Beam focusing method and system based on liquid neural network and meta learning

Abstract

The invention discloses a beam focusing method and system based on a liquid neural network and meta learning, and belongs to the technical field of wireless communication, and the method comprises the following steps: determining a system model; determining an optimization target; and joint optimization. The LNNM-BF algorithm with high robustness and unsupervised learning is provided, the LNNM-BF algorithm designs a phase shift matrix theta through an index matrix S and a phase compensation matrix phi, then an analog precoding matrix FPS and a digital precoding matrix FBB are designed at a BS end, and the near-field dual-beam splitting effect can be well relieved without introducing an extra true time delayer. Besides, the LNNM-BF algorithm enhances the adaptability of beam focusing to imperfect CSI through a meta-learning framework and improves the robustness of the algorithm, and the embedded LNN dynamically adjusts the topological structure and the connection weight between neurons through the currently input and previously implied iteration information to realize the maximization of SE.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically to a beam focusing method based on liquid neural networks and meta-learning. Background Technology

[0002] Sixth-generation mobile networks (6G) are considered a key infrastructure supporting the future digital society, but 6G's key performance indicators far exceed those of fifth-generation mobile networks (5G). To achieve this, researchers are actively exploring breakthrough technologies to meet 6G's key performance requirements, such as Ultra-massive Multiple Input Multiple Output (UM-MIMO), Extremely Large-scale Intelligent Reflecting Surface (XL-IRS), Terahertz (THz) communication, and cell-free massive MIMO communication technologies. Among these breakthrough technologies, THz communication has attracted significant attention due to its ultra-wide bandwidth resources, making it possible to achieve Tbps-level high-speed transmission. THz high-frequency communication is often combined with Extremely Large-scale Array (ELAA) technology to improve communication capacity.

[0003] However, with the widespread application of ELAA and THz band communication, the Rayleigh distance has gradually increased, making near-field effects more prevalent in wireless networks. The assumption of far-field uniform plane wave propagation no longer holds, necessitating the use of near-field spherical waves to accurately model the electromagnetic radiation field. The introduction of near-field effects changes the structure and modeling methods of communication channels, posing new challenges to key technologies such as beam focusing, channel estimation, and resource allocation. Furthermore, when both the base station (BS) and the IRS employ ELAA technology, THz broadband communication will simultaneously exhibit beam splitting at both the BS and IRS ends, i.e., a double beam splitting effect. This double beam splitting effect significantly impacts the system's spectral efficiency (SE). More complexly, the coupling effect between near-field effects and double beam splitting further exacerbates the design difficulty of beam focusing. Therefore, compared to far-field ELAA communication, XL-IRS-assisted near-field broadband THz massive MIMO beam focusing will face even greater challenges.

[0004] While there is considerable research on beam splitting effects, studies on near-field broadband beam splitting in XL-IRS-assisted THz massive MIMO systems are scarce. Therefore, in XL-IRS-assisted near-field broadband THz massive MIMO systems, it is necessary to investigate beam focusing algorithms that possess strong robustness, low cost, and the ability to mitigate near-field dual-beam splitting effects. Summary of the Invention

[0005] The technical problem to be solved by this invention is: how to alleviate the near-field dual-beam splitting effect and maximize the system SE in an XL-IRS-assisted near-field broadband THz massive MIMO system, and provides a beam focusing method based on liquid neural network and meta-learning.

[0006] like Figure 7 As shown, the present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0007] S1: Determine the system model

[0008] Establish an XL-IRS-assisted near-field broadband THz massive MIMO system, including one equipped with N t A base station with 1 antenna, an XL-IRS with N reflector elements, and a single user equipment (UE) with U antennas deployed.

[0009] S2: Determine the optimization objective

[0010] The simulation precoding matrix F will be jointly optimized. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is optimized by maximizing SE;

[0011] S3: Joint Optimization

[0012] Joint optimization using the LNNM-BF algorithm based on LNN and meta-learning is employed. LNN is then applied to an XL-IRS-assisted near-field wideband THz massive MIMO system, and the precoding matrix F is simulated iteratively. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is maximized to achieve the SE of the XL-IRS-assisted near-field broadband THz massive MIMO system, which can effectively alleviate the near-field dual-beam splitting effect without introducing an additional true time delay unit. At the same time, a meta-learning framework with three nested loops is adopted to enhance the adaptability of beam focusing to imperfect CSI and improve the robustness of the system.

[0013] Furthermore, in the XL-IRS-assisted near-field broadband THz massive MIMO system described in step S1, the direct communication between the BS and the UE is blocked by buildings. The UE can only communicate with the BS via the XL-IRS, employing orthogonal frequency division multiplexing with M subcarriers. The BS simultaneously transmits N... S A data stream, the UE's received signal at the m-th subcarrier. It is expressed as follows:

[0014] y m =H m ΘG m W m s m +n m

[0015] in, and Let Θ represent the channel matrices between XL-IRS and UE and between BS and XL-IRS at the m-th subcarrier, respectively, Θ = diag(θ1, θ2, ..., θ N ) represents the phase shift matrix of XL-IRS. ψ represents the reflection coefficient of the nth XL-IRS reflective unit. n ∈[0,2π), ψ n This represents the phase shift caused by the nth XL-IRS reflective unit. This represents the hybrid precoding matrix at the m-th subcarrier. It is a frequency-independent analog precoding matrix. It is the digital precoding matrix at the m-th subcarrier. It is the transmitted signal at the m-th subcarrier, satisfying It follows a Gaussian distribution. The additive white Gaussian noise has a variance of σ. 2 N S =U≤N RF <<N t N RF The number of radio frequency chains to be deployed at the BS end.

[0016] Furthermore, in step S2, the achievable SE quantization of the UE on subcarrier m is as follows:

[0017]

[0018] in, Indicates a cascaded channel, I U It is an identity matrix of size U×U, [·] H The expression represents the conjugate transpose, and det(·) represents the determinant operation.

[0019] Furthermore, in step S2, the optimization problem of maximizing SE is formulated as follows:

[0020]

[0021] in, This represents the average SE over all subcarriers, used to quantize the SE of an XL-IRS-assisted near-field wideband THz massive MIMO system. BB =(F BB,1 ,F BB,2 …,F BB,M P represents the set of all subcarrier digital precoding matrices, i.e., the digital precoding matrix. t For the transmit power of each data stream, the C1 constraint describes that each item of the analog precoding matrix must satisfy the normalization constraint, the C2 constraint indicates that the total transmit power of the BS is finite, and the C3 constraint is the equal modulus constraint of the XL-IRS reflector unit.

[0022] Furthermore, in step S3, the LNNM-BF algorithm includes two sub-networks, LNN1 and LNN2, and three nested loops: a sub-loop, a main loop, and an iterative loop. The specific details of the three nested loops are as follows:

[0023] Sub-loop: The sub-loop is used to optimize the analog precoding matrix F through the LNN1 and LNN2 sub-networks. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS;

[0024] Main Loop: The main loop is used to accumulate the loss function. To achieve unsupervised learning, the loss function in the j-th main loop is represented by the negative of SE.

[0025]

[0026] Among them, F PS * F BB * and Θ * These represent the analog precoding matrix, digital precoding matrix, and phase shift matrix after each main loop update;

[0027] Iterative Loop: The iterative loop is used to update the parameters in the LNN1 and LNN2 subnetworks. In each iteration loop, there is I... o The main loop accumulates the average of the loss function and uses the Adam optimizer for backpropagation to update the parameter set θ in the LNN1 and LNN2 subnetworks. Θ and θ W .

[0028] Furthermore, the LNN1 sub-network is used to optimize the phase shift matrix Θ of the XL-IRS design. It includes an LNN, parallel fully connected layers FC1 and FC2, and parallel Lambda1 and Lambda2 layers. The LNN consists of three layers of liquid neurons whose synapses are connected using a neural circuit strategy, used to select the optimal trajectory and generate shared features. The two parallel fully connected layers FC1 and FC2 are used to output the index matrix updated in the current iteration. and phase compensation matrix The output of the fully connected layer FC1 is passed through a sigmoid function to ensure that the output is controlled within the range of 0 to 1. Then, it is processed by a Lambda1 layer to output an index matrix containing only 0 and 1 elements, and satisfies... Similarly, to ensure the row summation is 1, the output of the fully connected layer FC2 is controlled within the range of 0 to 1 by using a sigmoid function, and then processed by a Lambda2 layer to adjust the phase compensation matrix Φ. * Within the range of 0 to 2π, the index matrix and the phase compensation matrix are then multiplied to obtain the updated phase shift for each XL-IRS reflector element. Subsequently, to satisfy the equal modulus constraint C3 of the XL-IRS reflector unit, the updated reflection coefficient θ is obtained using Euler's formula. * Finally, through diagonal operations Θ * =diag(θ) * The updated phase shift matrix Θ is obtained. * .

[0029] Furthermore, in the LNN1 sub-network, the SE representation in the i-th sub-loop and the j-th main loop is as follows:

[0030]

[0031] Where, Θ (i,j) This represents the phase shift matrix in the i-th sub-loop and the j-th main loop. It is the hybrid precoding matrix at the m-th subcarrier after initialization or update.

[0032] Furthermore, the LNN2 sub-network is used to optimize the analog precoding matrix F. PS and digital precoding matrix F BB It includes an LNN, parallel fully connected layers FC3 and FC4, a parallel Lambda3 layer, and a BS total emission power C2 constraint unit. The LNN consists of three layers of liquid neurons with synapses connected using a neural circuit strategy, used to select the optimal trajectory and generate shared features. The two parallel fully connected layers FC3 and FC4 are used to output the simulated precoding matrix updated in each iteration. and digital precoding matrix The output of the fully connected layer FC3 is passed through a sigmoid function to ensure that the output is controlled within the range of 0 to 1. Then, after processing by the Lambda3 layer, the updated phase shift angle is output within the range of 0 to 2π. Finally, the analog precoding matrix that satisfies the normalized C1 constraint is obtained. Output of the fully connected layer FC4 The updated digital precoding matrix is ​​obtained by using the total transmit power C2 constraint unit.

[0033] Furthermore, in the LNN2 network, the SE representation in the i-th sub-loop and the j-th main loop is as follows:

[0034]

[0035] in, This represents the hybrid precoding matrix of the i-th sub-loop and the j-th main loop at the m-th subcarrier. It is the phase shift matrix for initialization or updating.

[0036] Furthermore, the three liquid neurons in the LNN are the interneuron layer, the command layer, and the motor layer. The interneuron layer is used to perform nonlinear transformations on the input data and store the features of previous iterations. The command layer is used to integrate the features from the interneuron layer and generate decision signals to select the optimal trajectory. The motor layer generates the final shared features based on the output of the command layer.

[0037] This invention also provides a beam-focusing system based on liquid neural networks and meta-learning, which uses the above-mentioned method to alleviate the near-field dual-beam splitting effect in XL-IRS-assisted near-field broadband THz massive MIMO systems, including:

[0038] The system model determination module is used to establish an XL-IRS-assisted near-field broadband THz massive MIMO system, including N... t A base station with 1 antenna, an XL-IRS with N reflector elements, and a single user equipment (UE) with U antennas deployed.

[0039] The optimization objective determination module is used to jointly optimize the simulated precoding matrix F. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is optimized by maximizing SE;

[0040] The joint optimization module utilizes the LNNM-BF algorithm based on LNN and meta-learning for joint optimization, applying LNN to an XL-IRS-assisted near-field broadband THz massive MIMO system, and iteratively simulating the precoding matrix F. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is used to maximize the SE of the XL-IRS-assisted near-field broadband THz massive MIMO system. At the same time, a meta-learning framework with three nested loops is adopted to enhance the adaptability of beam focusing to imperfect CSI and improve the robustness of the system.

[0041] Compared with existing technologies, this invention has the following advantages: This beam focusing method based on liquid neural networks and meta-learning proposes an LNNM-BF algorithm with strong robustness and unsupervised learning. The LNNM-BF algorithm designs the phase shift matrix Θ using the index matrix S and the phase compensation matrix Φ, and then designs the analog precoding matrix F at the BS end. PS and digital precoding matrix F BB This algorithm effectively mitigates the near-field dual-beam splitting effect without introducing an additional true time delay unit. Furthermore, the LNNM-BF algorithm enhances the adaptability of beam focusing to imperfect CSI through a meta-learning framework, improving its robustness. Simultaneously, the embedded LNN dynamically adjusts the topology and connection weights between neurons based on the current input and previously implicit iterative information, maximizing SE. Extensive simulation experiments demonstrate that the LNNM-BF algorithm, compared to existing beam focusing algorithms, better mitigates the near-field dual-beam splitting effect, thus providing a high SE and robust algorithm for XL-IRS-assisted near-field broadband THz large-scale MIMO scenarios. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the near-field broadband THz massive MIMO system model structure assisted by XL-IRS in an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of the network structure of the LNNM-BF algorithm in an embodiment of the present invention, wherein the network structure of LNN is within the green dashed box;

[0044] Figure 3 In the embodiments of this invention, under the perfect CSI assumption and P t A comparison of the convergence process of the proposed algorithm and the benchmark algorithm when the value is 10dBm;

[0045] Figure 4 This is a comparison diagram of the impact of different distances from XL-IRS to UE on SE in an embodiment of the present invention, where P t =10dBm;

[0046] Figure 5 This is a comparison diagram of the impact of different transmit powers on SE under different CSI assumptions in the embodiments of the present invention, where (a) is under the perfect CSI assumption and (b) is under the imperfect CSI assumption.

[0047] Figure 6 P is an embodiment of the present invention. t SE curves for different CEE values ​​when CEE = 10dBm;

[0048] Figure 7 This is a flowchart of the main steps of the beam focusing method based on liquid neural network and meta-learning in this invention. Detailed Implementation

[0049] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0050] This embodiment provides a technical solution: a beam focusing method based on liquid neural networks and meta-learning, the specific details of which are as follows:

[0051] I. Algorithm Introduction

[0052] To mitigate the near-field dual-beam splitting effect, this invention proposes a Liquid Neural Network and Meta-learning based Beam Focusing (LNNM-BF) algorithm for near-field broadband THz massive MIMO systems assisted by XL-IRS. The LNNM-BF algorithm significantly improves the system's beam splitting (SE) by jointly optimizing the phase shift matrix, analog precoding matrix, and digital precoding matrix. First, to implement a frequency-dependent XI-IRS phase shift matrix design and alleviate the beam splitting effect at the XI-IRS, this invention divides the XI-IRS into multiple VSAs (Virtual Subarrays) by introducing an index matrix with only 0 and 1 elements and a row sum of 1. Within the same column, XI-IRS reflector units with index 1 are grouped into the same subarray, and this subarray is assigned the same phase shift through a phase compensation matrix. The row sum of 1 ensures that each XI-IRS reflector unit undergoes only one partitioning and phase shift design. The partitioning is based on an index matrix, not limited by whether the XI-IRS reflection units are adjacent or in the same Fresnel interval, nor by the number of reflection units in each subarray. The ultimate goal is to alleviate beam splitting at the XI-IRS and maximize SE. The introduction of the index matrix avoids the use of a true delay unit and overcomes the drawbacks of fixed VSA and Fresnel-based XI-IRS partitioning. Furthermore, considering the excessively high hardware cost and power consumption of all-digital precoding at the BS (base station), which is often impractical, the LNNM-BF algorithm optimizes both frequency-independent analog precoding matrices and frequency-dependent digital precoding matrices at the BS. This hybrid precoding structure avoids the introduction of a true delay unit module while also incorporating a frequency-dependent hybrid precoding matrix, mitigating beam splitting at the BS. Finally, the LNNM-BF algorithm iterates multiple times through a meta-learning framework, jointly optimizing the phase shift matrix, analog precoding matrix, and digital precoding matrix to enhance adaptability to imperfect CSI (channel state information) and improve algorithm robustness. Meanwhile, the LNNM-BF algorithm is designed using a Liquid Neural Network (LNN) as its core. By dynamically adjusting the topology and connection weights between neurons based on the current input and previously implicit iterative information, it fully extracts the implicit angle and distance features of the near-field channel, determines the optimal strategy, and maximizes the SE (Sequence Optimization). Simulation results show that the proposed LNNM-BF algorithm has strong robustness and can effectively mitigate the near-field dual-beam splitting effect.

[0053] Note: Unless otherwise specified, matrices are represented by bold uppercase letters (e.g., H), vectors by bold lowercase letters (e.g., h), and scalars by plain letters (e.g., d). and Let these represent the set of complex numbers and the set of real numbers, respectively. [·] -1 、[·] T 、[·] H ,Tr(·), diag(·), |·|, ||·||2 and ||·|| F These represent the inverse, transpose, conjugate transpose, trace, diagonal operation, modulo operation, and L, respectively. 2 Norms and Frobenius norms. I N It is an N×N identity matrix. The mean is u and the covariance is... It follows a complex Gaussian random distribution. It represents the statistical expectation. This represents the asymptotic time complexity.

[0054] II. System Model and Optimization Problem

[0055] A. System Model

[0056] This embodiment considers an XL-IRS-assisted near-field broadband THz massive MIMO system, such as Figure 1 As shown. Includes equipment with N t The system consists of a Base Station (BS) with 10 antennas, an XL-IRS with N reflector elements, and a single User Equipment (UE) with U antennas. The BS uses a uniform linear array, while the XL-IRS uses a uniform planar array. Assuming both the BS and XL-IRS are located in the yOz plane, N1 and N2 represent the number of reflector elements in the z and y axes, respectively (N = N1 × N2). d is the spacing between adjacent antennas and reflector elements, and the center of the BS antenna array is located at the origin. A traditional fully connected hybrid precoding architecture is used, deploying N antennas at the BS. RF The root radio-frequency (RF) chain is considered. Assuming direct communication between the BS and UE is obstructed by buildings, the UE can only communicate with the BS via the XL-IRS. The BS simultaneously transmits N... S N data streams S =U≤N RF <<N t This embodiment employs orthogonal frequency division multiplexing with M subcarriers. Therefore, the received signal of the UE at the m-th subcarrier... It can be represented as:

[0057] y m =H m ΘG m W m s m +n m (1)

[0058] in, and Let Θ represent the channel matrices between XL-IRS and UE and between BS and XL-IRS at the m-th subcarrier, respectively, Θ = diag(θ1, θ2, ..., θ N ) represents the phase shift matrix of XL-IRS. ψ represents the reflection coefficient of the nth XL-IRS reflective unit. n This represents the phase shift caused by the nth XL-IRS reflective unit. This represents the hybrid precoding matrix at the m-th subcarrier. It is a frequency-independent analog precoding matrix. It is the digital precoding matrix at the m-th subcarrier. It is the transmitted signal at the m-th subcarrier, satisfying It follows a Gaussian distribution. The additive white Gaussian noise has a variance of σ. 2 .

[0059] B. Near-field wideband channel model

[0060] In XL-IRS-assisted near-field communication, the cascaded reflection links include the BS to XL-IRS and the XL-IRS to UE. According to the near-field boundary delineation criteria, the near-field region of XL-IRS-assisted communication can be represented as follows:

[0061]

[0062] Where r1 and r2 represent the distances from BS to XL-IRS and from XL-IRS to UE, respectively, D represents the maximum aperture of the XL-IRS array, and λ represents the signal wavelength. It is clear from formula (2) that when either r1 or r2 is less than the Rayleigh distance... In such cases, near-field communication must be considered in the XL-IRS system. Furthermore, when the BS is equipped with a large number of antennas, both the BS and XL-IRS will experience beam splitting effects. Therefore, this embodiment considers the common scenario where both the BS and UE are located in the near-field region of the XL-IRS and the transmitted signals both have time delays.

[0063] In this embodiment, the system bandwidth B is divided into M orthogonal subcarriers, and the center carrier frequency is set to f. c Then the communication frequency f at subcarrier m m It can be represented as:

[0064]

[0065] The near-field THz broadband channel from BS to XL-IRS at the m-th subcarrier can be composed of one line-of-sight (LoS) path and L non-line-of-sight (NLoS) paths. The near-field THz broadband channel from BS to XL-IRS at the m-th subcarrier is represented as follows:

[0066]

[0067] Where, α l,m (l∈[0,L]) represents the path loss of the THz signal propagating from the BS to the XL-IRS. and These represent the received responses of the XL-IRS arrays for the LoS and NLoS paths, respectively. and r l R These represent the distances from the center of the XL-IRS array to the center of the BS array and the l-th scatterer, respectively. and These represent the azimuth and elevation angles of the signal as it travels along the LoS path to the XL-IRS. and These represent the azimuth and elevation angles of the signal as it travels through the NLoS path to the XL-IRS. and Regarding the transmit response of the BS arrays for LoS and NLoS paths respectively, r l BR , and Let represent the distance from the center of the BS array to the l-th scatterer, and the departure angle of the BS end when the signal propagates along the LoS and NLoS paths, respectively. and These represent the time delays of the signal propagating to the XL-IRS via the LoS and NLoS paths, respectively. In near-field channel modeling, the array response must consider both angle and distance information. Therefore, this embodiment uses a spherical wave model to describe the near-field broadband array response. and They can be represented as follows:

[0068]

[0069] in, This indicates the maximum index of the antenna at point BS. This indicates the nth node in the Loss path. t The distance from the antenna to the XL-IRS, Indicates the index of each XL-IRS reflective unit. This represents the distance from the reflecting unit (n1, n2) to the BS in the LoS path. According to the literature (Z. Wu and L. Dai. Multiple Access for Near-Field Communications: SDMA or LDMA?. IEEE J. Select. Areas Commun., 2023, 41(6): 1918–1935), in the th LoS path, and They can be represented as follows:

[0070]

[0071] Similarly, and The definitions can be found by referring to formulas (5) and (6).

[0072] The near-field THz wideband channel from XL-IRS to UE at the m-th subcarrier can also be composed of one LoS path and L NLoS paths. Therefore, the near-field THz wideband channel from XL-IRS to UE at the m-th subcarrier is represented as:

[0073]

[0074] Where, β l,m (l∈[0,L]) represents the path loss of the THz signal propagating from the XL-IRS to the UE. and These represent the transmit responses of the XL-IRS array with respect to the LoS and NLoS paths, respectively. and r l RU These represent the distances from the center of the XL-IRS array to the center of the UE array and the l-th scatterer, respectively. and These represent the azimuth and elevation angles at which the signal leaves the XL-IRS via the LOS path, respectively. and These represent the azimuth and elevation angles at which the signal leaves the XL-IRS via the NLoS path, respectively. and Regarding the received responses of the UE arrays for the LoS and NLoS paths respectively, r l U , and These represent the distance from the center of the UE array to the l-th scatterer, and the angle of arrival at the UE when the signal propagates along the LoS and NLoS paths, respectively. and These represent the time delays of the signal propagating to the UE via the LoS and NLoS paths, respectively. Similarly, a spherical wave model is used to describe the array response of the XL-IRS and the UE. Therefore, the array response of the XL-IRS and the UE can be defined with reference to formulas (5) and (6), respectively.

[0075] C. Channel estimation error

[0076] In THz near-field broadband communication systems, channel estimation error (CEE) is one of the key factors affecting system security (SE) and reliability. Due to the extremely high path loss, strong molecular absorption effect, and complex near-field propagation characteristics of THz band signals, accurately capturing the true channel index (CSI) is often difficult in practice. Furthermore, broadband signals in the near-field environment introduce frequency-selective fading and spatial non-stationarity, further exacerbating the difficulty of channel estimation. Therefore, CEE is unavoidable in practical systems.

[0077] This embodiment studies the case where CEE exists in both the BS-to-XL-IRS and XL-IRS-to-UE channels. To evaluate CEE, the actual channel is denoted as X, and the estimated channel is denoted as... Therefore, CEE can be represented as:

[0078]

[0079] Channel Estimation Error (CEE) is a key indicator for measuring the accuracy of channel estimation, and its value directly reflects the degree of deviation between the estimated channel and the actual channel. A larger CEE value indicates a more significant deviation in channel estimation, severely impacting channel accuracy (SE), which poses a serious challenge to the design of broadband beamforming algorithms. Therefore, it is necessary to design robust algorithms to mitigate the negative impact of CEE on communication performance.

[0080] D. Optimization Problem

[0081] The objective of this invention is to jointly optimize the analog precoding matrix F PS Digital precoding matrix F BB The phase shift matrix Θ of the XL-IRS is used to maximize the SE. The achievable SE of the UE on subcarrier m can be quantized as follows:

[0082]

[0083] in, Indicates a cascaded channel, I U It is an identity matrix of size U×U, [·] H `det(·)` represents the conjugate transpose, and `det(·)` represents the determinant operation. Therefore, the optimization problem of maximizing SE can be formulated as:

[0084]

[0085] in, This invention uses R to quantize the SE of the system over all subcarriers, and F represents the average SE of the system. BB =(F BB,1 ,F BB,2 …,F BB,M P represents the set of all subcarrier digital precoding matrices, i.e., the digital precoding matrix. t For the transmit power of each data stream, the C1 constraint describes that each item of the analog precoding matrix must satisfy the normalization constraint, the C2 constraint indicates that the total transmit power of the BS is finite, and the C3 constraint is the equal modulus constraint of the XL-IRS reflector, that is, the reflection coefficient of the XL-IRS reflector lies on the unit circle, thereby simplifying the hardware implementation of XL-IRS.

[0086] III. Beamforming Algorithm Based on LNN and Meta-learning

[0087] This section describes the LNNM-BF algorithm to overcome the XL-IRS-assisted THz near-field dual-beam splitting effect, including its design concept, architecture, and implementation process.

[0088] A. LNN structure

[0089] LNNs describe the information transmission process between neurons using Ordinary Differential Equations (ODEs), and the hidden states of these ODEs can remember historical information about the data. Furthermore, the topology and connection weights of an LNN are adjusted in real time as the input data changes. Therefore, this invention applies LNNs to an XL-IRS-assisted THz near-field broadband communication system, iteratively simulating the precoding matrix F... PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is used to maximize the system's SE. LNN exhibits dual advantages in XL-IRS-assisted THz near-field broadband communication systems. Not only does it implicitly incorporate previously optimized gradient information in each iteration, avoiding convergence oscillations caused by discretization, but it also automatically adjusts the topology and connection weights between neurons based on the input of the current iteration, thereby maximizing SE. The core of LNN is a continuous-time state update equation describing the dynamic evolution of the hidden state. However, continuous-time neural networks based on ODE are computationally inefficient during training and inference. Therefore, this invention adopts a closed-form continuous-time model of LNN, replacing the numerical solution of ODE with a closed-form approximation. The specific core expression is:

[0090]

[0091] Where x(t) represents the hidden state of the network, storing the input feature information of the current iteration, σ(·) is the activation function, f(·), g(), and h() are the three functional modules of the neuron, controlling the dynamic update, gating regulation, and synaptic integration of the neuron, respectively, and θ f θ g and θ h These are the learnable parameter sets for the three functional modules, used to control the time decay and response intensity of neurons. x represents the hidden state of the previous iteration, and I represents the input feature of the current iteration. The closed-form continuous-time model skips the iterative calculation of ODE through closed-form solutions, directly outputting the results. Its running speed is comparable to that of ordinary recurrent neural networks, but it retains continuous-time modeling capabilities. Furthermore, the LNN wiring method in this invention adopts a neural circuit strategy, introducing bio-inspired local connection structures to replace the traditional fully connected approach, significantly reducing the network's learnable parameters.

[0092] B. Meta-learning framework

[0093] Meta-learning, as a method of "learning how to learn," has been gradually introduced into wireless communication systems. Its common application involves extensive offline pre-training followed by further online adaptive optimization. However, these methods rely excessively on perfect CSI (Constant Sound Indicator) and are sensitive to changes in CEE (Constant Effectiveness) and data distribution. Therefore, the LNNM-BF algorithm proposed in this invention employs a meta-learning framework with three nested loops. This framework enhances the adaptability of beam focusing to imperfect CSI, improving system robustness. The LNNM-BF algorithm mainly consists of two sub-networks, LNN1 and LNN2, with the network structure as follows: Figure 2 As shown, the LNNM-BF algorithm does not require pre-training; it iterates through multiple loops during runtime to find the optimal simulated precoding matrix F. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is used to obtain the maximum SE. The three nested loops consist of a child loop, a main loop, and an iteration loop. The specific details of the three nested loops are as follows:

[0094] Sub-loop: The sub-loop is responsible for optimizing the simulated precoding matrix F using LNN1 and LNN2 loops. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS.

[0095] Main Loop: The main loop's function is to accumulate the loss function. To achieve unsupervised learning, the loss function in the j-th main loop is represented by the negative of SE.

[0096]

[0097] Among them, FPS * F BB * and Θ * These represent the analog precoding matrix, digital precoding matrix, and phase shift matrix after each main loop update, respectively.

[0098] Iterative Loop: The iterative loop is mainly responsible for updating the parameters in the LNN1 and LNN2 subnetworks. Each iterative loop has an I... o The main loop iterates through the sum of the average loss function values, which is expressed as:

[0099]

[0100] Backpropagation using the Adam optimizer updates the parameter set θ in the LNN1 and LNN2 subnetworks. Θ and θ W , where θ Θ Including the learnable parameter set θ in LNN1 f θ g θ h and the weight parameter set θ of the two fully connected layers FC Composition, similarly θ W It consists of the learnable parameter set of LNN2 and the weight parameter sets of the two fully connected layers. The entire optimization process has I e The iteration cycle is repeated, with the update interval set to a constant n. o In every n o The parameter sets in LNN1 and LNN2 are updated once in each iteration loop. The optimization objective of the LNNM-BF algorithm proposed in this invention is not a single variable, but rather to continuously select the optimal trajectory to optimize the simulated precoding matrix F. PS Digital precoding matrix F BB The phase shift matrix Θ of the XL-IRS algorithm is jointly optimized. Therefore, the impact of CEE on SE is minimized, significantly improving the robustness of the LNNM-BF algorithm.

[0101] C. Joint optimization of beam focusing and XL-IRS phase shift

[0102] The LNNM-BF algorithm proposed in this invention uses two sub-networks, LNN1 and LNN2, to optimize the phase shift matrix Θ and the analog precoding matrix F, respectively. PS and digital precoding matrix F BB ,like Figure 2 As shown.

[0103] The LNN1, which optimizes the phase shift matrix, consists of an LNN (within the green dashed box), parallel fully connected layers FC1 and FC2, and parallel Lambda1 and Lambda2 layers. The LNN is composed of three layers of liquid neurons connected by neural circuits, named the interneuron layer, command layer, and motor layer. The interneuron layer primarily performs nonlinear transformations on the input data and stores features from previous iterations. The command layer integrates features from the interneuron layer and generates decision signals to select the optimal trajectory. The motor layer generates the final shared features based on the output of the command layer. The two parallel fully connected layers output the updated index matrix for the current iteration. and phase compensation matrix First, the output of the fully connected layer FC1 is passed through a sigmoid function to ensure that the output is controlled within the range of 0 to 1. Then, the updated index matrix S of the current iteration is output through the Lambda1 layer. * The Lambda1 layer uses the Gumbel-Softmax function to implement differentiable discrete decision-making, outputting an index matrix with only 0 and 1 elements, and satisfying... The constraint that the sum of rows must be 1. Similarly, the output of the fully connected layer FC2 is controlled by a sigmoid function to ensure that the output is controlled within the range of 0 to 1, and then the phase compensation matrix Φ is ensured by a Lambda2 layer. * Within the range of 0 to 2π. Next, the index matrix and the phase compensation matrix are multiplied to obtain the updated phase shift for each XL-IRS reflector element. Subsequently, to satisfy the equal modulus constraint C3 of the XL-IRS reflector unit, this invention obtains the updated reflection coefficient θ using Euler's formula. * , can be represented as:

[0104]

[0105] in, This represents the updated reflection coefficient of the nth reflection unit. Finally, Θ is calculated using diagonal operations. * =diag(θ) * The updated phase shift matrix Θ is obtained. * In the LNN1 subnetwork, the SE in the i-th sub-loop and the j-th main loop can be represented as:

[0106]

[0107] Where, Θ (i,j) This represents the phase shift matrix in the i-th sub-loop and the j-th main loop. It is the hybrid precoding matrix at the m-th subcarrier after initialization or update.

[0108] Optimize the analog precoding matrix F PS and digital precoding matrix F BB The LNN2 sub-network structure consists of an LNN (within the green dashed box), parallel fully connected layers FC3 and FC4, a parallel Lambda3 layer, and a BS total transmit power constraint C2. The structure and function of the LNN are the same as the LNN in LNN1, responsible for selecting the optimal trajectory and generating shared features. The two parallel fully connected layers are used to output the simulated precoding matrix updated in each iteration. and digital precoding matrix First, to ensure the input to the Lambda3 layer is controlled within the range of 0 to 1, the output of the fully connected layer FC3 is processed by a sigmoid function. Then, the phase shift angle, updated to a range of 0 to 2π, is output through the Lambda3 layer. Finally, the analog precoding matrix that satisfies the normalized C1 constraint is obtained. It can be represented as:

[0109]

[0110] Output of the fully connected layer FC4 By constraining the total transmit power C2, the updated digital precoding matrix is ​​obtained. It can be represented as:

[0111]

[0112] According to known and Calculate the hybrid precoding matrix W after the current iteration update. * , can be represented as:

[0113]

[0114] In the LNN2 network, the SE in the i-th sub-loop and the j-th main loop can be represented as:

[0115]

[0116] in, This represents the hybrid precoding matrix of the i-th sub-loop and the j-th main loop at the m-th subcarrier. This is the phase shift matrix for initialization or updating. The specific flowchart of the LNNM-BF algorithm proposed in this invention is shown in Table 1.

[0117] Table 1 Key steps of the LNNM-BF algorithm

[0118]

[0119]

[0120]

[0121] D. Complexity Analysis

[0122] The complexity of the LNNM-BF algorithm proposed in this invention mainly comes from the LNN1 sub-network, the LNN2 sub-network, and the three nested loops. Firstly, the complexity of the LNN1 sub-network mainly stems from the calculation of the SE, the embedded LNN, the fully connected layer, and the phase shift ψ = SΦ of the reflection unit. This invention considers an XL-IRS-assisted near-field broadband THz massive MIMO system, where the BS is equipped with N antennas. t The number of reflective units N in XL-IRS is much greater than the number of RF chains N. RF The number of antennas U and data stream N of the UE S (N S =U≤N RF < <N t ≤N), so the complexity of calculating the SE of the UE on subcarrier m using formula (11) is Then formula (11) is repeated M times, and finally the computational complexity of SE is obtained as The computational complexity of the phase shift ψ = SΦ of the embedded LNN network, fully connected layers, and reflection units is... Therefore, the complexity of a single iteration within LNN1 can be expressed as:

[0123] Next, the complexity of the LNN2 subnetwork mainly consists of the computation of SE, the embedded LNN, the fully connected layer, and the precoding matrix W. Therefore, the complexity of a single iteration within LNN2 can be expressed as... Finally, considering the three-level nested loop iteration, the overall complexity of the LNNM-BF algorithm proposed in this invention is...

[0124] Among them I i This indicates the number of iterations in the sub-loop.

[0125] IV. Simulation Results

[0126] This section presents simulation results to quantify the advantages of the proposed LNNM-BF algorithm. XL-IRS-assisted near-field broadband THz massive MIMO systems, such as... Figure 1 As shown. This invention assumes that the direct link is blocked by an obstacle, and the user can only communicate with the BS through the passive reflection of the XL-IRS. Channel modeling uses formulas (4) and (9). The THz channel is assumed to contain one LoS path and three NLoS paths, and the noise is calculated as σ.2 = -174 + 10lgB. In the simulation, the proposed LNNM-BF algorithm in I s The average result on independent channel samples is compared with the benchmark algorithm. Parameter I s I e 、I0、I i n0 is set to 100, 500, 1, 1, and 5, respectively. Unless otherwise specified, the main parameter settings of the simulation system of this invention are shown in Table 2, and the algorithm parameter settings are shown in Table 3. Furthermore, the benchmark algorithm compared to this invention is shown below:

[0127] Baseline 1 (GMML): It uses a gradient-based manifold learning algorithm to solve the SE maximization problem, takes the gradient as the network input, and uses manifold learning to reduce the overhead of high-dimensional signal processing.

[0128] Baseline 2 (FZ-SPM): Based on the Fresnel zone design of XL-IRS phase shift. Reflector units located in the same Fresnel zone are designed with the same phase shift, and ideal beamforming is used at the BS end to suppress near-field dual-beam splitting effect.

[0129] Baseline 3 (VSA-BF): Phase shift design of reflection units based on XL-IRS virtual subarray. Each subarray is designed with a phase shift for the center frequency of different subcarriers, while maximum ratio combining is used at the BS end to optimize the received signal, thereby mitigating the near-field dual-beam splitting effect.

[0130] Baseline 4 (Ref-BF): Based on the literature (Y. Cheng, C. Huang, W. Peng, M. Debbah, L. Hanzo, and C.

[0131] Yuen, “Achievable rate optimization of the RIS-aided near-fieldwideband uplink,” IEEE Trans.

[0132] The phase shift design of the upper bound of the SE in Wireless Commun., vol.23, no.3, pp.2296–2311, Mar.2024. ignores hardware limitations and assumes that the phase shift of the XL-IRS reflector unit can be designed according to the frequency of different subcarriers, while the BS end uses maximum ratio combining.

[0133] Baseline 5 (PDF): A phase delay focusing algorithm with an alternating delay phase precoding structure for handling beam splitting effects in near-field broadband MIMO systems.

[0134] Table 2 Simulation System Parameter Settings

[0135] Parameter name value Number of BS transmitting antennas <![CDATA[N t =256]]> XL-IRS reflective unit number N＝512 Number of user receiving antennas U＝4 RF chain number <![CDATA[N RF =4]]> Data Stream <![CDATA[N S =4]]> Center frequency <![CDATA[f c =300GHz]]> bandwidth B = 30GHz XL-IRS reflector spacing d=λ / 2 Distance between the scatterer (or UE) and the origin r = 5m ~ 50m BS maximum transmit power <![CDATA[P t =-10dBm~20dBm]]>

[0136] Table 3 LNNM-BF Algorithm Parameter Settings

[0137]

[0138]

[0139] Under the perfect CSI assumption and P t When the value is 10dBm, the convergence process of the algorithm is as follows: Figure 3As shown in the simulation results, the LNNM-BF algorithm proposed in this invention outperforms the PDF, VSA-BF, and FZ-SPM algorithms in the 20th, 29th, and 76th iterations, respectively. Furthermore, the LNNM-BF algorithm exhibits a faster convergence speed and a better final convergence value compared to the GMML algorithm. The GMML algorithm has the lowest SE value because it is a far-field narrowband algorithm that designs phase shifts based on the center carrier frequency, which cannot effectively alleviate SE loss at edge frequencies. Simultaneously, the GMML algorithm can only update weight parameters based on the current iteration input, limiting its learning ability and making it difficult to learn nonlinear phase characteristics and subtle changes in the near-field channel environment. The PDF algorithm's SE value is not ideal because it employs an alternating delay phase precoding structure based on a true delayer at the BS end, which can alleviate beam splitting effects at the BS end, but cannot specifically address the beam splitting problem at the XI-IRS end. This also illustrates the importance of simultaneously and rationally designing beam focusing at both the BS and XI-IRS ends when dealing with near-field dual-beam splitting effects. The SE value of the VSA-BF algorithm is lower than the final convergence value of the LNNM-BF algorithm proposed in this invention. This is because the VSA-BF algorithm designs the phase shift individually for each subarray, which, although it can alleviate the beam splitting effect at the XI-IRS end, suffers a severe gain loss. The FZ-SPM algorithm designs the XL-IRS phase shift based on the Fresnel zone, and the reflection units located in the same Fresnel zone are designed with the same phase shift, so that signals of different frequencies are coherently superimposed at the user position. Although this avoids virtual subarray division, the Fresnel zone is a continuous region, while the reflection units of the XL-IRS are discrete. The phase shift design of the reflection units at the edge of the Fresnel zone is obviously not optimal, resulting in a lower SE value than the LNNM-BF algorithm. The LNNM-BF algorithm proposed in this invention is closest to the ideal optimal value in broadband beam focusing performance. This is attributed to the LNNM-BF algorithm's introduction of an index matrix to flexibly divide the reflection units of the XL-IRS, and the design of frequency-related hybrid precoding at the BS end, which aims to maximize the system SE and effectively alleviate the near-field dual-beam splitting effect. While the Ref-BF algorithm can achieve the maximum SE, the XL-IRS reflector unit cannot be configured with a different phase shift matrix at each frequency, making it impractical for broadband systems. Therefore, the LNNM-BF algorithm proposed in this invention exhibits significant advantages in convergence and near-field feature learning, mitigating the near-field dual-beam splitting effect by iteratively converging to the optimal solution.

[0140] Under the perfect CSI assumption, the impact of different distances from XL-IRS to UE on SE, such as Figure 4As shown, in XL-IRS-assisted near-field broadband THz massive MIMO systems, the closer the distance between the XL-IRS and the UE, the more pronounced the near-field effect. Compared to benchmark algorithms, the LNNM-BF algorithm proposed in this invention exhibits near-optimal SE performance as the near-field effect becomes increasingly significant. This is attributed to the introduction of an index matrix to partition the XL-IRS array, which not only solves the SE loss caused by fixed subarray partitioning but also overcomes the SE loss caused by inaccurate phase shift of edge reflection units when partitioning the XL-IRS array based on Fresnel zones, effectively mitigating the beam splitting effect at the XL-IRS end. Furthermore, the LNNM-BF algorithm iteratively optimizes both the frequency-independent analog precoding matrix and the frequency-dependent digital precoding matrix simultaneously, mitigating the beam splitting effect at the BS end and improving the system's SE. It is noteworthy that the SE of all algorithms in the figure gradually decreases with increasing distance r. This is because the greater the distance r from the XL-IRS to the user, the greater the path loss, thus leading to a gradual decrease in SE. Excluding the Ref-BF algorithm, the LNNM-BF algorithm proposed in this invention outperforms other benchmark algorithms in terms of SE within a distance of 5 to 50 meters from XL-IRS to UE, proving the effectiveness of the LNNM-BF algorithm in mitigating the near-field two-beam splitting effect.

[0141] To verify the robustness of the proposed LNNM-BF algorithm, the impact of different transmit powers on the SE under different CSI assumptions was simulated. Figure 5 The SE comparison graph (a) for different transmit powers in Figure 1 shows that, under the perfect CSI assumption, the LNNM-BF algorithm outperforms other benchmark algorithms except the Ref-BF algorithm in the SE performance range of -10dBm to 20dBm. This indicates that the LNNM-BF algorithm can fully learn the near-field broadband beam focusing characteristics assisted by XL-IRS, capture the nonlinear phase shift relationship of the near-field channel, and effectively alleviate the near-field dual-beam splitting effect, thus improving SE performance. Notably, when the transmit power is 20dBm, the SE of the LNNM-BF algorithm is improved by 29.93%, 20.95%, and 7.87% compared to the PDF, VSA-BF, and FZ-SPM algorithms, respectively, proving that the LNNM-BF algorithm achieves higher SE in XL-IRS-assisted near-field broadband THz massive MIMO systems. Figure 5Figure (b) shows the SE comparison for different transmit powers when CEE=1. Simulation results show that when CEE=1, the proposed LNNM-BF algorithm consistently outperforms the benchmark algorithm in the range of -10dBm to 20dBm. Specifically, the SE performance of the LNNM-BF algorithm in this invention reaches 88.16% of the perfect CSI assumption when CEE=1, while the SE performance of the GMML, PDF, VSA-BF, FZ-SPM, and Ref-BF algorithms are 74.00%, 70.45%, 67.92%, 64.90%, and 67.90% respectively under the perfect CSI assumption. The PDF, VSA-BF, FZ-SPM, and Ref-BF algorithms all require accurate CSI to achieve effective beam focusing optimization, resulting in low SE in scenarios with CEE. Specifically, the PDF algorithm compensates for beam splitting effects based on the phase difference between arrays, thus requiring accurate CSI information for phase compensation through the joint design of phase shifters and true time delayers. Under the imperfect CSI assumption, the VSA-BF and Ref-BF algorithms cannot accurately focus the phase shift at the user's location, resulting in signal superposition mismatch and severe SE loss. The FZ-SPM algorithm requires accurate Cartesian coordinates of the BS and UE, which are then converted into corresponding Fresnel zone coordinates. Therefore, in scenarios with CEE, using the FZ-SPM algorithm will cause severe SE loss. The GMML algorithm has the lowest SE in the XL-IRS-assisted near-field broadband THz massive MIMO system, indicating that phase shift design based on center frequency is not suitable for broadband systems in narrowband systems, causing substantial SE loss. The above results demonstrate that the LNNM-BF algorithm proposed in this invention exhibits significant advantages in the XL-IRS-assisted near-field broadband THz massive MIMO system. It not only effectively alleviates the near-field dual-beam splitting effect but also demonstrates excellent robustness, providing an innovative solution for achieving high SE communication.

[0142] P t When CEE = 10dBm, the SE curves for different CEE values ​​are as follows: Figure 6As shown, by changing the value of CEE, the corresponding changes in system SE can be observed. Simulation results show that as CEE increases, the SE of all algorithms gradually decreases. Among them, the PDF, VSA-BF, FZ-SPM, and Ref-BF algorithms show the most significant SE decrease with increasing CEE. This is because these algorithms require accurate CSI information to design the optimal phase shift, and the SE loss is severe when CEE is present. In particular, the Ref-BF algorithm has a lower SE than the LNNM-BF algorithm proposed in this invention when CEE = 0.7, demonstrating the importance of robust algorithms in the design of XL-IRS-assisted near-field broadband THz massive MIMO systems. The LNNM-BF algorithm shows a more gradual decrease in SE with increasing CEE compared to the benchmark algorithms. This is attributed to the algorithm continuously iterating through the meta-learning architecture and learning the optimal decision through the embedded LNN, thereby obtaining the optimal phase shift matrix Θ and the simulated precoding matrix F. PS and digital precoding matrix F BB Therefore, the LNNM-BF algorithm proposed in this invention maintains high SE performance as the CEE value increases, proving that the LNNM-BF algorithm significantly reduces the channel estimation accuracy requirements of broadband near-field applications.

[0143] In summary, the beam focusing method based on liquid neural networks and meta-learning described in the above embodiments proposes an LNNM-BF algorithm with strong robustness and unsupervised learning capabilities. The LNNM-BF algorithm designs the phase shift matrix Θ using an index matrix and a phase compensation matrix, and then designs the analog precoding matrix F at the BS end. PS and digital precoding matrix F BB This algorithm effectively mitigates the near-field dual-beam splitting effect without introducing an additional true time delay unit. Furthermore, the LNNM-BF algorithm enhances the adaptability of beam focusing to imperfect CSI through a meta-learning framework, improving its robustness. Simultaneously, the embedded LNN dynamically adjusts the topology and connection weights between neurons based on the current input and previously implicit iterative information, maximizing SE. Extensive simulation experiments demonstrate that the LNNM-BF algorithm, compared to existing beam focusing algorithms, better mitigates the near-field dual-beam splitting effect, thus providing a high SE and robust algorithm for XL-IRS-assisted near-field broadband THz large-scale MIMO scenarios.

[0144] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A beam focusing method based on liquid neural networks and meta-learning, characterized in that, Includes the following steps: S1: Determine the system model Establish an XL-IRS-assisted near-field broadband THz massive MIMO system, including one equipped with N t A base station with 1 antenna, an XL-IRS with N reflector elements, and a single user equipment (UE) with U antennas deployed. S2: Determine the optimization objective The simulation precoding matrix F will be jointly optimized. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is optimized by maximizing SE; S3: Joint Optimization Joint optimization using the LNNM-BF algorithm based on LNN and meta-learning is employed. LNN is then applied to an XL-IRS-assisted near-field broadband THz massive MIMO system, and the precoding matrix F is simulated iteratively. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is used to maximize the SE of the XL-IRS-assisted near-field broadband THz massive MIMO system. At the same time, a meta-learning framework with three nested loops is adopted to enhance the adaptability of beam focusing to imperfect CSI and improve the robustness of the system.

2. The beam focusing method based on liquid neural network and meta-learning according to claim 1, characterized in that, In the XL-IRS-assisted near-field broadband THz massive MIMO system described in step S1, the direct communication between the BS and UE is blocked by buildings. The UE can only communicate with the BS via the XL-IRS, employing orthogonal frequency division multiplexing with M subcarriers. The BS simultaneously transmits N... S A data stream, the UE's received signal at the m-th subcarrier. It is expressed as follows: y m =H m ΘG m W m s m +n m in, and Let Θ represent the channel matrices between XL-IRS and UE and between BS and XL-IRS at the m-th subcarrier, respectively, Θ = diag(θ1, θ2, ..., θ N ) represents the phase shift matrix of XL-IRS. ψ represents the reflection coefficient of the nth XL-IRS reflective unit. n ∈[0,2π), ψ n This represents the phase shift caused by the nth XL-IRS reflective unit. This represents the hybrid precoding matrix at the m-th subcarrier. It is a frequency-independent analog precoding matrix. It is the digital precoding matrix at the m-th subcarrier. It is the transmitted signal at the m-th subcarrier, satisfying It follows a Gaussian distribution. The additive white Gaussian noise has a variance of σ. 2 N S =U≤N RF < <N t N RF The number of radio frequency chains to be deployed at the BS end.

3. The beam focusing method based on liquid neural network and meta-learning according to claim 2, characterized in that, In step S2, the achievable SE quantization of the UE on subcarrier m is as follows: in, Indicates a cascaded channel, I U It is an identity matrix of size U×U, [·] H The expression represents the conjugate transpose, and det(·) represents the determinant operation.

4. The beam focusing method based on liquid neural network and meta-learning according to claim 3, characterized in that, In step S2, the optimization problem of maximizing SE is formulated as follows: in, This represents the average SE over all subcarriers, used to quantize the SE of an XL-IRS-assisted near-field wideband THz massive MIMO system. BB =(F BB,1 ,F BB,2 …,F BB,M P represents the set of all subcarrier digital precoding matrices, i.e., the digital precoding matrix. t For the transmit power of each data stream, the C1 constraint describes that each item of the analog precoding matrix must satisfy the normalization constraint, the C2 constraint indicates that the total transmit power of the BS is finite, and the C3 constraint is the equal modulus constraint of the XL-IRS reflector unit.

5. The beam focusing method based on liquid neural network and meta-learning according to claim 4, characterized in that, In step S3, the LNNM-BF algorithm includes two sub-networks, LNN1 and LNN2, and three nested loops: a sub-loop, a main loop, and an iterative loop. The specific details of the three nested loops are as follows: Sub-loop: The sub-loop is used to optimize the analog precoding matrix F through the LNN1 and LNN2 sub-networks. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS; Main Loop: The main loop is used to accumulate the loss function. To achieve unsupervised learning, the loss function in the j-th main loop is represented by the negative of SE. Among them, F PS * F BB * and Θ * These represent the analog precoding matrix, digital precoding matrix, and phase shift matrix after each main loop update; Iterative Loop: The iterative loop is used to update the parameters in the LNN1 and LNN2 subnetworks. In each iteration loop, there is I... o The main loop accumulates the average of the loss function and uses the Adam optimizer for backpropagation to update the parameter set θ in the LNN1 and LNN2 subnetworks. Θ and θ W .

6. The beam focusing method based on liquid neural network and meta-learning according to claim 5, characterized in that, The LNN1 subnetwork is used to optimize the phase shift matrix Θ of the XL-IRS design. It includes an LNN, parallel fully connected layers FC1 and FC2, and parallel Lambda1 and Lambda2 layers. The LNN consists of three layers of liquid neurons whose synapses are connected using a neural circuit strategy. These neurons are used to select the optimal trajectory and generate shared features. The two parallel fully connected layers FC1 and FC2 are used to output the index matrix updated in the current iteration. and phase compensation matrix The output of the fully connected layer FC1 is passed through a sigmoid function to ensure that the output is controlled within the range of 0 to 1. Then, it is processed by a Lambda1 layer to output an index matrix containing only 0 and 1 elements, and satisfies... Similarly, to ensure the row summation is 1, the output of the fully connected layer FC2 is controlled within the range of 0 to 1 by using a sigmoid function, and then processed by a Lambda2 layer to adjust the phase compensation matrix Φ. * Within the range of 0 to 2π, the index matrix and the phase compensation matrix are then multiplied to obtain the updated phase shift for each XL-IRS reflector element. Subsequently, to satisfy the equal modulus constraint C3 of the XL-IRS reflector unit, the updated reflection coefficient θ is obtained using Euler's formula. * Finally, through diagonal operations Θ * =diag(θ) * The updated phase shift matrix Θ is obtained. * .

7. The beam focusing method based on liquid neural network and meta-learning according to claim 6, characterized in that, In the LNN1 sub-network, the SE representation in the i-th sub-loop and the j-th main loop is as follows: Where, Θ (i,j) This represents the phase shift matrix in the i-th sub-loop and the j-th main loop. It is the hybrid precoding matrix at the m-th subcarrier after initialization or update.

8. The beam focusing method based on liquid neural network and meta-learning according to claim 5, characterized in that, The LNN2 subnetwork is used to optimize the analog precoding matrix F. PS and digital precoding matrix F BB It includes an LNN, parallel fully connected layers FC3 and FC4, a parallel Lambda3 layer, and a BS total emission power C2 constraint unit. The LNN consists of three layers of liquid neurons with synapses connected using a neural circuit strategy, used to select the optimal trajectory and generate shared features. The two parallel fully connected layers FC3 and FC4 are used to output the simulated precoding matrix updated in each iteration. and digital precoding matrix The output of the fully connected layer FC3 is passed through a sigmoid function to ensure that the output is controlled within the range of 0 to 1. Then, after processing by the Lambda3 layer, the updated phase shift angle is output within the range of 0 to 2π. Finally, the analog precoding matrix that satisfies the normalized C1 constraint is obtained. Output of the fully connected layer FC4 The updated digital precoding matrix is ​​obtained by using the total transmit power C2 constraint unit.

9. A beam focusing method based on liquid neural network and meta-learning according to claim 8, characterized in that, In the LNN2 network, the SE representation in the i-th sub-loop and the j-th main loop is as follows: in, This represents the hybrid precoding matrix of the i-th sub-loop and the j-th main loop at the m-th subcarrier. It is the phase shift matrix for initialization or updating.

10. A beam-focusing system based on liquid neural networks and meta-learning, employing the method described in any one of claims 1 to 9 to mitigate the near-field dual-beam splitting effect in an XL-IRS-assisted near-field broadband THz massive MIMO system, comprising: The system model determination module is used to establish an XL-IRS-assisted near-field broadband THz massive MIMO system, including N... t A base station with 1 antenna, an XL-IRS with N reflector elements, and a single user equipment (UE) with U antennas deployed. The optimization objective determination module is used to jointly optimize the simulated precoding matrix F. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is optimized by maximizing SE; The joint optimization module utilizes the LNNM-BF algorithm based on LNN and meta-learning for joint optimization, applying LNN to an XL-IRS-assisted near-field broadband THz massive MIMO system, and iteratively simulating the precoding matrix F. PS Digital precoding matrix F BB The phase shift matrix Θ of XL-IRS is used to maximize the SE of the XL-IRS-assisted near-field broadband THz massive MIMO system. At the same time, a meta-learning framework with three nested loops is adopted to enhance the adaptability of beam focusing to imperfect CSI and improve the robustness of the system.

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