High-precision sensing and positioning method for near-field millimeter wave system of super-large scale array

Abstract

The invention belongs to the technical field of 6G wireless communication, and particularly relates to a high-precision sensing positioning method design in a near-field millimeter wave / sub-terahertz system. According to the method, more accurate estimation angles are obtained by utilizing block sparse features in near-field channel representation and adopting a low-complexity block sparse scheme, and a triangular geometrical relationship is strictly met by automatically adapting to the estimation angles corresponding to the two sub-arrays, so that distance information does not need to be given to a user, and the user experience is improved. And then an estimated distance is obtained by using a triangular geometrical relationship of the two sub-arrays, and a dictionary matrix representing a channel is continuously updated by using a dictionary learning scheme, so that more accurate angle and distance sensing performance is obtained, and high-precision sensing positioning is realized. Simulation results show that the near-field positioning scheme of the invention better balances low complexity, strong noise robustness, no need of user distance information and good performance, and has practical application significance in low-altitude network and agent communication.

Description

Technical Field

[0001] This invention belongs to the field of 6G wireless communication technology, specifically relating to a high-precision positioning and sensing method for a near-field millimeter-wave / Asia Pacific Hertz system with a large-scale array, applicable to practical scenarios such as low-altitude networks and intelligent agent communication. Background Technology

[0002] With the increasing application of millimeter-wave / Asia-Pacific Hertz VMI arrays in low-altitude networks and agent communications, the demand for joint estimation of user angle and distance in the near-field region has significantly increased. The positioning accuracy of user angle and distance is mainly determined by two factors: the dictionary matrix in the sparse representation of the near-field millimeter-wave channel and the sensing positioning estimation method. When using a traditional far-field dictionary, the sensing positioning scheme faces performance loss in the near field. When using a search scheme, which generates a dictionary learning matrix composed of a series of near-field steering vectors at different distances and angles, the large dimension of the dictionary matrix will impose a codebook storage burden on the system and will also increase pilot overhead. When using the latest near-field millimeter-wave positioning scheme, by using a near-field dictionary matrix coupled with angle and distance, and continuously updating the dictionary matrix representing the channel using a dictionary learning scheme, good performance and a small dictionary matrix dimension are achieved. However, this scheme is limited to needing to accurately know the user's distance range to select a suitable dictionary matrix, and also suffers performance loss under low signal-to-noise ratio conditions. Summary of the Invention

[0003] The purpose of this invention is to propose a near-field millimeter-wave / Asia-Pacific Hertz positioning and sensing scheme that is low-complexity, noise-robust, requires no user distance information, and offers superior performance. The proposed scheme mainly consists of three steps: First, utilizing the block sparsity feature in the near-field channel representation, a low-complexity block sparsity scheme is employed to obtain a more accurate estimated angle. By automatically adapting the estimated angles corresponding to the two subarrays, the triangular geometric relationship is strictly satisfied, allowing this invention to obtain the estimated distance without requiring user distance information. Then, the estimated distance is obtained using the triangular geometric relationship between the two subarrays. Second, based on the updated estimated angle and distance information, the near-field dictionary matrix representing the channel is updated. Third, after the two subarrays obtain the updated near-field dictionary matrix, steps one and two are repeated until the algorithm converges and outputs. Finally, this invention achieves a block sparse Bayesian learning algorithm (UDL-BSBL) based on a unitary dictionary learning framework.

[0004] The technical solution adopted in this invention is: A near-field sensing and localization method for millimeter-wave / Asia-Pacific Hertz systems using ultra-large-scale arrays, specifically for uplink communication systems of single-antenna users, wherein the operating frequency of the uplink system is [missing information]. The base station (BS) is equipped with two sub-array structures with a spacing between them. Serving single-antenna users, each subarray has the following number of receiving antennas: Antenna spacing Half the wavelength, Represents the speed of light; the observation vectors corresponding to the two subarrays are respectively and The corresponding angles of arrival are respectively and The corresponding user distances are respectively and The high-precision positioning and sensing method includes the following steps: S1. Construct a block sparse recovery algorithm based on unitary matrices: make Representing the discrete Fourier transform matrix, considering the general block sparse model, the channel... Block sparsity can be characterized as ,here Represents a unitary dictionary matrix. For near-field equivalent distance, It is a sparse signal; for the observation vector Then the block sparse recovery model can be expressed as: , in To handle zero-mean complex Gaussian noise; based on the existing pattern-coupled sparse Bayesian framework (PC-SBL) and the feature that the dictionary matrix is ​​a unitary matrix, the recovery of the block sparse signal does not require inverse operations. For the obtained posterior distribution estimate, it is continuously updated alternately until convergence, thus obtaining the unitary matrix-based block sparse recovery algorithm (U-PCSBL). The recovery of the block sparse signal can be expressed as:

[0005] The specific updates are as follows:

[0006] Here, The value is 1, representing the inverse variance of noise. The initial value is set to 1, and the inverse variance of each element is... The initial value is set to 1; parameter , , and For very small real values, such as ; Represents the diagonal covariance matrix The diagonal elements, Represents the mean of the block sparse signal The One element, The conjugate of the symbol, express The conjugate transpose of . express The second norm; Indicates to Seeking traces; S2. Obtain the estimated angle and estimated distance that satisfy strict trigonometric relations; For each subarray, using the DFT matrix as the initial dictionary matrix, the low-complexity block sparse recovery algorithm of U-PCSBL is used to obtain the block sparse recovery signal, represented as:

[0007] here and These correspond to the block sparse signals of the two subarrays, respectively. and The near-field unitary dictionary matrices for block sparse recovery correspond to the two subarrays respectively; firstly, Sort by amplitude in descending order; the angle corresponding to the largest amplitude is represented as follows: Next Sort by magnitude in descending order, and the corresponding new index order is denoted as follows: ,make This invention represents the set of angles corresponding to all angle grid points of the DFT matrix, and will proceed from the index order from front to back. Find the first less than Angle corresponding to the angle grid point To satisfy strict trigonometric relations, that is

[0008] If the above relationships cannot be satisfied, it is necessary to choose another set of initial dictionaries to avoid this problem. In this case, the DFT matrix is ​​replaced with the following new initial dictionary.

[0009] in, Indicates The elements of the random variable form a diagonal matrix. satisfy Uniform distribution between, random variables satisfy The uniform distribution between them, in this invention and The values ​​are all 0.1; new initial dictionaries are continuously generated until a certain value exists. This satisfies strict trigonometric relationships; After being updated and The distance between the two subarrays and the user can be obtained through trigonometric relationships, i.e.

[0010] here This represents the estimated distance between the first subarray and the user. This represents the estimated distance between the second subarray and the user; S3. Update the unitary dictionary matrix: Once the updated angle and distance are obtained, the corresponding dictionary matrix can be updated to...

[0011] Repeat steps S1, S2, and S3 until the algorithm converges. This completes the Block Sparse Bayes Learning (UDL-BSBL) method based on the unitary dictionary learning framework, achieving high-precision positioning and sensing.

[0012] The beneficial effects of this invention are: The UDL-BSBL perception and localization method proposed in this invention has the advantages of better performance, stronger noise robustness, and no need for prior user location information, while maintaining low complexity compared to existing methods. Attached Figure Description

[0013] Figure 1 To illustrate the relationship between the mean square error performance and signal-to-noise ratio of near-field angle estimation for each method, the operating frequency is set. .

[0014] Figure 2 To establish the relationship between near-field range estimation error and signal-to-noise ratio for each method, the operating frequency is set. .

[0015] Figure 3 To establish the relationship between the mean square error of near-field angle estimation for each method and the operating frequency, the signal-to-noise ratio (SNR) is set to 0 dB.

[0016] Figure 4 To establish the relationship between the near-field distance estimation error of each method and the operating frequency, the signal-to-noise ratio (SNR) is set to 0 dB. Detailed Implementation

[0017] The present invention will now be described in detail with reference to the accompanying drawings and simulation examples to demonstrate its practicality.

[0018] This invention addresses the near-field sensing and localization problem in millimeter-wave / Asia-Pacific Hertz systems using ultra-large-scale arrays. Specifically, it considers the uplink communication system for a single-antenna user, with the system operating at a frequency of [insert frequency here]. The base station (BS) is equipped with two subarray structures to serve single-antenna users, and each subarray has a number of receiving antennas. Meanwhile, the number of radio frequency links is Antenna spacing Half the wavelength, Represents the speed of light. For a single subarray, the angle of arrival corresponding to the visible path (LoS) is defined as... The distance and time delay between the user and the first antenna are respectively... and The corresponding path gain is ; Define the first The angle of arrival for each non-visible path (NLoS) is The distance and time delay between the user and the first antenna are respectively... and The corresponding path gain is Therefore, the near-field millimeter-wave channel can be represented as...

[0019] Among them, the near-field steering vector The The elements are

[0020] The approximate expression can be obtained through Taylor expansion.

[0021] in,

[0022] here It represents the Hadamardi (or Hadama) stack.

[0023] To obtain the near-field unitary matrix, the effective distance is defined. The reciprocal of is

[0024] So in the effective distance The reciprocal is near-field unitary matrix It can be represented as

[0025] here ,at the same time .here This represents the discrete Fourier transform matrix. The advantage of this design is that it separates the search for angle and distance, allowing the invention to efficiently search within a one-dimensional dimension of effective distance or angle. Simultaneously, the invention continuously updates the near-field unitary matrix. To achieve higher accuracy in angle and distance estimation performance.

[0026] When the near-field unitary matrix When not optimal, the channel exhibits blocky sparsity, which can be represented as: So, the observed signal It can be represented as , Here the observed signal It is easy to obtain, in one case. It can be channel estimation. This corresponds to the channel estimation error; in another case, the transmitted symbol is set to 1, and the pilot number is defined as T, satisfying... If the receiver matrix is ​​set to be an identity matrix, then... It is the received signal of the sub-array. This is noise. From this invention onwards, it will be referred to as... In order to receive signals, For a valid signal, To obey zero mean and variance Complex Gaussian noise. Here The dimension is The unit array.

[0027] First, this invention employs the existing pattern-coupled sparse Bayesian framework. When the dictionary matrix is ​​a near-field unitary matrix, this invention obtains a block sparse recovery scheme with extremely low complexity and good robustness to noise, termed U-PCSBL. The core idea is to maximize the lower bound of evidence relaxation by coupling neighboring elements to perform variational inference, obtaining the variational distribution to obtain the posterior estimate. Specifically, consider a general block sparse model...

[0028] Block sparse signal The prior distribution is set as , Among them, sparse signal The element The inverse variance satisfies , This setting couples adjacent elements, leading to block sparse signaling. Blocky sparse recovery, here the parameters It can be set to a positive real number between 0 and 1. This invention is applicable to... The value is 1. Meanwhile, the inverse variance variable... satisfy , variable It follows a gamma distribution with parameters and For very small real values, such as .

[0029] The received signal follows a complex Gaussian distribution. , Meanwhile, the inverse variance of the noise follows a Gamma distribution, i.e. , parameter and For very small real values, such as .

[0030] According to the variational Bayesian framework, we have 1) Variational distribution The update satisfies

[0031] here Therefore, its posterior distribution satisfies

[0032] Because the near-field unitary matrix satisfies This will ultimately yield a diagonal covariance matrix. This avoids matrix inversion operations, resulting in very low complexity for the block sparse recovery algorithm. (Diagonal covariance matrix) The The diagonal elements are

[0033] in

[0034] 2) Variational distribution The update satisfies:

[0035] in

[0036] Then variables The mean of each element in is

[0037] 3) Variational distribution The update satisfies: , in

[0038] Then the inverse variance of the noise can be updated to:

[0039] Thus, we have obtained a low-complexity block sparse Bayesian recovery with the measurement matrix being a near-field unitary matrix. The algorithm can be represented as follows:

[0040] Next, this invention utilizes the U-PCSBL channel recovery algorithm, combined with a two-subarray structure, to obtain accurate distance estimates by using estimated angles of arrival (Angles of Arrival) and triangular geometric relationships. The overall scheme can be summarized as follows: First, we select a Discrete Fourier Transform (DFT) matrix as the initial dictionary. Using the U-PCSBL channel block sparse recovery algorithm, we estimate the user's angle. Combining this with the two-subarray structure and triangular geometric relationships, we estimate the distance. To satisfy the triangular geometric relationship, the user angles corresponding to the second subarray need to be appropriately selected to meet this relationship. If a user angle satisfying the triangular geometric relationship cannot be found, a new random near-field unitary matrix is ​​generated to replace the DFT matrix as the dictionary matrix, until a user angle satisfying the triangular geometric relationship is found. The dictionary unitary matrix is ​​continuously updated using the estimated angles of arrival and user distances corresponding to each subarray. This update process is repeated until the algorithm converges, outputting the estimated user angles and distances. The specific steps are as follows: The triangulation relationship based on a dual-subarray structure can achieve efficient and high-precision distance positioning. Assuming each subarray is configured with... There are one antenna, and the spacing between the two subarrays is... According to trigonometric relations, it satisfies

[0041] here and The range of variation is all To satisfy strict trigonometric relations, the following conditions must be met.

[0042] Otherwise, distance estimation algorithms based on trigonometric relationships will not function properly, leading to significant distance estimation errors. Existing learnable dictionary schemes typically assume prior information such as the user's minimum and maximum distances, facilitating the pre-acquisition of estimated angles. The minimum and maximum values ​​of the distances are required to establish the triangular geometric relationship. However, in practical applications, the true distance range is often difficult to obtain accurately. To overcome this difficulty, this invention proposes a unitary dictionary learning block sparse Bayesian learning (UDL-BSBL) algorithm based on a unitary dictionary learning framework, which can automatically obtain reasonable user angles to satisfy the triangular geometric relationship.

[0043] The proposed UDL-BSBL localization algorithm specifically uses the DFT matrix as the initial dictionary matrix and leverages the low-complexity block sparse recovery algorithm of U-PCSBL to obtain the block sparse recovery signal, represented as follows:

[0044] here and These correspond to the block sparse signals of the two subarrays, respectively. and These correspond to the received signals of the two sub-arrays, respectively. and These are the near-field unitary dictionary matrices for block sparse recovery, corresponding to the two subarrays respectively. First, let's... Sort by amplitude in descending order; the angle corresponding to the largest amplitude is represented as follows: Next Sort by magnitude in descending order, and the corresponding new index order is denoted as follows: ,make This invention represents the set of angles corresponding to all angle grid points of the DFT matrix, and will proceed from the index order from front to back. Find the first less than Angle corresponding to the angle grid point To satisfy strict trigonometric relations, that is

[0045] Furthermore, it should be noted that since the initial matrix and DFT matrix are not optimal dictionary matrices, the blocky sparse signal... and The estimation error may lead to The special case caused by the initial dictionary matrix renders the localization scheme based on triangular geometry ineffective. To avoid this problem, a different initial dictionary needs to be chosen. Specifically, the DFT matrix can be replaced with the following new initial dictionary:

[0046] Here, random variables satisfy Uniform distribution between, random variables satisfy The uniform distribution between them, in this invention and The values ​​are all 0.1. A new initial dictionary is continuously generated until a certain value exists. This satisfies strict trigonometric relationships.

[0047] After being updated and The distance between the two subarrays and the user can be obtained through trigonometric relationships, i.e.

[0048] Once the updated angle and distance are obtained, the corresponding dictionary matrix can be updated to...

[0049] Notice, and All are unitary matrices, which ensures that the block sparse recovery of this invention still maintains the advantage of low complexity.

[0050] After obtaining the new dictionary matrix, the block sparse signals corresponding to the two subarrays can be recovered separately.

[0051] Repeat the above steps until convergence.

[0052] The simulation considers near-field scenarios in millimeter-wave and even Asia-Pacific Hertz (APH) frequencies. Since millimeter-wave / APH channels are primarily dominated by the line-of-sight path, only the line-of-sight scenario needs to be considered in the millimeter-wave APH scenario. The number of subarray antennas is set to M=256, and the system operating frequency is... The antenna spacing is half a wavelength, and the antennas are distributed in the user direction within the range. The distance between the user and the first subarray is within the range of [10, 30] meters. The parameter N = 3M is set between the two subarrays. This invention names the proposed block sparse Bayesian learning-based perceptual localization scheme based on a unitary dictionary learning scheme as the UDL-BSBL algorithm. Comparison algorithms include the DFT-OMP algorithm, the Searching Scheme algorithm, and the DL-OMP algorithm based on a dictionary learning scheme. Here: The DFT-OMP contrast algorithm refers to the localization using triangular geometric relationships in a twin array structure, using the DFT matrix as the dictionary matrix, and using OMP (Orthogonal Matching Pursuit) for sparse recovery, without employing a dictionary learning scheme. The Searching Scheme algorithm refers to a dictionary learning matrix generated from a series of near-field steering vectors at different distances and angles within a single-array structure. The distance step size used to generate the dictionary is... Mi still hasn't adopted a dictionary learning approach; The DL-OMP comparison algorithm is a high-performance and low-complexity comparison scheme. It adopts a dictionary learning scheme, which generates a dictionary by coupling distance and angle (by assuming that the maximum and minimum distance values ​​of the user are known, then taking M distance values ​​at equal intervals, and dividing the angle values ​​into M equally spaced points, M near-field steering vectors coupled with distance and angle are obtained, resulting in a low-dimensional dictionary learning matrix).

[0053] Meanwhile, the signal-to-noise ratio (SNR) is the ratio between the useful channel power and the noise power. Finally, regarding the sensing performance between the user and the base station antenna, the performance metrics for evaluating the positioning accuracy of angle and distance are as follows. The angle estimation performance is measured using the mean square error (MSE), i.e. The distance estimation performance is measured by the average error, i.e. .

[0054] First, we consider the impact of noise on the performance of angle estimation and user distance estimation, which is presented in... Figure 1 and Figure 2 In the middle. Among them, Figure 1 This demonstrates the impact of different SNR values ​​on the angle estimation performance MSE. Figure 2 This paper demonstrates the impact of different SNRs on distance estimation errors. Using the classic far-field DFT as the dictionary matrix, the DFT-OMP algorithm shows significant performance loss in both angle and distance estimation. Furthermore, under low SNR conditions, it may fail to strictly satisfy triangular geometric relationships, leading to malfunctions. While the Searching Scheme uses near-field steering vectors to construct the dictionary matrix and performs well in angle estimation, it lacks a dictionary update learning scheme, resulting in a performance loss in positioning accuracy compared to the proposed UDL-BSBL algorithm and the comparative DL-OMP algorithm. Moreover, the search algorithm's high-dimensional dictionary matrix increases system storage and pilot overhead. In contrast, compared to the dictionary-based DL-OMP algorithm, the proposed UDL-BSBL algorithm not only employs a dictionary learning scheme but also effectively utilizes the sparse block structure, resulting in significant performance improvements in both angle and distance estimation. The proposed UDL-BSBL algorithm is also more robust to noise and does not require prior knowledge of the user's distance, making it more suitable for practical applications.

[0055] Finally, this invention investigated the impact of different operating frequencies on angle and distance estimation performance, with SNR set to 0 dB in the experiment. As the operating frequency increased, the angle estimation performance of each positioning and sensing method improved to some extent, while the distance estimation performance decreased to some extent. This is because, from the perspective of the near-field channel model, the approximate steering vector in the near field... As the frequency increases, the error caused by the quadratic term in the Taylor expansion becomes smaller, which is beneficial for angle estimation. However, due to the increasingly high frequency, the quadratic term in the channel expansion becomes weaker, resulting in a smaller phase difference between the two subarrays, making distance estimation increasingly difficult and leading to a decrease in distance accuracy. Nevertheless, the UDL-BSBL algorithm proposed in this invention still exhibits optimal sensing accuracy performance at different operating frequencies.

[0056] In summary, this invention studies the high-precision sensing and positioning problem in near-field millimeter-wave / Asia-Pacific Hertz. Utilizing the triangular geometric relationship of two subarrays, angle estimation is obtained through a low-complexity block sparse scheme. By automatically finding an initial unitary dictionary matrix that conforms to strict triangular geometric relationships, this invention eliminates the need for user distance information. Furthermore, by combining a dictionary learning scheme, this invention obtains a block sparse Bayesian learning algorithm, UDL-BSBL, based on unitary dictionary learning. Simulation results show that, compared to existing schemes, this invention achieves a high-precision sensing and positioning scheme with low complexity, strong noise robustness, and no need for prior distance information.

[0057] The above is a further detailed description of the present invention and should not be considered as a limitation on the specific implementation of the present invention. For those skilled in the art, simple deductions or substitutions without departing from the concept of the present invention are all within the protection scope of the present invention.

Claims

1. A near-field sensing and localization method in a millimeter-wave / Asia-Pacific Hertz system using ultra-large-scale arrays, for an uplink communication system of a single-antenna user, wherein the operating frequency of the uplink communication system is [insert frequency here]. The base station is equipped with two sub-array structures with a spacing between them. Serving single-antenna users, each subarray has the following number of receiving antennas: Antenna spacing The wavelength is half that of light, representing the speed of light; the observation vectors corresponding to the two subarrays are respectively and The corresponding angles of arrival are respectively and The corresponding user distances are respectively and Its characteristics are, The high-precision sensing and positioning method includes the following steps: S1. Construct a block sparse recovery algorithm based on unitary matrices: make Representing the discrete Fourier transform matrix, considering the general block sparse model, the channel... Block sparsity can be characterized as , Represents a unitary dictionary matrix. For near-field equivalent distance, It is a sparse signal; for the observation vector Then the block sparse recovery model can be expressed as: ， In the formula To handle zero-mean complex Gaussian noise; based on the existing pattern-coupled sparse Bayesian framework, and considering the feature that the dictionary matrix is ​​a unitary matrix, the recovery of block sparse signals does not require inverse operations. For the obtained posterior distribution estimate, it is continuously updated alternately until convergence, thus obtaining the unitary matrix-based block sparse recovery algorithm U-PCSBL. The recovery can be expressed as The specific updates are as follows: In the formula, The value is 1, representing the inverse variance of noise. The initial value is set to 1, and the inverse variance of each element is... The initial value is set to 1; parameter , , and For very small real values, such as ; Represents the diagonal covariance matrix The diagonal elements, Represents the mean of the block sparse signal The One element, express conjugate, express The conjugate transpose of . express The second norm; Indicates to Seeking traces; S2. Obtain the estimated angle and estimated distance that satisfy strict trigonometric relations; For each subarray, using the DFT matrix as the initial dictionary matrix, the low-complexity block sparse recovery algorithm of U-PCSBL is used to obtain the block sparse recovery signal, represented as: In the formula, and These correspond to the block sparse signals of the two subarrays, respectively. and The near-field unitary dictionary matrices for block sparse recovery correspond to the two subarrays respectively; firstly, Sort by amplitude in descending order, with the angle corresponding to the largest amplitude value represented as follows: Next Sort by magnitude in descending order, and the corresponding new index order is denoted as follows: ,make This represents the set of angles corresponding to all angle grid points in the DFT matrix, ordered from front to back by index. Find the first less than Angle corresponding to the angle grid point To satisfy strict trigonometric relations, that is If the above relationships cannot be satisfied, choose another set of initial dictionaries to avoid this problem, and replace the DFT matrix with the following new initial dictionary. in, Indicates The elements of the random variable form a diagonal matrix. satisfy Uniform distribution between, random variables satisfy Uniform distribution between and The values ​​are all 0.1; new initial dictionaries are continuously generated until a certain value exists. This satisfies strict trigonometric relationships; After being updated and The distance between the two subarrays and the user can be obtained through trigonometric relationships, i.e. In the formula, This represents the estimated distance between the first subarray and the user. This represents the estimated distance between the second subarray and the user; S3. Update the unitary dictionary matrix: Once the updated angle and distance are obtained, the corresponding dictionary matrix is ​​updated as follows: Repeat steps S1, S2, and S3 until the algorithm converges. This completes the UDL-BSBL method based on the unitary dictionary learning framework, achieving high-precision positioning and sensing.

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