Large-scale MIMO channel estimation method and system based on circular antenna array

Abstract

The invention discloses a circular antenna array-based maximum-scale MIMO (Multiple Input Multiple Output) channel estimation method and a circular antenna array-based maximum-scale MIMO channel estimation system, an uplink communication link of a time division duplex-based communication system is considered, users are randomly distributed in a three-dimensional space, and a hybrid precoding architecture is adopted. Different from a previous method which only considers a polar domain of a user plane angle and a distance to represent a near-field channel, the method also considers an elevation angle of a user, uses a ball domain codebook to represent the near-field channel, analyzes how to sample the elevation angle, an azimuth angle and the distance in a ball domain to reduce column coherence of a transformation matrix, and improves the accuracy of the near-field channel. In addition, a synchronous orthogonal matching pursuit algorithm based on a sphere domain codebook is provided, and finally, the effectiveness of the algorithm is verified under the condition of users distributed in any space.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and more specifically, to a very large-scale MIMO channel estimation method and system based on a circular antenna array. Background Art

[0002] With the development of science and technology, the ultra-large-scale MIMO (XL-MIMO) system has gradually become a research hotspot in wireless communications. 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 using beamforming and spatial multiplexing technologies. However, as the size of the antenna array increases, the limitations of the traditional far-field plane wave model in describing signal propagation become increasingly prominent, especially in the near-field communication environment, where the signal propagation characteristics are more consistent with the spherical wave model. Therefore, it is particularly important to develop new channel estimation algorithms to adapt to the channel characteristics under near-field conditions.

[0003] Uniform circular array (UCA) has significant advantages in beamforming and spatial processing due to its unique rotational symmetry. UCA can provide uniform beam patterns at different azimuth angles, which is suitable for achieving omnidirectional coverage and improving beamforming gain. Especially in near-field communications, UCA can better maintain the directionality of the beam and ensure accurate transmission and reception of signals. In addition, the uniformity of UCA enables it to reduce performance losses caused by the complexity of the signal propagation path when processing near-field signals.

[0004] However, UCA systems face multiple challenges in channel estimation. First, UCA requires channel estimation in three-dimensional space, which increases the complexity of the problem because it must consider both angle and distance information, especially in environments where users are unevenly distributed or dynamically changing. 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. In addition, the design of the three-dimensional codebook is also a difficult problem, which needs to effectively cover all users while maintaining low complexity.

[0005] In traditional channel models, it may not be possible to accurately describe the actual propagation environment of signals under complex user distribution conditions, especially under near-field conditions, where the spherical wave model of signal propagation is significantly different from the plane wave model of the far field. The limitations of UCA in angle and distance resolution will hinder its accurate estimation of user signals from different directions and distances. At the same time, if the complex multipath effects in near-field communications are not properly handled, it will lead to inaccurate signal delay and phase estimation, affecting signal detection and demodulation.

[0006] Therefore, in response to these challenges, the present invention aims to improve the accuracy and efficiency of channel estimation and ensure the quality of signal transmission under extreme climate conditions. By combining advanced signal processing technology and optimization algorithms, this method can effectively cope with the complexity of UCA system in channel estimation and improve the overall system performance. Summary of the invention

[0007] In order to overcome the defects of inaccurate signal delay and phase estimation in the prior art, the present invention provides a very large-scale MIMO channel estimation method and system based on a circular antenna array.

[0008] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0009] The present invention provides a very large-scale MIMO channel estimation method based on a circular antenna array, comprising:

[0010] Obtain received signals, simulated combination matrices, user channel paths, sparsity support sets, residual sets, and spherical codebooks;

[0011] Starting a loop to traverse the channel path, calculating a support matrix based on a simulated combination matrix, a spherical codebook and a residual set;

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

[0013] Perform orthogonal projection based on the received signal, the spherical codebook and the simulated combination matrix to obtain a spherical sparse channel matrix;

[0014] Update the residual set according to the spherical channel matrix, the simulated combination matrix, the spherical codebook and the residual set;

[0015] Until all communication paths are traversed, the loop is exited and the estimated channel is obtained.

[0016] Preferably, obtaining a spherical domain 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 a sample value of the current elevation angle according to the number of antennas, the spacing between antennas, and the wavelength;

[0019] Select an azimuth angle under the current elevation angle, and calculate the sampling value of the azimuth angle under the current elevation angle according to the range column coherence threshold, the number of antennas, the antenna spacing and the wavelength;

[0020] Calculate the distance sampling value at the current elevation angle and azimuth angle according to the minimum communication distance, the distance column coherence threshold, the number of antennas, the spacing between antennas and the wavelength, and generate a corresponding set of wave speed steering vectors based on the calculated distance sampling value;

[0021] Until all azimuth angles at the current elevation angle are selected, and the initial codebook is obtained by integrating the corresponding wave speed steering vector set;

[0022] This continues until all elevation angles are selected and a spherical codebook is obtained based on the initial codebook.

[0023] Preferably, the formula for obtaining the sampling value of the current elevation angle according to the number of antennas, the spacing between antennas and the wavelength is:

[0024]

[0025] Among them, λ is the wavelength of the antenna; α is the zero point; and m is the number of sampling points of the elevation angle.

[0026] Preferably, the formula for calculating the sampling value of the azimuth angle under the current elevation angle according to the distance column coherence threshold, the number of antennas, the spacing between antennas and the wavelength is:

[0027]

[0028] Among them, θ is the elevation angle; λ is the wavelength of the antenna; α is the zero point; and s is the number of sampling points of the azimuth angle under θ.

[0029] Preferably, the formula for calculating the distance sampling value at the current elevation angle and azimuth angle according to the minimum communication distance, the distance column coherence threshold, the number of antennas, the spacing between antennas and the wavelength is:

[0030]

[0031] Among them, z is the sampling index; r min 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:

[0033] T=(AW) H R

[0034] Among them, A is the simulation combination matrix; W is the spherical codebook; R is the residual set.

[0035] Preferably, the formula for obtaining a new support number according to the support matrix is:

[0036]

[0037] Among them, T is the support matrix; M is the frequency number; p is the number of support sets.

[0038] Preferably, orthogonal projection is performed based on the received signal, the spherical codebook and the simulated combination matrix to obtain the formula for the spherical sparse channel matrix:

[0039]

[0040] Wherein, 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 according to the spherical channel matrix, the simulated combination matrix, the spherical codebook and the residual set is:

[0042]

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

[0044] The present invention also provides an extremely large-scale MIMO channel estimation system based on a circular antenna array, which is used to implement the above method, and is characterized by comprising:

[0045] A data acquisition module acquires received signals, simulated combination matrices, user channel paths, sparsity support sets, residual sets, and spherical codebooks;

[0046] A traversal module starts a loop to traverse the channel path, and calculates a support matrix according to a simulation combination matrix, a spherical codebook and a residual set;

[0047] The support set update module obtains the new support number according to the support matrix and updates the sparse support set based on the new support number;

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

[0049] A residual set updating module, which updates the residual set according to the spherical channel matrix, the simulation combination matrix, the spherical codebook and the residual set;

[0050] The channel estimation module continues until all communication paths are traversed, then exits the loop and obtains the estimated channel.

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

[0052] The present invention considers the uplink communication link of a communication system based on time division duplex, in which users are randomly distributed in three-dimensional space and a hybrid precoding architecture is adopted. Different from the previous polar domain representation of near-field channels that only considers the user's plane angle and distance, the work done by the present invention also considers the user's elevation angle, uses a spherical codebook to represent the near-field channel, analyzes how to sample the elevation angle, azimuth angle and distance in the spherical domain to reduce the 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a flowchart of the extremely 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 extremely large-scale MIMO channel estimation system model based on the circular antenna array described in Example 2;

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

[0056] Figure 4 This is a flow chart of generating a spherical domain codebook as described in Embodiment 2;

[0057] Figure 5 Schematic diagram of the structure of the three-dimensional space codebook based on UCA described in Example 2;

[0058] Figure 6 Schematic diagram of performance comparison of UCA and ULA under different algorithms with signal-to-noise ratio in Example 2;

[0059] Figure 7 Schematic diagram of performance comparison of UCA and ULA under different algorithms with signal-to-noise ratio in Example 2;

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

[0061] Fig. 9 It is a schematic diagram of the performance of different algorithms under different pilot lengths described in Example 2;

[0062] Fig.10 It is a schematic diagram of the performance of different algorithms under different pilot lengths described in Example 2;

[0063] Fig.11 A schematic diagram of the variation of the communication calculation delay of the extremely large-scale MIMO channel estimation system based on the circular antenna array with each time slot described in Example 2;

[0064] Fig.12 A schematic diagram of the variation of the communication calculation delay of the extremely large-scale MIMO channel estimation system based on the circular antenna array with each time slot described in Example 2;

[0065] Fig.13 A schematic diagram of the variation of the communication calculation delay of the extremely large-scale MIMO channel estimation system based on the circular antenna array with each time slot described in Example 2;

[0066] Fig.14 Schematic diagram of the relationship between NMSE performance and user distance in Example 3;

[0067] Fig.15 This is a schematic diagram of the structure of the extremely large-scale MIMO channel estimation system based on the circular antenna array described in Example 3. DETAILED DESCRIPTION

[0068] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0069] In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product;

[0070] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0071] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0072] Example 1

[0073] This embodiment provides a very large-scale MIMO channel estimation method based on a circular antenna array, such as Figure 1 As shown, including:

[0074] Obtain received signals, simulated combination matrices, user channel paths, sparsity support sets, residual sets, and spherical codebooks;

[0075] Starting a loop to traverse the channel path, calculating a support matrix based on a simulated combination matrix, a spherical codebook and a residual set;

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

[0077] Perform orthogonal projection based on the received signal, the spherical codebook and the simulated combination matrix to obtain a spherical sparse channel matrix;

[0078] Update the residual set according to the spherical channel matrix, the simulated combination matrix, the spherical codebook and the residual set;

[0079] Until all communication paths are traversed, the loop is exited and the estimated channel is obtained.

[0080] This embodiment considers the uplink communication link of a communication system based on time division duplex, in which users are randomly distributed in three-dimensional space and a hybrid precoding architecture is adopted. Different from the previous polar domain representation of near-field channels that only considers the user's plane angle and distance, this embodiment also considers the user's elevation angle, uses a spherical codebook to represent the near-field channel, analyzes how to sample the elevation angle, azimuth angle and distance in the spherical domain to reduce the 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 very large-scale MIMO channel estimation method based on a circular antenna array, including:

[0083] Obtain received signals, simulated combination matrices, user channel paths, sparsity support sets, residual sets, and spherical codebooks;

[0084] Starting a loop to traverse the channel path, calculating a support matrix based on a simulated combination matrix, a spherical codebook and a residual set;

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

[0086] Perform orthogonal projection based on the received signal, the spherical codebook and the simulated combination matrix to obtain a spherical sparse channel matrix;

[0087] Update the residual set according to the spherical channel matrix, the simulated combination matrix, the spherical codebook and the residual set;

[0088] Until all communication paths are traversed, the loop is exited and the estimated channel is obtained.

[0089] Get the spherical 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 a sample value of the current elevation angle according to the number of antennas, the spacing between antennas, and the wavelength;

[0092] Select an azimuth angle under the current elevation angle, and calculate the sampling value of the azimuth angle under the current elevation angle according to the range column coherence threshold, the number of antennas, the antenna spacing and the wavelength;

[0093] Calculate the distance sampling value at the current elevation angle and azimuth angle according to the minimum communication distance, the distance column coherence threshold, the number of antennas, the spacing between antennas and the wavelength, and generate a corresponding set of wave speed steering vectors based on the calculated distance sampling value;

[0094] Until all azimuth angles at the current elevation angle are selected, and the initial codebook is obtained by integrating the corresponding wave speed steering vector set;

[0095] This continues until all elevation angles are selected and a spherical codebook is obtained based on the initial codebook.

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

[0097]

[0098] Among them, λ is the wavelength of the antenna; α is the zero point, and m is the number of sampling points of the elevation angle.

[0099] The formula for calculating the sampling value of the azimuth angle under the current elevation angle based on the distance column coherence threshold, the number of antennas, the antenna spacing and the wavelength is:

[0100]

[0101] Among them, θ is the elevation angle; λ is the wavelength of the antenna; α is the zero point, and s is the number of sampling points of the azimuth angle under θ.

[0102] The formula for calculating the distance sampling value at the current elevation angle and azimuth angle based on the minimum communication distance, distance column coherence threshold, number of antennas, antenna spacing and wavelength is:

[0103]

[0104] Among them, z is the sampling index; r min 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, spherical codebook and residual set is:

[0106] T=(AW) H R

[0107] Among them, A is the simulation combination matrix; W is the spherical codebook; R is the residual set.

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

[0109]

[0110] Among them, T is the support matrix; M is the frequency number, and p is the number of support sets.

[0111] Based on the orthogonal projection of the received signal, the spherical codebook and the simulated combination matrix, the formula for obtaining the spherical sparse channel matrix is:

[0112]

[0113] Wherein, 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 according to the spherical channel matrix, the analog combination matrix, the spherical codebook and the residual set is:

[0115]

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

[0117] In a specific embodiment, Figure 1 The figure 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 is the carrier wavelength. K single-antenna users are served by M subcarriers at the same time, where K≤N RF For uplink channel estimation, it is assumed that K users send mutually orthogonal pilot sequences to the BS, that is, different users use orthogonal time or frequency resources to send pilot sequences. Therefore, the channel estimation of each user is independent. Without loss of generality, consider an arbitrary user. The position of the antenna can be expressed in spherical coordinates as in n=(0,1,…,N-1), converted into Cartesian coordinates as The position of the kth user can be expressed 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 subsequent discussion for easier viewing. That is, the propagation distance from user k to the nth antenna is:

[0118]

[0119] where (a) is approximated by the second-order Taylor formula It is worth noting that this approximation is valid for most near field communication systems.m,p is represented as the transmitted pilot at the mth subcarrier in time slot p. Then the received pilot for:

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

[0121] in, represents the simulation combination matrix and satisfies It means that the mean is 0 and the variance is σ 2 I N Gaussian white noise. m represents the wireless channel. By defining the pilot length as P, then p = 1, 2, ..., P, assuming x m,p =1, the pilot sequence y received at the mth subcarrier m =[y m,1 ,…,y m,P ] T It can be expressed as

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

[0123] in, represents noise, Represents the overall observation simulation matrix, where each element in A is independent, given by 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, is the wave number, c is the speed of light, g is l ,r l ,θ l ,φ l They represent the complex path gain, distance, elevation angle and azimuth angle of the lth path respectively. l ,φ l ) is given by θ l ∈(0,π) and φ l The plane wave assumption of ∈(0,2π) is derived and expressed as:

[0126]

[0127] However, due to the significantly increased array aperture of ELAA, the near-field area is greatly expanded, and the user is likely to be located in the near-field area, so the spherical wave propagation model must be used. Therefore, the far-field beam steering vector based on the plane wave propagation model cannot characterize the spherical wave propagation in the ELAA system. In order to solve the mismatch problem of the propagation model, a more accurate UCA near-field beam steering vector can be used, which is expressed as:

[0128]

[0129]

[0130] Where (b) is obtained by substituting the second-order Taylor expansion in 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 space plane, that is, φ l =φ 0 is a constant value and will not change with the path. m It can be regarded as a weighted sum of the finite near-field steering vectors b(r,θ), and the channel It can be transformed into its polar domain representation through the polar domain transformation matrix Right now:

[0133]

[0134] in W represents the polar domain sampling codebook, and Q represents the number of near-field steering vectors sampled in the polar domain. P Contains Q steering vectors with uniform angle sampling and non-uniform distance sampling, and in the polar domain It is usually sparse. Taking advantage of this channel sparsity, some channel estimation algorithms based on compressed sensing (CS) are proposed to effectively recover P with low pilot overhead.

[0135] 2.2 Near-field spherical codebook establishment

[0136] As shown in formula (8), the number of channel paths in the near field is still limited, that is, L<<N. This shows that the number of channel parameters that need to be estimated is still limited, so the near-field channel in three-dimensional space is also compressible. In order 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 the weighted sum of the finite near-field steering vectors b(r,θ,φ), where b(r,θ,φ) is not only related 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 design of , a new transformation matrix W is proposed, which consists 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 distance domain and angular domain. In this way, w makes full use of all the elevation, azimuth, and distance information of the near-field path components. Since the elevation, azimuth, and distance represent coordinates in a spherical coordinate system, the spatial angular distance domain is called the spherical domain. Therefore, the matrix W is called the spherical domain transformation matrix.

[0137] With polar domain representation Similarly, the proposed near-field channel 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 domain transformation matrix W can simultaneously consider the elevation angle, azimuth angle and distance information of the near-field path component. Therefore, the matrix W is used to make 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 the matrix W samples two different angles and distances at the same time, it is not assumed that the number of sampling vectors U is equal to N. In general, U>>N.

[0140] After the CS framework is determined, in order to achieve the channel recovery accuracy requirement, sampling is performed at different distances, elevation angles, and azimuth angles. The column coherence of the codebook 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 When , the Fresnel approximation (a) in formula (1) is accurate, and this distance is much lower than the Rayleigh distance Where D represents the array aperture. For example, if the array aperture D is 0.82m, the wavelength λ c is 1cm, the Rayleigh distance is 134.5m, and This is negligible. Therefore, the column coherence f(r 1 ,r 2 ,θ 1 ,θ 2 ,φ 1 ,φ 2 ) can be approximated as

[0141]

[0142] It is still difficult to directly obtain the distance and angle sampling method from equation (11), but the phase can be decoupled into two parts. The first term It is only related to the angle, the second term Based on this observation, 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 Elevation Angle Sampling Method

[0144] Since the coherence between column vectors needs to be guaranteed, the angular resolution is used as the standard for the sampling interval. 1 ≠θ 2 ) has a column vector correlation of 0, which meets the sampling requirements. To obtain the elevation angle that satisfies the minimum coherence, assume r 1 =r 2 ,φ 1 =φ 2 .

[0145] Lemma 1: According to the properties of the near-field beam focusing gain, the near-field beamforming vector b(r,θ 1 ,φ) at position (r,θ 2 The beamforming gain obtained at ,φ) can be shown to be similar to the far-field beamforming gain, that is:

[0146]

[0147] In the formula, J 0 (·) is the first kind of zero-order Bessel function, Δθ=sinθ 1 -sinθ 2 .

[0148] The proof process is as follows:

[0149]

[0150] Where approximation (a) is obtained by keeping only the first order of the Taylor series expansion, and (b) is obtained by setting Δθ = sinθ 1 -sinθ 2 Then we use the properties of Bessel functions:

[0151]

[0152] Where J m (·) is the first-kind m-order Bessel function, and the beamforming gain can be rewritten as:

[0153]

[0154] Then, by summing the geometric series over n, we can derive a piecewise function:

[0155]

[0156] Then according to the asymptotic properties of Bessel function:

[0157]

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

[0159]

[0160] The above proof is complete. It can be seen that the angular resolution of θ is related to |J 0 (x)| has a direct relationship, such as Figure 3 As shown, it is |J 0 (x)|, by setting |J 0 (α)|=0 gives the first zero point α≈2.4, then Right now Therefore, the elevation sampling and the existing polar domain transformation matrix W P The sampling method is the same, which is uniform sampling, that is:

[0161]

[0162]

[0163] 2.2.2 Azimuth sampling method

[0164] Similar to the elevation sampling method, the azimuth angle resolution is also used as the sampling interval, that is, assuming r 1 =r 2 ,θ 1 =θ 2 , from Lemma 1 we can get:

[0165]

[0166] Where (a) is the product formula of sum and difference of trigonometric functions We get (b) through the trigonometric transformation formula Get, (c) is through shilling Then substitute the Bessel function properties into formula (14) to obtain (d), which is similar to formula (18). When N is very large, the function is not equal to 0 only when m = 0, so m = 0 is taken as the approximation.

[0167] It can be seen that the angular resolution of φ varies with the change of θ, but the overall resolution is also affected by |J 0 (x)| function constraints, let |J 0 (α)|=0, we get The angular resolution So the sampling point interval of azimuth is:

[0168]

[0169] So the sampling points of the azimuth are:

[0170]

[0171] 2.2.3 Distance sampling method

[0172] Similar to the angle sampling method, since the distance information is only contained in the quadratic term Therefore, we will focus on this part and deduce the distance sampling method, that is, φ = φ 1 =φ 2 ,θ=θ 1 =θ 2 , so the first phase of formula (11) is removed, in which case the column coherence is only related to the phase of the second quadratic term. It is dependent on the item Its physical meaning is to sample two positions at the same elevation angle θ and azimuth angle φ. The column coherence is given by Determine, on this basis, the distance sampling method can be obtained. Therefore, the column coherence at the same angle can be approximated as:

[0173]

[0174] In the formula, (a) is obtained by substituting the double angle formula into the trigonometric function Simplify, and then propose quadratic terms that are independent of n, (b) is to eliminate the terms that are independent of the sum of n, (c) is to introduce the properties of Bessel functions Then the terms related to the n summation are separated and summed separately. (d) is similar to formula (16), only m = N·t, hour, In other cases, s is taken as 0, and then the asymptotic property of the Bessel function is substituted into formula (17). Since N is large, an approximate approximation can be obtained by taking s=0.

[0175] Formula (24) shows that the column coherence of distance depends largely on the function |J 0 (x)| and parameter θ. Given by Figure 2 It can be seen that |J 0 The (x)| function shows a clear downward trend in the range (0,2). Therefore, in order to minimize the coherence, let |J 0(β)|≤Δ, Δ represents the expected threshold. For example, Δ=0.5,|J 0 (β Δ )|≈1.6, then β≥β Δ =1.6, therefore, the sampling distance r 1 and r 2 The following conditions should be met:

[0176]

[0177]

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

[0179]

[0180] In the formula, z is the sampling index, represents the number of sampling points at the minimum communication distance. z = 0 represents the beamforming vector with energy focused on infinity, where the near-field beamforming vector degenerates into the far-field beamforming vector. Therefore, the far-field ULA codebook can be regarded as a special case of the proposed near-field spherical codebook and is included in the proposed near-field codebook. When mixed-field communication occurs, that is, the user has a mixed near-field or far-field channel, the proposed codebook can still work by assigning near-field (far-field) beams to near-field (far-field) users.

[0181] According to the above sampling method, the spherical codebook design scheme of UCA can be obtained, such as Figure 4 As shown, the specific algorithm 1 is:

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

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

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

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

[0186] (5) Generate codebook steering vector:

[0187] (6) Jump out of the first layer loop and get the codebook:

[0188] (7) Jump out of the second layer loop and get the codebook:

[0189] 2.4 Channel Estimation Based on UCA Spherical Codebook

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

[0191]

[0192] Due to the spherical channel discussed above is sparse, so spherical channel estimation can be expressed 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 Under this condition, the sparsity support of the polar domain channel is also the same, and the estimation can be performed simultaneously to improve the estimation accuracy. Therefore, the signal can be rearranged as:

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

[0194] In the formula, Y=[y 1 ,y 2 ,…,y M ], n=[n 1 ,n 2 ,…,n M ], since the channel WH is estimated from the known Y and AW S , and H S Since it is sparse, the channel estimation problem can be solved by the existing polar domain synchronous orthogonal matching pursuit (P-SOMP) grid-based near-field channel estimation algorithm, 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 loop channel path number

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

[0198] (4) Find the new support number. The row vector of the correlation matrix takes the row with the largest square modulus absolute value:

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

[0200] (6) Orthogonal projection obtains the spherical sparse channel matrix:

[0201] (7) Update the residual matrix:

[0202] (8) Know that all channel path information has been collected and exit the loop

[0203] (9) Get the estimated channel:

[0204] like Figure 5 As shown in the figure, when the number of antennas is 512, the carrier frequency is 30 GHz, and the antenna spacing is half a wavelength, the three-dimensional codebook generated based on Algorithm 1 can sample all users in the space, where the blue ring represents the set of sampling points. and elevation sampling spacing is very small, so the distance between adjacent sampling points on the ring is very small. Therefore, the subsequent channel estimation only needs to fine-tune the distance domain, which can reduce the overall algorithm complexity and overhead.

[0205] like Figure 6 and Figure 7 As shown in Figure 1, the performance analysis of ULA and UCA with the same array aperture and the same number of antennas with the signal-to-noise ratio (SNR) is shown in Figure 2. Figure 6 As shown in Figure 1, it is a performance analysis diagram of ULA and UCA with the same antenna array aperture. Figure 7As shown in the figure, it is a performance analysis diagram of ULA and UCA with the same number of antennas. The SOMP algorithm is a far-field sampling algorithm that only considers angles, and S-SOMP is a near-field sampling algorithm that considers angles and distances. From the figure, the following conclusions can be drawn: (1) As the number of antennas increases, the performance of ULA decreases, and when the number of antennas is the same as that of UCA, the performance of the two is the same under the SOMP algorithm. The reason is that the sampling angles of the two are directly related to the number of antennas, and both are equally spaced. (2) For the near-field sampling algorithm S-SOMP, the performance of UCA is far better than that of ULA. The main reason is that the proposed UCA spherical codebook can accurately sample and capture users at any angle and distance in space, while ULA can only accurately sample and capture users in the same plane as the antenna array. For users in different planes, ULA can only capture their azimuth and distance values, and cannot obtain their elevation angles. Therefore, it illustrates the excellence of the solution proposed in this patent 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 , Fig. 9 and Fig.10 As shown in the figure, the performance of different algorithms changes with the change of pilot length in different distance ranges. Since the array aperture D = 2R = 0.82m and the wavelength λ = 0.01m, the Rayleigh distance therefore Figure 8 The users are distributed in (5m, 15m) which belongs to near field communication. Fig. 9 The users are distributed in (100m, 150m) and belong to mixed field communication. Fig.10 The users are distributed at (160m, 200m) which belongs to far-field communication. The spherical domain S-SOMP algorithm proposed in this paper is compared with the existing orthogonal matching pursuit algorithm OMP, grid angular domain SOMP algorithm, off-grid angular domain SIGW algorithm, polar domain synchronous iterative orthogonal matching pursuit algorithm P-SOMP and LS method. In addition, the Oracle LS method assuming the real distance and angle of reception and scattering is available as the NMSE performance limit is also compared. As can be seen from the figure, regardless of whether the user is located in the near field, mixed field or far-field communication, with the increase of the time slot pilot overhead, the performance of the S-SOMP algorithm is getting better and better, and the downward trend of the curve is steeper than that of other algorithms, which may mean that it can converge to a lower error value faster during the iteration process. However, no matter what the conditions are, the proposed algorithm is better than other existing algorithms, which shows the excellence of the spherical codebook channel estimation scheme proposed in this patent, and also shows that the spherical codebook can provide more design space for improving system performance.

[0207] like Fig.11 , Fig.12 and Fig.13As shown in Figure 2, the performance of different algorithms varies with the pilot length at different distance ranges. Fig.11 The users are distributed in (5m, 15m), Fig.12 The users are distributed in (100m, 150m), Fig.13 The users are distributed at (160m, 200m). As can be seen from the figure, the NMSE of all algorithms shows a downward trend with the increase of SNR, but the proposed S-SOMP has a smaller NMSE index than other algorithms regardless of the 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 close to that of 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 in the case of low SNR. 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, thereby maintaining a low error even at a low SNR. (4) The S-SOMP algorithm shows good robustness when the signal-to-noise ratio changes, and its performance decreases slower than that of OMP and P-SOMP. This shows that S-SOMP can provide relatively stable performance under different signal-to-noise ratio conditions. Therefore, the excellence of the S-SOMP algorithm proposed in this patent is demonstrated.

[0208] like Fig.14 As shown in Figure 7, the S-SOMP algorithm proposed in this embodiment is superior to other algorithms in terms of NMSE performance, regardless of the near field, mixed field or far field. Due to the geometric symmetry of the UCA array and the very small sampling angle interval, the positions of all users in the plane can be sampled. As can be seen from formula (7b), the near-field beam steering vector phase Since R=0.41m,r>5, So the phase value mainly depends on the first part It can be clearly seen that its value is only related to the array radius R, the elevation angle θ, and the azimuth angle φ, and has no great relationship with the user distance r. This also explains why NMSE does not fluctuate much with the change of distance. It can also be seen from the figure that the S-SOMP algorithm based on the spherical codebook proposed in this embodiment fully considers the spatial elevation angles of all users, so that the performance is also better than other existing algorithms, which illustrates 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, which is used to implement the method described in Embodiment 1 or Embodiment 2, such as Fig.15 As shown, including:

[0211] A data acquisition module acquires received signals, simulated combination matrices, user channel paths, sparsity support sets, residual sets, and spherical codebooks;

[0212] A traversal module starts a loop to traverse the channel path, and calculates a support matrix according to a simulation combination matrix, a spherical codebook and a residual set;

[0213] The support set update module obtains the new support number according to the support matrix and updates the sparse support set based on the new support number;

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

[0215] A residual set updating module, which updates the residual set according to the spherical channel matrix, the simulation combination matrix, the spherical codebook and the residual set;

[0216] The channel estimation module continues until all communication paths are traversed, then exits the loop and obtains the estimated channel.

[0217] The same or similar reference numerals correspond to the same or similar components;

[0218] The terms used in the drawings to describe positional relationships are only used for illustrative purposes 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 embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A very large-scale MIMO channel estimation method based on a circular antenna array, characterized in that: include: Obtain received signals, simulated combination matrices, user channel paths, sparsity support sets, residual sets, and spherical codebooks; Starting a loop to traverse the channel path, calculating a support matrix based on a simulated combination matrix, a spherical codebook and a residual set; Obtain new support numbers according to the support matrix, and update the sparsity support set based on the new support numbers; Perform orthogonal projection based on the received signal, the spherical codebook and the simulated combination matrix to obtain a spherical sparse channel matrix; Update the residual set according to the spherical channel matrix, the simulated combination matrix, the spherical codebook and the residual set; Until all communication paths are traversed, the loop is exited and the estimated channel is obtained.

2. The extremely large-scale MIMO channel estimation method based on circular antenna array according to claim 1, characterized in that: Get the spherical codebook, including: Obtain the minimum communication distance, distance column coherence threshold, number of antennas, antenna spacing and wavelength; Select an elevation angle and obtain a sample value of the current elevation angle according to the number of antennas, the spacing between antennas, and the wavelength; Select an azimuth angle under the current elevation angle, and calculate the sampling value of the azimuth angle under the current elevation angle according to the range column coherence threshold, the number of antennas, the antenna spacing and the wavelength; Calculate the distance sampling value at the current elevation angle and azimuth angle according to the minimum communication distance, the distance column coherence threshold, the number of antennas, the spacing between antennas and the wavelength, and generate a corresponding set of wave speed steering vectors based on the calculated distance sampling value; Until all azimuth angles at the current elevation angle are selected, and the initial codebook is obtained by integrating the corresponding wave speed steering vector set; This continues until all elevation angles are selected and a spherical codebook is obtained based on the initial codebook.

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

4. The extremely large-scale MIMO channel estimation method based on circular antenna array according to claim 2, characterized in that: The formula for calculating the sampling value of the azimuth angle under the current elevation angle based on the distance column coherence threshold, the number of antennas, the antenna spacing and the wavelength is: Among them, θ is the elevation angle; λ is the wavelength of the antenna; α is the zero point, and s is the number of sampling points of the azimuth angle under θ.

5. The extremely large-scale MIMO channel estimation method based on circular antenna array according to claim 2, characterized in that: The formula for calculating the distance sampling value at the current elevation angle and azimuth angle based on the minimum communication distance, distance column coherence threshold, number of antennas, antenna spacing and wavelength is: Among them, z is the sampling index; r min is the minimum communication distance; Z is the number of sampling points at the minimum communication distance; θ is the elevation angle.

6. The extremely large-scale MIMO channel estimation method based on circular antenna array according to claim 1, characterized in that: The formula for calculating the support matrix based on the simulated combination matrix, spherical codebook and residual set is: T=(AW) H R Among them, A is the simulation combination matrix; w is the spherical codebook; R is the residual set.

7. The extremely large-scale MIMO channel estimation method based on circular antenna array according to claim 1, characterized in that: The formula for obtaining the new support number based on the support matrix is: Among them, T is the support matrix; M is the frequency number, and p is the number of support sets.

8. The extremely large-scale MIMO channel estimation method based on circular antenna array according to claim 1, characterized in that: Based on the orthogonal projection of the received signal, the spherical codebook and the simulated combination matrix, the formula for obtaining the spherical sparse channel matrix is: Wherein, Y is the received signal; A is the analog combination matrix; and W is the spherical codebook.

9. The extremely large-scale MIMO channel estimation method based on circular antenna array according to claim 1, characterized in that: The formula for updating the residual set according to the spherical channel matrix, the analog combination matrix, the spherical codebook and the residual set is: Where R is the residual set; A is the simulated combination matrix; W is the spherical codebook; is the spherical sparse channel matrix.

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 to 9, characterized in that: include: A data acquisition module acquires received signals, simulated combination matrices, user channel paths, sparsity support sets, residual sets, and spherical codebooks; A traversal module starts a loop to traverse the channel path, and calculates a support matrix according to a simulation combination matrix, a spherical codebook and a residual set; The support set update module obtains the new support number according to 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 simulated combination matrix to obtain a spherical sparse channel matrix; A residual set updating module, which updates the residual set according to the spherical channel matrix, the simulation combination matrix, the spherical codebook and the residual set; The channel estimation module continues until all communication paths are traversed, then exits the loop and obtains the estimated channel.

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