Channel gain map reconstruction method and device based on analytical log-norm norm matrix

Abstract

The application discloses a channel gain map reconstruction method and device based on analytic logarithmic norm matrix, and relates to the technical field of wireless communication and signal processing. The method comprises the following steps: taking a complete channel gain matrix to be recovered as a solving variable, and constructing a channel map reconstruction optimization objective function; establishing an optimality benchmark equation of a regularization coefficient; introducing relative reconstruction accuracy and sampling missing rate, and quantifying a fidelity term gradient norm; deducing a closed-form expression of a regularization term gradient norm; using a matrix norm order relationship to establish an analytic expression of a non-zero singular value; substituting the quantified expression, the closed-form expression and the analytic expression into the optimality benchmark equation to obtain a regularization coefficient determined completely by physical parameters; and substituting the regularization coefficient into the optimization objective function, taking a partial observation matrix and an observation position set as inputs to iteratively solve, and outputting a reconstructed complete channel gain map matrix. According to the application, the channel gain map can be reconstructed without manual intervention.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and signal processing technology, and in particular to a method and apparatus for channel gain map reconstruction based on the analytical logarithmic norm matrix. Background Technology

[0002] A Channel Gain Map (CGM) is a spatial distribution map of large-scale channel gain across different spatial locations in a wireless communication environment. It is widely used in scenarios such as base station deployment optimization, mobility management, beam alignment, and spectrum resource allocation. Since dense measurements of the entire area are extremely costly, only sparse sampled data is available in practice. Therefore, it is necessary to reconstruct a complete channel gain map from sparse samples. This problem is essentially a matrix completion problem: the space is discretized into M×N grids, where the channel gain value of each grid point constitutes an element of the matrix, and sparse measurements correspond to some observation entries. The goal is to recover the entire matrix.

[0003] The core challenge of matrix completion lies in how to utilize low-rank prior information. Wireless channel gain maps typically exhibit low-rank characteristics because path loss and shadow fading vary smoothly with spatial location. Traditional methods employ the kernel norm as a convex relaxation of the matrix rank function. However, the kernel norm proportionally shrinks all singular values, leading to over-penalization of even large singular values, resulting in "biased estimations" and thus reducing the accuracy of channel map reconstruction.

[0004] To overcome the shortcomings of the nuclear norm, non-convex regularization methods have been extensively studied. Among them, the reweighted logarithmic norm (RLNM) has achieved superior performance to the nuclear norm in tasks such as image inpainting by assigning adaptive weights to different singular values, lightly penalizing larger singular values ​​and strongly penalizing smaller singular values. However, the RLNM method has a fundamental drawback: the selection of the regularization parameter λ and the internal shape parameters (p, γ, ε, c) heavily relies on manual empirical tuning or cross-validation. In practical channel map reconstruction tasks, different regions, different sampling rates, and different noise levels all require trial and error, which is inefficient and lacks theoretical guidance. More importantly, existing methods cannot establish a direct mathematical relationship between λ and the physical parameters of the channel map (such as grid size, sampling missing rate, channel dynamic range, expected rank, etc.), resulting in a lack of interpretability and difficulty in applying the methods to practical communication systems.

[0005] Therefore, the key technical challenge to improve the practicality, interpretability and automation of channel gain map reconstruction methods lies in how to rigorously derive the closed analytical relationship between the regularization parameter λ and the physical parameters of the channel map from the underlying mathematical structure of optimization theory, so that λ can be directly calculated rather than adjusted empirically. Summary of the Invention

[0006] To address the technical problems of existing technologies that rely on empirical parameter tuning and lack theoretical guidance, this invention provides a method and apparatus for reconstructing a channel gain map based on an analytical logarithmic norm matrix. The technical solution is as follows:

[0007] On the one hand, a channel gain map reconstruction method based on the analytic logarithmic norm matrix is ​​provided. This method is implemented by a channel gain map reconstruction device based on the analytic logarithmic norm matrix, and includes: S1. Obtain sparsely sampled channel gain data within the target area, construct a partial observation matrix and the corresponding set of observation locations, and determine the physical parameters of the channel map. The physical parameters include matrix dimension, sampling missing rate, channel gain magnitude, expected channel rank, relative reconstruction accuracy, structure coefficient, and log-norm shape parameter. S2. Using the complete channel gain matrix to be recovered as the solution variable, and the partial observation matrix and the set of observation locations as the fitting constraints, construct a channel map reconstruction optimization objective function with the reweighted log norm as the low-rank regularization term. The objective function includes a data fidelity term and a regularization term with undetermined regularization coefficients. S3. Based on the first-order optimality condition of the optimization objective function, establish the optimality benchmark equation between the regularization coefficient and the gradient norm of the fidelity term and the gradient norm of the regularization term; S4. Introducing the relative reconstruction accuracy and sampling missing rate, and combining the statistical characteristics of random uniform sampling, the gradient norm of the fidelity term is quantized into an expression related to the energy and physical parameters of the complete matrix. S5. Based on the low-rank characteristics of the channel gain map, and using the flat singular value assumption, derive the closed-form expression for the gradient norm of the regularization term. S6. Using the order of magnitude of the matrix norm, combined with the channel gain magnitude, structure coefficients, matrix dimension and expected channel rank, establish analytical expressions for non-zero singular values; S7. Substitute the physical quantization expression of the gradient norm of the fidelity term in S4, the closed expression of the gradient norm of the regularization term in S5, and the analytical expression of the non-zero singular value in S6 into the optimality benchmark equation in S3, eliminate intermediate variables, and obtain the regularization coefficient that is completely determined by the physical parameters. S8. Substitute the calculated regularization coefficient and log-norm shape parameter into the optimization objective function of S2, and iteratively solve the problem using the partial observation matrix and the set of observation locations as input. After the iteration converges, output the reconstructed complete channel gain map matrix.

[0008] On the other hand, a channel gain map reconstruction apparatus based on an analytic logarithmic norm matrix is ​​provided. This apparatus is applied to a channel gain map reconstruction method based on an analytic logarithmic norm matrix. The apparatus includes: The acquisition unit is used to acquire sparsely sampled channel gain data within the target area, construct a partial observation matrix and the corresponding set of observation locations, and determine the physical parameters of the channel map. The physical parameters include matrix dimension, sampling missing rate, channel gain magnitude, expected channel rank, relative reconstruction accuracy, structure coefficient, and log-norm shape parameter. The construction unit is used to construct a channel map reconstruction optimization objective function with the reweighted log norm as the low-rank regularization term, using the complete channel gain matrix to be recovered as the solution variable and the partial observation matrix and the set of observation positions as the fitting constraint. The objective function includes a data fidelity term and a regularization term with undetermined regularization coefficients. Establishment unit, used to establish the optimality benchmark equation between the regularization coefficient and the gradient norm of the fidelity term and the gradient norm of the regularization term based on the first-order optimality condition of the optimization objective function; The quantization unit is used to introduce the relative reconstruction accuracy and sampling missing rate, and combine the statistical characteristics of random uniform sampling to quantize the gradient norm of the fidelity term into an expression related to the energy and physical parameters of the complete matrix. The derivation unit is used to derive the closed-form expression of the gradient norm of the regularization term based on the low-rank characteristics of the channel gain map and the flat singular value assumption. Establish a unit to use the matrix norm order of magnitude relationship, combined with channel gain magnitude, structure coefficients, matrix dimension and expected channel rank, to establish analytical expressions for non-zero singular values; The analytical calculation unit is used to substitute the physical quantization expression of the gradient norm of the fidelity term of the quantization unit, the closed expression of the gradient norm of the regularization term of the derivation unit, and the analytical expression of the non-zero singular value of the establishment unit into the optimality benchmark equation of the establishment unit, eliminate intermediate variables, and obtain the regularization coefficient that is completely determined by the physical parameters. The optimization solution unit is used to substitute the calculated regularization coefficients and log-norm shape parameters into the optimization objective function of the construction unit, and iteratively solves the problem using the partial observation matrix and the set of observation locations as input. After the iteration converges, it outputs the reconstructed complete channel gain map matrix.

[0009] On the other hand, a channel gain map reconstruction device based on an analytic log-norm matrix is ​​provided. The channel gain map reconstruction device based on an analytic log-norm matrix includes: a processor; a memory, wherein computer-readable instructions are stored in the memory, and when the computer-readable instructions are executed by the processor, any one of the methods described above for channel gain map reconstruction based on an analytic log-norm matrix is ​​implemented.

[0010] On the other hand, a computer-readable storage medium is provided, wherein at least one instruction is stored therein, the at least one instruction being loaded and executed by a processor to implement any of the above-described methods for channel gain map reconstruction based on the analytic logarithmic norm matrix.

[0011] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: This invention utilizes the first-order optimality condition from optimization theory, combined with matrix spectral analysis theory and the low-rank statistical properties of channel gain maps, to establish a strict analytical equation relationship between the regularization parameter λ and the physical parameters of the channel map itself (spatial grid size, sampling missing rate, channel gain magnitude, expected channel rank, reconstruction accuracy requirements, etc.). This allows λ to be directly calculated rather than through cross-validation trial and error. Simultaneously, this invention provides analytical constraints on the shape parameters within the logarithmic norm, forming a complete channel gain map reconstruction technique that requires no manual intervention. This overcomes the shortcomings of existing RLNM methods in CGM reconstruction applications, which rely on empirical parameter tuning and lack theoretical guidance. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart of a channel gain map reconstruction method based on an analytical logarithmic norm matrix provided by an embodiment of the present invention; Figure 2 This is a schematic diagram of a channel gain map reconstruction system scenario provided by an embodiment of the present invention; Figure 3 This is a block diagram of a channel gain map reconstruction device based on an analytical logarithmic norm matrix provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of a channel gain map reconstruction device based on an analytical logarithmic norm matrix provided in an embodiment of the present invention. Detailed Implementation

[0014] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0015] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0016] In the embodiments of this invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning. Similarly, the terms "of," "corresponding (relevant)," and "corresponding" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning.

[0017] In this embodiment of the invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0018] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0019] This invention provides a channel gain map reconstruction method based on an analytic logarithmic norm matrix. This method can be implemented by a channel gain map reconstruction device based on an analytic logarithmic norm matrix, which can be a terminal or a server. Figure 1 The flowchart shown is for a channel gain map reconstruction method based on the analytic logarithmic norm matrix. The processing flow of this method may include the following steps:

[0020] S1. Obtain sparsely sampled channel gain data within the target area, construct a partial observation matrix and the corresponding set of observation locations, and determine the physical parameters of the channel map.

[0021] The physical parameters include matrix dimension, sampling missing rate, channel gain magnitude, expected channel rank, relative reconstruction accuracy, structural coefficients, and log-norm shape parameter.

[0022] In one feasible implementation, the partial observation matrix to be completed is obtained. and its set of observation locations Statistically analyze or set the following physical parameters:

[0023] (1) Matrix dimension , ; (2) Sampling missing rate (i.e., the proportion of unobserved elements, by) Size determines); (3) Channel gain amplitude (The maximum absolute value of the elements of the observation matrix can be taken) ); (4) Expected channel rank It can be estimated through prior knowledge or information theory criteria, reflecting the low-rank degree of the channel map.

[0024] (5) Relative reconstruction accuracy (The noise environment is determined by the standard deviation of the channel noise). (6) Log-norm shape parameter , , , ; (7) Structural coefficient It reflects the uniformity of the distribution of elements within the channel gain map, which can be achieved through... Estimate or adaptive update.

[0025] Among them, relative reconstruction accuracy δ These are user-specified physical parameters whose values ​​reflect the ratio of the energy of the fitted residuals to the energy of the observed data. In the presence of noise, the values ​​are determined by the noise standard deviation.

[0026] Structural coefficient k It reflects the distribution characteristics of the elements inside the matrix, is inversely proportional to the matrix size, and is obtained through a small amount of sampling or adaptive updates.

[0027] Shape parameters , , , Determined by analyzing the constraint relationships. γ The value is determined by the user, and the larger the value, the stronger the regularization constraint effect.

[0028] Optionally, the logarithmic norm shape parameter includes a power parameter. p and global scale coefficient γ The shape parameters are determined through analytical constraints: Power parameter p The channel rank is selected based on its low rank in the channel map; the lower the expected channel rank, the better. p The smaller the value, the wider the range of values ​​(0 < 0). p ≤1.

[0029] Global scale coefficient γ The value is determined based on the magnitude matching relationship between the regularization term and the fidelity term, and its range is 0.1 < γ ≤10.

[0030] All shape parameters are determined analytically from the channel's physical characteristics, eliminating the need for manual parameter tuning through cross-validation.

[0031] Optionally, structural coefficient k Determined using an adaptive update mechanism, including: In the initial iteration phase, the structure coefficients are estimated based on the statistical characteristics of a small amount of sampled data. k The initial value.

[0032] During the iteration process, the structure coefficients are updated in real time based on the singular value distribution characteristics of the channel gain matrix obtained in the current iteration. k The value of .

[0033] Updated structural coefficients k The feedback is used to calculate the regularization coefficient, achieving an adaptive match between the regularization strength and the actual low-rank characteristics of the channel.

[0034] S2. Using the complete channel gain matrix to be recovered as the solution variable and the partial observation matrix and observation location set as the fitting constraints, construct a channel map reconstruction optimization objective function with the reweighted logarithmic norm as the low-rank regularization term. The objective function includes a data fidelity term and a regularization term with undetermined regularization coefficients.

[0035] Alternatively, the objective function in S2 can be in the form of equation (1): (1) Among them, the fidelity term measures the relationship between the recovery matrix X and the observed data. The fitting error at the known location, This is the complete channel matrix to be recovered. The observed sparse channel matrix. This is a sampling operator that retains only known elements within the set of observed locations. This is a regularization term used to constrain the low-rank property of a matrix. The regularization coefficient balances the data fitting term and the regularization term. In existing technologies, manual adjustment is required; this invention will provide a closed-form analytical solution through theoretical derivation.

[0036] The specific form of the reweighted logarithmic norm Φ(X) is as follows (2): (2) Among them, the weighting coefficient satisfy , The first of the channels to be recovered is the complete channel gain matrix. i There are singular values, and the log-norm shape parameter satisfies... , , It is a very small constant.

[0037] S3. Based on the first-order optimality condition of the objective function, establish the optimality benchmark equation between the regularization coefficient and the gradient norm of the fidelity term and the gradient norm of the regularization term.

[0038] In one feasible implementation, let X be the optimal solution to the optimization problem. According to the first-order necessary condition, the gradient of the objective function is... The value is zero, as shown in equation (3):

[0039] (3) After rearranging and taking the F-norm, we get The expression is as follows (4): (4) This formula will This is expressed as the ratio of the gradient norm of the fidelity term to the gradient norm of the regularization term, laying the foundation for subsequent analytical calculations.

[0040] S4. Introducing relative reconstruction accuracy and sampling missing rate, and combining the statistical characteristics of random uniform sampling, the gradient norm of the fidelity term is quantized into an expression related to the energy and physical parameters of the complete matrix.

[0041] In one feasible implementation, molecules It is the energy of the fitting residual at the observation location. The relative fitting accuracy is defined as follows (5):

[0042] (5) The physical meaning of δ is the ratio of residual energy to observed data energy, set by the user based on noise level or desired accuracy. Under the statistical assumption of random uniform missing data, the observed data energy and the complete data energy satisfy... And the energy of the optimal solution is approximately equal to Therefore, the following equation (6) is given:

[0043] (6) S5. Based on the low-rank characteristics of the channel gain map, and using the flat singular value assumption, a closed-form expression for the gradient norm of the regularization term is derived.

[0044] In one feasible implementation, an optimal solution is assumed. The rank is And all non-zero singular values ​​are approximately equal: (Low-rank flat singular value assumption). Under this assumption:

[0045] (1) The F-norm of the matrix simplifies to .

[0046] (2) For the reweighted log-norm, by taking the derivative using the chain rule and substituting the flatness assumption, we obtain the concise expression for the gradient F-norm as shown in equation (7): (7) S6. Using the matrix norm order relationship, combined with the channel gain magnitude, structure coefficient, matrix dimension and expected channel rank, establish the analytical expression for the non-zero singular value.

[0047] Alternatively, the analytic expression for the non-zero singular values ​​in S6 is as follows (8): (8) in, k For structural coefficients, M and N Represents the matrix dimension. A Indicates the channel gain magnitude. r This represents the expected channel rank.

[0048] In one feasible implementation, using matrix norm theory, the F-norm and the infinite norm satisfy... .set up = (Estimated from observational data), introducing structural coefficients. The uniformity of the energy distribution of the channel gain elements ∈(0,1] is given by the following equation (9):

[0049] (9) Combined with the flatness assumption Solving equation (8) yields the above equation.

[0050] S7. Substitute the physical quantization expression of the gradient norm of the fidelity term in S4, the closed-form expression of the gradient norm of the regularization term in S5, and the analytical expression of the non-zero singular values ​​in S6 into the optimality benchmark equation in S3, eliminate intermediate variables, and obtain the regularization coefficient that is completely determined by the physical parameters.

[0051] Alternatively, the closed-form analytical expression for the regularization coefficients in S7, which are entirely determined by the physical parameters, is as follows (10): (10) in, For relative reconstruction accuracy, B The sampling missing rate, Non-zero singular values, p and Let be the logarithmic norm shape parameter, where p This represents the power parameter of the regularization term. Represents the global scale coefficient. and To ensure the non-negativity and numerical stability of the logarithmic terms, a minimal constant is used.

[0052] In one feasible implementation, Substituting the values, we get the following equation (12): (12) S8. Substitute the calculated regularization coefficients and log-norm shape parameters into the optimization objective function of S2, and iteratively solve the problem using the partial observation matrix and the set of observation locations as inputs. After the iteration converges, output the reconstructed complete channel gain map matrix.

[0053] Optionally, S8 employs the Alternating Direction Method of Multipliers (ADMM) for iterative solution. The iterative process includes: X-sub-problem update: By fusing partial observation matrix data and auxiliary variables from the observation location set, the update of the complete channel gain matrix to be recovered is completed through closed-form calculation.

[0054] Z-subproblem update: Perform singular value decomposition on the auxiliary variable, solve the one-dimensional non-convex optimization problem using the convex function difference algorithm or Newton's method, and complete the threshold update of the singular values.

[0055] Multiplier and parameter update: Synchronously update the Lagrange multipliers and penalty parameters.

[0056] The iteration terminates when the relative change in the channel gain matrix to be recovered obtained from two consecutive iterations is less than the preset convergence threshold, or when the number of iterations reaches the preset maximum number of iterations.

[0057] In one feasible implementation, when the relative change of the recovery matrix between two adjacent iterations is less than a threshold or the maximum number of iterations is reached, the final reconstructed complete channel gain map matrix is ​​output. The system scenario for reconstructing the channel gain map can be as follows: Figure 2 As shown in the diagram. This matrix can be used for downstream applications such as wireless network planning, beam management, and mobility prediction.

[0058] This invention utilizes the first-order optimality condition from optimization theory, combined with matrix spectral analysis theory and the low-rank statistical properties of channel gain maps, to establish a strict analytical equation relationship between the regularization parameter λ and the physical parameters of the channel map itself (spatial grid size, sampling missing rate, channel gain magnitude, expected channel rank, reconstruction accuracy requirements, etc.). This allows λ to be directly calculated rather than through cross-validation trial and error. Simultaneously, this invention provides analytical constraints on the shape parameters within the logarithmic norm, forming a complete channel gain map reconstruction technique that requires no manual intervention. This overcomes the shortcomings of existing RLNM methods in CGM reconstruction applications, which rely on empirical parameter tuning and lack theoretical guidance.

[0059] Figure 3 This is a block diagram of a channel gain map reconstruction device based on an analytic logarithmic norm matrix, provided by an embodiment of the present invention. This device is used in a channel gain map reconstruction method based on an analytic logarithmic norm matrix. (Refer to...) Figure 3 The device includes an acquisition unit 310, a construction unit 320, an establishment unit 330, a quantization unit 340, a derivation unit 350, an establishment unit 360, an analytical calculation unit 370, and an optimization solution unit 380. Wherein:

[0060] The acquisition unit 310 is used to acquire sparsely sampled channel gain data within the target area, construct a partial observation matrix and the corresponding set of observation locations, and determine the physical parameters of the channel map. The physical parameters include matrix dimension, sampling missing rate, channel gain magnitude, expected channel rank, relative reconstruction accuracy, structure coefficient, and log-norm shape parameter. Construction unit 320 is used to construct a channel map reconstruction optimization objective function with the reweighted log norm as the low-rank regularization term, using the complete channel gain matrix to be recovered as the solution variable and the partial observation matrix and the set of observation positions as the fitting constraint basis. The objective function includes a data fidelity term and a regularization term with undetermined regularization coefficients. Establishment unit 330 is used to establish an optimality benchmark equation between the regularization coefficient and the gradient norm of the fidelity term and the gradient norm of the regularization term based on the first-order optimality condition of the optimization objective function; The quantization unit 340 is used to introduce the relative reconstruction accuracy and sampling missing rate, and combine the statistical characteristics of random uniform sampling to quantize the gradient norm of the fidelity term into an expression related to the energy and physical parameters of the complete matrix. Derivation unit 350 is used to derive the closed-form expression of the gradient norm of the regularization term based on the low-rank characteristics of the channel gain map and the flat singular value assumption. Unit 360 is established to utilize the matrix norm order of magnitude relationship, combined with channel gain magnitude, structure coefficients, matrix dimension and expected channel rank, to establish analytical expressions for non-zero singular values; The analytical calculation unit 370 is used to substitute the physical quantization expression of the gradient norm of the fidelity term of the quantization unit, the closed expression of the gradient norm of the regularization term of the derivation unit, and the analytical expression of the non-zero singular value of the establishment unit into the optimality benchmark equation of the establishment unit, eliminate intermediate variables, and obtain the regularization coefficient that is completely determined by the physical parameters. The optimization solution unit 380 is used to substitute the calculated regularization coefficients and log-norm shape parameters into the optimization objective function of the construction unit, and perform iterative solution with the partial observation matrix and the set of observation positions as input. After the iteration converges, the reconstructed complete channel gain map matrix is ​​output.

[0061] This invention utilizes the first-order optimality condition from optimization theory, combined with matrix spectral analysis theory and the low-rank statistical properties of channel gain maps, to establish a strict analytical equation relationship between the regularization parameter λ and the physical parameters of the channel map itself (spatial grid size, sampling missing rate, channel gain magnitude, expected channel rank, reconstruction accuracy requirements, etc.). This allows λ to be directly calculated rather than through cross-validation trial and error. Simultaneously, this invention provides analytical constraints on the shape parameters within the logarithmic norm, forming a complete channel gain map reconstruction technique that requires no manual intervention. This overcomes the shortcomings of existing RLNM methods in CGM reconstruction applications, which rely on empirical parameter tuning and lack theoretical guidance.

[0062] Figure 4 This is a schematic diagram of a channel gain map reconstruction device based on an analytic logarithmic norm matrix provided in an embodiment of the present invention, as shown below. Figure 4 As shown, the channel gain map reconstruction device based on the analytical logarithmic norm matrix can include the above-mentioned... Figure 3 The illustrated channel gain map reconstruction apparatus based on the analytic log-norm matrix is ​​shown. Optionally, the channel gain map reconstruction apparatus 410 based on the analytic log-norm matrix may include a first processor 2001.

[0063] Optionally, the channel gain map reconstruction device 410 based on the analytic logarithmic norm matrix may also include a memory 2002 and a transceiver 2003.

[0064] The first processor 2001, memory 2002, and transceiver 2003 can be connected via a communication bus.

[0065] The following is combined with Figure 4 The various components of the channel gain map reconstruction device 410 based on the analytic logarithmic norm matrix are described in detail below: The first processor 2001 is the control center of the channel gain map reconstruction device 410 based on the analytical logarithmic norm matrix. It can be a single processor or a collective term for multiple processing elements. For example, the first processor 2001 can be one or more central processing units (CPUs), application-specific integrated circuits (ASICs), or one or more integrated circuits configured to implement embodiments of the present invention, such as one or more digital signal processors (DSPs), or one or more field-programmable gate arrays (FPGAs).

[0066] Optionally, the first processor 2001 can perform various functions of the channel gain map reconstruction device 410 based on the analytic logarithmic norm matrix by running or executing software programs stored in the memory 2002 and calling data stored in the memory 2002.

[0067] In a specific implementation, as one example, the first processor 2001 may include one or more CPUs, for example... Figure 4 CPU0 and CPU1 are shown in the diagram.

[0068] In a specific implementation, as one example, the channel gain map reconstruction device 410 based on the analytic logarithmic norm matrix may also include multiple processors, for example... Figure 4 The first processor 2001 and the second processor 2004 are shown in the diagram. Each of these processors can be a single-core processor or a multi-core processor. Here, a processor can refer to one or more devices, circuits, and / or processing cores used to process data (such as computer program instructions).

[0069] The memory 2002 is used to store the software program that executes the present invention, and is controlled by the first processor 2001 to execute it. The specific implementation method can be referred to the above method embodiment, and will not be repeated here.

[0070] Optionally, the memory 2002 may be a read-only memory (ROM) or other type of static storage device capable of storing static information and instructions, random access memory (RAM) or other type of dynamic storage device capable of storing information and instructions, or electrically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto. The memory 2002 may be integrated with the first processor 2001 or may exist independently, and may be connected via the interface circuit of the channel gain map reconstruction device 410 based on the analytic logarithmic norm matrix. Figure 4 (Not shown in the image) is coupled to the first processor 2001, and this embodiment of the invention does not specifically limit this.

[0071] The transceiver 2003 is used to communicate with network devices or with terminal devices.

[0072] Alternatively, transceiver 2003 may include a receiver and a transmitter. Figure 4 (Not shown separately). The receiver is used to implement the receiving function, and the transmitter is used to implement the transmitting function.

[0073] Optionally, the transceiver 2003 can be integrated with the first processor 2001 or exist independently, and can be connected to the interface circuit of the channel gain map reconstruction device 410 based on the analytical logarithmic norm matrix. Figure 4 (Not shown in the image) is coupled to the first processor 2001, and this embodiment of the invention does not specifically limit this.

[0074] It should be noted that, Figure 4 The structure of the channel gain map reconstruction device 410 based on the analytic log-norm matrix shown in the figure does not constitute a limitation on the router. Actual channel gain map reconstruction devices based on the analytic log-norm matrix may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0075] Furthermore, the technical effect of the channel gain map reconstruction device 410 based on the analytical logarithmic norm matrix can be referred to the technical effect of the channel gain map reconstruction method based on the analytical logarithmic norm matrix described in the above method embodiments, and will not be repeated here.

[0076] It should be understood that the first processor 2001 in the embodiments of the present invention may be a central processing unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor, or it may be any conventional processor, etc.

[0077] It should also be understood that the memory in the embodiments of the present invention can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDR SDRAM), enhanced synchronous DRAM (ESDRAM), synchronous linked DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0078] The above embodiments can be implemented, in whole or in part, by software, hardware (such as circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0079] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. A and B can be singular or plural. Additionally, the character " / " in this article generally indicates an "or" relationship between the preceding and following related objects, but it can also represent an "and / or" relationship. Please refer to the context for a more accurate understanding.

[0080] In this invention, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of a single item or a plurality of items. For example, at least one of a, b, or c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be a single item or multiple items.

[0081] It should be understood that, in various embodiments of the present invention, the order of the above-mentioned process numbers does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0082] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0083] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices, apparatuses, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0084] In the several embodiments provided by this invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0085] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0086] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0087] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0088] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A channel gain map reconstruction method based on the analytic logarithmic norm matrix, characterized in that, The method includes: S1. Obtain sparsely sampled channel gain data within the target area, construct a partial observation matrix and the corresponding set of observation locations, and determine the physical parameters of the channel map. The physical parameters include matrix dimension, sampling missing rate, channel gain magnitude, expected channel rank, relative reconstruction accuracy, structure coefficient, and log-norm shape parameter. S2. Using the complete channel gain matrix to be recovered as the solution variable, and the partial observation matrix and the set of observation locations as the fitting constraints, construct a channel map reconstruction optimization objective function with the reweighted log norm as the low-rank regularization term. The objective function includes a data fidelity term and a regularization term with undetermined regularization coefficients. S3. Based on the first-order optimality condition of the optimization objective function, establish the optimality benchmark equation between the regularization coefficient and the gradient norm of the fidelity term and the gradient norm of the regularization term; S4. Introducing the relative reconstruction accuracy and sampling missing rate, and combining the statistical characteristics of random uniform sampling, the gradient norm of the fidelity term is quantized into an expression related to the energy and physical parameters of the complete matrix. S5. Based on the low-rank characteristics of the channel gain map, and using the flat singular value assumption, derive the closed-form expression for the gradient norm of the regularization term. S6. Using the order of magnitude of the matrix norm, combined with the channel gain magnitude, structure coefficients, matrix dimension and expected channel rank, establish analytical expressions for non-zero singular values; S7. Substitute the physical quantization expression of the gradient norm of the fidelity term in S4, the closed expression of the gradient norm of the regularization term in S5, and the analytical expression of the non-zero singular value in S6 into the optimality benchmark equation in S3, eliminate intermediate variables, and obtain the regularization coefficient that is completely determined by the physical parameters. S8. Substitute the calculated regularization coefficient and log-norm shape parameter into the optimization objective function of S2, and iteratively solve the problem using the partial observation matrix and the set of observation locations as input. After the iteration converges, output the reconstructed complete channel gain map matrix.

2. The channel gain map reconstruction method based on the analytic logarithmic norm matrix according to claim 1, characterized in that, The closed-form analytical expression for the regularization coefficient in S7, which is entirely determined by the physical parameters, is as follows: (1) （1） in, For relative reconstruction accuracy, B The sampling missing rate, Non-zero singular values, p and Let be the logarithmic norm shape parameter, where p This represents the power parameter of the regularization term. Represents the global scale coefficient. and To ensure the non-negativity and numerical stability of the logarithmic terms, a minimal constant is used.

3. The channel gain map reconstruction method based on the analytic logarithmic norm matrix according to claim 1, characterized in that, The analytical expression for the non-zero singular values ​​in S6 is as follows (2): （2） Where k is the structure coefficient, M and N represent the matrix dimensions, A represents the channel gain magnitude, and r represents the expected channel rank.

4. The channel gain map reconstruction method based on the analytic logarithmic norm matrix according to claim 3, characterized in that, The logarithmic norm shape parameter includes a power parameter p and a global scaling coefficient γ, and the shape parameter is determined through analytical constraints: The power parameter p is selected based on the low rank of the channel map; the lower the expected channel rank, the smaller the value of p, with a range of 0. <p≤1; The global scaling coefficient γ is determined based on the order of magnitude of the regularization term and the fidelity term, and its value range is 0.1 < γ ≤ 10. All shape parameters are determined analytically from the channel's physical characteristics, eliminating the need for manual parameter tuning through cross-validation.

5. The channel gain map reconstruction method based on the analytic logarithmic norm matrix according to claim 1, characterized in that, The objective function in S2 is in the form of the following equation (3): （3） in, The complete channel matrix to be recovered; The observed sparse channel matrix; As a sampling operator, only known elements within the set of observed locations are retained; This is a regularization term used to constrain the low-rank property of the matrix; This is the regularization coefficient, which balances the data fitting term and the regularization term. The specific form of the reweighted log-norm Φ(X) is as follows (4): （4） Among them, the weighting coefficient satisfy , The first of the channels to be recovered is the complete channel gain matrix. i There are singular values, and the log-norm shape parameter satisfies... , , It is a very small constant.

6. The channel gain map reconstruction method based on the analytic logarithmic norm matrix according to claim 1, characterized in that, The S8 solution employs the Alternating Direction Multiplier Method (ADMM) for iterative solving. The iterative process includes: X Subproblem Update: By fusing partial observation matrix data and auxiliary variables from the observation location set, the update of the complete channel gain matrix to be recovered is completed through closed-form calculation; Z-subproblem update: Perform singular value decomposition on the auxiliary variable, solve the one-dimensional non-convex optimization problem by convex function difference algorithm or Newton's method, and complete the threshold update of singular values; Multiplier and parameter update: Synchronously update the Lagrange multipliers and penalty parameters; The iteration terminates when the relative change in the channel gain matrix to be recovered obtained from two consecutive iterations is less than the preset convergence threshold, or when the number of iterations reaches the preset maximum number of iterations.

7. The channel gain map reconstruction method based on the analytic logarithmic norm matrix according to claim 1, characterized in that, The structural coefficient k is determined using an adaptive update mechanism, including: In the initial iteration phase, the initial value of the structure coefficient k is estimated based on the statistical characteristics of a small amount of sampled data; During the iteration process, the value of the structure coefficient k is updated in real time based on the singular value distribution characteristics of the channel gain matrix obtained in the current iteration. The updated structural coefficient k is fed back into the calculation process of the regularization coefficient to achieve adaptive matching between the regularization strength and the actual low-rank characteristics of the channel.

8. A channel gain map reconstruction apparatus based on an analytic log-norm matrix, wherein the channel gain map reconstruction apparatus based on an analytic log-norm matrix is ​​used to implement the channel gain map reconstruction method based on an analytic log-norm matrix as described in any one of claims 1-7, characterized in that, The device includes: The acquisition unit is used to acquire sparsely sampled channel gain data within the target area, construct a partial observation matrix and the corresponding set of observation locations, and determine the physical parameters of the channel map. The physical parameters include matrix dimension, sampling missing rate, channel gain magnitude, expected channel rank, relative reconstruction accuracy, structure coefficient, and log-norm shape parameter. The construction unit is used to construct a channel map reconstruction optimization objective function with the reweighted log norm as the low-rank regularization term, using the complete channel gain matrix to be recovered as the solution variable and the partial observation matrix and the set of observation positions as the fitting constraint. The objective function includes a data fidelity term and a regularization term with undetermined regularization coefficients. Establishment unit, used to establish the optimality benchmark equation between the regularization coefficient and the gradient norm of the fidelity term and the gradient norm of the regularization term based on the first-order optimality condition of the optimization objective function; The quantization unit is used to introduce the relative reconstruction accuracy and sampling missing rate, and combine the statistical characteristics of random uniform sampling to quantize the gradient norm of the fidelity term into an expression related to the energy and physical parameters of the complete matrix. The derivation unit is used to derive the closed-form expression of the gradient norm of the regularization term based on the low-rank characteristics of the channel gain map and the flat singular value assumption. Establish a unit to use the matrix norm order of magnitude relationship, combined with channel gain magnitude, structure coefficients, matrix dimension and expected channel rank, to establish analytical expressions for non-zero singular values; The analytical calculation unit is used to substitute the physical quantization expression of the gradient norm of the fidelity term of the quantization unit, the closed expression of the gradient norm of the regularization term of the derivation unit, and the analytical expression of the non-zero singular value of the establishment unit into the optimality benchmark equation of the establishment unit, eliminate intermediate variables, and obtain the regularization coefficient that is completely determined by the physical parameters. The optimization solution unit is used to substitute the calculated regularization coefficients and log-norm shape parameters into the optimization objective function of the construction unit, and iteratively solves the problem using the partial observation matrix and the set of observation locations as input. After the iteration converges, it outputs the reconstructed complete channel gain map matrix.

9. A channel gain map reconstruction device based on an analytic logarithmic norm matrix, characterized in that, The channel gain map reconstruction device based on the analytic logarithmic norm matrix includes: processor; A memory storing computer-readable instructions that, when executed by the processor, implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium contains program code that can be invoked by a processor to execute the method as described in any one of claims 1 to 7.

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