A user terminal direct positioning method in a millimeter wave MIMO system

Abstract

The application discloses a kind of millimeter wave MIMO system in user terminal direct positioning method, and the present application includes the following steps: S1: establish two-dimensional space coordinate system, determine the physical coordinate of millimeter wave MIMO base station, each base station will received user signal be returned to data center and be handled jointly;S2: grid discretization and angle discretization are carried out to positioning area, according to the geometric relation between user position and angle of arrival, list the optimization problem of direct positioning, and the optimization target is user position information;S3: using alternating direction multiplier method (ADMM) to transform direct positioning optimization problem, derive the iteration formula of this problem;S4: ADMM iteration parameter is learned using deep unfolding network, and the iteration formula is calculated until convergence, and the user position is obtained.The present application can realize millimeter wave MIMO system sub-millimeter level high-precision positioning, simultaneously through ADMM iterative algorithm and deep unfolding network, the complexity and time overhead of direct positioning algorithm are greatly reduced, and the demand of fast positioning is achieved.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method for direct positioning of user terminals in a millimeter-wave MIMO system. Background Technology

[0002] In fifth- and sixth-generation cellular communication networks, millimeter-wave MIMO systems are considered a crucial technology. Thanks to the high spectral efficiency of millimeter-wave MIMO systems, cellular wireless communication can achieve greater system capacity and higher communication reliability. Furthermore, because millimeter-wave arrays have high angular resolution, sub-meter-level positioning can be achieved using millimeter-wave MIMO systems, enabling efficient deployment of applications such as the Internet of Things, autonomous driving, and social networks.

[0003] The fundamental characteristic of millimeter-wave MIMO system positioning is that it utilizes user signals received by the base station to extract location-related information such as time delay, angle of arrival, and signal strength, and then accurately reconstructs the user terminal's location based on this information. Therefore, developing an efficient millimeter-wave MIMO system positioning method is essential.

[0004] Current multi-base station MIMO positioning algorithms are generally divided into two categories: two-step positioning methods and direct positioning methods. In the two-step positioning method, the base station first estimates the user's signal delay, angle of arrival, and received signal strength based on the received signal, and then determines the user's location using triangulation or triangulation techniques. In the direct positioning method, the base station directly recovers the user's location based on the received signal, without the need for intermediate parameter estimation, enabling high-precision positioning in multi-base station systems.

[0005] However, both positioning methods have significant drawbacks in existing research. For two-step positioning, the intermediate parameters estimated by the base station often contain large errors, which amplify the errors in subsequent user terminal location estimation. While direct positioning methods offer far superior accuracy compared to two-step methods, they often require constructing large-scale, high-dimensional optimization problems. Solving these problems demands substantial computational resources and time, which is unacceptable in positioning applications. Summary of the Invention

[0006] Technical Problem: To address the high complexity of existing methods for direct user terminal positioning using millimeter-wave multi-MIMO base stations, this invention proposes a direct user terminal positioning method in millimeter-wave MIMO systems. This invention enables high-precision user positioning in multi-base station millimeter-wave MIMO systems with arbitrary array configurations. Furthermore, the proposed algorithm significantly reduces the complexity and computational resource overhead of direct positioning.

[0007] Technical Solution: To achieve the objectives of this invention, a direct positioning method for user terminals in a millimeter-wave MIMO system specifically includes the following steps:

[0008] S1: Establish a two-dimensional spatial coordinate system, determine the physical coordinates of the millimeter-wave MIMO base station, and each base station transmits the received user signals back to the data center for joint processing;

[0009] S2: Discretize the positioning area into a grid and an angle. Based on the geometric relationship between the user's location and the angle of arrival, list the optimization problem for direct positioning. The optimization objective is the user's location information.

[0010] S3: The direct localization optimization problem is transformed using the Alternating Direction Multiplier Method (ADMM), and the iterative formula for the problem is derived.

[0011] S4: Use a deep unfolded network to learn the ADMM iterative parameters, calculate the iterative formula until convergence, and obtain the user's position.

[0012] in,

[0013] The specific steps of S1 are as follows:

[0014] S1.1: Define the two-dimensional target positioning area By region Establish a two-dimensional coordinate system with the center as the origin, and let the location of the m-th millimeter-wave MIMO base station be... The location of the user to be tested is p = [p x ,p y ];

[0015] S1.2: Define the narrowband signal transmitted by the user terminal as s d Each base station receives the following signals:

[0016]

[0017] Where: ρ is the transmission signal-to-noise ratio, h m Let n be the channel vector between the user and the m-th base station. m To receive the noise vector;

[0018] S1.3: Based on the sparsity characteristics of millimeter-wave channels, the channel vector representation is determined as follows:

[0019]

[0020] Where: P m a represents the number of non-line-of-sight paths. m (·) represents the array response vector, α m and θ m (p) represent the gain and angle of arrival for the line-of-sight path, respectively. and These represent the gain and angle of arrival for non-line-of-sight paths, respectively.

[0021] S1.4: The spatial geometric relationship between the user terminal location and the angle of arrival of the line-of-sight path can be expressed as:

[0022]

[0023] Based on the geometric relationship between the line-of-sight paths between each base station and the terminal, the user's specific location is obtained through angle-position information mapping.

[0024] Step S2 specifically involves:

[0025] S2.1: The millimeter-wave channel is sparsely represented in the beam domain. Based on this characteristic, the channel vector between the user and the m-th base station is sparsely represented by performing grid discretization and angle discretization on the positioning area; for grid discretization, the target area is... The grid is uniformly divided into K grid locations, i.e.:

[0026]

[0027] in: This represents the coordinates of the k-th grid position, and the two-dimensional target location area. As shown in step S1.1; further, for the m-th base station, define L m Uniformly discrete angles Right now:

[0028]

[0029] Where: L m >>P m m = 1, 2, ..., M;

[0030] S2.2: Based on the discretization information given in S2.1, the millimeter-wave channel can be sparsely represented in the beam domain. In this case, the received signal is further represented as:

[0031] y m =A m x m +B m z m +n m m = 1, 2, ..., M

[0032] Among them, A m =[a m (θ m (Φ1)),...,a m (θ m (Φ K))], θ m (Φ k () represents the angle of arrival between the k-th grid location and the m-th base station. It is a sparse vector, x m,k ,k=1,...,K represents the effective gain of the line-of-sight path between the k-th grid location and the m-th base station. Let z be a sparse vector. m,k ,k=1,...,K represents the effective gain of the non-line-of-sight path between the k-th grid location and the m-th base station;

[0033] S2.3: Define matrix X = [x1, x2, ..., x...] M ], because vector x m Since X contains only one non-zero element whose position is related to the user's location information, X is a row-sparse matrix. Based on this property, direct location can be represented as an optimization problem, specifically:

[0034] min

[0035] st

[0036] in, and Let X and z represent respectively m The estimate, w m Represents the weighting coefficient, usually By solving the above optimization problem, the user's location estimation can be expressed as: in Corresponding to matrix Non-zero rows.

[0037] Step S3 specifically involves:

[0038] S3.1: The augmented Lagrangian form of the direct location optimization problem can be expressed as:

[0039]

[0040] Where A = blkdiag(A1, A2, ..., A M ), B = blkdiag(B1, B2, ..., B M ), Let ρ denote a Lagrange multiplier, where ρ is defined as a positive penalty parameter;

[0041] S3.2: For the augmented Lagrangian function of the direct location optimization problem in S3.1, the alternating direction multiplier method is used to iteratively solve for the parameters to be estimated, specifically:

[0042]

[0043]

[0044]

[0045] Iteratively update the above three equations until convergence to obtain the estimated value.

[0046] S3.3: For S3.2 The update equation is further transformed to obtain the following minimization problem:

[0047]

[0048] After transformation, the above equation is further converted into the following optimization problem:

[0049]

[0050] Where λ1=τ1 / ρ, Note that the above equation is optimized to address the multi-observation vector problem in compressed sensing, and its closed-form solution is expressed as:

[0051]

[0052] Among them, C (i) =[[c (i) ] 1:K ,[c (i) ] K+1:2K ,...,[c (i) ] (M-1)K+1:MK ];

[0053] S3.4: For S3.2 The update equation is further transformed to obtain the following minimization problem:

[0054]

[0055] in, τ2 is defined as a positive penalty parameter; after simplification, the optimization problem in the above equation can be further expressed as:

[0056]

[0057] Where λ2=τ2 / ρ, Note that the above equation is optimized to solve a single-observation vector problem in compressed sensing, and its closed-form solution can be expressed as:

[0058]

[0059] in,

[0060] Step S4 specifically involves:

[0061] S4.1: Establish a deep unfolded network to learn the penalty parameters ρ, τ1, and τ2 that need to be determined in the iterative update of step S3.2; in the i-th layer of the deep unfolded network, the parameters to be trained are ρ. (i) ,

[0062] S4.2: The deep unfolded network is trained using unsupervised learning. Under this condition, the loss function is defined as:

[0063]

[0064] Wherein, the received signal y is the training dataset;

[0065] S4.3: The above deep unfolded network is trained using stochastic gradient descent and mini-batch training methods. To avoid the vanishing gradient problem, incremental training is used; specifically, all parameters are learned sequentially from the first layer to the last layer. That is, after the current i-th layer of the network is trained, the learned parameters are... As initial values, the new i+1 layer network is relearned; finally, the actual received signal from the base station is used as the input to the trained deep unfolded network to output the user's location information.

[0066] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0067] The fast direct positioning method of this invention employs the alternating direction multiplier method and a deep unfolded network for multi-base station user positioning in millimeter-wave MIMO systems. First, the positioning area is discretized into a grid and its angles, and the millimeter-wave channel is represented sparsely in the beam domain. Then, based on the geometric relationship between the user's location and angle of arrival, a direct positioning optimization problem is derived. The alternating multiplier method and a deep unfolded network are used to solve the direct optimization problem, ultimately obtaining the user's location information.

[0068] This invention enables high-precision user positioning in multi-base station millimeter-wave MIMO systems with arbitrary array configurations. Furthermore, the proposed algorithm significantly reduces the complexity and computational resource overhead of direct positioning. Attached Figure Description

[0069] Figure 1 This is an application environment diagram of the millimeter-wave MIMO system positioning in an embodiment of the present invention;

[0070] Figure 2 This is the overall flowchart of the present invention;

[0071] Figure 3 This is a flowchart of the fast direct positioning method for millimeter-wave MIMO systems of the present invention;

[0072] Figure 4 This is a flowchart of the alternating multiplier method of the present invention;

[0073] Figure 5 This is a schematic diagram of the deep unfolded network structure of the present invention;

[0074] Figure 6 This is a comparison chart of the sub-meter positioning performance of the direct positioning method of the present invention and the existing base station positioning method;

[0075] Figure 7 This is a comparison chart of the convergence performance of the direct localization method of this invention with other direct localization algorithms. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only some, not all, of the embodiments of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention.

[0077] Example 1

[0078] The rapid positioning method provided in this application can be applied to, for example... Figure 1 The application environment shown depicts a user terminal communicating with a base station. For example, the base station receives a target signal sent by a terminal at a preset location, thus obtaining the actual received signal. The terminal can be, but is not limited to, various personal computers, laptops, smartphones, tablets, and portable wearable devices. The base station can be a standalone base station or a cluster of multiple base stations.

[0079] refer to Figure 2 The overall flowchart for direct positioning of the millimeter-wave MIMO system provided in the embodiments of this application includes:

[0080] The terminal equipped with a signal source transmits a positioning reference signal, i.e., a received signal, while the array antenna in the base station receives the signal. The base station then transmits the received signal back to the data center for joint processing. At the data center, the signals received by each base station are input into a trained deep unfolded network without intermediate processing. After iterative calculation, the deep unfolded network directly outputs the user's location information.

[0081] refer to Figure 3This embodiment provides a method for fast and direct positioning of user terminals in a millimeter-wave MIMO system, which specifically includes the following steps:

[0082] Step S1: As Figure 3 As shown, a two-dimensional spatial coordinate system is established to determine the physical coordinates of the millimeter-wave MIMO base station. Each base station transmits the received user signals back to the data center for joint processing, as detailed below:

[0083] Step S1.1: Define the two-dimensional target positioning area By region Establish a two-dimensional coordinate system with the center as the origin, and let the location of the m-th millimeter-wave MIMO base station be... The location of the user to be tested is p = [p x ,p y ].

[0084] Step S1.2: Define the narrowband signal transmitted by the user as s d Each base station receives the following signals:

[0085]

[0086] Where: ρ is the transmission signal-to-noise ratio, h m Let n be the channel vector between the user terminal and the m-th base station. m This is for receiving noise vectors. Each base station will receive signal y. m It is then sent back to the data center for joint processing.

[0087] Step S1.3: Based on the sparsity characteristics of millimeter-wave channels, determine the channel vector representation, specifically as follows:

[0088]

[0089] Where: P m a represents the number of non-line-of-sight paths. m (θ) is the array response vector, α m and θ m (p) represent the gain and angle of arrival for the line-of-sight path, respectively. and These represent the gain and angle of arrival for non-line-of-sight paths, respectively.

[0090] Step S1.4: As Figure 1 As shown, the spatial geometric relationship between the user terminal's location and the angle of arrival of the line-of-sight path can be expressed as:

[0091]

[0092] Based on the geometric relationship between the line-of-sight paths between each base station and the terminal, the user's specific location can be obtained through angle-location information mapping.

[0093] Step S2: Specifically, millimeter-wave channels exhibit beam domain sparsity. The positioning area is discretized into a grid and its angles, and the millimeter-wave channel is sparsely represented using this discretized information. Based on the geometric relationship between the user's location and the angle of arrival, an optimization problem for direct positioning is formulated, with the user's location information as the optimization objective, as follows:

[0094] Step S2.1: Since the user terminal location and angle of arrival are interrelated, the millimeter-wave channel h can be determined by performing grid discretization and angle discretization on the positioning area. m Sparse representation is used. In this case, the target region can be represented. The grid is uniformly divided into K grid locations, i.e.:

[0095]

[0096] in: Let L represent the coordinates of the k-th grid position. Furthermore, for the m-th base station, define L... m A uniformly discrete angle, namely:

[0097]

[0098] Where: L m >>P m m = 1, 2, ..., M.

[0099] Step S2.2: Based on the discretization information given in S2.1, the received signal can be represented as:

[0100] y m =A m x m +B m z m +n m m = 1, 2, ..., M

[0101] Among them, A m =[a m (θ m (Φ1)),...,a m (θ m (Φ K ))], θ m (Φ k ) represents the angle of arrival between the k-th grid location and the m-th base station, x m =[x m,1 ,x m,2 ,...,x m,K ] T It is a sparse vector, x m,lThis represents the effective gain of the line-of-sight path between the k-th grid location and the m-th base station. Let z be a sparse vector. m,l This represents the effective gain of the non-line-of-sight path between the k-th grid location and the m-th base station.

[0102] Step S2.3: Define matrix X = [x1, x2, ..., x...] M ], because vector x m Since X contains only one non-zero element whose position is related to the user's location information, X is a row-sparse matrix. Based on these properties, direct location can be represented as an optimization problem, specifically:

[0103] min

[0104] st

[0105] in, and Let X and z represent respectively m The estimate, w m Represents the weighting coefficient, usually By solving the above optimization problem, the user's location estimation can be expressed as: in Corresponding to matrix Non-zero rows.

[0106] Step S3: Reference Figure 4 The direct location optimization problem in step S2.3 is transformed using the Alternating Direction Multiplier Method (ADMM), and the iterative solution formula for this problem is derived as follows:

[0107] Step S3.1: The augmented Lagrangian form of the direct location optimization problem can be expressed as:

[0108]

[0109] Where A = blkdiag(A1, A2, ..., A M ), B = blkdiag(B1, B2, ..., B M ), Let ρ denote the Lagrange multiplier, and ρ is defined as a positive penalty parameter.

[0110] Step S3.2: For the augmented Lagrangian function of the direct location optimization problem in S3.1, the alternating direction multiplier method is used to iteratively solve for the parameters to be estimated, specifically:

[0111]

[0112]

[0113]

[0114] By iteratively updating the above three equations until convergence, we can obtain the estimated value.

[0115] Step S3.3: For S3.2 Further transformation of the update equation yields the following minimization problem:

[0116]

[0117] After a series of mathematical transformations, the above formula can be further transformed into the following optimization problem:

[0118]

[0119] Where λ1=τ1 / ρ, Note that the above equation is optimized to address the multi-observation vector problem in compressed sensing, and its closed-form solution can be expressed as:

[0120]

[0121] Among them, C (i) =[[c (i) ] 1:K ,[c (i) ] K+1:2K ,…,[c (i) ] (M-1)K+1:MK ].

[0122] Step S3.4: For S3.2 Further transformation of the update equation yields the following minimization problem:

[0123]

[0124] in, τ2 is defined as the positive penalty parameter. After a series of mathematical simplifications, the optimization problem above can be further expressed as:

[0125]

[0126] Where λ2=τ2 / ρ, Note that the above equation is optimized to solve a single-observation vector problem in compressed sensing, and its closed-form solution can be expressed as:

[0127]

[0128] in,

[0129] Step S4: Use a deep unfolded network to learn the ADMM iterative parameters, calculate the iterative formula until convergence, and finally obtain the user's location, as follows:

[0130] Step S4.1: Establish a deep unfolded network to learn the penalty parameters ρ, τ1, and τ2 that need to be determined in the iterative update of step S3.2. In the i-th layer of the deep unfolded network, set the parameters to be trained as ρ. (i) ,

[0131] Step S4.2: Train the deep unfolded network using unsupervised learning. Under this condition, the loss function is defined as:

[0132]

[0133] Wherein, the received signal y is the training dataset.

[0134] Step S4.3: The deep unfolded network described above is trained using stochastic gradient descent and mini-batch training methods. The deep unfolded network structure is as follows: Figure 5 As shown. To avoid the vanishing gradient problem, incremental training is used for learning. Specifically, all parameters are learned sequentially from the first layer to the last layer. That is, after the current i-th layer of the network is trained, the learned parameters are... As initial values, the new i+1-level network is relearned.

[0135] In this embodiment, each layer of the deep unfolded network is trained 700 times, and the commonly used Adam optimizer is selected as the trainer. Specifically, the learning rate of the Adam optimizer is set to 0.05 during the training of the first 5 layers of the network, and the learning rate of the Adam optimizer is set to 0.01 during the training of the subsequent 5 layers.

[0136] When testing the deep unfolded network, the cross-validation set contains 200 samples of received signal data. The deep unfolded network completes training when the cross-validation loss function no longer decreases, and the trained parameters are retained.

[0137] Finally, the actual received signal from the base station is used as the input to the trained deep unfolded network. After iterative calculation of the deep unfolded network data, the user's location information is directly output.

[0138] refer to Figure 6 , Figure 6This is a probability comparison chart showing the sub-meter level positioning accuracy of the fast direct positioning method in this embodiment and existing positioning methods. In the simulation parameter settings, the number of base stations M = 4, located at coordinate points [-50m, -50m], [-50m, 50m], [50m, 50m], and [50m, -50m]. Each base station uses a uniform circular array with N antennas. m =50, m=1,2,3,4, carrier frequency is 30GHz millimeter wave band. The channel generation model adopts the Urban Marco scenario defined by the 3GPP standard. The number of discrete points in the positioning area is K=900, L m =100, m=1,2,3,4. Users are randomly generated and distributed within the target location area. From this, we can discover that:

[0139] Compared to other base station positioning algorithms, the fast direct positioning algorithm in this embodiment can achieve a higher probability of sub-meter positioning accuracy.

[0140] refer to Figure 7 The setting of simulation parameters and Figure 6 The simulation parameters are set the same. From this, we can see that:

[0141] Compared to the pure alternating multiplier direct localization algorithm, the fast direct localization algorithm in this embodiment can converge faster and achieve efficient localization.

[0142] Refer to Table 1, where the simulation parameters are set and Figure 6 , 7 The simulation parameters are set the same. It can be observed that:

[0143] Compared to other direct positioning methods, the fast direct positioning algorithm in this embodiment has a significantly reduced running time, enabling real-time and rapid positioning in base station positioning systems.

[0144] The present invention and its embodiments have been described above illustratively. This description is not restrictive, and the figures shown are only one embodiment of the present invention. The actual structure and method are not limited thereto. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs shall fall within the protection scope of the present invention.

[0145] Table 1 shows the running time comparison data of the direct positioning method of the present invention and other direct positioning algorithms;

[0146]

[0147] Table 1

Claims

1. A method for direct positioning of a user terminal in a millimeter-wave MIMO system, characterized in that, The direct positioning method specifically includes the following steps: S1: Establish a two-dimensional spatial coordinate system, determine the physical coordinates of the millimeter-wave MIMO base station, and each base station transmits the received user signals back to the data center for joint processing; S2: Discretize the positioning area into a grid and an angle. Based on the geometric relationship between the user's location and the angle of arrival, list the optimization problem for direct positioning. The optimization objective is the user's location information. S3: The direct localization optimization problem is transformed using the Alternating Direction Multiplier Method (ADMM), and the iterative formula for this problem is derived; specifically: S3.1: The augmented Lagrangian form of the direct location optimization problem can be expressed as: in, , , , , , Represents the Lagrange multipliers. Defined as a positive penalty parameter; S3.2: For the augmented Lagrangian function of the direct location optimization problem in S3.1, the alternating direction multiplier method is used to iteratively solve for the parameters to be estimated, specifically: Iteratively update the above three equations until convergence to obtain the estimated value. , ; S3.3: For S3.2 The update equation is further transformed to obtain the following minimization problem: After transformation, the above equation is further converted into the following optimization problem: in, , Note that the above equation is optimized to solve the multi-observation vector problem in compressed sensing, and its closed-form solution is expressed as: ， in, ; S3.4: For S3.2 The update equation is further transformed to obtain the following minimization problem: in, , Defined as a positive penalty parameter; after simplification, the optimization problem in the above equation can be further expressed as: in, , Note that the above equation is optimized to solve a single-observation vector problem in compressed sensing, and its closed-form solution can be expressed as: ， in, , ; S4: Utilize a deep unfolded network to learn the ADMM iterative parameters, calculate the iterative formula until convergence, and obtain the user's location; specifically: S4.1: Establish a deep unfolded network and iteratively update the penalty parameters that need to be determined in step S3.

2. , , Learning; in the first stage of deep unfolded networks Layer, parameters to be trained are , , ; S4.2: The deep unfolded network is trained using unsupervised learning. Under this condition, the loss function is defined as: ， Among them, the received signal For the training dataset; S4.3: The above deep unfolded network is trained using stochastic gradient descent and mini-batch training methods. To avoid the vanishing gradient problem, incremental training is used; specifically, all parameters are learned sequentially from the first layer to the last layer; that is, the current... After the multilayer network is trained, the learned parameters will be... As an initial value, for the new The deep unfolded network is relearned; finally, the actual received signal from the base station is used as the input to the trained deep unfolded network to output the user's location information.

2. The direct positioning method for user terminals in a millimeter-wave MIMO system according to claim 1, characterized in that, The specific steps of S1 are as follows: S1.1: Define the two-dimensional target positioning area , in the region Establish a two-dimensional coordinate system with the center as the origin, and let the first... The locations of the millimeter-wave MIMO base stations are as follows: The location of the user to be tested is ; S1.2: Define the narrowband signal transmitted by the user terminal as... The signals received by each base station are as follows: in: To improve the transmission signal-to-noise ratio, Let m be the channel vector between the user and the m-th base station. To receive the noise vector; S1.3: Based on the sparsity characteristics of millimeter-wave channels, the channel vector representation is determined as follows: ， in: This represents the number of non-line-of-sight paths. For array response vectors, and These represent the gain and angle of arrival for the line-of-sight path, respectively. and These represent the gain and angle of arrival for non-line-of-sight paths, respectively. S1.4: The spatial geometric relationship between the user terminal location and the angle of arrival of the line-of-sight path can be expressed as: ， Based on the geometric relationship between the line-of-sight paths between each base station and the terminal, the user's specific location is obtained through angle-position information mapping.

3. A method for direct positioning of a user terminal in a millimeter-wave MIMO system according to claim 1 or 2, characterized in that, Step S2 specifically involves: S2.1: The millimeter-wave channel is sparsely represented in the beam domain. Based on this characteristic, the channel vector between the user and the m-th base station is sparsely represented by performing grid discretization and angle discretization on the positioning area; for grid discretization, the target area is... Evenly divided into One grid position, that is: in: Indicates the first The coordinates of each grid location represent the two-dimensional target positioning area. As shown in step S1.1; further, for the first... One base station, defined Uniformly discrete angles ,Right now: in: ; S2.2: Based on the discretization information given in S2.1, the millimeter-wave channel can be sparsely represented in the beam domain. In this case, the received signal is further represented as: in, , , Indicates the first The grid position and the first Angle of arrival between base stations It is a sparse vector. Indicates the first The grid position and the first Effective gain of the line-of-sight path between base stations Given a sparse vector, Indicates the first The grid position and the first Effective gain of non-line-of-sight paths between base stations; S2.3: Define the matrix Because of vector There is only one non-zero element in the array, and the position of this element is related to the user's location information. Given a row-sparse matrix, based on the above properties, direct positioning can be represented as an optimization problem, specifically: in, and They represent and The estimated quantity, Represents the weighting coefficient, usually By solving the above optimization problem, the user's location estimate can be expressed as: ,in Corresponding to matrix Non-zero rows.

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