A method for near-field beamforming and codebook design of a columnar antenna array

Abstract

The application discloses a kind of near-field beamforming and codebook design method of columnar antenna array, comprising: modeling near-field columnar antenna array, by the geometric position relationship of user and antenna array, expression of beam focusing vector is obtained by simplifying;Respectively in elevation angle domain, azimuth angle domain and distance domain, the closed-form solution of corresponding beamforming gain is obtained by calculating beamforming gain;By controlling the correlation of beam focusing vector focused on different positions, respectively, the sampling method of elevation angle domain, azimuth angle domain and distance domain is obtained;Sampling is carried out to elevation angle domain, and azimuth angle sampling value and distance sampling value are obtained on the plane corresponding to elevation angle sampling value, finally obtain the three-dimensional codebook for near-field columnar antenna array beamforming.The application can effectively represent the beamforming gain of near-field columnar antenna array, meet the constraint of the correlation between code words, and focus signals to the expected position.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a near-field beamforming and codebook design method for a cylindrical antenna array, applicable to near-field communication scenarios where base stations are equipped with ultra-large-scale cylindrical antenna arrays. Background Technology

[0002] Very Large Array (ELAA) antennas can provide additional spatial resolution, thus greatly improving spectral efficiency, and are therefore considered one of the most important technologies in 6G communication. Another significant characteristic of 6G communication is that it may use frequencies far higher than previous communication systems. While 6G communication will bring many new possibilities, such as augmented reality (AR) and virtual reality (VR), it also brings many new challenges. For example, the advent of ELAA technology not only means an increase in the number of antennas, but also a corresponding increase in antenna aperture. Therefore, the Rayleigh distance in 6G communication may reach tens or even hundreds of meters, meaning that near-field communication will be very common in next-generation communication systems.

[0003] The biggest difference between near-field communication and traditional far-field communication lies in their electromagnetic wave models. In traditional far-field communication, electromagnetic waves are often approximated as plane waves. However, in the near field, the spherical wave characteristics of electromagnetic waves cannot be ignored. The biggest difference between the spherical wave model and the traditional plane wave model is that for plane waves, we can only control their angle, while spherical waves are related not only to the angle but also to the distance. We can control them in both angle and distance dimensions. Given that near-field communication based on spherical waves provides additional distance resolution, traditional far-field beam steering has evolved into near-field beam focusing. That is, unlike far-field beamforming, which can only control the beam direction, near-field communication based on spherical wavefronts allows us to control both the beam direction and distance simultaneously, concentrating the signal energy at a specific location. This significantly improves energy efficiency and reduces energy loss. In near-field beamforming research, predefined codebook-based schemes are frequently used because, with the help of predefined codebooks, beamforming can be achieved without channel estimation. Considering that it is difficult to obtain accurate channel state information when users are constantly moving, codebook-based beamforming can greatly improve the beamforming effect.

[0004] A literature search of existing technologies revealed that Z. Ding et al. published a paper entitled "NOMA-Based Coexistence of Near-Field and Far-Field Massive MIMO Communications" in *IEEE Wireless Communications Letters*, vol. 12, no. 8, pp. 1429-1433, August 2023. This paper studies the performance of non-orthogonal multiple access (NOMA) systems in the case of near-field and far-field coexistence. By solving a resource allocation optimization problem aimed at maximizing system rate, it proves that a near-field and far-field hybrid NOMA system can effectively achieve high user numbers and rates while ensuring the quality of service for incoming users. Further research revealed that Emil... In their paper titled "A Primer on Near-Field Beamforming for Arrays and Reconfigurable Intelligent Surfaces" published at the 55th Asilomar Conference on Signals, Systems, and Computers, 2021, pp. 105-112, this paper investigates how near-field beamforming should be performed when a single antenna and intelligent reflector are used at the transmitting end. It further infers the near-field range within which beam focusing can be achieved. However, the paper does not propose any effective beamforming schemes, and in practical communication systems, antenna arrays often employ more complex structures than single-antenna structures. In practical communication systems, cylindrical antennas are widely used because they can be fixed to the surfaces of many objects. However, as a commonly used antenna array form in practical communication systems, cylindrical antenna arrays have not been addressed in previous near-field related work. Summary of the Invention

[0005] Technical problem to be solved: This invention focuses on near-field ultra-large-scale cylindrical antenna array systems and proposes a near-field beamforming and codebook design method for cylindrical antenna arrays. It can effectively characterize the beamforming gain of near-field cylindrical antenna arrays, and the codebook proposed in this invention can well satisfy the constraints of correlation between codewords and can effectively focus the signal to the expected position.

[0006] Technical solution:

[0007] A near-field beamforming and codebook design method for a cylindrical antenna array, the near-field beamforming and codebook design method comprising the following steps:

[0008] Step A: Model the near-field cylindrical antenna array, use three-dimensional polar coordinates to represent the positional relationship between the array elements and the user, and simplify the expression of the beam focusing vector by using the geometric positional relationship between the user and the antenna array.

[0009] Step B: Based on the relationship of the beam focusing vector, calculate the beamforming gain in the elevation, azimuth, and range domains respectively, and simplify using the trigonometric relationship and Taylor expansion to obtain the closed-form solutions of the beamforming gain in the elevation, azimuth, and range domains.

[0010] Step C: By controlling the correlation of the beam focusing vectors focused at different positions, sampling methods for the elevation, azimuth, and range domains are obtained respectively.

[0011] Step D: When acquiring the codebook, the elevation domain is first sampled, and the azimuth and range sampling values ​​are obtained on the plane corresponding to the elevation sampling values, so as to finally obtain a three-dimensional codebook for beamforming of the near-field cylindrical antenna array.

[0012] Further, in step A, the process of modeling the near-field cylindrical antenna array, using three-dimensional polar coordinates to represent the positional relationship between the array elements and the user, and simplifying the expression for the beam focusing vector based on the geometric positional relationship between the user and the antenna array includes the following steps:

[0013] Step A1: Model the near-field cylindrical antenna array:

[0014] In near-field downlink transmission scenarios, the transmitter is equipped with a columnar array, which consists of 2M+1 identical uniform circular arrays. The columnar array is symmetrical about the z=0 plane, meaning that M uniform circular arrays are distributed on the upper and lower sides of the z=0 plane. Each uniform circular array contains N elements, and the radius of each uniform circular array is denoted as R. The distance between each layer of uniform circular arrays is d. The nth antenna element on the mth uniform circular array is denoted as the (n, m)th element on the columnar array, where m∈{-M, -M+1, ..., M-1, M}, and n∈{0, 1, ..., N}. In this scenario, the signal y received by a single-antenna user from the transmitter is:

[0015] y = h H vx+n

[0016] In the formula, h is the channel vector, v is the beamforming vector, x is the transmitted signal, and n is additive white Gaussian noise with variance δ;

[0017] Step A2: Use three-dimensional polar coordinates to represent the geometric position of the user relative to the antenna element. The user's position is represented as... Where r is the distance from the user to the center of the antenna array, and θ is the elevation angle of the user's position with respect to the center of the antenna array. The azimuth angle of the user's position with respect to the center of the antenna array; the azimuth angle φ of the nth element on each uniform circular array. n Represented as: The elevation angle θ corresponding to the m-th uniform circular array m Represented as:

[0018] Step A3, the beam focusing vector b(Y) corresponding to the user's position Y is expressed as:

[0019]

[0020] In the formula, λ is the wavelength. Let be the total number of layers in the cylindrical antenna array, which satisfies r (m，n) This represents the distance between the user and the (n, m)th element in the column array, expressed as:

[0021]

[0022] Further, in step B, the process of calculating the beamforming gain in the elevation, azimuth, and range domains based on the beam focusing vector relationship, and simplifying it using trigonometric relations and Taylor expansions to obtain closed-form solutions for the beamforming gain in the elevation, azimuth, and range domains includes the following steps:

[0023] Step B1: Use the Taylor expansion to calculate the distance r between the user and the (n, m)th element in the columnar array. (m ，n) Simplify:

[0024]

[0025] Step B2: In the elevation domain, keeping the user's distance and azimuth constant, for matched filter beamforming, the beamforming gain is considered as the correlation between two beam focusing vectors. For focusing on the user's position... With user location The two beam focusing vectors have a beamforming gain g. * (Y1, Y2) are:

[0026]

[0027] By simplifying the beamforming gain formula using Taylor expansions of trigonometric functions and Bessel function expansions respectively, we obtain an approximate beamforming gain expression g(Y1, Y2) in the elevation domain:

[0028]

[0029] In the formula, The expression for the zeroth-order Bessel function of the first kind is given; the beamforming gain in the elevation domain is approximated as a function g of the elevation difference θ1-θ2. E (θ1-θ2);

[0030] Step B3: For the azimuth domain, keeping the distance and elevation angle constant, study the user's position. and user location The beamforming gain between the two sides is obtained by using the expansion of the first kind of Bessel function to obtain the approximate beamforming gain g(Ξ1, Ξ2) in the azimuth domain:

[0031]

[0032] The beamforming gain in the azimuth domain is approximated as follows:

[0033] Step B4, in the distance domain, only change the distance research to focus on the user's location. and user location The beamforming gain in the range domain is approximated by using Fresnel functions and Bessel functions of the first kind, resulting in the approximate beamforming gain g(Ω1, Ω2) in the range domain:

[0034]

[0035] In the formula, G(·) represents the Fresnel function;

[0036] The approximate beamforming gain in the range domain is simplified to:

[0037] Furthermore, in step C, the process of obtaining the sampling methods for the elevation, azimuth, and range domains by controlling the correlation of the beam focusing vectors at different positions includes the following steps:

[0038] Step C1: Set the correlation threshold to Δ;

[0039] Step C2: In the elevation angle domain, for a given correlation threshold Δ, find the corresponding elevation angle difference θ. Δ This makes the approximate beamforming gain g in the elevation domain... E (θ Δ Elevation domain sampling is performed using the following formula: ) = Δ;

[0040] θi =iθ Δ i = 0, 1, 2, ..., I

[0041] In the formula, I is the total number of samples in the elevation angle domain. θ i This represents the sampling of the i-th elevation angle;

[0042] Step C3: In the azimuth domain, for the i-th elevation angle sample, obtain... This improves the beamforming gain in the azimuth domain. The following formula is used to calculate the t-th azimuth angle sample on the i-th elevation angle sample.

[0043]

[0044] Among them, T i It is the total number of azimuth angle samples on the i-th elevation angle sample. Make the azimuth angle take values ​​in [0, 2π);

[0045] Step C4: In the distance domain, for the i-th elevation angle sample, obtain δ. i This makes the approximate beamforming gain g in the range domain... r (δ i θ i ) = Δ; On the i-th elevation angle sampling, set the s-th distance sampling as in, and These represent the minimum near-field distance r. min Maximum distance r in the near field max The corresponding sampling numbers satisfy the following conditions:

[0046] Furthermore, in step D, the three-dimensional codebook W used for beamforming of the near-field cylindrical antenna array is:

[0047] W = [W1, ..., W] I ]

[0048] in Focus on location The beam focusing vector.

[0049] Beneficial effects:

[0050] First, the near-field beamforming and codebook design method for the cylindrical antenna array of the present invention addresses the technical problem that existing near-field beamforming research is often limited to two-dimensional planes. It extends the problem to three-dimensional space, studying the elevation, azimuth, and range domains separately, and approximately deriving closed-form solutions for beamforming gain in each of the three domains. This is closer to the situation in actual communication scenarios where users may be distributed at any location in three-dimensional space. By concentrating the beam at a specific location, energy leakage is greatly reduced.

[0051] Second, the near-field beamforming and codebook design method of the cylindrical antenna array of the present invention combines near-field communication with cylindrical antennas for the first time, studies the beamforming problem of near-field cylindrical antennas, and proposes a corresponding codebook for beamforming. The codebook-based beamforming scheme can eliminate the need for channel estimation when performing beamforming, thereby greatly reducing system overhead. Attached Figure Description

[0052] Figure 1 This is a flowchart of the near-field beamforming and codebook design method for a cylindrical antenna array according to an embodiment of the present invention;

[0053] Figure 2 This is a schematic diagram of the columnar antenna array structure according to an embodiment of the present invention.

[0054] Figure 3 This is a schematic diagram of the elevation domain beamforming gain derived from an embodiment of the present invention.

[0055] Figure 4 This is a schematic diagram of the azimuth domain beamforming gain derived from an embodiment of the present invention.

[0056] Figure 5 This is a schematic diagram of the range-domain beamforming gain derived from an embodiment of the present invention.

[0057] Figure 6 This is a beam pattern obtained by beamforming using the proposed codebook in an embodiment of the present invention. Detailed Implementation

[0058] The following embodiments are provided to enable those skilled in the art to more fully understand the present invention, but do not limit the invention in any way.

[0059] This invention discloses a near-field beamforming and codebook design method for a cylindrical antenna array, the near-field beamforming and codebook design method comprising the following steps:

[0060] Step A: Model the near-field cylindrical antenna array, use three-dimensional polar coordinates to represent the positional relationship between the array elements and the user, and simplify the expression of the beam focusing vector by using the geometric positional relationship between the user and the antenna array.

[0061] Step B: Based on the beam focusing vector relationship proposed in Step A, calculate the beamforming gain in the elevation, azimuth, and range domains respectively, and simplify the closed-form solution of the beamforming gain in the three domains using methods such as trigonometric relations and Taylor expansion of special functions.

[0062] Step C: By controlling the correlation of the beam focusing vectors focused at different positions, sampling methods for the elevation, azimuth, and range domains are obtained respectively.

[0063] Step D: When acquiring the codebook, the elevation domain is first sampled, and then the azimuth and range sampling values ​​are obtained on the plane corresponding to the elevation sampling values, finally obtaining a three-dimensional codebook suitable for beamforming of near-field cylindrical antenna arrays.

[0064] Figure 1 This is a flowchart of the near-field beamforming and codebook design method for a cylindrical antenna array according to an embodiment of the present invention; see also Figure 1 The near-field beamforming and codebook design method specifically includes the following steps:

[0065] Step one involves modeling the near-field cylindrical antenna array. Three-dimensional polar coordinates are used to represent the positional relationship between the array elements and the user. The expression for the beam focusing vector is then simplified using the geometric positional relationship between the user and the antenna array. This invention considers a near-field downlink transmission scenario where the transmitter is equipped with a cylindrical array (CLA), which consists of… This is constructed using N uniform circular arrays (UCAs). In this scenario, the signal received by a single-antenna user from the transmitter is:

[0066] y = h H vx+n (1);

[0067] In the formula, h is the channel vector, v is the beamforming vector, x is the transmitted signal, and n is additive white Gaussian noise with variance δ.

[0068] The cylindrical antenna model considered in this invention is as follows: it consists of 2M+1 identical UCAs, and the CLA is symmetric about the z=0 plane, that is, M UCAs are distributed on the upper and lower sides of the z=0 plane, each UCA contains N elements, and the distance between each layer of UCAs is d. The nth antenna element on the mth UCA of the antenna array can be represented as the (n, m)th element on the CLA, where m∈{-M, -M+1, ..., M-1, M}, and n∈{0, 1, ..., N}.

[0069] We use three-dimensional polar coordinates to represent the geometric position of the user relative to the antenna elements. The user's position is represented as... Where r is the distance from the user to the center of the antenna array, i.e., the origin of the coordinate axis, and θ is the elevation angle of the user's position with respect to the center of the antenna array. Let φ be the azimuth angle of the user's position with respect to the center of the antenna array. The radius of each UCA constituting the CLA is denoted as R, and the spacing between UCAs is d. Therefore, the azimuth angle φ of the nth element in each UCA is... n It can be represented as: The elevation angle θ corresponding to the m-th UCA m It can be represented as:

[0070] In traditional far-field planar wavefront-based communication, beam control vectors are typically used to direct the signal in a specific direction to reduce energy leakage. However, in near-field communication scenarios, due to the characteristics of spherical wavefronts, we can control not only the beam direction but also the beam in the range domain. Therefore, traditional far-field beam steering has evolved into near-field beam focusing. If the user is located in... Where r, θ, Let represent the user's distance, elevation angle, and azimuth angle relative to the origin, respectively. Then, the beam focusing vector corresponding to the user's location can be expressed as:

[0071]

[0072] Where λ is the wavelength, r (n，m) This represents the distance between the user and the (n, m)th element in the CLA, which can be expressed as:

[0073]

[0074] As we can see from the expression, the near-field beam focusing vector can simultaneously control the beam's angle and distance. Therefore, the near-field beam focusing vector can perform beamforming better than the traditional far-field beam steering vector.

[0075] Step 2: Based on the beamforming vector relationship proposed in Step 1, we calculate the beamforming gain in the elevation, azimuth, and range domains, respectively, and simplify it using trigonometric relationships and Taylor expansions of special functions to obtain closed-form solutions for the beamforming gain in the three domains. This invention studies the beamforming gain of the near-field CLA system in the range, elevation, and azimuth domains. This invention considers the use of matched filter beamforming, therefore the beamforming vector is the near-field beam focusing vector focused at the corresponding position. Since formula (3) will be used repeatedly in the following calculations, and its radical form is not conducive to further simplification, we first simplify it using Taylor expansions.

[0076]

[0077] Below, we investigate the beamforming gain of the near-field CLA system in the elevation, azimuth, and range domains. First, in the elevation domain, we keep the user's range and azimuth constant and only study the effect of elevation on beamforming gain. For matched filter beamforming, beamforming gain can also be viewed as the correlation between two beam focusing vectors; that is, for beams focused on… and The two beam focusing vectors have the following beamforming gain:

[0078]

[0079] We simplify Equation (4) by retaining the first-order Taylor expansion to obtain Equation (5), which consists of the product of two sums. We simplify the two sums using the Taylor expansion of trigonometric functions and the expansion of Bessel functions to obtain the approximate beamforming gain expression in the elevation domain:

[0080]

[0081] in, This is the expression for a zero-order Bessel function of the first kind. From equation (6), it can be seen that the beamforming gain in the elevation domain can be approximately simplified to a function g of the elevation difference θ1-θ2. E (θ1-θ2).

[0082] For the azimuth domain, we adopt a similar method to the elevation domain, keeping the distance and elevation constant, and study... The beamforming gain between beams can also be approximated using the first-kind Bessel function expansion:

[0083]

[0084] It can be seen that the beamforming gain in the azimuth domain is related not only to the elevation difference but also to the elevation value; therefore, it can be expressed as:

[0085] In the range domain, we study beamforming gain by varying only the range. Using Fresnel functions and Bessel functions of the first kind for approximation, the range domain beamforming gain can be approximated as:

[0086]

[0087] The beamforming gain in the range domain is mainly affected by the elevation angle and the absolute value of the inverse difference of the range, which can be expressed as:

[0088] Step 3: By controlling the correlation of beam focusing vectors at different positions, sampling methods are obtained for the elevation, azimuth, and range domains. After obtaining the beamforming gain expressions in the three domains, we obtain the sampling methods for the elevation, azimuth, and range domains by controlling the correlation of beam focusing vectors at different positions. The beam focusing vectors corresponding to the sampling positions are used as codewords to construct the codebook. Controlling the correlation between codewords is crucial in codebook design. Using the previously derived elevation domain beamforming gain, we set the correlation threshold to Δ. Since the elevation domain beamforming gain is a function of the elevation difference, for a given Δ, we can find the corresponding elevation difference θ. Δ , making g E (θ Δ Therefore, when sampling in the elevation domain, we need to ensure that the difference between sampled values ​​is θ. Δ This satisfies the established correlation constraints. Therefore, angle domain sampling can be performed as follows:

[0089] θ i =iθ Δ ,i=0,1,2,…,I (9);

[0090] in θ i This represents the sampling of the i-th elevation angle.

[0091] Next, in the azimuth domain, since the beamforming gain in the azimuth domain is related to both the elevation angle and the azimuth difference, we study the azimuth sampling problem based on the I elevation angle samples we have already obtained. For the i-th elevation angle sample, we obtain... Make Thus, we can obtain the azimuth sampling method for the i-th elevation angle sampling.

[0092]

[0093] in Ensure that the azimuth angle takes values ​​in [0, 2π).

[0094] In the distance domain, we also study the sampling method over all 1 elevation angles. Similar to the previous method, we obtain g. r (δ i θ i ) = Δ. At this point, we find that if we take a distance sample value as... Then r2 must satisfy... or Therefore, for the i-th elevation angle sampling, we set the distance sampling as... It can satisfy the correlation constraint.

[0095] Step four: When acquiring the codebook, firstly, sampling is performed in the elevation domain. Then, azimuth and range sampling values ​​are obtained on the plane corresponding to the elevation sampling values, ultimately obtaining a three-dimensional codebook suitable for beamforming of near-field cylindrical antenna arrays. After obtaining the sampling methods for each domain, we found that the sampling in both the azimuth and range domains is related to the elevation angle. This means that when generating the codebook, we first need to sample in the elevation domain, and then perform azimuth and range sampling on all I elevation sampling planes respectively. Finally, the beam focusing vectors corresponding to all sampling points are used as codewords to synthesize the three-dimensional CLA codebook proposed in this invention.

[0096] W = [W1, ..., W] I ]

[0097] in,

[0098] The elevation, azimuth, and range domain beamforming gains derived in this invention are shown in the appendix. Figure 3 To be continued Figure 5 As shown, in the elevation domain, the main lobe of the beamforming gain decreases more rapidly as the antenna radius increases, meaning that denser sampling is required in the elevation domain. (See attached image.) Figure 4 and attached Figure 5 The beamforming gain in the azimuth and range domains are shown respectively. As can be seen from the figure, when the elevation sampling is closer to... That is, when the elevation sampling plane is closer to the z=0 plane, the main lobe of the beamforming gain in the azimuth domain decreases faster. This means that the azimuth difference corresponding to the preset threshold Δ=0.5 is smaller, i.e., we need to perform denser sampling in the azimuth domain. In the range domain, when the elevation angle is close to... At this point, the main lobe of the beamforming gain corresponding to the reciprocal range difference decreases more rapidly. This also means that more range sampling loops need to be generated in the range domain.

[0099] The beam pattern obtained by the specific beamforming of the codebook designed in this invention is attached. Figure 6 As shown in the figure, the codewords in our designed codebook can effectively guide the channel to the expected location, thereby effectively reducing the energy leakage problem.

[0100] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A near-field beamforming and codebook design method for a cylindrical antenna array, characterized in that, The near-field beamforming and codebook design method includes the following steps: Step A: Model the near-field cylindrical antenna array, use three-dimensional polar coordinates to represent the positional relationship between the array elements and the user, and simplify the expression of the beam focusing vector by using the geometric positional relationship between the user and the antenna array. Includes the following steps: Step A1: Model the near-field cylindrical antenna array: In near-field downlink transmission scenarios, the transmitting end is equipped with a columnar array, which consists of... Composed of identical uniform circular arrays, the columnar array is about Planar symmetry, that is The plane has distributions on both the upper and lower sides. There are uniform circular arrays, each containing... There are n elements, and the radius of each uniform circular matrix is ​​represented as... The distance between each layer of uniform circular arrays is ; the first antenna array The first uniform circular array The nth antenna element is represented as the nth antenna element on the columnar array. There are elements, among which In this scenario, the signal received by a single-antenna user from the transmitter... for: ； In the formula, For channel vectors, For beamforming vectors, For the transmitted signal, The variance is Additive white Gaussian noise; Step A2: Use three-dimensional polar coordinates to represent the geometric position of the user relative to the antenna element. The user's position is represented as... ,in, The distance from the user to the center of the antenna array. The elevation angle of the user's location with respect to the center of the antenna array. The azimuth angle of the user's position with respect to the center of the antenna array; the first [angle] on each uniform circular array. The azimuth angle of each element Represented as: , No. The elevation angle corresponding to a uniform circular array Represented as: ; Step A3, User Location Corresponding beam focusing vector Represented as: ； In the formula, It's the wavelength. Let be the total number of layers in the cylindrical antenna array, which satisfies , Represents the user and the first in the column array The distance between elements is expressed as: ； Step B: Based on the relationship of the beam focusing vector, calculate the beamforming gain in the elevation, azimuth, and range domains respectively, and simplify using the trigonometric relationship and Taylor expansion to obtain the closed-form solutions of the beamforming gain in the elevation, azimuth, and range domains. Step C: By controlling the correlation of the beam focusing vectors focused at different positions, sampling methods for the elevation, azimuth, and range domains are obtained respectively. Step D: When acquiring the codebook, the elevation domain is first sampled, and the azimuth and range sampling values ​​are obtained on the plane corresponding to the elevation sampling values, so as to finally obtain a three-dimensional codebook for beamforming of the near-field cylindrical antenna array.

2. The near-field beamforming and codebook design method for a cylindrical antenna array according to claim 1, characterized in that, Step B involves calculating the beamforming gain in the elevation, azimuth, and range domains based on the beam focusing vector relationship, and then simplifying the equations using trigonometric relations and Taylor expansions to obtain closed-form solutions for the beamforming gain in the elevation, azimuth, and range domains. This process includes the following steps: Step B1, using Taylor expansion to compare the user with the first column in the column array. Distance between elements Simplify: ； Step B2: In the elevation domain, keeping the user's distance and azimuth constant, for matched filter beamforming, the beamforming gain is considered as the correlation between two beam focusing vectors. For focusing on the user's position... With user location The two beam focusing vectors, their beamforming gain for: ； By simplifying the beamforming gain formula using Taylor expansions of trigonometric functions and Bessel function expansions respectively, an approximate beamforming gain expression for the elevation domain is obtained. : ； In the formula, The expression for the zeroth-order Bessel function of the first kind is given; the beamforming gain in the elevation domain is approximated as the elevation difference. function ; Step B3: For the azimuth domain, keeping the distance and elevation angle constant, study the user's position. and user location The beamforming gain in the azimuth domain is obtained by using the expansion of the first kind of Bessel function. : ； The beamforming gain in the azimuth domain is approximated as follows: ; Step B4, in the distance domain, only change the distance research to focus on the user's location. and user location The beamforming gain in the range domain is approximated by using Fresnel functions and Bessel functions of the first kind, resulting in an approximate beamforming gain in the range domain. : ； In the formula, Represents Fresnel functions; The approximate beamforming gain in the range domain is simplified to: .

3. The near-field beamforming and codebook design method for a cylindrical antenna array according to claim 1, characterized in that, Step C, which involves controlling the correlation of beam focusing vectors at different positions to obtain sampling methods for the elevation, azimuth, and range domains, includes the following steps: Step C1, set the correlation threshold to ; Step C2, in the elevation angle domain, for a given correlation threshold Find the corresponding elevation angle difference This results in an approximate beamforming gain in the elevation domain. The following formula is used for sampling in the elevation region: ； In the formula, It is the total number of samples in the elevation angle region. , Representing the Sampling at an elevation angle; Step C3, in the azimuth domain, for the first... Sampling at an elevation angle yields... This improves the beamforming gain in the azimuth domain. The following formula is used to calculate the first... Sampling the t-th azimuth angle on the elevation angle sampling. : ； in, It is the first The total number of azimuth angles sampled from each elevation angle sampling point. , so that the azimuth angle is Take the value from; Step C4, in the distance domain, for the first... Sampling at an elevation angle yields... This makes the approximate beamforming gain in the range domain... ; in the On the first elevation angle sampling, set the first... Each distance sampling is , ; in, and These represent the minimum near-field distances. Maximum distance from near field The corresponding sampling numbers satisfy the following conditions: .

4. The near-field beamforming and codebook design method for a cylindrical antenna array according to claim 3, characterized in that, In step D, a three-dimensional codebook is used for beamforming of the near-field cylindrical antenna array. for: ； in , Focus on location The beam focusing vector.

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