A multi-terminal near-field communication method based on non-uniform antenna array

Abstract

The present invention relates to a multi-terminal near-field communication method based on a non-uniform antenna array. First, based on the construction of a near-field communication signal model between a base station and each terminal, the optimal position of each antenna in the base station is solved with the goal of maximizing the near-field communication and rate of multiple terminals. Then, an algorithm based on orthogonal matching pursuit and iterative super-resolution estimation is used to estimate channel parameters and calculate the channel estimation vector between each terminal and the base station. Finally, based on the channel estimation vector between each terminal and the base station, a digital precoding matrix at the base station is constructed to eliminate multi-terminal interference. The overall scheme design effectively improves the near-field communication and rate of multiple terminals.

Description

Technical Field

[0001] The present invention relates to a multi-terminal near-field communication method based on a non-uniform antenna array, and belongs to the technical field of non-uniform antenna arrays. Background Art

[0002] The next generation of wireless communications is expected to enhance the user experience and support diverse application scenarios. This has placed higher demands on transmission speeds and network connectivity, and has spawned a host of new technologies. Near-field communication (NFC) has garnered significant attention due to its potential to improve spatial resolution, communication capacity, and transmission security.

[0003] Based on the antenna aperture and propagation distance, the radiation area of ​​electromagnetic waves can be divided into the far field, the radiating near field, and the inductive near field. The far-field electromagnetic waves exhibit a planar waveform, while as the transmission distance decreases, the electromagnetic waves in the radiating near field exhibit a spherical waveform with different phase differences between antennas, while the amplitude of the electromagnetic waves in the inductive near field varies between antennas.

[0004] By utilizing the characteristics of electromagnetic waves in the near field, communication performance can be improved. Reference 1 (Z. Wu and L. Dai, "Multiple Access for Near-Field Communications: SDMA or LDMA?" in IEEE Journal on Selected Areas in Communications, vol. 41, no. 6, pp. 1918-1935, June 2023) utilizes the improvement of spatial resolution in near-field multi-terminal communications to provide services to terminals located at the same distance but at different angles. Reference 2 (A. Chen, L. Chen, Y. Chen, C. You, G. Wei and FR Yu,"Cramér-Rao Bounds of Near-Field Positioning Based on Electromagnetic Propagation Model," in IEEE Transactions on Vehicular Technology, vol. 72, no. 11, pp. 13808-13825, Nov. 2023.) utilizes the characteristics of near-field electromagnetic waves as spherical waves and realizes near-field target perception and positioning based on the channel steering vector that depends on angle and distance. Reference 3 (Z. Zhang, Y. Liu, Z. Wang, X. Mu and J. Chen, "Physical Layer Security in Near-Field Communications," in IEEE Transactions on Vehicular Technology, pp. 1–6, 2024.) uses near-field beamforming to improve physical layer security. The base station uses near-field beamforming to provide high beamforming gain and suppressed beamforming gain to the target terminal and malicious terminal located at the same angle but at different distances.

[0005] Near-field communication relies on large antenna apertures to ensure the spherical shape of electromagnetic waves. The above-mentioned literature mainly uses ultra-large-scale multiple-input multiple-output arrays, that is, compared with traditional large-scale multiple-input multiple-output arrays, more antennas are adopted. However, the design greatly increases the hardware cost, and the spacing between array elements cannot be flexibly adjusted, which greatly limits the design freedom. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a multi-terminal near-field communication method based on a non-uniform antenna array, which can effectively improve the near-field communication speed of the multi-terminal.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solution: The present invention designs a multi-terminal near-field communication method based on a non-uniform antenna array, comprising the following steps:

[0008] Step A. Based on each terminal within the near-field communication range transmitting an orthogonal pilot signal via a wireless channel to a base station equipped with a non-uniform antenna array, a channel vector is constructed between each terminal and the base station based on the multipath path between each terminal and the base station, and a near-field communication signal model is constructed between the base station and each terminal, and then the process proceeds to step B.

[0009] Step B: Based on the channel vectors between each terminal and the base station, with the goal of maximizing multi-terminal near-field communication and rate, the optimal position of each antenna in the base station is solved.

[0010] As a preferred technical solution of the present invention: it also includes the following steps C to D, after executing step B, proceed to step C;

[0011] Step C. Based on the optimized positions of the antennas in the base station, a two-dimensional sparse model of the equivalent distance domain and angle domain between the base station and the terminal is constructed. An algorithm based on orthogonal matching pursuit and iterative super-resolution estimation is used to estimate the channel parameters and calculate the channel estimation vector between each terminal and the base station.

[0012] Step D: constructing a digital precoding matrix at the base station according to the channel estimation vectors between each terminal and the base station.

[0013] The multi-terminal near-field communication method based on a non-uniform antenna array described in the present invention has the following technical effects compared with the prior art by using the above technical solution:

[0014] (1) The present invention designs a multi-terminal near-field communication method based on a non-uniform antenna array. First, based on the construction of a near-field communication signal model between a base station and each terminal, the optimal position of each antenna in the base station is solved with the goal of maximizing the near-field communication and rate of multiple terminals. Then, an algorithm based on orthogonal matching pursuit and iterative super-resolution estimation is used to estimate the channel parameters, and the channel estimation vector between each terminal and the base station is calculated. Finally, according to the channel estimation vector between each terminal and the base station, a digital precoding matrix at the base station end is constructed to eliminate multi-terminal interference. The overall scheme design can effectively improve the near-field communication and rate of multiple terminals. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a schematic diagram of an application of a multi-terminal near-field communication method based on a non-uniform antenna array designed by the present invention;

[0016] Figure 21. This is a comparison chart of the normalized mean square error of channel estimation between the channel estimation method designed in an embodiment of the present invention and different channel estimation methods;

[0017] Figure 3 This is a comparison diagram of multi-user sum rates between a non-uniform array designed in an embodiment of the present invention and different arrays at different signal-to-noise ratios;

[0018] Figure 4 This is a comparison diagram of multi-user sum rates between a non-uniform array designed in an embodiment of the present invention and different arrays under different numbers of users. DETAILED DESCRIPTION

[0019] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0020] The present invention designs a multi-terminal near-field communication method based on a non-uniform antenna array. In the process of implementing near-field communication, Figure 1 As shown, it is used to improve the near-field communication and speed of multiple terminals. In actual application, the specific design executes the following steps A to D.

[0021] Step A: Based on each terminal within the near-field communication range sending an orthogonal pilot signal via a wireless channel to a base station equipped with a non-uniform antenna array, a channel vector is constructed between each terminal and the base station based on the multipath path between each terminal and the base station, and a near-field communication signal model is constructed between the base station and each terminal, and then the process proceeds to step B. Each antenna in the base station is connected to a radio frequency link.

[0022] In actual application, the above step A is specifically designed to execute the following steps A1 to A4.

[0023] Step A1. Based on the terminal sending an orthogonal pilot signal to the base station via a wireless channel, for each multipath path between each terminal and the base station, a channel vector between each terminal and the base station is constructed as follows:

[0024]

[0025] Among them, 1≤k≤K, K represents the number of terminals within the near field communication range, h k represents the channel vector between the kth terminal and the base station, 1≤l k ≤L k , L k represents the number of multipath paths between the kth terminal and the base station, represents the lth connection between the kth terminal and the base station k The gain of the multipath, x=[x1,…,x n ,…,x N ], N represents the number of antennas in the base station, xn It represents the coordinate value of the nth antenna arranged along the X-axis in the coordinate system of the base station. x represents the arrangement vector of each antenna in the base station. represents the lth connection between the kth terminal and the base station k The distance of the multipath, Indicates the kth terminal to the lth base station k The multipath departure angles, represents the lth connection between the kth terminal and the base station k The transmit channel steering vector of the multipath path, [·] n represents the nth element in the vector, j represents an imaginary number, represents the distance between the nth antenna in the base station and the kth terminal, and λ represents the wavelength.

[0026] Step A2. Based on the law of cosines, The relationship between the three According to Taylor expansion, the relationship between the three is simplified to And based on the definition of equivalent angle and the equivalent distance Substitute the same amount into the transmission channel steering vector to obtain when When and build The corresponding probability density function

[0027] when As it approaches infinity, the equivalent distance tends to 0; when is equal to 0, and When it is the minimum distance for near field communication, the equivalent distance Reaching the maximum value b max ,but and build The corresponding probability density function In applications, the minimum distance for near field communication is the Fresnel distance, that is,

[0028] Step A3. Construct a near-field communication signal model between the base station and each terminal, that is, the received signal matrix y obtained by the base station is as follows:

[0029]

[0030] Among them, s k represents the orthogonal pilot signal sent by the kth terminal to the base station, (·) HIndicates transposition, g indicates that the mean is 0 and the variance is the preset σ 2 The channel additive white Gaussian noise vector.

[0031] Step A4. The base station performs an inner product on the received signal matrix y and the orthogonal pilot signals sk sent by each terminal according to the following formula:

[0032] y k =y·S k =h k z k +η k

[0033] Get the measurement vector y corresponding to each terminal in the received signal matrix y k , where y k represents the measurement vector of the kth terminal in the received signal matrix y, z k Indicates that the kth terminal sends an orthogonal pilot signal s k The pilot gain, η k Indicates that the orthogonal pilot signal s is sent to the kth terminal k The equivalent noise.

[0034] Step B. Based on the channel vectors between each terminal and the base station, with the goal of maximizing multi-terminal near-field communication and rate, the optimal position of each antenna in the base station is solved, and then step C is entered.

[0035] In actual application, the above step B is specifically designed to execute the following steps B1 to B6.

[0036] Step B1. Construct multi-terminal near-field communication and rate R sum as follows:

[0037]

[0038] in, Γ k represents the signal-to-interference-and-noise ratio of the kth terminal, 1≤i≤K, f i represents the beamforming vector of the base station for the i-th terminal, f k represents the beamforming vector of the base station for the kth terminal, that is, update

[0039] Step B2. Based on the layout of each antenna along the X-axis of the base station's coordinate system, with the midpoint of the distribution length of each antenna layout as the origin of the coordinate system, and with the goal of maximizing multi-terminal near-field communication and rate, the optimization problem of the antenna position arrangement in the base station is constructed as follows:

[0040]

[0041] stx n ≥-D / 2,x n ≤D / 2

[0042] x m -x m-1 ≥λ / 2

[0043] n=1,…,N

[0044] m=2,…,N

[0045] Objective function Indicates taking R sum where D represents the distribution length of each antenna along the X-axis in the coordinate system of the base station.

[0046] Step B3. Update the objective function of the optimization problem according to Jensen inequality as follows:

[0047]

[0048] Then the objective function of the optimization problem is transformed into And according to Then the objective function of the updated optimization problem is converted to

[0049] Step B4. Based on the channel vector h between each terminal and the base station k , then the objective function of the updated optimization problem is transformed as follows:

[0050]

[0051] Where 1≤l i ≤L i , L i Represents the number of multipath paths between the i-th terminal and the base station.

[0052] Step B5. Based on the definition of equivalent distance difference and the equivalent angle difference Substitute into the probability density function Probability density function Constructing equivalent distance difference The probability density function of and the equivalent angle difference The probability density function of as follows:

[0053]

[0054] And bring it into the objective function of the optimization problem updated in step B4, then the objective function of the optimization problem is further updated as follows:

[0055]

[0056] That is, the updated optimization problem is as follows:

[0057]

[0058] stx n ≥-D / 2,x n ≤D / 2

[0059] x m -x m-1 ≥λ / 2

[0060] n=1,…,N

[0061] m=2,…,N

[0062] Step B6. For the optimization problem updated in step B5, execute the non-uniform array antenna position optimization algorithm based on continuous convex approximation according to the following steps B6-1 to B6-4 to solve the optimal position of each antenna in the base station, that is, the antenna arrangement vector x of each antenna in the base station.

[0063] Step B6-1. Randomly generate an initial value x (0) , initialize the number of iterations q = 0, and the maximum number Q max , then go to step B6-2.

[0064] Step B6-2. Update q by adding 1. According to Taylor's theorem, we get the following:

[0065]

[0066] Among them, x (q-1) represents the antenna arrangement vector in the base station at the q-1th iteration, represents the first derivative of the h function with respect to each antenna arrangement vector at the q-1th iteration, and χ is the Hessian matrix The maximum eigenvalue of It represents the second derivative of the h function with respect to each antenna arrangement vector in the q-1th iteration, and then proceeds to step B6-3.

[0067] here, and The expressions are as follows.

[0068]

[0069] in,[·] s,trepresents the element in the sth row and tth column of the matrix, [·] s Represents the sth element of the vector, where v, s, and t are the indices of the antennas in the base station.

[0070] Step B6-3. Convert the optimization problem of the antenna position arrangement in the base station into a convex problem as follows:

[0071]

[0072] st|x m -x m-1 |≥λ / 2

[0073] x n ≥-D / 2,x n ≤D / 2

[0074] m=2,…,N,n=1,…,N

[0075] And use the CVX toolbox to solve, and record the result x as x (q) , then go to step B6-4.

[0076] Step B6-4. Determine whether q is equal to Q max , then what is obtained That is, the optimized position of each antenna in the base station, otherwise return to step B6-2.

[0077] Step C. Based on the optimized position of each antenna in the base station, a two-dimensional sparse model of the equivalent distance domain and angle domain between the base station and the terminal is constructed. An algorithm based on orthogonal matching pursuit and iterative super-resolution estimation is used to estimate the channel parameters and calculate the channel estimation vector between each terminal and the base station.

[0078] In actual application, the above step C is specifically designed to execute the following steps C1 to C5.

[0079] Step C1. The base station obtains the measurement vector y of each terminal in the received signal matrix y k Sparse signal model;

[0080] y k =Wγ k +η k

[0081] Among them, γ k The measurement vector y of the kth terminal of each terminal obtained by the base station k The corresponding sparse coefficient vector has a dimension of T×1, where W represents the dictionary matrix, [W] :,t =a(x,[b] f ,[Θ] e ), [·] :,tis the t-th column of the matrix, t = (f-1)E + e, t = 1, 2, ..., T, b represents the equivalent distance domain vector between the base station and the terminal, [b] f =b max (f-1) / F, [b] f represents the fth equivalent distance domain sampling value of the equivalent distance domain vector between the base station and the terminal, f=1,2,…,F, F represents the number of equivalent distance domain samples, [·] f represents the fth sampling value of the vector; Θ represents the equivalent angle domain vector between the base station and the terminal, [Θ] e represents the e-th equivalent angle domain sampling value of the equivalent angle domain vector between the base station and the terminal, e=1,2,…,E, E represents the number of equivalent angle domain samples, [·] e Represents the e-th sample value of the vector, the sparse coefficient vector γ k The dimension T=FE.

[0082] Step C2. Based on the measurement vector y of each terminal in the received signal matrix y k The sparse signal model of the near field communication channel parameter estimation problem is constructed as follows:

[0083]

[0084] in, represents the sparse coefficient vector γ k The number of non-zero elements in , To γ k The new coefficient vector after deleting the zero elements in is of dimension The first elements; δ represents the preset adjustment parameter, δ is used to ensure γ k The sparsity of , ω represents the preset weighting parameter to ensure the balance between sparsity and fitting accuracy; ||·||2 is the 2-norm of the vector.

[0085] Step C3. According to the mini-maximum method, the near field communication channel parameter estimation problem is converted into iterative minimization of the maximum value of the objective function in the near field communication channel parameter estimation problem. Then, in the pth iteration, the near field communication channel parameter estimation problem is converted to:

[0086]

[0087] Among them, D (p) is the weight matrix at the pth iteration, which is a diagonal matrix and is the estimated coefficient matrix for the kth terminal obtained in the p-1th iteration, B k Represents The channel matrix composed of the corresponding channel steering vector is based on the definition b k and Θ k Respectively represent The equivalent distance vector and the equivalent angle vector in the corresponding channel steering vector are: Represents The first Equivalent distance vectors, Represents The first Equivalent angle vectors.

[0088] Step C4. Solve the near field communication channel parameter estimation problem according to the following formula to obtain the optimal estimation coefficient vector for the pth iteration:

[0089]

[0090] and will Substituting the expression into the near field communication channel parameter estimation problem, we get the following:

[0091]

[0092] Then use the gradient descent method to solve the optimal b k and Θ k The results are recorded as Then we get the channel estimation matrix

[0093]

[0094] Then, we can obtain the coefficient vector estimate according to the following formula:

[0095]

[0096] Step C5. Based on the orthogonal matching pursuit and iterative super-resolution estimation algorithm, perform channel parameter estimation according to the following steps C5-1 to C5-11, and calculate and obtain the channel estimation vector between each terminal and the base station.

[0097] Step C5-1. Initialize the maximum number of orthogonal matching pursuit iterations Initialize the residual vector Initialize the estimated index set φ is an empty set, the number of iterations corresponding to orthogonal matching pursuit is set to l'=0, and then step C5-2 is entered.

[0098] Step C5-2. For the number of iterations l', add 1 to update, calculate the inner product vector value of the residual vector r and the dictionary matrix W according to the following formula, and take the index t of the maximum modulus value in the inner product vector value * , is the index set of the l'-1th iteration, and then enters step C5-3.

[0099]

[0100] Step C5-3. Update the estimated index set of the l'th iteration according to the following formula And proceed to step C5-4;

[0101]

[0102] Step C5-4. Based on the estimated index set The channel steering matrix between the base station and the kth terminal in the l'th iteration is obtained as follows: Then proceed to step C5-5;

[0103]

[0104] in, Indicates that the column number in the dictionary matrix W is a set The matrix consisting of column vectors of the element values ​​in .

[0105] Step C5-5. Use the following formula:

[0106]

[0107] Update the residual vector And go to step C5-6.

[0108] Step C5-6. Determine whether the number of iterations l' is equal to the maximum number of iterations If yes, then get And the channel steering matrix of the corresponding base station and the kth terminal Then go to step C5-7; otherwise return to step C5-2.

[0109] Step C5-7. Initialize the number of iterations corresponding to the minimization maximum value i'=0, the maximum number of iterations is I max ,according to Initialize the channel estimation matrix for the 0th iteration Initialize estimated sparsity Initialize the adjustment parameter ε and weighting parameter ω to ensure the balance between sparsity and fitting accuracy, initialize the channel coefficient estimation error threshold μ', and initialize the 0th iteration coefficient vector estimate Indicates the dimension A vector in which each element is 1; the minimum power value of the channel coefficient value is initialized to ρ; and then step C5-8 is entered.

[0110] Step C5-8. Update the number of iterations i' by 1 and use the gradient descent method to solve the following optimization problem:

[0111]

[0112] Get the optimal b k and Θ k , respectively And according to the following formula:

[0113]

[0114] Get the channel estimation matrix Then proceed to step C5-9.

[0115] Step C5-9. Based on the channel estimation matrix According to the following formula:

[0116]

[0117] Calculate the coefficient vector estimate Then proceed to steps C5-10.

[0118] Step C5-10. Judgment coefficient vector estimate Is the element modulus less than ρ? If so, delete the element and update As dimension, then go to step C5-11; otherwise, go directly to step C5-11.

[0119] Step C5-11. Determine whether i' is equal to the maximum number of iterations I max , then we get the estimated value of the coefficient vector And its corresponding channel estimation matrix Then according to the following formula:

[0120]

[0121] Calculate the channel estimation vector Otherwise, return to step C5-8.

[0122] Step D: Based on the channel estimation vectors between each terminal and the base station, execute the following steps D1 to D3 to construct a digital precoding matrix at the base station.

[0123] Step D1. According to the channel estimation vector, the following formula is used:

[0124]

[0125] Calculate the multi-terminal channel estimation matrix And proceed to step D2.

[0126] Step D2. Use the minimum mean square error method according to the following formula:

[0127]

[0128] Get the digital precoding matrix at the base station Among them, I K Represent a matrix with dimensions of K×K and all diagonal elements are 1, and proceed to step D3.

[0129] Step D3. Press For digital precoding matrix Normalize to get Among them, ||·|| F Refers to the Frobenius norm of the matrix.

[0130] The multi-terminal near-field communication method based on the non-uniform antenna array is applied in practice. The simulation conditions and results are further described. The number of antennas in the non-uniform antenna array at the base station is N = 33, the operating frequency is 30 GHz, that is, the wavelength is λ = 0.01 m, and it serves K terminals. The number of distinguishable multipath paths in the near-field communication channel is 3, that is, L k =3, including 1 line-of-sight path and 2 non-line-of-sight paths, and the power ratio between the line-of-sight path and the non-line-of-sight path is set to κ, and the total power of all terminals is normalized to K.

[0131] (1) Figure 2 As shown in the figure, under different signal-to-noise ratios, the normalized mean square error of channel estimation when the base station uses the same non-uniform antenna array and different channel estimation methods, and the cosine value of the multipath departure angle from the terminal to the base station is randomly distributed in The distance between the base station and the terminal is randomly distributed in [10,100]m, and κ = -20dB, K = 28. The number of antennas in the non-uniform array at the base station is N = 33, the antenna panel length is D = 4.95, and the least square method with known channel angle information is used as the lower bound of the normalized mean square error of the channel estimation. Figure 2It can be seen that the far-field orthogonal matching pursuit has the worst performance. This is because the increase in antenna aperture in the non-uniform array causes the far-field channel model assumption to no longer apply to near-field communication. The channel estimation scheme of the present invention is better than the near-field orthogonal matching pursuit. This is because the scheme of the present invention fully utilizes the spatial sparsity of the near-field channel and high-precision iterative super-resolution, while the near-field orthogonal matching pursuit does not fully utilize the spatial sparsity and has quantization errors.

[0132] (2) Figure 3 The figure shows the comparison of multiple terminals and rates when the base station uses different arrays under different signal-to-noise ratios. Assume k = -20dB, k = 28, and the other parameters are set to the same as Figure 2 Same. From Figure 3 It can be seen that when the signal-to-noise ratio is lower than -10dB, the performance of the non-uniform array, uniform circular array and traditional large-scale half-wavelength array of the present invention is similar. This is because severe noise affects the effectiveness of the solution. At higher signal-to-noise ratios, the non-uniform antenna array of the present invention is significantly better than the uniform circular array and traditional large-scale half-wavelength array. This is because the present invention utilizes the design freedom of the non-uniform array to increase the antenna aperture and uses the near-field effect to improve the spatial resolution, thereby effectively improving multi-terminal and rate.

[0133] (3) Figure 4 The figure shows the comparison of multi-terminal sum rate when the base station uses different arrays under different terminal numbers. Assume that the signal-to-noise ratio is 20dB and the other parameters are set to the same as Figure 3 Same. From Figure 4 It can be seen that when the number of terminals is less than 5, the performance of the non-uniform array, uniform circular array, and traditional large-scale half-wavelength array of the present invention is similar. This is because all schemes can provide sufficient degrees of freedom to distinguish different terminals. As the number of terminals increases, the sum rate first increases with the increase in the number of terminals. In the non-uniform array, uniform circular array, and traditional large-scale half-wavelength array of the present invention, the sum rate reaches the maximum value when the number of terminals is 10, 21, and 28, respectively. This verifies that the non-uniform array of the present invention can serve more terminals to achieve a higher sum rate.

[0134] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. A multi-terminal near-field communication method based on a non-uniform antenna array, characterized in that: The steps include: Step A. Based on each terminal within the near-field communication range transmitting an orthogonal pilot signal via a wireless channel to a base station equipped with a non-uniform antenna array, a channel vector is constructed between each terminal and the base station based on the multipath path between each terminal and the base station, and a near-field communication signal model is constructed between the base station and each terminal, and then the process proceeds to step B. Step B. Based on the channel vectors between each terminal and the base station, with the goal of maximizing multi-terminal near-field communication and rate, the optimal position of each antenna in the base station is solved, and then the process proceeds to step C; Step C. Based on the optimized positions of the antennas in the base station, a two-dimensional sparse model of the equivalent distance domain and angle domain between the base station and the terminal is constructed. An algorithm based on orthogonal matching pursuit and iterative super-resolution estimation is used to estimate the channel parameters and calculate the channel estimation vector between each terminal and the base station. Step D: constructing a digital precoding matrix at the base station according to the channel estimation vectors between each terminal and the base station.

2. The multi-terminal near-field communication method based on a non-uniform antenna array according to claim 1, characterized in that: The step A comprises the following steps: Step A1. Based on the terminal sending an orthogonal pilot signal to the base station via a wireless channel, for each multipath path between each terminal and the base station, a channel vector between each terminal and the base station is constructed as follows: Among them, 1≤k≤K, K represents the number of terminals within the near field communication range, h k represents the channel vector between the kth terminal and the base station, 1≤l k ≤L k , L k represents the number of multipath paths between the kth terminal and the base station, represents the lth connection between the kth terminal and the base station k The gain of the multipath, x=[x1,…,x n ,…,x N ], N represents the number of antennas in the base station, x n It represents the coordinate value of the nth antenna arranged along the X-axis in the coordinate system of the base station. x represents the arrangement vector of each antenna in the base station. represents the lth connection between the kth terminal and the base station k The distance of the multipath, Indicates the kth terminal to the lth base station k The multipath departure angles, represents the lth connection between the kth terminal and the base station k The transmit channel steering vector of the multipath path, [·] n represents the nth element in the vector, j represents an imaginary number, represents the distance between the nth antenna in the base station and the kth terminal, and λ represents the wavelength; Step A2. Based on The relationship between the three According to Taylor expansion, the relationship between the three is simplified to And based on the definition of equivalent angle and the equivalent distance Substitute the same amount into the transmission channel steering vector to obtain when When and build The corresponding probability density function when As it approaches infinity, the equivalent distance tends to 0; when is equal to 0, and When it is the minimum distance for near field communication, the equivalent distance Reaching the maximum value b max ,but and build The corresponding probability density function Step A3. Construct a near-field communication signal model between the base station and each terminal, that is, the received signal matrix y obtained by the base station is as follows: Among them, s k represents the orthogonal pilot signal sent by the kth terminal to the base station, (·) H Indicates transposition, g indicates that the mean is 0 and the variance is the preset σ 2 The channel additive white Gaussian noise vector of ; Step A4: The base station combines the received signal matrix y with the orthogonal pilot signals s sent by each terminal. k , perform the inner product according to the following formula: y k =y·s k =h k z k +η k Get the measurement vector y corresponding to each terminal in the received signal matrix y k , where y k represents the measurement vector of the kth terminal in the received signal matrix y, z k Indicates that the kth terminal sends an orthogonal pilot signal s k The pilot gain, η k Indicates that the orthogonal pilot signal s is sent to the kth terminal k The equivalent noise.

3. The multi-terminal near-field communication method based on a non-uniform antenna array according to claim 2, characterized in that: The minimum distance for near field communication is the Fresnel distance, that is, D represents the distribution length of each antenna along the X-axis of the coordinate system where the base station is located.

4. The multi-terminal near-field communication method based on a non-uniform antenna array according to claim 2, characterized in that: Described step B comprises the following steps: Step B1. Construct multi-terminal near-field communication and rate R sum as follows: in, Γ k represents the signal-to-interference-and-noise ratio of the kth terminal, 1≤i≤K, f i represents the beamforming vector of the base station for the i-th terminal, f k represents the beamforming vector of the base station for the kth terminal, that is, update Step B2. Based on the layout of each antenna along the X-axis of the base station's coordinate system, with the midpoint of the distribution length of each antenna layout as the origin of the coordinate system, and with the goal of maximizing multi-terminal near-field communication and rate, the optimization problem of the antenna position arrangement in the base station is constructed as follows: Objective function Indicates taking R sum , where D represents the distribution length of each antenna along the X-axis of the coordinate system where the base station is located; Step B3. Update the objective function of the optimization problem according to Jensen inequality as follows: Then the objective function of the optimization problem is transformed into And according to Then the objective function of the updated optimization problem is converted to Step B4. Based on the channel vector h between each terminal and the base station k , then the objective function of the updated optimization problem is transformed as follows: Where 1≤l i ≤L i , L i represents the number of multipath paths between the i-th terminal and the base station; Step B5. Based on the definition of equivalent distance difference and the equivalent angle difference Substitute into the probability density function Probability density function Constructing equivalent distance difference The probability density function of and the equivalent angle difference The probability density function of as follows: And bring it into the objective function of the optimization problem updated in step B4, then the objective function of the optimization problem is further updated as follows: That is, the updated optimization problem is as follows: Step B6. For the optimization problem updated in step B5, execute the non-uniform array antenna position optimization algorithm based on continuous convex approximation to solve the optimal position of each antenna in the base station, that is, the antenna arrangement vector x of each antenna in the base station.

5. The multi-terminal near-field communication method based on a non-uniform antenna array according to claim 4, characterized in that: Step B6 includes the following steps: Step B6-1. Randomly generate an initial value x (0) , initialize the number of iterations q = 0, and the maximum number Q max , then proceed to step B6-2; Step B6-2. Update q by adding 1. According to Taylor's theorem, we get the following: Among them, x (q-1) represents the antenna arrangement vector in the base station at the q-1th iteration, represents the first derivative of the h function with respect to each antenna arrangement vector at the q-1th iteration, and χ is the Hessian matrix The maximum eigenvalue of represents the second derivative of the h function with respect to each antenna arrangement vector at the q-1th iteration, and then proceeds to step B6-3; Step B6-3. Convert the optimization problem of the antenna position arrangement in the base station into a convex problem as follows: And use the CVX toolbox to solve, and record the result x as x (q) , then proceed to step B6-4; Step B6-4. Determine whether q is equal to Q max , then what is obtained That is, the optimized position of each antenna in the base station, otherwise return to step B6-2.

6. The multi-terminal near-field communication method based on a non-uniform antenna array according to claim 5, characterized in that: and The expressions are as follows: in,[·] s,t represents the element in the sth row and tth column of the matrix, [·] s Represents the sth element of the vector, where v, s, and t are the indices of the antennas in the base station.

7. The multi-terminal near-field communication method based on a non-uniform antenna array according to claim 1, characterized in that: Described step C comprises the following steps: Step C1. The base station obtains the measurement vector y of each terminal in the received signal matrix y k Sparse signal model; y k =Wγ k +n k Among them, γ k The measurement vector y of the kth terminal of each terminal obtained by the base station k The corresponding sparse coefficient vector has a dimension of T×1, where W represents the dictionary matrix, [W] :,t =a(x,[b] f ,[Θ] e ), [·] :,t is the t-th column of the matrix, t = (f-1)E + e, t = 1, 2, ..., T, b represents the equivalent distance domain vector between the base station and the terminal, [b] f =b max (f-1) / F, [b] f represents the fth equivalent distance domain sampling value of the equivalent distance domain vector between the base station and the terminal, f=1,2,…,F, F represents the number of equivalent distance domain samples, [·] f represents the fth sampling value of the vector; Θ represents the equivalent angle domain vector between the base station and the terminal, [Θ] e represents the e-th equivalent angle domain sampling value of the equivalent angle domain vector between the base station and the terminal, e=1,2,…,E, E represents the number of equivalent angle domain samples, [·] e Represents the e-th sample value of the vector, the sparse coefficient vector γ k The dimension T = FE; Step C2. Based on the measurement vector y of each terminal in the received signal matrix y k The sparse signal model of the near field communication channel parameter estimation problem is constructed as follows: in, represents the sparse coefficient vector γ k The number of non-zero elements in , To γ k The new coefficient vector after deleting the zero elements in is of dimension The first elements; δ represents the preset adjustment parameter, ω represents the preset weighting parameter; ||·||2 is the 2-norm of the vector; Step C3. According to the mini-maximum method, the near field communication channel parameter estimation problem is converted into iterative minimization of the maximum value of the objective function in the near field communication channel parameter estimation problem. Then, in the pth iteration, the near field communication channel parameter estimation problem is converted to: Among them, D (p) is the weight matrix at the pth iteration, which is a diagonal matrix and is the estimated coefficient matrix for the kth terminal obtained in the p-1th iteration, B k Represents The channel matrix composed of the corresponding channel steering vector is based on the definition b k and Θ k Respectively represent The equivalent distance vector and the equivalent angle vector in the corresponding channel steering vector are: Represents The first Equivalent distance vectors, Represents The first Equivalent angle vectors; Step C4. Solve the near field communication channel parameter estimation problem according to the following formula to obtain the optimal estimation coefficient vector for the pth iteration: and will Substituting the expression into the near field communication channel parameter estimation problem, we get the following: Then use the gradient descent method to solve the optimal b k and Θ k The results are recorded as Then we get the channel estimation matrix Then, we can obtain the coefficient vector estimate according to the following formula: Step C5: Based on the orthogonal matching pursuit and iterative super-resolution estimation algorithm, channel parameter estimation is performed, and the channel estimation vector between each terminal and the base station is calculated.

8. The multi-terminal near-field communication method based on a non-uniform antenna array according to claim 7, characterized in that: The step C5 comprises the following steps: Step C5-1. Initialize the maximum number of orthogonal matching pursuit iterations Initialize the residual vector Initialize the estimated index set If it is an empty set, set the number of iterations corresponding to orthogonal matching pursuit l'=0, and then go to step C5-2; Step C5-2. For the number of iterations l', add 1 to update, calculate the inner product vector value of the residual vector r and the dictionary matrix W according to the following formula, and take the index t of the maximum modulus value in the inner product vector value * , is the index set of the l'-1th iteration, and then goes to step C5-3; Where D represents the distribution length of each antenna along the X-axis of the coordinate system where the base station is located; Step C5-3. Update the estimated index set of the l'th iteration according to the following formula And proceed to step C5-4; Step C5-4. Based on the estimated index set The channel steering matrix between the base station and the kth terminal in the l'th iteration is obtained as follows: Then proceed to step C5-5; in, Indicates that the column number in the dictionary matrix W is a set A matrix consisting of column vectors of element values ​​in ; Step C5-5. Use the following formula: Update the residual vector And proceed to step C5-6; Step C5-6. Determine whether the number of iterations l' is equal to the maximum number of iterations If yes, then get And the channel steering matrix of the corresponding base station and the kth terminal Then go to step C5-7; otherwise return to step C5-2; Step C5-7. Initialize the number of iterations corresponding to the minimization maximum value i'=0, the maximum number of iterations is I max ,according to Initialize the channel estimation matrix for the 0th iteration Initialize estimated sparsity Initialize the adjustment parameter δ and the weighting parameter ω, initialize the channel coefficient estimation error threshold μ', and initialize the estimation coefficient matrix for the kth terminal at the 0th iteration Indicates the dimension and each element is a vector of 1; initialize the channel coefficient value to the minimum power value ρ; then proceed to step C5-8; Step C5-8. Update the number of iterations i' by 1 and use the gradient descent method to solve the following optimization problem: Get the optimal b k and Θ k , respectively And according to the following formula: Get the channel estimation matrix Then proceed to step C5-9; Step C5-9. Based on the channel estimation matrix According to the following formula: Calculate the coefficient vector estimate Then proceed to step C5-10; Step C5-10. Judgment coefficient vector estimate Is the element modulus less than ρ? If so, delete the element and update As dimension, then go to step C5-11; otherwise, go directly to step C5-11; Step C5-11. Determine whether i' is equal to the maximum number of iterations I max , then we get the estimated value of the coefficient vector And its corresponding channel estimation matrix Then according to the following formula: Calculate the channel estimation vector Otherwise, return to step C5-8.

9. The multi-terminal near-field communication method based on a non-uniform antenna array according to claim 7, characterized in that: Described step D comprises the following steps: Step D1. According to the channel estimation vector, the following formula is used: Calculate the multi-terminal channel estimation matrix And proceed to step D2; Step D2. Use the minimum mean square error method according to the following formula: Get the digital precoding matrix at the base station Among them, I K represents a matrix of dimension K×K with all diagonal elements being 1, and proceeds to step D3; Step D3. Press For digital precoding matrix Normalize to get Among them, ||·|| F Refers to the Frobenius norm of the matrix.

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