Method and system for massive mimo channel estimation based on circular antenna array

Abstract

The application discloses a kind of based on circular antenna array's extremely large scale MIMO channel estimation method and system, consider the uplink of communication system based on time division duplex, wherein, user is located in three-dimensional space arbitrary distribution, and using hybrid precoding architecture.Different from the past only considering the polar region representation near-field channel of user plane angle and distance, the application also considers the elevation angle of user, and uses spherical domain codebook to represent near-field channel, analyzes how to sample elevation angle, azimuth and distance in spherical domain to reduce column coherence of transformation matrix, and proposes synchronous orthogonal matching pursuit algorithm based on spherical domain codebook, finally, for the case of arbitrary spatial distribution of user, the effectiveness of the algorithm is verified.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically, to a method and system for estimating ultra-large-scale MIMO channels based on a circular antenna array. Background Technology

[0002] With the development of technology, ultra-large-scale MIMO (XL-MIMO) systems have gradually become a research hotspot in wireless communication. The goal of XL-MIMO is to significantly improve the spectral efficiency and connection density of the system by deploying a large number of antennas at the base station and utilizing beamforming and spatial multiplexing techniques. However, as the size of antenna arrays increases, the limitations of traditional far-field plane wave models in describing signal propagation become increasingly apparent, especially in near-field communication environments where signal propagation characteristics are more consistent with spherical wave models. Therefore, developing new channel estimation algorithms to adapt to the channel characteristics under near-field conditions is particularly important.

[0003] Uniform Circular Arrays (UCAs) exhibit significant advantages in beamforming and spatial processing due to their unique rotational symmetry. UCAs can provide uniform beam patterns at different azimuth angles, making them suitable for achieving omnidirectional coverage and improving beamforming gain. Particularly in near-field communication, UCAs can better maintain beam directivity, ensuring accurate signal transmission and reception. Furthermore, the uniformity of UCAs reduces performance losses caused by the complexity of signal propagation paths when processing near-field signals.

[0004] However, UCA systems face several challenges in channel estimation. First, UCA requires channel estimation in three-dimensional space, which increases the complexity of the problem because it must simultaneously consider angle and distance information, especially in environments with uneven or dynamically changing user distribution. Second, the angular resolution of UCA relies on a non-uniform sampling strategy, which is more complex than the uniform sampling of a Uniform Linear Array (ULA) and requires precise design to ensure signal orthogonality and coverage. Furthermore, the design of the three-dimensional codebook is also challenging, needing to effectively cover all users while maintaining low complexity.

[0005] Traditional channel models may fail to accurately describe the actual propagation environment of signals under complex user distribution conditions, especially in the near field, where the spherical wave model of signal propagation differs significantly from the plane wave model in the far field. Limitations in angular and distance resolution of UCA hinder its accurate estimation of user signals from different directions and distances. Furthermore, if complex multipath effects in near-field communication are not properly addressed, they will lead to inaccurate signal delay and phase estimation, affecting signal detection and demodulation.

[0006] Therefore, to address these challenges, this invention aims to improve the accuracy and efficiency of channel estimation and ensure signal transmission quality under extreme weather conditions. By combining advanced signal processing techniques and optimization algorithms, this method can effectively address the complexity of channel estimation in UCA systems and improve overall system performance. Summary of the Invention

[0007] To overcome the shortcomings of inaccurate signal delay and phase estimation in existing technologies, this invention provides a method and system for estimating ultra-large-scale MIMO channels based on a circular antenna array.

[0008] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0009] This invention provides a method for estimating the channel of extremely large-scale MIMO based on a circular antenna array, comprising:

[0010] Acquire the received signal, analog combination matrix, user channel path, sparse support set, residual set, and sphere codebook;

[0011] Start the loop to traverse the channel path and calculate the support matrix based on the simulated combination matrix, the sphere codebook, and the residual set;

[0012] Obtain the new support number based on the support matrix, and update the sparse support set based on the new support number;

[0013] Orthogonal projection is performed based on the received signal, the spherical codebook, and the analog combination matrix to obtain the sparse channel matrix in the spherical domain.

[0014] Update the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set;

[0015] The loop continues until all communication paths have been traversed, at which point the loop is exited and the estimated channel is obtained.

[0016] Preferably, obtaining the sphere codebook includes:

[0017] Obtain the minimum communication distance, distance column coherence threshold, number of antennas, antenna spacing, and wavelength;

[0018] Select an elevation angle, and obtain the sampled value of the current elevation angle based on the number of antennas, the spacing between antennas, and the wavelength;

[0019] Select an azimuth angle at the current elevation angle, and calculate the sampled value of the azimuth angle at the current elevation angle based on the range column coherence threshold, the number of antennas, the antenna spacing, and the wavelength.

[0020] The distance sampling values ​​at the current elevation and azimuth angles are calculated based on the minimum communication distance, the distance column coherence threshold, the number of antennas, the antenna spacing and wavelength, and the corresponding wave speed steering vector set is generated based on the calculated distance sampling values.

[0021] The process continues until all azimuth angles at the current elevation angle have been selected, and the initial codebook is obtained by integrating the corresponding wave speed steering vector sets.

[0022] This continues until all elevation angles have been selected, and the sphere codebook is obtained based on the initial codebook.

[0023] Preferably, the formula for obtaining the sampled value of the current elevation angle based on the number of antennas, the spacing between antennas, and the wavelength is as follows:

[0024]

[0025] Where λ is the wavelength of the antenna; α is the null point; and m is the number of sampling points at the elevation angle.

[0026] Preferably, the formula for calculating the sampled value of the azimuth angle below the current elevation angle based on the range column coherence threshold, the number of antennas, the antenna spacing, and the wavelength is as follows:

[0027]

[0028] Where θ is the elevation angle; λ is the wavelength of the antenna; α is the null point; and s is the number of sampling points for the azimuth angle at θ.

[0029] Preferably, the formula for calculating the distance sampling values ​​at the current elevation and azimuth angles based on the minimum communication distance, the distance column coherence threshold, the number of antennas, the antenna spacing, and the wavelength is as follows:

[0030]

[0031] Where z is the sampling index; r min Z is the minimum communication distance; Z is the number of sampling points at the minimum communication distance; θ is the elevation angle.

[0032] Preferably, the formula for calculating the support matrix based on the simulated combination matrix, the spherical codebook, and the residual set is as follows:

[0033] T = (AW) H R

[0034] Where A is the simulated combination matrix; W is the spherical codebook; and R is the residual set.

[0035] Preferably, the formula for obtaining the new support number based on the support matrix is:

[0036]

[0037] Where T is the support matrix; M is the frequency count; and p is the number of support sets.

[0038] Preferably, the formula for obtaining the sparse channel matrix in the spherical domain by orthogonal projection based on the received signal, the spherical codebook, and the analog combination matrix is ​​as follows:

[0039]

[0040] Where Y is the received signal; A is the analog combination matrix; and W is the spherical codebook.

[0041] Preferably, the formula for updating the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set is as follows:

[0042]

[0043] Where R is the residual set; A is the simulated combination matrix; W is the spherical codebook; It is a sparse channel matrix in the spherical domain.

[0044] The present invention also provides a very large-scale MIMO channel estimation system based on a circular antenna array, for implementing the above method, characterized in that it includes:

[0045] The data acquisition module acquires the received signal, analog combination matrix, user channel path, sparsity support set, residual set, and sphere codebook.

[0046] The traversal module begins a loop to traverse the channel path and calculates the support matrix based on the simulated combination matrix, the spherical codebook, and the residual set.

[0047] The support set update module obtains the new number of supports based on the support matrix and updates the sparse support set based on the new number of supports.

[0048] The channel matrix acquisition module performs orthogonal projection based on the received signal, the spherical codebook, and the analog combination matrix to obtain the sparse spherical channel matrix.

[0049] The residual set update module updates the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set.

[0050] The channel estimation module continues until all communication paths have been traversed, then breaks out of the loop to obtain the estimated channel.

[0051] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0052] This invention considers the uplink communication link of a time-division duplex communication system, where users are arbitrarily distributed in three-dimensional space and a hybrid precoding architecture is employed. Unlike previous methods that only considered the user's plane angle and distance in polar domain representation of the near-field channel, this invention also considers the user's elevation angle, using a spherical codebook to represent the near-field channel. It analyzes how to sample elevation, azimuth, and distance in the spherical domain to reduce column coherence of the transformation matrix, and proposes a synchronous orthogonal matching pursuit algorithm based on the spherical codebook. Finally, the effectiveness of the algorithm is verified for users with arbitrary spatial distribution. Attached Figure Description

[0053] Figure 1 This is a flowchart of the ultra-large-scale MIMO channel estimation method based on a circular antenna array described in Example 1;

[0054] Figure 2 This is a schematic diagram of the structure of the ultra-large-scale MIMO channel estimation system model based on a circular antenna array described in Example 2;

[0055] Figure 3 This is a schematic diagram of the absolute value of the first type of zeroth-order Bessel function in Example 2;

[0056] Figure 4 This is a flowchart of the process for generating the sphere codebook as described in Example 2;

[0057] Figure 5 This is a schematic diagram of the structure of the three-dimensional spatial codebook based on UCA described in Example 2;

[0058] Figure 6 This is a schematic diagram comparing the performance of UCA and ULA under different algorithms with signal-to-noise ratio in Example 2;

[0059] Figure 7 This is a schematic diagram comparing the performance of UCA and ULA under different algorithms with signal-to-noise ratio in Example 2;

[0060] Figure 8 This is a schematic diagram illustrating the performance of different algorithms under different pilot lengths as described in Example 2;

[0061] Figure 9 This is a schematic diagram illustrating the performance of different algorithms under different pilot lengths as described in Example 2;

[0062] Figure 10 This is a schematic diagram illustrating the performance of different algorithms under different pilot lengths as described in Example 2;

[0063] Figure 11 This is a schematic diagram illustrating the variation of communication computation delay in each time slot of the ultra-large-scale MIMO channel estimation system based on a circular antenna array described in Example 2.

[0064] Figure 12 This is a schematic diagram illustrating the variation of communication computation delay in each time slot of the ultra-large-scale MIMO channel estimation system based on a circular antenna array described in Example 2.

[0065] Figure 13 This is a schematic diagram illustrating the variation of communication computation delay in each time slot of the ultra-large-scale MIMO channel estimation system based on a circular antenna array described in Example 2.

[0066] Figure 14 This is a schematic diagram illustrating the relationship between NMSE performance and user distance as described in Example 3;

[0067] Figure 15 This is a schematic diagram of the structure of the ultra-large-scale MIMO channel estimation system based on a circular antenna array described in Example 3. Detailed Implementation

[0068] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0069] To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions.

[0070] It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings.

[0071] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0072] Example 1

[0073] This embodiment provides a method for estimating the channel of extremely large-scale MIMO based on a circular antenna array, such as... Figure 1 As shown, it includes:

[0074] Acquire the received signal, analog combination matrix, user channel path, sparse support set, residual set, and sphere codebook;

[0075] Start the loop to traverse the channel path and calculate the support matrix based on the simulated combination matrix, the sphere codebook, and the residual set;

[0076] Obtain the new support number based on the support matrix, and update the sparse support set based on the new support number;

[0077] Orthogonal projection is performed based on the received signal, the spherical codebook, and the analog combination matrix to obtain the sparse channel matrix in the spherical domain.

[0078] Update the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set;

[0079] The loop continues until all communication paths have been traversed, at which point the loop is exited and the estimated channel is obtained.

[0080] This embodiment considers the uplink communication link of a time-division duplex communication system, where users are arbitrarily distributed in three-dimensional space, and a hybrid precoding architecture is employed. Unlike previous polar domain representations of near-field channels that only consider user plane angles and distances, this embodiment also considers user elevation angles, using a spherical codebook to represent the near-field channel. It analyzes how to sample elevation, azimuth, and distance in the spherical domain to reduce column coherence of the transformation matrix, and proposes a synchronous orthogonal matching pursuit algorithm based on the spherical codebook. Finally, the effectiveness of the algorithm is verified for users with arbitrary spatial distribution.

[0081] Example 2

[0082] This embodiment provides a method for estimating the channel of extremely large-scale MIMO based on a circular antenna array, including:

[0083] Acquire the received signal, analog combination matrix, user channel path, sparse support set, residual set, and sphere codebook;

[0084] Start the loop to traverse the channel path and calculate the support matrix based on the simulated combination matrix, the sphere codebook, and the residual set;

[0085] Obtain the new support number based on the support matrix, and update the sparse support set based on the new support number;

[0086] Orthogonal projection is performed based on the received signal, the spherical codebook, and the analog combination matrix to obtain the sparse channel matrix in the spherical domain.

[0087] Update the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set;

[0088] The loop continues until all communication paths have been traversed, at which point the loop is exited and the estimated channel is obtained.

[0089] Retrieve the ball domain codebook, including:

[0090] Obtain the minimum communication distance, distance column coherence threshold, number of antennas, antenna spacing, and wavelength;

[0091] Select an elevation angle, and obtain the sampled value of the current elevation angle based on the number of antennas, the spacing between antennas, and the wavelength;

[0092] Select an azimuth angle at the current elevation angle, and calculate the sampled value of the azimuth angle at the current elevation angle based on the range column coherence threshold, the number of antennas, the antenna spacing, and the wavelength.

[0093] The distance sampling values ​​at the current elevation and azimuth angles are calculated based on the minimum communication distance, the distance column coherence threshold, the number of antennas, the antenna spacing and wavelength, and the corresponding wave speed steering vector set is generated based on the calculated distance sampling values.

[0094] The process continues until all azimuth angles at the current elevation angle have been selected, and the initial codebook is obtained by integrating the corresponding wave speed steering vector sets.

[0095] This continues until all elevation angles have been selected, and the sphere codebook is obtained based on the initial codebook.

[0096] The formula for obtaining the sampled value of the current elevation angle based on the number of antennas, the spacing between antennas, and the wavelength is:

[0097]

[0098] Where λ is the wavelength of the antenna; α is the null point; and m is the number of sampling points at the elevation angle.

[0099] The formula for calculating the sampled value of the apex angle below the current elevation angle based on the range coherence threshold, the number of antennas, the antenna spacing, and the wavelength is as follows:

[0100]

[0101] Where θ is the elevation angle; λ is the wavelength of the antenna; α is the null point; and s is the number of sampling points for the azimuth angle at θ.

[0102] The formula for calculating the distance sample values ​​at the current elevation and azimuth angles based on the minimum communication distance, range coherence threshold, number of antennas, antenna spacing, and wavelength is as follows:

[0103]

[0104] Where z is the sampling index; r min Z is the minimum communication distance; Z is the number of sampling points at the minimum communication distance; θ is the elevation angle.

[0105] The formula for calculating the support matrix based on the simulated combination matrix, the spherical codebook, and the residual set is as follows:

[0106] T = (AW) H R

[0107] Where A is the simulated combination matrix; W is the spherical codebook; and R is the residual set.

[0108] The formula for obtaining new support numbers based on the support matrix is:

[0109]

[0110] Where T is the support matrix; M is the frequency count; and p is the number of support sets.

[0111] The formula for obtaining the sparse channel matrix in the spherical domain by orthogonal projection based on the received signal, the spherical codebook, and the analog combination matrix is ​​as follows:

[0112]

[0113] Where Y is the received signal; A is the analog combination matrix; and W is the spherical codebook.

[0114] The formula for updating the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set is as follows:

[0115]

[0116] Where R is the residual set; A is the simulated combination matrix; W is the spherical codebook; It is a sparse channel matrix in the spherical domain.

[0117] In a specific embodiment, such as Figure 1 The diagram shows an uplink communication link between a base station equipped with an N-element uniform circular antenna array and K single-antenna users. The antenna spacing is d = λ. c / 2, where λ c Let N be the carrier wavelength. K single-antenna users are simultaneously served by M subcarriers, where K ≤ N. RF For uplink channel estimation, assume that K users send mutually orthogonal pilot sequences to the BS, meaning different users use orthogonal time or frequency resources to send pilot sequences. Therefore, the channel estimation for each user is independent. Without loss of generality, consider an arbitrary user. The antenna position can be represented in spherical coordinates as follows: in n = (0, 1, ..., N-1), which can be represented in Cartesian coordinates as follows: The position of the kth user can be represented in Cartesian coordinates as (r k sinθ k cosφ k ,r k sinθ k sinφ k ,r k cosθ k Since we are considering any user, the subscript k will be removed in the following discussion for easier viewing. That is, the propagation distance from user k to the nth antenna is:

[0118]

[0119] Where approximation (a) is derived from the second-order Taylor formula. Expanding, we get... It's worth noting that this approximation is valid for most near-field communication systems. Let x...m,p This is represented as the transmit pilot at the m-th subcarrier in time slot p. Then the receive pilot... for:

[0120] y m,p =A p h m x m,p +n m,p (2)

[0121] in, Denotes the simulated combination matrix, and satisfies This indicates that the mean is 0 and the variance is σ. 2 I N Gaussian white noise. h m This represents a wireless channel. By defining the pilot length as P, then p = 1, 2, ..., P. Assume x... m,p =1, the pilot sequence y received at the m-th subcarrier m =[y m,1 ,…,y m,P ] T It can be represented as

[0122] y m =Ah m +n m (3)

[0123] in, Indicates noise. Let A represent the overall observation simulation matrix, where each element in A is independent and derived from... Equal probability random generation. In traditional XL-MIMO, the channel can be modeled using a far-field plane wave model:

[0124]

[0125] Where L is the number of communication paths, Where c is the wave number, and g is the speed of light. l ,r l ,θ l ,φ l These represent the multiplex gain, range, elevation angle, and azimuth angle of the l-th path, respectively. The steering vector a(θ) l ,φ l ) by θ l ∈(0,π) and φ l The plane wave hypothesis ∈(0,2π) is derived as follows:

[0126]

[0127] However, due to the significantly increased array aperture of ELAA, the near-field region expands dramatically, and users are likely located in this region. Therefore, a ball wave propagation model must be used. Consequently, the far-field beam steering vector based on the plane wave propagation model cannot characterize ball wave propagation in the ELAA system. To address this propagation model mismatch, a more accurate UCA near-field beam steering vector can be used, expressed as:

[0128]

[0129]

[0130] Where (b) is obtained by substituting the second-order Taylor expansion of formula (1) into (5a). Therefore, the spherical wave channel model in the near-field region can be expressed as:

[0131]

[0132] For a two-dimensional plane, i.e. φ l =φ0 is a constant and will not change with the path. Therefore, h m It can be viewed as a weighted sum of finite near-field steering vectors b(r,θ), while the channel... It can be transformed into its polar domain representation by polar domain transformation matrix. Right now:

[0133]

[0134] in W represents the polar-domain sampling codebook, where Q represents the number of near-field steering vectors sampled in the polar domain. P It contains Q uniformly sampled angles and non-uniformly sampled distances for the steering vector, and in the polar domain Channel sparsity is typically sparse. Leveraging this channel sparsity, several channel estimation algorithms based on compressed sensing (CS) have been proposed to efficiently recover channel data with low pilot overhead P.

[0135] 2.2 Near-field ball domain codebook establishment

[0136] As shown in formula (8), the number of channel paths in the near field is still finite, i.e., L << N. This indicates that the number of channel parameters that need to be estimated is still finite, and therefore the near field channel in three-dimensional space is also compressible. To find a sparse representation of the near field channel, we can refer to the derivation of the polar-domain sparse representation of the near field channel (9). Specifically, as shown in (8), hm can be regarded as a weighted sum of finite near-field turning vectors b(r,θ,φ), where b(r,θ,φ) is related not only to the channel distance and elevation angle, but also to the channel azimuth angle. Compared with the existing polar-domain matrix W PSimilar to the previous design, a new transformation matrix W is proposed, consisting of multiple near-field steering vectors b(r,θ,φ), where the distance r, elevation angle θ, and azimuth angle φ are sampled from the entire spatial range and angular domains. In this way, w fully utilizes all elevation, azimuth, and range information of the near-field path components. Since elevation, azimuth, and range represent coordinates in a spherical coordinate system, the spatial angular range domain is called the spherical domain. Therefore, matrix W is called the spherical domain transformation matrix.

[0137] With polar field representation Similarly, the proposed near-field channel polar domain representation for:

[0138]

[0139] In the formula, U represents the number of near-field steering vectors sampled in the polar domain. Similar to the polar domain sparsity, the proposed spherical transformation matrix W can simultaneously consider the elevation angle, azimuth angle, and range information of the near-field path components. Therefore, matrix W makes the near-field channel sparse in the polar domain, thereby avoiding the energy diffusion effect of the near-field channel in the polar domain. Since matrix W samples two different angles and distances simultaneously, it is not assumed that the number of sampled vectors U is equal to N; in general, U >> N.

[0140] After the CS framework is determined, in order to achieve the required channel recovery accuracy, sampling is performed at different distances, elevation angles, and azimuth angles, and the column coherence of the codebook is considered. It should be as small as possible. Studies have shown that when the distance between the base station and the user or scattering point is greater than... At that time, the Fresnel approximation (a) in formula (1) is accurate, and the distance is much lower than the Rayleigh distance. Where D represents the array aperture. For example, if the array aperture D is 0.82m and the wavelength λ... c The value is 1 cm, the Rayleigh distance is 134.5 m, and This is negligible. Therefore, the column coherence f(r1,r2,θ1,θ2,φ1,φ2) can be approximated as:

[0141]

[0142] It is still difficult to directly obtain the sampling methods for distance and angle from equation (11), but the phase can be decoupled into two parts, the first term It only depends on the angle, the second item Based on this observation, which relates to angle and distance, we will first derive the angle sampling method from the first linear phase part, and then derive the distance sampling method from the second quadratic phase part.

[0143] 2.2.1 Sampling method for elevation angle

[0144] To ensure coherence between column vectors, angular resolution is used as the standard for sampling interval. This ensures that the correlation between any two column vectors with different elevation angles (θ1≠θ2) is zero, thus satisfying the sampling requirements. To determine the elevation angle that minimizes coherence, we assume r1 = r2 and φ1 = φ2.

[0145] Lemma 1: Based on the properties of near-field beamforming gain, the beamforming gain obtained by the near-field beamforming vector b(r,θ1,φ) at position (r,θ2,φ) can be proven to be approximately the same as the far-field beamforming gain, i.e.:

[0146]

[0147] In the formula, J0(·) is the zeroth order Bessel function of the first kind, and Δθ=sinθ1-sinθ2.

[0148] The proof is as follows:

[0149]

[0150] In the formula, approximation (a) is obtained by keeping only the first order of the Taylor series expansion, and (b) is obtained by letting Δθ = sinθ1 - sinθ2, and then using the properties of the Bessel function:

[0151]

[0152] In the formula J m (·) represents a first-order m-th order Bessel function, and the beamforming gain can be rewritten as:

[0153]

[0154] Then, by summing the geometric series over n, it can be derived as a piecewise function:

[0155]

[0156] Then, by the asymptotic property of Bessel functions:

[0157]

[0158] When N is very large, m = N·t, t ≠ 0, |J |m| (β)|≈0, therefore, equation (15) can be approximated by summation through m=0, that is:

[0159]

[0160] The above completes the proof. It can be seen that the angular resolution of θ is directly related to |J0(x)|, as follows: Figure 3 The figure shows the graph of the function |J0(x)|. By setting |J0(α)|=0, we obtain the first zero point α≈2.4. Right now Therefore, elevation angle sampling and the existing polar domain transformation matrix W P The sampling methods are the same, both being uniform sampling, i.e.:

[0161]

[0162]

[0163] 2.2.2 Azimuth sampling method

[0164] Similar to the elevation angle sampling method, the azimuth angle resolution is also used as the sampling interval, i.e., assuming r1 = r2, θ1 = θ2, from Lemma 1 we can obtain:

[0165]

[0166] In the formula, (a) is the product-to-sum formula using trigonometric functions. We obtain (b) through trigonometric transformation formulas. We obtain (c) through a pre-order. Then, by substituting the properties of the Bessel function into formula (14), we get (d), which is similar to formula (18). When N is very large, the function is not equal to 0 only when m = 0. Therefore, we take m = 0 to approximate it.

[0167] It can be seen that the angular resolution of φ changes with θ, but it is also constrained by the function |J0(x)|. Setting |J0(α)|=0, we get... Then angular resolution Therefore, the sampling point interval for the azimuth angle is:

[0168]

[0169] Therefore, the sampling points for the azimuth angle are:

[0170]

[0171] 2.2.3 Distance Sampling Method

[0172] Similar to the angle sampling method, since distance information is only contained in the quadratic term... Therefore, this part will be the focus of the study, thus deriving the distance sampling method, i.e., φ=φ1=φ2, θ=θ1=θ2, thus the first phase of formula (11) It is then eliminated; in this case, the column coherence is only in phase with the second quadratic term. It is related to the item. The physical meaning of this is sampling two positions at the same elevation angle θ and azimuth angle φ, and the column coherence is determined by... Based on this, a distance sampling method can be derived. Therefore, column coherence at the same angle can be approximated as:

[0173]

[0174] In the formula, (a) is achieved by substituting the double-angle formula of trigonometric functions. Simplify, then introduce quadratic terms that are independent of n; (b) remove terms that are independent of the summation of n; (c) introduce the properties of the Bessel function. Then, the terms related to the summation of n are summed separately. (d) is similar to formula (16), except that m = N·t. hour, In other cases, take 0, and then substitute it into the asymptotic property of the Bessel function in formula (17). Since N is large, it can be approximated by taking an approximate value at s = 0.

[0175] Equation (24) shows that the column coherence of the distance depends to a large extent on the function |J0(x)| and the parameter θ. From Figure 2 It can be seen that the |J0(x)| function exhibits a significant decreasing trend in the range (0,2). Therefore, to minimize the coherence, we should ensure that |J0(β)| ≤ Δ, where Δ represents the desired threshold. For example, Δ = 0.5, |J0(β)| ≤ Δ. Δ If |≈1.6, then β≥β Δ =1.6, therefore, the sampling distances r1 and r2 should satisfy the following condition:

[0176]

[0177]

[0178] In formula (26) It can be seen that the reciprocal difference between the two distances should be greater than Therefore, an effective distance sampling method is proposed:

[0179]

[0180] In the formula, z is the sampling index. This represents the number of sampling points at the minimum communication distance. z = 0 indicates that energy is focused on the beamforming vector at infinity, where the near-field beamforming vector degenerates into the far-field beamforming vector. Therefore, the far-field ULA codebook can be considered a special case of the proposed near-field spherical domain codebook and is included in the proposed near-field codebook. When mixed-field communication occurs, i.e., when the user has a mixture of near-field and far-field channels, the proposed codebook can still work by allocating near (far) field beams to near (far) field users.

[0181] Based on the sampling method described above, the design scheme for the UCA sphere codebook can be obtained, such as... Figure 4 As shown, the specific algorithm one is as follows:

[0182] (1) Initialize the minimum communication distance r min The distance column coherence threshold Δ, the number of antennas N, the antenna spacing d, and the wavelength λ.

[0183] (2) The sampled value of the elevation angle is obtained by formula (20).

[0184] (3) Enter the first loop and obtain the azimuth angle sampling value through formula (23).

[0185] (4) Enter the second loop and obtain the distance sampling value through formula (27).

[0186] (5) Generate codebook turning vector:

[0187] (6) Exit the first loop and obtain the codebook:

[0188] (7) Exit the second loop to obtain the codebook:

[0189] 2.4 Channel Estimation Based on UCA Ball Domain Codebook

[0190] Based on the above sampling method, a three-dimensional spherical codebook W is obtained. Since K users send mutually orthogonal pilot sequences, the uplink channel estimation for each user can be performed independently. For any user, based on the spherical representation (10), in (3) f m Pilot y received at frequency m It can be represented as:

[0191]

[0192] Due to the spherical channel discussed above It is sparse, therefore spherical channel estimation can be represented as a sparse signal recovery problem. In general, the steering vectors at different subcarriers are the same, just like the frequency-independent steering vectors b(r,θ,φ) and a(θ,φ). Therefore, at different subcarriers f... m Furthermore, the sparsity support of the polar-domain channel is the same, allowing for simultaneous estimation and improved estimation accuracy. Therefore, the signal can be rearranged as follows:

[0193] Y = AWH S +n (29)

[0194] In the formula, Y=[y1,y2,…,y M ], n = [n1, n2, ..., n M Since the channel WH is estimated from the known Y and AW. S And H S Since the channel is sparse, the channel estimation problem can be solved using the existing near-field channel estimation algorithm on the grid of polar-domain synchronous orthogonal matching pursuit (P-SOMP), and then extended to the spherical domain S-SOMP algorithm to recover the near-field XL-MIMO channel. The specific steps are shown in Algorithm 2:

[0195] (1) Initialize the received signal Y, the simulated combination matrix A, the user's communication path L, the sparsity support set P, the residual set R, and the spherical codebook W obtained by Algorithm 1.

[0196] (2) Start the number of looping channel paths

[0197] (3) Calculate the correlation matrix: T = (AW) H R

[0198] (4) Find the new support numbers, and take the row with the largest absolute square of the modulus of the row vectors in the correlation matrix:

[0199] (5) Update the support set: P = P ∪ p *

[0200] (6) Orthogonal projection yields the sparse channel matrix in the spherical domain:

[0201] (7) Update the residual matrix:

[0202] (8) Once all channel path information has been collected, exit the loop.

[0203] (9) Obtain the estimated channel:

[0204] like Figure 5As shown, with 512 antennas, a carrier frequency of 30 GHz, and an antenna spacing of half a wavelength, the 3D spatial codebook generated based on Algorithm 1 can sample all users in space. The blue rings represent the set of sampling points, and the azimuth sampling spacing... and elevation angle sampling interval Since the distance is very small, the spacing between adjacent sampling points on the ring is very small. Therefore, channel estimation only needs to perform fine optimization on the distance domain, which can reduce the overall algorithm complexity and overhead.

[0205] like Figure 6 and Figure 7 The figure shows the performance analysis of ULA and UCA with signal-to-noise ratio (SNR) under the same array aperture and the same number of antennas. Figure 6 The figure shows the performance analysis of ULA and UCA with the same antenna array aperture. Figure 7 As shown, the performance analysis diagrams of ULA and UCA with the same number of antennas are presented. SOMP is a far-field sampling algorithm that only considers angle, while S-SOMP is a near-field sampling algorithm that considers both angle and distance. From the diagrams, the following conclusions can be drawn: (1) As the number of antennas increases, the performance of ULA decreases. When the number of antennas is the same as that of UCA, the performance of both is the same under the SOMP algorithm. This is because the sampling angle of both is directly related to the number of antennas, and both are equally spaced sampling. (2) For the near-field sampling algorithm S-SOMP, the performance of UCA is far superior to that of ULA. This is mainly because the proposed UCA spherical codebook can accurately sample and capture users at any different angles and distances in space, while ULA can only accurately sample and capture users on the same plane as the antenna array. For users on different planes, ULA can only capture their azimuth and distance values, but cannot obtain their elevation angle. Therefore, this demonstrates the superiority of the proposed scheme and the effectiveness of the spherical codebook, and also shows that UCA can provide more performance accuracy space in channel estimation.

[0206] like Figure 8 , Figure 9 and Figure 10 The figure shows the performance variation of different algorithms with varying pilot lengths over different distance ranges. Given the array aperture D = 2R = 0.82m and wavelength λ = 0.01m, the Rayleigh distance... therefore Figure 8 The user distribution is located at (5m, 15m), which falls under the category of near-field communication. Figure 9 The user distribution is located at (100m, 150m), which belongs to mixed field communication. Figure 10The user distribution is located at (160m, 200m), which falls under far-field communication. The proposed spherical S-SOMP algorithm is compared with existing orthogonal matching pursuit algorithms (OMP, lattice-top corner domain SOMP, off-network corner domain SIGW, polar-domain synchronous iterative orthogonal matching pursuit algorithm (P-SOMP), and the LS method. Furthermore, the Oracle LS method, assuming the actual receiving and scattering distances and angles are available, is compared as a performance bound for NMSE. As shown in the figure, regardless of whether the user is in near-field, mixed-field, or far-field communication, the performance of the S-SOMP algorithm improves with increasing time slot pilot overhead, and the curve's downward trend is steeper than other algorithms. This may indicate that it converges to a lower error value faster during iteration. However, under all conditions, the proposed algorithm outperforms other existing algorithms, demonstrating the superiority of the spherical codebook channel estimation scheme proposed in this patent, and also showing that the spherical codebook can provide more design space for improving system performance.

[0207] like Figure 11 , Figure 12 and Figure 13 The figure shows the performance changes of different algorithms with varying pilot lengths over different distance ranges. Figure 11 The users are distributed in (5m, 15m). Figure 12 The users are distributed in the range of (100m, 150m). Figure 13 The users are distributed in (160m, 200m). As can be seen from the figure, the NMSE of all algorithms decreases with the increase of the signal-to-noise ratio, but the proposed S-SOMP has a smaller NMSE than other algorithms under any communication conditions. The following conclusions are also drawn: (1) The performance of the S-SOMP algorithm is close to that of Oracle LS, which shows that in channel estimation, S-SOMP can achieve performance similar to the least squares algorithm under ideal conditions. This is very attractive in practical applications because Oracle LS is usually not feasible because it requires complete channel state information. (2) The performance of the S-SOMP algorithm is significantly better than that of the traditional LS algorithm, especially under low signal-to-noise ratio and high performance conditions. This shows that the S-SOMP algorithm is more effective in handling noise and can provide more accurate channel estimation. (3) The performance of the S-SOMP algorithm is better than that of the OMP and P-SOMP algorithms. This means that S-SOMP is more effective in spherical sampling and can better utilize the sparsity of the signal, thus maintaining a low error even under low signal-to-noise ratio. (4) The S-SOMP algorithm exhibits good robustness under varying signal-to-noise ratios, and its performance degrades more slowly than that of OMP and P-SOMP. This indicates that S-SOMP can provide relatively stable performance under different signal-to-noise ratio conditions. Therefore, this demonstrates the superiority of the S-SOMP algorithm proposed in this patent.

[0208] like Figure 14 As shown, regardless of near-field, mixed-field, or far-field, the S-SOMP algorithm proposed in this embodiment outperforms other algorithms in terms of NMSE performance. Due to the geometric symmetry of the UCA array and the very small sampling angle interval, it can sample the positions of all users in the plane. From formula (7b), it can be seen that the near-field beam steering vector phase... Since R = 0.41m and r > 5, therefore Therefore, the phase value mainly depends on the first part. It is evident that its value is only related to the array radius R, elevation angle θ, and azimuth angle φ, and has little to do with the user distance r. This also explains why NMSE does not fluctuate much with the change of distance. As can be seen from the figure, the S-SOMP algorithm based on the spherical codebook proposed in this embodiment fully considers the spatial elevation angle of all users, thus its performance is better than other existing algorithms. This demonstrates the feasibility of the UCA spherical codebook proposed in this patent and the effectiveness of the S-SOMP algorithm.

[0209] Example 3

[0210] This embodiment also provides a very large-scale MIMO channel estimation system based on a circular antenna array, used to implement the method described in Embodiment 1 or Embodiment 2, such as... Figure 15 As shown, it includes:

[0211] The data acquisition module acquires the received signal, analog combination matrix, user channel path, sparsity support set, residual set, and sphere codebook.

[0212] The traversal module begins a loop to traverse the channel path and calculates the support matrix based on the simulated combination matrix, the spherical codebook, and the residual set.

[0213] The support set update module obtains the new number of supports based on the support matrix and updates the sparse support set based on the new number of supports.

[0214] The channel matrix acquisition module performs orthogonal projection based on the received signal, the spherical codebook, and the analog combination matrix to obtain the sparse spherical channel matrix.

[0215] The residual set update module updates the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set.

[0216] The channel estimation module continues until all communication paths have been traversed, then breaks out of the loop to obtain the estimated channel.

[0217] The same or similar labels correspond to the same or similar parts;

[0218] The terms used to describe positional relationships in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0219] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for estimating the channel of a very large-scale MIMO based on a circular antenna array, characterized in that, include: Acquire the received signal, analog combination matrix, user channel path, sparse support set, residual set, and sphere codebook; Start the loop to traverse the channel path and calculate the support matrix based on the simulated combination matrix, the sphere codebook, and the residual set; Obtain the new support number based on the support matrix, and update the sparse support set based on the new support number; Orthogonal projection is performed based on the received signal, the spherical codebook, and the analog combination matrix to obtain the sparse channel matrix in the spherical domain. Update the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set; The loop continues until all communication paths have been traversed, at which point the loop is exited and the estimated channel is obtained.

2. The method for estimating the ultra-large-scale MIMO channel based on a circular antenna array according to claim 1, characterized in that, Retrieve the ball domain codebook, including: Obtain the minimum communication distance, distance column coherence threshold, number of antennas, antenna spacing, and wavelength; Select an elevation angle, and obtain the sampled value of the current elevation angle based on the number of antennas, the spacing between antennas, and the wavelength; Select an azimuth angle at the current elevation angle, and calculate the sampled value of the azimuth angle at the current elevation angle based on the range column coherence threshold, the number of antennas, the antenna spacing, and the wavelength. The distance sampling values ​​at the current elevation and azimuth angles are calculated based on the minimum communication distance, the distance column coherence threshold, the number of antennas, the antenna spacing and wavelength, and the corresponding wave speed steering vector set is generated based on the calculated distance sampling values. The process continues until all azimuth angles at the current elevation angle have been selected, and the initial codebook is obtained by integrating the corresponding wave speed steering vector sets. This continues until all elevation angles have been selected, and the sphere codebook is obtained based on the initial codebook.

3. The ultra-large-scale MIMO channel estimation method based on a circular antenna array according to claim 2, characterized in that, The formula for obtaining the sampled value of the current elevation angle based on the number of antennas, the spacing between antennas, and the wavelength is: in, The wavelength of the antenna; Zero point m The number of sampling points for the elevation angle.

4. The ultra-large-scale MIMO channel estimation method based on a circular antenna array according to claim 2, characterized in that, The formula for calculating the sampled value of the apex angle below the current elevation angle based on the range coherence threshold, the number of antennas, the antenna spacing, and the wavelength is as follows: in, Angle of elevation; The wavelength of the antenna; Zero point s for θ The number of sampling points for the azimuth angle below.

5. The method for estimating the ultra-large-scale MIMO channel based on a circular antenna array according to claim 2, characterized in that, The formula for calculating the distance sample values ​​at the current elevation and azimuth angles based on the minimum communication distance, range coherence threshold, number of antennas, antenna spacing, and wavelength is as follows: Where z is the sampling index; Z represents the minimum communication distance; Z is the number of sampling points at the minimum communication distance. The angle of elevation.

6. The method for estimating the ultra-large-scale MIMO channel based on a circular antenna array according to claim 1, characterized in that, The formula for calculating the support matrix based on the simulated combination matrix, the spherical codebook, and the residual set is as follows: in, For simulating the combination matrix; For the sphere codebook; It is a residual set.

7. The method for estimating the ultra-large-scale MIMO channel based on a circular antenna array according to claim 1, characterized in that, The formula for obtaining new support numbers based on the support matrix is: in, For support matrix; M For frequency numbers, p To support the number of episodes.

8. The method for estimating the ultra-large-scale MIMO channel based on a circular antenna array according to claim 1, characterized in that, The formula for obtaining the sparse channel matrix in the spherical domain by orthogonal projection based on the received signal, the spherical codebook, and the analog combination matrix is ​​as follows: in, To receive signals; For simulating the combination matrix; For the sphere codebook.

9. The method for estimating the ultra-large-scale MIMO channel based on a circular antenna array according to claim 1, characterized in that, The formula for updating the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set is as follows: in, It is a residual set; For simulating the combination matrix; For the sphere codebook; It is a sparse channel matrix in the spherical domain.

10. A very large-scale MIMO channel estimation system based on a circular antenna array, used to implement the method according to any one of claims 1-9, characterized in that, include: The data acquisition module acquires the received signal, analog combination matrix, user channel path, sparsity support set, residual set, and sphere codebook. The traversal module begins a loop to traverse the channel path and calculates the support matrix based on the simulated combination matrix, the spherical codebook, and the residual set. The support set update module obtains the new support number based on the support matrix and updates the sparse support set based on the new support number. The channel matrix acquisition module performs orthogonal projection based on the received signal, the spherical codebook, and the analog combination matrix to obtain the sparse spherical channel matrix. The residual set update module updates the residual set based on the spherical channel matrix, the analog combination matrix, the spherical codebook, and the residual set. The channel estimation module continues until all communication paths have been traversed, then breaks out of the loop to obtain the estimated channel.

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