantly improves beam performance by utilizing the geometric characteristics of the arc array. Furthermore, this invention can be applied to both near-field and far-field environments, exhibiting good versatility and practicality.

[0194] This invention proposes a three-dimensional codebook design theory and method for ultra-large-scale arc array systems applicable to near-field communication scenarios. The disclosed three-dimensional codebook design method is adapted to arc antenna array structures, achieving adaptive joint optimization in the angle and range domains through precise mathematical modeling and beamforming gain analysis. These innovative designs result in generated beams with the following characteristics: First, precise beam focusing is achieved in the near-field region, fully utilizing the range dimension of freedom; second, low inter-beam correlation significantly reduces inter-user interference; third, the codebook size is compact, reducing storage overhead and training time; and fourth, it supports efficient hierarchical beam training algorithms. Furthermore, by utilizing the unique geometric characteristics of arc arrays, this invention further optimizes beam coverage and directivity, improving the overall performance of the communication system, and enabling simultaneous service to users across the entire range through adaptive parameter adjustments.

[0195] Figure 1 shows a flowchart of the three-dimensional codebook design for near-field arc-shaped large-scale antenna arrays according to the present invention. The specific implementation process of the functions and roles of each unit in the system can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0196] On the other hand, the present invention also provides a codebook design system, a system for implementing a general codebook design method for near-field ultra-large-scale arc arrays, comprising:

[0197] Antenna parameter acquisition unit: used to acquire the type, geometric parameters, and operating frequency of the antenna array;

[0198] Polar coordinate angle mesh generation unit: used to generate adaptive polar coordinate angle mesh, including: beamwidth calculation module, radial layering module, circumferential sampling module, and coordinate transformation module.

[0199] Effective Rayleigh distance calculation unit: used to calculate the effective Rayleigh distance for each angle, including: direction projection factor calculation module, near-field boundary determination module, and distance division module.

[0200] Adaptive distance sampling unit: used to generate distance sampling points, including: near field Domain sampling module, far-field logarithmic sampling module, and sampling point optimization module.

[0201] Codeword construction and optimization unit: used to construct codewords and optimize codebooks, including: array response vector calculation module, phase quantization module, redundancy removal module, and hierarchical codebook generation module.

[0202] Performance verification unit: used to verify codebook performance, including: coverage testing module, correlation analysis module, and training cost evaluation module.

[0203] This invention proposes a near-field spherical wave range approximation model applicable to curved ULAs and curved UPAs, laying a mathematical foundation for codebook design. It innovatively employs polar coordinates to describe beam pointing, fully utilizing the rotational symmetry of the curved array to achieve efficient angle-domain sampling. The concept of direction-dependent effective Rayleigh distance is proposed, based on which an adaptive range sampling strategy for near and far fields is implemented. A codebook design framework for joint optimization in the angle and range domains is established, minimizing codebook size while ensuring performance. Through the three-dimensional codebook design method provided by this invention, ultra-large-scale curved array systems can achieve precise beam focusing in the near field and maintain efficient beam coverage in the far field, providing an efficient and practical solution for future wireless communication systems.

[0204] This invention may be embodied in other specific forms without departing from the subject matter of the claims. The exemplary embodiments described are merely illustrative in all respects and not restrictive. Selected features from one or more of the foregoing embodiments may be combined to create alternative embodiments not explicitly described, and features suitable for such combinations are to be understood to fall within the scope of the invention. For example, although the computational order of the disclosed 3D codebook design method is shown, other representations and solution orders may be used.

[0205] Furthermore, while the systems, algorithms, and processes disclosed and illustrated herein may include a specific number of elements / components and solution methods, these systems, devices, and components can be modified to include more or fewer such elements / components and the same solution methods for key steps. For example, although any disclosed 3D codebook design algorithm may be the result of calculations under specific conditions, the embodiments disclosed herein may be modified to include more or fewer such conditions and calculation results with different steps. This invention is intended to cover all reasonable technical variations and modifications.

[0206] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this application. This application is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A general codebook design method for near-field ultra-large-scale arc arrays, characterized in that, Includes the following steps: Step 1: Establish an arc-shaped antenna array model, including an arc-shaped ULA antenna model or an arc-shaped UPA antenna model; Step 2: Perform Taylor expansion on the distance between the transmitting antenna and the receiving end to obtain an approximate formula for the distance. Substitute this formula into the response vector to obtain the array response vector generated by the entire antenna array. Step 3: Decompose the phase part of the correlation function of any two antenna response vectors into two parts: one containing only angle and the other containing both angle and distance. Based on the goal of minimizing the correlation function, use a polar coordinate angle grid and an adaptive distance sampling strategy based on effective Rayleigh distance to find the optimal sampling angle and sampling distance. The objectives based on minimizing the correlation function include: (1) Angle domain design: For the arc-shaped ULA, a polar coordinate grid is used, and polar coordinates are defined. : ； Where θ represents the elevation angle of the user's position, The azimuth angle is the user's location; therefore, the angle sampling interval is determined by the beamwidth. ； in, , Based on The first zero sampling point; λ represents the wavelength, β is the bending angle, and R is the radius of curvature. The predetermined threshold; For an arc-shaped UPA, the definition is... ,exist Uniform sampling over a domain, the horizontal sampling interval is calculated as follows: ; Where r is the radial distance between the origin and the user. The horizontal preset threshold is used; the sampling interval in the arc direction is calculated as follows: ; where M is the number of arc ULA, d x is the X-direction antenna spacing; therefore, the final sampling interval is obtained by combining the horizontal direction and the arc direction as follows: ; (2) Distance domain design: for each direction on the angle grid The effective Rayleigh distance is calculated using the following formula: Arc-shaped ULA: ,in, , For gain descent tolerance; Curved UPA: ; in, The effective Rayleigh distance in the horizontal direction. ; Step 4: Construct codewords based on the optimal sampling angle and sampling distance to obtain the optimal three-dimensional codebook.

2. The general codebook design method for near-field ultra-large-scale arc-shaped arrays according to claim 1, characterized in that, The arc-shaped antenna array model specifically includes: Arc-shaped ULA antenna: Composed of N antenna elements, uniformly arranged along an arc of radius R and bending angle β; the coordinates of the nth antenna element are: ； The central angle corresponding to the nth element is defined as... , ; Arc-shaped UPA antenna: Composed of M*N antenna elements, with M arc-shaped ULAs arranged along the X-axis, each arc-shaped ULA containing N antenna elements; the coordinates of the (m, n)th antenna element are: ； in, d x This represents the antenna spacing in the X direction.

3. The general codebook design method for near-field ultra-large-scale arc-shaped arrays according to claim 2, characterized in that, The Taylor expansion of the distance between the transmitting antenna and the receiving end specifically includes: The distance of the arc-shaped ULA can be approximated as follows: ； Where, r n This represents the precise distance between the user and the nth element; similarly, the distance in the arc-shaped UPA is approximated as: ； Where m represents the m-th arc-shaped ULA in the arc-shaped UPA array composed of M arc-shaped arrays. This represents the precise distance between the user and the nth element of the m-th arc array.

4. The general codebook design method for near-field ultra-large-scale arc arrays according to claim 3, characterized in that, The correlation function of any two antenna response vectors specifically includes: Related functions for curved ULA and curved UPA: ； in, and This indicates the distance, elevation angle, and azimuth angle between the user and different antenna elements; is the near-field beam focusing vector, used to compensate for the phase change of the spherical wave at the array aperture; H represents the conjugate transpose function.

5. The general codebook design method for near-field ultra-large-scale arc-shaped arrays according to claim 4, characterized in that, The phase decomposition in step 3 specifically involves: For an arc-shaped ULA, the phase difference is decomposed into a phase containing only angular information as follows: ； Therefore, the phase, which contains both angle and distance information, is: ； Where F is a function related to array geometry; For an arc-shaped UPA, the phase difference can be decomposed into an angle-dependent component and an angle-distance hybrid component.

6. The general codebook design method for near-field ultra-large-scale arc arrays according to claim 1, characterized in that, The specific operation steps of the angle sampling scheme include: for an arc-shaped ULA, Step 6.1: Establish a polar coordinate angle grid and determine the maximum coverage angle. Calculate the radial spacing of the foundation Generate radial stratification ;in, It is the maximum radial angle covered. ; Step 6.2: Generate circumferential sampling for each layer and calculate the circumferential resolution of that layer. , ； Therefore, the number of circumferential samples is determined as follows: ； Step 6.3: Convert to spherical coordinates for each Calculate the corresponding spherical coordinates: 。 7. The general codebook design method for near-field ultra-large-scale arc arrays according to claim 1, characterized in that, The specific operation steps of the angle sampling scheme include: for an arc-shaped UPA, The number of circumferential samples is determined as follows: ; Merge near-field and far-field sampling points, remove duplicates, and sort by distance from smallest to largest.

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