Terahertz Ultra-Large-Scale Intelligent Meta-Surface Assisted Communication and Positioning Integration Method

Abstract

A communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurfaces belongs to the field of communication and sensing integration in wireless communication. Based on the assistance of intelligent metasurfaces, the present invention uses the relevant operations in the channel estimation of the orthogonal matching pursuit algorithm to provide initial conditions for positioning, and optimizes the dictionary in the channel estimation with the positioning results, bringing performance gain to the channel estimation. At the same time, positioning is completed during the process of channel estimation; by extending the orthogonal matching pursuit algorithm, multiple atoms are selected simultaneously during the iteration process, effectively overcoming the problem of large correlation of the hybrid field dictionary, and at the same time using the polar coordinate domain frequency-dependent dictionary to effectively overcome the beam offset effect; by using the polar coordinate domain gradient descent algorithm and the method of the polar coordinate domain hierarchical dictionary respectively when the intelligent metasurface is turned off and on, the user is effectively positioned. The present invention is applicable to scenarios such as communication, vehicle networking, smart cities, and smart factories, realizing an efficient combination of communication and positioning.

Description

Technical Field

[0001] The present invention relates to a communication and positioning integration method assisted by a terahertz ultra-large-scale intelligent metasurface, belonging to the field of communication and sensing integration in wireless communication. Background Art

[0002] In the complex application scenarios of future 6G, the information processing process presents the characteristics of highly coupled communication and sensing. The white paper "Research Report on Communication and Sensing Integration Technology" of the IMT-2030 (6G) Promotion Group points out that communication and sensing integration will simultaneously realize the coordination of sensing and communication functions based on the sharing of software and hardware resources or information sharing, which can effectively improve the system spectrum efficiency, hardware efficiency and information processing efficiency. Channel estimation and positioning are two basic and important tasks in communication and sensing.

[0003] From 5G to 6G, the frequency band is continuously increasing, and the carrier frequency will move from millimeter wave to terahertz; at the same time, a higher frequency band means a smaller carrier wavelength, which also means a smaller element spacing, making it possible to deploy an array with more elements in a limited area. Therefore, compared with the large-scale array of 5G, 6G will adopt an ultra-large-scale array to improve the spectrum efficiency. The high-frequency band and large array of 5G and 6G bring the sparsity characteristics in the channel delay domain and angle domain, so many compressed sensing methods have been proposed. The compressed sensing methods in channel estimation can be roughly divided into three categories: a. Optimization methods, such as the LASSO algorithm; b. Greedy methods, such as the orthogonal matching pursuit algorithm; c. Message passing methods, such as approximate message passing. Due to the complex application scenarios of future 6G, channel estimation based on the extended methods of the above three categories has attracted great attention in both academia and industry. At the same time, research on network positioning using the high angle resolution or high delay resolution brought by large arrays or large bandwidths has emerged in an endless stream. There are studies using the orthogonal matching pursuit algorithm and the expectation maximization algorithm to estimate the delay and angle of the user arriving at the base station, which relies on the existence of scatterers and determines the position of the user itself while estimating the position of the scatterers; there are studies using multiple base stations as anchor points to directly estimate the user position instead of estimating the angle of arrival and delay first and then performing positioning; there are also studies that have derived the Cramer-Rao lower bound in positioning and quantitatively analyzed the gain that can be obtained in positioning with the assistance of a flexibly deployable low-power intelligent metasurface, providing theoretical guidance for designing corresponding positioning algorithms and deploying intelligent metasurfaces.

[0004] However, the above research did not consider how to combine channel estimation and positioning in the 6G communication network. At the same time, under the hybrid field offset effect caused by the extremely large bandwidth and extremely large array in the 6G communication network, how to accurately locate users and how to perfectly recover the channel state information have not been solved. Therefore, there is an urgent need to further study a communication and positioning integration method that can overcome the terahertz hybrid field beam offset effect with the assistance of intelligent metasurfaces. Summary of the Invention

[0005] Aiming at the problem of how to overcome the hybrid field beam offset effect caused by terahertz and extremely large arrays with the assistance of extremely large-scale intelligent metasurfaces and efficiently combine channel estimation in communication and positioning in sensing, the main purpose of the present invention is to provide a communication and positioning integration method assisted by terahertz extremely large-scale intelligent metasurfaces. By combining the generalized orthogonal matching pursuit algorithm, the polar coordinate domain gradient descent algorithm, and the polar coordinate domain hierarchical dictionary, high-precision positioning of users is completed while estimating the channel, and the positioning result is used to improve the accuracy of channel estimation.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] The communication and positioning integration method assisted by terahertz extremely large-scale intelligent metasurfaces disclosed in the present invention takes the initial correlation result of channel estimation as the initial condition for positioning. When the intelligent metasurface is turned off, the polar coordinate domain gradient descent algorithm is used, and when the intelligent metasurface is turned on, the polar coordinate domain hierarchical dictionary is used to obtain the angles of the user arriving at the base station and the intelligent metasurface respectively, thereby completing the high-precision positioning of the user. Using the user's position, the dictionary in the generalized orthogonal matching pursuit algorithm is updated, and then channel estimation operations are performed to obtain more accurate channel estimation results, thereby reducing or eliminating the hybrid field beam offset effect caused by terahertz and extremely large arrays.

[0008] The communication and positioning integration method assisted by terahertz extremely large-scale intelligent metasurfaces disclosed in the present invention includes the following steps:

[0009] Step 1: Use a polar coordinate domain frequency-dependent dictionary to divide the common area served by the base station and the intelligent metasurface.

[0010] The areas served by the base station and the intelligent metasurface are divided in terms of angle and distance to generate a polar coordinate domain frequency-dependent dictionary. This dictionary is evolved from the Fourier transform matrix, and each element in the dictionary has both sampling of angles and sampling of distances to reduce the adverse effects of the near-field energy diffusion effect; and the generated dictionary takes into account the differences in dictionaries on different subcarriers brought by the large bandwidth, so that the polar coordinate domain frequency-dependent dictionary can overcome the hybrid field beam offset effect.

[0011] The polar coordinate domain frequency-dependent dictionaries generated at the base station and the intelligent metasurface are represented by and respectively. θ BU and θ RU are the angles of the user arriving at the base station and the intelligent metasurface respectively, and r BU and r RU are the distances of the user arriving at the base station and the intelligent metasurface respectively. N / N RIS , Q NRIS / Q RIS and M are the number of array elements of the base station / intelligent metasurface, the number of atoms in the dictionary at the base station / intelligent metasurface, and the number of subcarriers respectively. The angles in the served area are uniformly sampled at N / N RIS points, and the distances are sampled at S points according to the inverse proportional function. Then Q NRIS =NS, Q RIS =N RIS S. "Polar coordinate domain" means that each element in the dictionary is composed of an angle and a distance in the served area. "Frequency dependence" means that the dictionaries for different subcarriers need to consider the specific subcarrier size instead of being replaced by the center carrier frequency uniformly. For a frequency of f m , the sine value of the central angle θ (i.e., the true angle ) to the base station or the intelligent metasurface, and the distance to the center of the base station or the intelligent metasurface is r, the element in the dictionary is expressed as

[0012]

[0013] where is the distance from a point in the area to the nth array element of the base station or the intelligent metasurface, δ n =(2×n - N + 1) / 2, n = 0, …, N - 1 / δ n =(2×n - N RIS +1) / 2, n = 0, …, N RIS -1 is the index of the array element of the base station or the intelligent metasurface, and the central array element is the zero point of the index; d is the array element spacing; is the wave number of the mth subcarrier, and λ m is the wavelength of the mth subcarrier.

[0014] Step 2: Turn off and turn on the intelligent metasurface, multiply the observation matrix by the polar coordinate domain frequency-dependent dictionary, correlate the result with the received signal, and obtain the rough angles of the user arriving at the base station and the intelligent metasurface respectively according to the correlation results.

[0015] Turn off the intelligent metasurface and turn on the intelligent metasurface. Perform the correlation operation of the product of the observation matrix and the polar coordinate domain frequency-dependent dictionary with the received signal, extract the angle index where the maximum correlation value is located, and obtain the preliminary angles of arrival from the user to the base station and the intelligent metasurface. The relevant expressions for turning off the intelligent metasurface and turning on the intelligent metasurface are as follows: and are as follows:

[0016]

[0017] where is the sine value of the angle from the user to the base station / intelligent metasurface ; is the base station observation matrix after stacking multiple time slots when the intelligent metasurface is not turned on; is the observation matrix jointly composed of the base station phase shift network, the channel from the intelligent metasurface to the base station, and the phase matrix of the intelligent metasurface after stacking multiple time slots when the intelligent metasurface is turned on. Since the intelligent metasurface is pre-deployed, the channel from the intelligent metasurface to the base station is completely known; and are the polar coordinate domain frequency-dependent dictionaries on the base station side and the intelligent metasurface side respectively. m represents the subcarrier index, and M is the number of subcarriers; and are the received signals on the m-th subcarrier when the intelligent metasurface is not turned on and when the intelligent metasurface is turned on respectively, received by the base station; and are the Gaussian noises on the m-th subcarrier when the intelligent metasurface is turned off and when the intelligent metasurface is turned on respectively. N is the number of base station antenna elements, and N RIS is the number of elements of the intelligent metasurface; N RF is the number of radio frequency links; P NRIS and P RIS are the uplink communication time slot numbers when the intelligent metasurface is turned off and when the intelligent metasurface is turned on respectively. Then, select the optimal angle according to the following formula:

[0018]

[0019] where I(θ BU ,r BU ) and I(θ RU ,r RU ) represent the row indices of Γ BU and Γ RU where θ NRIS and θ RIS are located respectively.

[0020] The received signals obtained by turning off the intelligent metasurface and turning on the intelligent metasurface are as follows:

[0021]

[0022]

[0023] Among them, are the channels from the user to the base station and the intelligent metasurface on the m-th subcarrier, respectively. The near-field multipath cluster sparse channel from the user to the base station is:

[0024]

[0025] where the subscripts m, l, and g represent the subcarrier, cluster, and the sequence number of the inner diameter of the cluster, respectively; the l-th cluster has paths, and there are a total of L BU clusters, and l = 0 represents the direct path; is the channel complex gain; f m is the subcarrier frequency; and represent the angle and distance from the user to the central element of the base station antenna, respectively; since the direct path does not form a cluster and has only one path, that is For simplicity, the subscript g of the direct path is omitted, and and represent the channel gain of the direct path, the angle at which the user arrives at the base station, and the distance, respectively. is the steering vector of the hybrid field and is modeled as follows

[0026]

[0027] where is the distance from the user to the n-th antenna element of the base station; The central element of the antenna is taken as the reference zero point; d is the element spacing of the antenna.

[0028] Similarly, the near-field multipath cluster sparse channel from the user to the intelligent metasurface is:

[0029]

[0030] where the l-th cluster has paths, and there are a total of L RU clusters, and l = 0 represents the direct path; is the channel complex gain; f m is the subcarrier frequency; and represent the angle and distance from the user to the central element of the base station antenna, respectively; since the direct path does not form a cluster and has only one path, that is For simplicity, the subscript g of the direct path is omitted, and and They represent the channel gain of the direct path, the angle at which the user reaches the smart metasurface, and the distance, respectively. is the steering vector of the mixed field, modeled as follows,

[0031]

[0032] in, is the distance from the user to the nth element of the smart metasurface; and The center array element is the reference zero point; d is the array element spacing.

[0033] Step 3: Use the polar coordinate domain gradient descent algorithm and the polar coordinate domain hierarchical dictionary to optimize the arrival angle of the user to the base station and the smart metasurface respectively.

[0034] First, the existing gradient descent algorithm is used to optimize the arrival angle from the user to the base station. Since the dictionary used in channel estimation and positioning is a frequency-dependent dictionary in the polar coordinate domain, the gradient descent algorithm in the case of a terahertz ultra-large-scale array is called the polar coordinate domain gradient descent algorithm. The difference between the polar coordinate domain gradient descent algorithm used and the traditional gradient descent algorithm lies mainly in the loss function v NRIS The structure of is as shown below:

[0035]

[0036] in, is the processed received signal; is the virtual direct path channel from the user to the base station, and its expression is:

[0037]

[0038] in, and are the estimated channel gain, angle, and distance from the user to the base station, respectively. Yes NRIS A variant of

[0039]

[0040] in, The premise is that the phase shift network of the base station needs to be specially processed as follows, that is, for

[0041]

[0042] and Each element from the second row to the last row of satisfies the constant modulus constraint, and the modulus value is The phase is randomly set and follows a uniform distribution from 0 to 2π. The influence of is removed from the received signal. Meanwhile, when generating the loss function, the virtual channel is also not This enables the angle from the user to the base station to be estimated without being affected by the not entirely accurate distance from the user to the base station so as to optimize the angle based on the not entirely accurate distance. For the derivative of the loss function with respect to the angle and the Armijo-Goldstein criterion for step size selection during the update process, the existing gradient descent algorithm is adopted.

[0043] Secondly, the polar coordinate domain hierarchical dictionary W RIS,PHD is used to optimize the angles of arrival from the user to the base station and the intelligent metasurface. The optimization objective function is constructed as follows.

[0044]

[0045] Then, according to the following formula, the optimal angle is selected

[0046]

[0047] where denotes the RIS th row of Γ. After each selection of the optimal angle, the angle sampling interval and sampling range of the next polar coordinate domain hierarchical dictionary will be reduced to of the previous iteration to gradually approach the true value until the sampling interval is reduced to the threshold γ and the iteration stops.

[0048] Step 4: Obtain the accurate position of the user using the positions of the base station and the intelligent metasurface and the angle of arrival information.

[0049] Based on the positions of the base station and the intelligent metasurface, and the estimated angles of arrival from the user to the base station and the intelligent metasurface, the position of the user is obtained through the intersection of straight lines Its expression is

[0050]

[0051] where (x BS , y BS ) and (x RIS , y RIS ) are the coordinates of the base station and the intelligent metasurface respectively, and are the slopes of the straight lines from the user to the base station and from the user to the intelligent metasurface respectively.

[0052] Step 5: Update the dictionary in the channel estimation process using the user location obtained in Step 4, and then perform the channel estimation operation to further improve the channel estimation performance from the user to the base station and from the user to the intelligent metasurface.

[0053] After obtaining the accurate user location, use the polar-domain frequency-dependent dictionary W NRIS and W RIS generated initially in Step 1 to generate the polar-domain frequency-dependent dictionaries and

[0054]

[0055] where, and are generated from the located user location coordinates. The assistance of the location information can significantly improve the performance of channel estimation at high signal-to-noise ratios. Then perform the channel estimation operation as follows:

[0056] 5.1. Construct the equivalent observation matrices for the case of turning off the intelligent metasurface and turning on the intelligent metasurface

[0057]

[0058] 5.2. Calculate the correlation matrices of the equivalent observation matrices and the residuals for the case of turning off the intelligent metasurface and turning on the intelligent metasurface, denoted as and

[0059]

[0060] where, R NRIS and R RIS are residual matrices, which take the values of Y NRIS and Y RIS respectively in the first iteration, and the calculation method in subsequent iterations is shown in Step 5.5.

[0061] 5.3. Superimpose the values of and on different subcarriers. The vectors representing the correlation magnitudes of different dictionary elements are and

[0062]

[0063] where, i represents the index of the dictionary element. Select the sets of the indices of the top and largest elements in the above formula, which are γ NRIS and γ RIS,

[0064]

[0065] wherein, is the nth element in the set γ NRIS / γ RIS Then, update the support sets of the estimated user-to-base station channel and the user-to-intelligent metasurface channel to Ω NRIS = Ω NRIS ∪γ NRIS and Ω RIS = Ω RIS ∪γ RIS . At the first iteration, Ω NRIS and Ω RIS are empty sets. The proposed terahertz massive intelligent metasurface-assisted communication and positioning integration method not only uses a polar coordinate domain frequency-dependent dictionary, but also, compared with the traditional orthogonal matching pursuit algorithm, the number of atoms selected each time is not limited to one, to adapt to the large correlation between the hybrid field steering vectors and reduce the adverse effects brought by spectral leakage. Compared with selecting only one atom per iteration, this method will have better performance under the same number of iterations.

[0066] 5.4. For each subcarrier, calculate the orthogonal projection matrices on the mth subcarrier for the case of turning off the intelligent metasurface and turning on the intelligent metasurface respectively and

[0067]

[0068] where the superscript represents the Moore-Penrose generalized inverse matrix of the matrix.

[0069] 5.5. Update the residual matrices for the case of turning off the intelligent metasurface and turning on the intelligent metasurface as follows,

[0070]

[0071] After going through the iterations of steps 5.2 to 5.5 for the case of turning off the intelligent metasurface and turning on the intelligent metasurface, where and are the estimated numbers of scatterers from the user to the base station and from the user to the intelligent metasurface respectively, the finally estimated user-to-base station channel and the user-to-intelligent metasurface channel are expressed as follows,

[0072]

[0073] Beneficial effects:​​

[0074] 1. The communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface disclosed in the present invention uses the relevant results of channel estimation in communication as the initial conditions for positioning, and completes high-precision positioning during the process of channel estimation; at the same time, the final positioning result is used to update the dictionary in the channel estimation process, bringing performance gain to channel estimation.

[0075] 2. The communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface disclosed in the present invention effectively overcomes the problem of large correlation of the hybrid field dictionary by expanding the orthogonal matching pursuit algorithm and selecting multiple atoms simultaneously during the iteration process. At the same time, the polar coordinate domain frequency-dependent dictionary is used to effectively overcome the beam offset effect, and good channel estimation performance can be obtained under various signal-to-noise ratios.

[0076] 3. The communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface disclosed in the present invention uses the polar coordinate domain gradient descent algorithm and the polar coordinate domain hierarchical dictionary to estimate the angle from the user to the base station and the angle from the user to the intelligent metasurface respectively. By using the base station and the intelligent metasurface as anchor points, the high-precision user position can be obtained.

[0077] 4. The communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface disclosed in the present invention uses the polar coordinate domain frequency-dependent dictionary, which has both angle sampling and distance sampling, and takes into account the differences in the dictionaries on different subcarriers. Therefore, this method can perform channel estimation and positioning both under far-field plane waves and under near-field spherical waves, and is not affected by the beam offset effect caused by large bandwidth. Description of the Drawings

[0078] Figure 1 is a flowchart of the communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface disclosed in the present invention;

[0079] Figure 2 is a schematic diagram of the application scenario of the communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface disclosed in this embodiment;

[0080] Figure 3 is a comparison chart of the channel estimation performance between this embodiment and a comparison scheme under near-field conditions, with the normalized mean square error as the evaluation index;

[0081] Figure 4 is a comparison chart of the channel estimation performance between this embodiment and a comparison scheme under far-field conditions, with the normalized mean square error as the evaluation index;

[0082] Figure 5Under the condition of a hybrid field, the root mean square error is used as an evaluation index, and the simulation diagram of the angle positioning performance of this embodiment;

[0083] Figure 6 Under the condition of a hybrid field, the root mean square error is used as an evaluation index, and the simulation diagram of the distance positioning performance of this embodiment. Detailed implementation manners

[0084] The present invention will be described in detail below in conjunction with the accompanying drawings and embodiments. At the same time, the technical problems solved by the technical solution of the present invention and the beneficial effects are also described. It should be noted that the described embodiments are only for facilitating the understanding of the present invention and do not limit it in any way.

[0085] Since many scenarios and applications in the future 6G communication network not only require data transmission but also need to know the specific location of the terminal, such as outdoor V2X (vehicle-to-everything) and indoor intelligent factories. Therefore, the present invention is applicable to indoor and outdoor scenarios in the future 6G communication network with data transmission requirements and high-precision user positioning requirements. And due to the extremely large bandwidth and ultra-large-scale antenna array of the 6G communication network, it generates a hybrid field beam offset effect that previous communication networks did not have. This embodiment provides a communication and positioning integration method assisted by a terahertz ultra-large-scale intelligent metasurface for such scenarios. The basic idea is that first, the area served by the base station and the intelligent metasurface is divided by angle and distance to generate a polar coordinate domain frequency-dependent dictionary; then, by turning off and turning on the intelligent metasurface, and calculating the product of the observation matrix and the polar coordinate domain frequency-dependent dictionary, using the result to correlate with the received signal, the preliminary angle information of the user to the base station and the intelligent metasurface is obtained, and the rough position of the user is obtained; secondly, the polar coordinate domain gradient descent algorithm and the polar coordinate domain hierarchical dictionary are respectively used to optimize the angle of the user to the base station and the intelligent metasurface, and the base station and the intelligent metasurface are used as anchor points to obtain the accurate position of the user; finally, the previously generated polar coordinate domain frequency-dependent dictionary is updated, and the subsequent iterative process of the orthogonal matching pursuit-like algorithm is completed to complete channel estimation. Since the present invention uses a polar coordinate domain frequency-dependent dictionary, it can work both under far-field plane waves and under near-field spherical waves, and can overcome the beam offset effect at the same time; the introduction of the generalized orthogonal matching pursuit algorithm can reduce the adverse effects of the large correlation of the polar coordinate domain dictionary and the spectral leakage caused by the fact that the true position of the user is not on the grid points sampled by the dictionary.

[0086] As Figure 2As shown in the figure, the scenario of this embodiment is an outdoor urban area with many building obstructions. The base station needs to provide navigation services while interacting with users for data. The base station serves users within a radius of 50 m centered on the central element of the base station antenna, and the angular range of the service sector is -45° to 45°. Both the base station and the intelligent metasurface have a large number of elements, which makes the Rayleigh distance increase in the terahertz band, and the communication scenario becomes a hybrid field with coexistence of near-field and far-field. At the same time, the terahertz band has a large bandwidth, and different subcarriers can no longer share the same dictionary elements, that is, the steering vector in modeling will be related to the subcarriers. The specific parameters are as follows: The base station antenna adopts a uniform linear array with the number of elements N = 256; the intelligent metasurface adopts a uniform linear array with the number of elements N RIS = 256; the number of radio frequency links of the base station N RF = 4; the carrier frequency f c = 0.1 THz; the bandwidth B = 10 GHz; the number of uplink pilot time slots is P NRIS = 16, P RIS = 32; when simulating in the near-field region, the positions of the center of the base station, the center of the intelligent metasurface, and the user are set to (5.96 m, -10.1 m); when simulating in the far-field region, the positions of the center of the base station, the center of the intelligent metasurface, and the user are set to (11.82 m, -20.1 m); since the scenario of the present invention is a hybrid field scenario, when modeling the channel, the scatterers cannot be regarded as point sources anymore, but the area of the scatterers needs to be considered. In this embodiment, the area of the scatterer is 1 m 2 , each scatterer represents a cluster, and there are 6 paths in a cluster. The channel is modeled as a multipath cluster sparse model. In this embodiment, the scatterers between the user and the base station and the scatterers between the user and the intelligent metasurface are both set to L BU = L RU = 5, and their positions are randomly generated in the area served by the base station through the rand function in MATLAB, and the average performance is obtained through multiple simulations. Specifically, the spherical wave steering vector has the following expression

[0087]

[0088]

[0089] where the subscripts m, l, and g represent the subcarrier, cluster, and the serial number of the path within the cluster respectively; f m is the frequency of the m-th subcarrier; is the distance from the user to the n-th element of the base station / intelligent metasurface; is the distance from the user to the central element of the base station / intelligent metasurface, sampled using a non-uniform inverse proportional function; δn =(2×n - N + 1) / 2, n = 0, …, N - 1 / δ n =(2×n - N RIS + 1) / 2, n = 0, …, N RIS - 1 represents the index of the nth array element, and the central array element of the base station / intelligent metasurface array is used as the reference point; is the sine value of the angle from the user to the base station / intelligent metasurface, uniformly sampled between - 1 and 1, is the angle from the user to the central array element of the base station / intelligent metasurface; d is the array element spacing of the base station / intelligent metasurface; is the wavenumber, λ is the wavelength of the mth sub - carrier. Since the wavelength in the wavenumber is no longer simplified to the carrier wavelength, different sub - carriers will correspond to the same angle and distance, eliminating the beam offset effect. After establishing the expression of the steering vector in the dictionary, the channel of the mth sub - carrier in the present invention can be established as follows, m where, the lth cluster has a total of

[0090]

[0091]

[0092] where, the lth cluster has a total of paths, and there are a total of L BU = L RU = 5 clusters; is the channel complex gain; for simplicity, since the direct path does not form a cluster and there is only one path, the subscript g of the direct path is omitted, and and respectively represent the channel gain of the direct path from the user to the base station / intelligent metasurface, the angle, and the distance. Based on the established channel model, the frequency - domain received signal model of this article can be derived,

[0093]

[0094]

[0095] where, and are the received signals of the mth sub - carrier with the intelligent metasurface turned off and on respectively; and are the observation matrices of the intelligent metasurface turned off and on respectively, and since the channel between the base station and the intelligent metasurface is a broadband channel when the intelligent metasurface is turned on, the observation matrix is frequency - dependent; and are the channels from the user to the base station and the intelligent metasurface, respectively; and are the Gaussian noises on the m-th subcarrier when the intelligent metasurface is turned off and on, respectively. Since the pilot is known to both the transmitter and the receiver and the pilot is set to 1, the transmitted pilot is hidden in the frequency-domain received signal model.

[0096] The terahertz ultra-massive intelligent metasurface-assisted communication and positioning integration method disclosed in this embodiment includes the following steps:

[0097] Step 1: Use a polar coordinate domain frequency-dependent dictionary to divide the common area served by the base station and the intelligent metasurface;

[0098] Divide the area served by the base station and the area served by the intelligent metasurface in terms of angle and distance to generate a polar coordinate domain frequency-dependent dictionary. This dictionary is evolved from the Fourier transform matrix. Each element in the dictionary has both a uniform sampling of the angle and a sampling of the distance in the form of an inverse proportional function to reduce the adverse effects of the near-field energy diffusion effect; and the generated dictionary takes into account the differences in the dictionaries on different subcarriers brought by the large bandwidth, so that the polar coordinate domain frequency-dependent dictionary can overcome the hybrid field beam offset effect. (For the sampling method of the distance, please refer to the literature "Title: Channel Estimation for Extremely Large-Scale MIMO: Far-Field or Near-Field?", its author, the English name source is "M. Cui and L. Dai, "Channel Estimation for Extremely Large-Scale MIMO: Far-Field or Near-Field?", in IEEE Trans. Commu., vol. 70, no. 4, pp. 2663-2677, April 2022.")

[0099] Figure 2 The dark area where the user is located in the figure is the position of the user in the polar coordinate domain dictionary. At the same time, since the present invention considers the beam offset effect under ultra-wideband, that is, the polar coordinate domain dictionary needs to be designed according to the corresponding subcarrier frequencies at different subcarriers, it is named the polar coordinate domain frequency-dependent dictionary W NRIS / W RIS 。N / N RIS is the number of array elements of the base station / intelligent metasurface, S is the number of distance sampling points, and M is the number of subcarriers. In order to reduce the influence of spectrum leakage and improve the performance of channel estimation, this embodiment uses a redundant dictionary, that is, the number of sampling points of the angle is no longer limited to N and N RIS , in Figure 3 , Figure 4 in the simulation, the number of sampling points of the angle is 2N and 2N RIS . Therefore, the dimension of the polar coordinate domain frequency-dependent dictionary is and The elements in the dictionary are valued according to formulas (1) and (2).

[0100] Step 2: Turn off and then turn on the intelligent metasurface, multiply the observation matrix by the polar coordinate domain frequency dependence dictionary, correlate the result with the received signal, and respectively obtain the rough angles of the user arriving at the base station and the intelligent metasurface according to the correlation results;

[0101] The received signals obtained by turning off and then turning on the intelligent metasurface can be modeled as shown in formulas (5) and (6). Turn off and then turn on the intelligent metasurface respectively, and use the correlation operation in formula (7), that is, the correlation of the product of the phase shift network and the polar coordinate domain frequency dependence dictionary with the received signal, extract the angle index where the maximum correlation value is located, and obtain the preliminary arrival angles of the user to the base station and the intelligent metasurface. The correlation expressions for turning off and then turning on the intelligent metasurface, that is, and are as follows

[0102]

[0103] where, θ BU and θ RU are respectively the angle of the user arriving at the base station and the angle of the user arriving at the intelligent metasurface, r BU and r RU are respectively the distance of the user arriving at the base station and the distance of the user arriving at the intelligent metasurface; is the observation matrix composed of the base station phase shift network after stacking multiple time slots when the intelligent metasurface is not turned on; is the observation matrix jointly constituted by the base station phase shift network after stacking multiple time slots when the intelligent metasurface is turned on, the channel from the intelligent metasurface to the base station (since the intelligent metasurface is pre-deployed, the channel from the intelligent metasurface to the base station is completely known), and the phase matrix of the intelligent metasurface; and are respectively the polar coordinate domain frequency dependence dictionaries on the base station side and the intelligent metasurface side, m represents the subcarrier index, and M is the number of subcarriers; and are respectively the received signals on the m-th subcarrier when the intelligent metasurface is not turned on and when the intelligent metasurface is turned on received by the base station; and are respectively the Gaussian noises on the m-th subcarrier when the intelligent metasurface is turned off and when the intelligent metasurface is turned on; N is the number of base station antenna elements, N RIS is the number of elements of the intelligent metasurface; N RF is the number of radio frequency links; P NRIS and P RIS are respectively the uplink communication time slot numbers when the intelligent metasurface is turned off and when the intelligent metasurface is turned on; Each element in satisfies the constant modulus constraint, and the phase satisfies a uniform distribution from 0 to 2π; The value on the m-th subcarrier is

[0104]

[0105] where is the base station phase shift network in the p-th time slot, and the value requirements of each element are the same as is the known channel from the intelligent metasurface to the base station; is the phase matrix of the intelligent metasurface in the p-th time slot, to all satisfy the uniform distribution from 0 to 2π. Then, according to the following formula, the optimal angle is selected,

[0106]

[0107] where I(θ BU ,r BU ) and I(θ RU ,r RU ) respectively represent the row indices of Γ BU and Γ RU where θ NRIS and θ RIS are located.

[0108] Step 3: Optimize the angles of arrival from the user to the base station and the intelligent metasurface using the polar coordinate domain gradient descent algorithm and the polar coordinate domain hierarchical dictionary respectively;

[0109] First, use the existing gradient descent algorithm to optimize the angle of arrival from the user to the base station. Since the dictionary used in channel estimation and positioning is a polar coordinate domain frequency-dependent dictionary, the gradient descent algorithm in the case of terahertz ultra-large-scale arrays is called the polar coordinate domain gradient descent algorithm. The difference between the polar coordinate domain gradient descent algorithm used and the traditional gradient descent algorithm mainly lies in the construction of the loss function, as shown in the following formula

[0110]

[0111] where is the processed received signal; is the virtual direct path channel from the user to the base station, and its expression is

[0112]

[0113] where and are the estimated channel gain, angle, and distance of the direct path from the user to the base station respectively. It is a variant of Y NRIS with the expression

[0114]

[0115] wherein The premise of doing this is that the phase shifter network of the base station needs to be specially designed as follows, that is, let be

[0116]

[0117] while each element from the second row to the last row of is randomly set, the modulus value is fixed as and the phase follows a uniform distribution from 0 to 2π; the purpose of doing this is to remove the influence of in the real channel from the received signal. At the same time, when generating the loss function, the virtual channel also has no In this way, when estimating the angle from the user to the base station, it will not be affected by the not completely accurate distance

[0118] from the user to the base station, so as to optimize the angle based on the not completely accurate distance. For the derivative of the loss function with respect to the angle and the Armijo-Goldstein criterion for step size selection in the update process, the existing gradient descent algorithm is adopted (for the existing gradient descent algorithm, see the literature "Title: Super-Resolution Channel Estimation for MmWave Massive MIMO With Hybrid Precoding" by its author, the English name source is "C. Hu, L. Dai, T. Mir, Z. Gao and J. Fang, "Super-Resolution Channel Estimation for MmWave Massive MIMO With Hybrid Precoding," in IEEE Trans. Veh. Technol., vol. 67, no. 9, pp. 8954 - 8958, Sept. 2018."). RIS,PHD Secondly, use the polar coordinate domain hierarchical dictionary W RIS,PHD to optimize the angles of arrival from the user to the base station and the intelligent metasurface. W RIS is constructed in the same way as the previous W

[0119]

[0120] Then, according to the following formula, select the optimal angle

[0121]

[0122] Among them, represents the row index in Γ RIS . After selecting the optimal angle each time, the angular sampling interval and sampling range of the next polar coordinate domain hierarchical dictionary will be reduced to of the previous iteration to gradually approach the true value until the sampling interval is reduced to the threshold γ = 0.0005 and the iteration stops.

[0123] Step 4: Obtain the accurate position of the user by using the positions of the base station and the intelligent metasurface and the angle of arrival information;

[0124] Through the positions of the base station and the intelligent metasurface, and the estimated angles of arrival of the user to the base station and the intelligent metasurface, the position of the user is obtained by the intersection of straight lines The expression is

[0125]

[0126] Among them, (x BS , y BS ) and (x RIS , y RIS ) are the coordinates of the base station and the intelligent metasurface respectively, and are the slopes of the straight lines from the user to the base station and from the user to the intelligent metasurface respectively.

[0127] Step 5: To further improve the channel estimation performance from the user to the base station and from the user to the intelligent metasurface, update the dictionary in the channel estimation process first, and then perform the channel estimation operation;

[0128] After obtaining the accurate user position, use the polar coordinate domain frequency-dependent dictionaries W NRIS and W RIS generated initially in Step 1 to generate the polar coordinate domain frequency-dependent dictionaries and

[0129]

[0130] Among them, and Generated from the located user position coordinates, the assistance of the positioning information can enable the channel estimation to have a greater performance improvement at high signal-to-noise ratios. Then, the channel estimation operation is performed. The subsequent channel estimation operation is a combination of the polar domain simultaneous orthogonal matching pursuit algorithm (PSOMP) and the generalized orthogonal matching pursuit algorithm (gOMP) (for the PSOMP algorithm, see specifically the literature "Title: Channel Estimation for Extremely Large-Scale MIMO: Far-Field or Near-Field?", its authors, the English name source is "M. Cui and L. Dai, "Channel Estimation for Extremely Large-Scale MIMO: Far-Field or Near-Field?", in IEEE Trans. Commu., vol. 70, no. 4, pp. 2663-2677, April 2022.") (for the gOMP algorithm, see specifically the literature "Title: Generalized Orthogonal Matching Pursuit", its authors, the English name source is "J. Wang, S. Kwon and B. Shim, "Generalized Orthogonal Matching Pursuit", in IEEE Trans. Signal Process., vol. 60, no. 12, pp. 6202-6216, Dec. 2012.").

[0131] 5.1. Construct the equivalent observation matrices for the closed intelligent metasurface and the open intelligent metasurface and

[0132]

[0133] 5.2. Calculate the correlation matrices of the equivalent observation matrices and the residuals for the closed intelligent metasurface and the open intelligent metasurface, denoted as and Their specific expressions are

[0134]

[0135] where R NRIS and R RIS are residual matrices, which take the values of Y NRIS and Y RIS respectively in the first iteration, and the calculation method in subsequent iterations is shown in step 5.5.

[0136] 5.3. Superimpose the values on different subcarriers of and The vector representing the correlation magnitudes of different dictionary elements is and

[0137]

[0138] Among them, \(i\) represents the index of the dictionary element. In the selection formula above, the set of subscripts of the top and elements is \(\gamma\) NRIS and \(\gamma\) RIS ,

[0139]

[0140] Among them, is the \(n\)th element in the set \(\gamma\) NRIS / \(\gamma\) RIS . Then, update the support sets of the estimated channel from the user to the base station and the channel from the user to the intelligent metasurface to \(\Omega\) NRIS = \(\Omega\) NRIS \(\cup\) \(\gamma\) NRIS and \(\Omega\) RIS = \(\Omega\) RIS \(\cup\) \(\gamma\) RIS . At the first iteration, \(\Omega\) NRIS and \(\Omega\) RIS are empty sets. The proposed terahertz very large-scale intelligent metasurface-assisted communication and positioning integration method not only uses a polar coordinate domain frequency-dependent dictionary, but also, compared with the traditional orthogonal matching pursuit algorithm, the number of atoms selected each time is not limited to one, so as to adapt to the large correlation between the hybrid field steering vectors and reduce the adverse effects brought by spectral leakage. Compared with selecting only one atom per iteration, this method has better performance under the same number of iterations.

[0141] 5.4. For each subcarrier, calculate the orthogonal projection matrices and for the case of turning off the intelligent metasurface and turning on the intelligent metasurface respectively, which are expressed as follows,

[0142]

[0143] Among them, the superscript represents the Moore-Penrose generalized inverse matrix of the matrix.

[0144] 5.5. Update the residual matrices of turning off the intelligent metasurface and turning on the intelligent metasurface as follows respectively,

[0145]

[0146] After going through the and iterations of steps 5.2 to 5.5 for turning off the intelligent metasurface and turning on the intelligent metasurface, where and are the estimated number of scatterers from the user to the base station and from the user to the intelligent metasurface, respectively. The finally estimated channel from the user to the base station and the channel from the user to the intelligent metasurface are expressed as follows

[0147]

[0148] So far, all the steps of the communication and positioning integration method assisted by terahertz large-scale intelligent metasurfaces have been introduced. We have tested it under near-field and far-field conditions respectively. Such as Figure 3 simulation under near-field Figure 4 and simulation under far-field. When estimating the channel between the user and the base station, if the transmit power is low, since the energy of the non-line-of-sight path from the user to the base station is small, it is easily overwhelmed by noise, and at the same time, the multiple atoms selected are very likely to be affected by noise. Therefore, when estimating the parameters of the non-line-of-sight path from the user to the base station at this time, selecting multiple atoms simultaneously will not bring performance gain. When the transmit power is below 6 dBm in the near field and below 16 dBm in the far field, the performance of selecting multiple atoms each iteration is worse than selecting only one atom. However, when the transmit power increases, compared with selecting only one atom reaching the performance bottleneck prematurely, selecting five atoms has obvious performance improvement, and there is no performance bottleneck in the simulated area. When estimating the channel from the user to the intelligent metasurface, since the observation matrix contains the broadband channel from the base station to the intelligent metasurface, this channel is frequency-dependent, and the phase shifter network of the base station is designed according to the center frequency, so the received signal on the edge subcarriers will be lost. In addition, under the same transmit power, due to large-scale fading via the intelligent metasurface, the received power is smaller than that without passing through the intelligent surface. Therefore, the overall channel estimation performance via the intelligent metasurface is worse than that without passing through the intelligent metasurface. From Figure 3 , Figure 4 the comparison between the proposed method and the polar coordinate domain simultaneous orthogonal matching pursuit algorithm (PSOMP), it can be seen that the channel estimation scheme proposed in the present invention has better performance than the comparison scheme of the polar coordinate domain simultaneous orthogonal matching pursuit algorithm under different parameter settings. There are three reasons. One is that the proposed channel estimation scheme considers the beam offset effect under ultra-widebandwidth and ultra-large array; the second is that the proposed channel estimation scheme can flexibly select the number of atom selections in the process of the orthogonal matching pursuit algorithm; the third is that the location information of the user is also used to improve the user channel estimation performance.

[0149] Through Figure 5 , Figure 6It can be seen that when estimating the user's location through the angles in the initial polar coordinate domain frequency-dependent dictionary, even with a redundant dictionary, it is limited by the accuracy of the angle sampling in the dictionary. Therefore, the angle from the user to the base station can be estimated using the polar coordinate domain gradient descent algorithm. For the angle from the user to the intelligent metasurface, a polar coordinate domain hierarchical dictionary is used based on the dictionary of uniformly sampled angles used in channel estimation. After each selection of the user angle using the polar coordinate domain hierarchical dictionary, the user location is updated using this angle, and then the distance from the user to the intelligent metasurface is fixed, and the polar coordinate domain hierarchical dictionary is updated with a smaller angle sampling interval. The above process is iterated until the sampling interval of the hierarchical dictionary is reduced to a given threshold. After optimizing the angles from the user to the base station and the intelligent metasurface using the polar coordinate domain gradient descent algorithm and the polar coordinate domain hierarchical dictionary respectively, the angle estimation accuracy is improved by 2-3 orders of magnitude, and the distance estimation accuracy is improved by more than 1 time. In Figure 3 and Figure 4 , it can be seen from the comparison of the results of channel estimation with and without positioning information assistance that positioning provides a gain of 1-2 dB for channel estimation with the assistance of accurate positioning information.

[0150] In summary, the above are only the preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface, characterized in that: It includes the following steps, Step 1: Use a polar coordinate domain frequency-dependent dictionary to divide the common area served by the base station and the intelligent metasurface; Step 2: Turn off and turn on the intelligent metasurface, multiply the observation matrix by the polar coordinate domain frequency-dependent dictionary, correlate the result with the received signal, and obtain the rough angles of the user arriving at the base station and the intelligent metasurface respectively according to the correlation results; Step 3: Optimize the arrival angles of the user to the base station and the intelligent metasurface using the polar coordinate domain gradient descent algorithm and the polar coordinate domain hierarchical dictionary respectively; Step 4: Obtain the accurate position of the user using the positions of the base station and the intelligent metasurface and the arrival angle information; Step 5: Update the dictionary in the channel estimation process using the user position obtained in Step 4, and then perform the channel estimation operation to further improve the channel estimation performance of the user to the base station and the user to the intelligent metasurface.

2. The communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface according to claim 1, characterized in that: The implementation method of Step 1 is, Divide the area served by the base station and the area served by the intelligent metasurface in terms of angle and distance to generate a polar coordinate domain frequency-dependent dictionary; this dictionary is evolved from the Fourier transform matrix, and each element in the dictionary has sampling of both angle and distance to reduce the adverse effects of the near-field energy diffusion effect; and the generated dictionary takes into account the differences in the dictionaries on different subcarriers brought by the large bandwidth, so that the polar coordinate domain frequency-dependent dictionary can overcome the hybrid field beam offset effect; The polar coordinate domain frequency-dependent dictionaries generated at the base station and the intelligent metasurface are denoted by and respectively. θ BU and θ RU are the angles of the user arriving at the base station and the intelligent metasurface respectively, and r BU and r RU are the distances of the user arriving at the base station and the intelligent metasurface respectively; N / N RIS , Q NRIS / Q RIS and M are the number of array elements of the base station / intelligent metasurface, the number of atoms of the dictionary at the base station / intelligent metasurface, and the number of subcarriers respectively; The angles of the served area are uniformly sampled at N / N RIS points, and the distances are sampled at S points according to the inverse proportional function, then Q NRIS = NS, Q RIS = N RIS S; "Polar coordinate domain" means that each element in the dictionary is composed of an angle and a distance in the served area; "Frequency dependence" means that the dictionaries of different subcarriers need to consider the specific subcarrier size, rather than being replaced by the center carrier frequency uniformly; For a frequency of f m , the sine value of the central angle θ (i.e., the true angle ) of the user arriving at the base station or the intelligent metasurface, and the distance to the center of the base station or the intelligent metasurface is r, the expression of the element in the dictionary is Among them, is the distance from a point in the region to the n-th array element of the base station or intelligent metasurface, and δ n =(2×n - N + 1) / 2, n = 0, …, N - 1 / δ n =(2×n - N RIS + 1) / 2, n = 0, …, N RIS - 1 is the index of the array element of the base station or intelligent metasurface, and the central array element is the zero point of the index; d is the array element spacing; is the wave number of the m-th subcarrier, and λ m is the wavelength of the m-th subcarrier.

3. The communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface according to claim 1, characterized in that: The implementation method of Step 2 is, Turn off the intelligent metasurface and turn on the intelligent metasurface respectively. Perform the correlation operation between the product of the observation matrix and the polar coordinate domain frequency-dependent dictionary and the received signal, extract the angle index where the maximum correlation value is located, and obtain the preliminary angles of arrival of the user to the base station and the intelligent metasurface; the relevant expressions for turning off the intelligent metasurface and turning on the intelligent metasurface, namely and are as follows Among them, is the sine value of the angle from the user to the base station / smart metasurface ; is the base station observation matrix after stacking multiple time slots when the smart metasurface is not turned on; is the observation matrix jointly composed of the base station phase shift network, the channel from the smart metasurface to the base station, and the phase matrix of the smart metasurface after stacking multiple time slots when the smart metasurface is turned on. Since the smart metasurface is pre-deployed, the channel from the smart metasurface to the base station is completely known; and are the polar coordinate domain frequency dependence dictionaries on the base station side and the smart metasurface side respectively. m represents the subcarrier index, and M is the number of subcarriers; and are the received signals on the m-th subcarrier when the smart metasurface is not turned on and when the smart metasurface is turned on respectively received by the base station; and are the Gaussian noises on the m-th subcarrier when the smart metasurface is turned off and when the smart metasurface is turned on respectively; N is the number of base station antenna elements, and N RIS is the number of elements of the smart metasurface; N RF is the number of radio frequency links; P NRIS and P RIS are the uplink communication time slot numbers when the smart metasurface is turned off and when the smart metasurface is turned on respectively; then, according to the following formula, the optimal angle is selected. where I(θ BU , r BU ) and I(θ RU , r RU ) respectively represent the row indices of θ BU and θ RU in Γ NRIS and Γ RIS ; The received signals obtained by turning off the intelligent metasurface and turning on the intelligent metasurface are as follows, wherein, and are the channels from the user to the base station and the intelligent metasurface on the m-th subcarrier respectively; the near-field multipath cluster sparse channel from the user to the base station is: where the subscripts m, l, and g represent the serial numbers of subcarriers, clusters, and inner cluster radii, respectively; the l-th cluster has paths, and there are a total of L BU clusters, and l = 0 represents the direct path; is the complex channel gain; f m is the subcarrier frequency; and represent the angle and distance from the user to the central element of the base station antenna, respectively; since the direct path does not form a cluster and has only one path, i.e., For simplicity, the subscript g of the direct path is omitted, and and represent the channel gain of the direct path, the angle of arrival of the user at the base station, and the distance, respectively; is the steering vector of the hybrid field and is modeled as follows: Among them, is the distance from the user to the nth antenna element of the base station; The center antenna element is the reference zero point; d is the element spacing of the antenna. Similarly, the near-field multipath cluster sparse channel from the user to the intelligent metasurface is as follows: Among them, the l-th cluster has paths in total, and there are L RU clusters, where l = 0 represents the direct path; is the channel complex gain; f m is the subcarrier frequency; and represent the angle and distance from the user to the central element of the base station antenna respectively; Since the direct path does not form a cluster and there is only one path, that is For simplicity, the subscript g of the direct path is omitted, and and represent the channel gain of the direct path, the angle at which the user arrives at the intelligent metasurface, and the distance respectively; is the steering vector of the hybrid field, which is modeled as follows, where, is the distance from the user to the n-th element of the intelligent metasurface; and the central element is the reference zero point; d is the element spacing.

4. The communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface according to claim 1, characterized in that: The implementation method of Step 3 is, First, use the existing gradient descent algorithm to optimize the angle of arrival from the user to the base station; since the dictionary used in channel estimation and positioning is a polar coordinate domain frequency-dependent dictionary, the gradient descent algorithm in the terahertz very large-scale array case is called the polar coordinate domain gradient descent algorithm; the difference between the used polar coordinate domain gradient descent algorithm and the traditional gradient descent algorithm mainly lies in the construction of the loss function v NRIS as shown in the following formula Among them, is the processed received signal; is the virtual direct path channel from the user to the base station, and its expression is Among them, and are the estimated channel gain, angle, and distance of the direct path from the user to the base station, respectively; is a variant of Y NRIS whose expression is Among them, provided that the phase shifter network of the base station needs to be specially processed as follows, that is, let be while each element from the second row to the last row satisfies a constant modulus constraint, with a modulus value of the phase is randomly set and follows a uniform distribution from 0 to 2π; the purpose of doing this is to remove the influence of in the real channel from the received signal. At the same time, when generating the loss function, the virtual channel also does not This can ensure that when estimating the angle from the user to the base station it will not be affected by the not completely accurate distance from the user to the base station so as to optimize the angle based on the not completely accurate distance; for the derivative of the loss function with respect to the angle and the Armijo - Goldstein criterion for step - size selection in the update process, the existing gradient descent algorithm is adopted; Secondly, use the polar coordinate domain hierarchical dictionary W RIS,PHD to optimize the angle of arrival of the user to the intelligent metasurface; the optimization objective function is constructed as follows, Then select the optimal angle according to the following formula Among them, denotes at the RIS th row of Γ; after each selection of the optimal angle, the angle sampling interval and sampling range of the next polar coordinate domain hierarchical dictionary will be reduced to of the previous iteration to gradually approach the true value until the sampling interval is reduced to the threshold γ and the iteration stops.

5. The communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface according to claim 1, characterized in that: The implementation method of Step 4 is, The position of the user is obtained by the intersection of straight lines through the positions of the base station and the intelligent metasurface, as well as the estimated angles of arrival of the user to the base station and the intelligent metasurface. Its expression is Among them, (x BS , y BS ) and (x RIS , y RIS ) are the coordinates of the base station and the intelligent metasurface respectively, and are the slopes of the straight lines from the user to the base station and from the user to the intelligent metasurface respectively.

6. The communication and positioning integration method assisted by terahertz ultra-large-scale intelligent metasurface according to claim 1, characterized in that: The implementation method of Step 5 is, After obtaining the accurate user location, use the polar-domain frequency-dependent dictionary W initially generated in step 1 NRIS and W RIS to generate the polar-domain frequency-dependent dictionaries used for subsequent channel estimation and Among them, and are generated from the located user position coordinates. The assistance of the positioning information can enable the channel estimation to have a large performance improvement at high signal-to-noise ratios; then, perform the channel estimation operation as follows: 5.

1. Construct the equivalent observation matrices for the closed intelligent metasurface and the open intelligent metasurface and 5.

2. Calculate the correlation matrices of the equivalent observation matrices and residuals for the case of turning off the intelligent metasurface and turning on the intelligent metasurface, which are respectively denoted as and wherein, R NRIS and R RIS are residual matrices, which take the values of Y NRIS and Y RIS respectively in the first iteration, and the calculation method in subsequent iterations is as shown in step 5.5; 5.

3. Superimpose the values on different subcarriers. The vector representing the correlation magnitudes of different dictionary elements is and and ​ where i represents the index of the dictionary element; in the above formula, select the set of subscripts of the top and largest elements, which are γ NRIS and γ RIS , wherein, is the n-th element of the set γ NRIS / γ RIS ; then, update the support sets of the estimated channel from the user to the base station and the channel from the user to the intelligent metasurface to be Ω NRIS = Ω NRIS ∪γ NRIS and Ω RIS = Ω RIS ∪γ RIS ; at the first iteration, Ω NRIS and Ω RIS are empty sets; the proposed terahertz massive intelligent metasurface-assisted communication and positioning integration method not only uses a polar coordinate domain frequency-dependent dictionary, but also, compared with the traditional orthogonal matching pursuit algorithm, the number of atoms selected each time is not limited to one to adapt to the large correlation between the hybrid field steering vectors and reduce the adverse effects brought by spectral leakage; compared with selecting only one atom per iteration, this method will have better performance under the same number of iterations; 5.

4. For each subcarrier, calculate the orthogonal projection matrix on the m-th subcarrier for the case of turning off the intelligent metasurface and the case of turning on the intelligent metasurface respectively. and Among them, the superscript represents finding the Moore-Penrose generalized inverse matrix of a matrix; 5.

5. Update the residual matrices of turning off the intelligent metasurface and turning on the intelligent metasurface respectively as follows, After closing and then turning on the intelligent metasurface, and going through the iterations in steps 5.2 to 5.5, where and are the number of scatterers estimated from the user to the base station and from the user to the intelligent metasurface respectively after the iterations, the finally estimated channel and from the user to the base station and from the user to the intelligent metasurface are expressed as follows: and ​

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