A sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition

Abstract

The application relates to a sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition, which comprises the following steps: S1, dividing a three-dimensional space corresponding to the three-dimensional spectrum map into equal grid points and numbering, and constructing a non-restriction condition sensing space; S2, using a RIP criterion in compression sensing to guide the selection of the non-restriction condition sensing space sampling grid points, performing principal component analysis preprocessing on a non-restriction condition sensing space channel matrix, and selecting a pre-sampling grid point set; S3, according to the restriction condition, distinguishing the grid points into a restriction sampling grid point set and a selectable sampling grid point set, and re-optimizing the restriction sampling grid points in the pre-sampling grid point set through a simulated annealing algorithm, so as to obtain a sampling grid point set of the selectable sampling grid points. The beneficial effect is that the three-dimensional spectrum map construction accuracy is effectively improved under the condition that the sampling is highly restricted.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication technology, and particularly relates to a sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition. BACKGROUND

[0002] Compressed sensing, also known as compressive sampling or sparse sampling, is a technology for finding a sparse solution of an underdetermined linear system. The theory proposes that sparse signals and compressible signals can be sampled at a rate much lower than the Nyquist sampling rate and still be reconstructed with high precision. It has been widely used in the field of signal processing in recent years. Sparsity is a prerequisite for using compressed sensing technology. When constructing a three-dimensional spectrum map, the three-dimensional space needs to be divided into grid points. Since the number of signal sources in the space is sparse compared to the number of grid points, we can use compressed sensing to sample in the space and then recover the signal source strength. Then, a three-dimensional spectrum map is constructed through a channel propagation model. Therefore, the accuracy of signal source strength estimation is particularly important for accurately constructing a three-dimensional spectrum map.

[0003] In recent years, with the rapid development of Internet technologies such as 5G, Internet of Things, and smart cities, more types and quantities of spectrum devices are being used. The use of spectrum resources in commercial construction, civilian life, and national defense construction is growing at an unprecedented rate. With the continuous expansion of business size and the increasing variety of spectrum devices, spectrum management is facing higher complexity and more diverse user demands. Rich spectrum resource information is the basis for spectrum management. The radio environment map, as a comprehensive database, can visualize the frequency resources in the environment in terms of time, space, and field strength. Therefore, accurately constructing a spectrum map of the environment is particularly important for spectrum management.

[0004] There are three main methods for constructing a spectrum map: direct construction, indirect construction, and hybrid construction. The widely used method for constructing a spectrum map is the Kriging interpolation algorithm in the direct construction method. The method consists of two steps: the first step is to sample the field strength of the points in the space, and the second step is to obtain the spectrum map of the entire space by fitting the variogram model. This algorithm requires a large amount of sampling data to fit the variogram model. The above spectrum map construction methods are mainly applied to small data processing and rich sampling conditions. Under high sampling constraints, the accuracy of the above spectrum map construction methods is significantly reduced.

[0005] RIP criterion (also known as: Restricted Isometry Property, RIP) in compressed sensing: the matrix satisfies 2K order RIP, which guarantees that any K sparse signal θK can be mapped to a unique y, that is, to recover the K sparse signal θK from the compressed observation y, it is necessary to ensure that the sensing matrix satisfies the 2K order RIP, and the matrix satisfying the 2K order RIP is any 2K column linearly independent. The RIP property (Restricted Isometry Property) ensures that the observation matrix does not map two different K sparse signals to the same set (ensures one-to-one mapping relationship from the original space to the sparse space), and requires that the matrix composed of every M column vectors extracted from the observation matrix is non-singular.

[0006] Principal Component Analysis (PCA) is a statistical method that converts a set of variables that may have correlations into a set of linearly uncorrelated variables through orthogonal transformation. The converted set of variables is called principal components.

[0007] Simulated annealing algorithm is derived from the principle of solid annealing, which is a probability-based algorithm. The solid is heated to a sufficiently high temperature and then slowly cooled. When heated, the particles in the solid become disordered with temperature rise, and the internal energy increases. When slowly cooled, the particles gradually become ordered, and at each temperature, the system reaches an equilibrium state. Finally, at room temperature, the system reaches the ground state, and the internal energy is minimized. Simulated annealing algorithm can be divided into three parts: solution space, objective function and initial solution. Simulated annealing algorithm is an optimization algorithm with a time-varying probability of sudden jump that tends to zero eventually, which can effectively avoid falling into local minimum and finally tend to global optimum.

[0008] Currently, no similar description or report has been found, and no similar data has been collected at home and abroad. The present application improves the placement method of the sampling receiver when constructing a three-dimensional spatial spectrum map by compressed sensing technology in a limited sampling area in space. SUMMARY

[0009] The purpose of the present application is to provide a sampling point selection method that effectively improves the accuracy of constructing a three-dimensional spectrum map under the condition of high sampling constraints.

[0010] To achieve the above purpose, the technical scheme adopted by the present application is a sampling point selection method for constructing a three-dimensional spectrum map under limited conditions, comprising the following steps:

[0011] S1, divide the three-dimensional space corresponding to the three-dimensional spectrum map into equal grid points and number them to construct a sensing space under non-limiting conditions;

[0012] S2, using the RIP criterion in compressed sensing to guide the selection of non-restricted condition perception space sampling grid points, performing principal component analysis preprocessing on the non-restricted condition perception space channel matrix, and selecting a pre-sampling grid point set;

[0013] S3, according to the restriction condition, the grid points are divided into a restricted sampling grid point set and a selectable sampling grid point set, and the restricted sampling grid points in the pre-sampling grid point set are re-optimized through the simulated annealing algorithm, so as to obtain the sampling grid point set of the selectable sampling grid points.

[0014] Preferably, the above-mentioned sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition comprises the following steps:

[0015] Preferably, the above-mentioned sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition comprises the following steps:

[0016] S21, the spectrum energy of each grid point in the non-restricted condition perception space is linearly superimposed by different source energies after path loss, and the number of sources is sparse compared with the total number of grid points, and the corresponding source sparse vector is wherein each element x i of the source sparse vector is: wherein is the source power at the grid point x i ;

[0017] S22, since the path loss is related to the distance, the channel f ij between the grid point i and the grid point j can be obtained: The non-restricted condition perception space channel matrix F is: wherein, α represents the path loss index, d ij represents the distance between the grid point i and the grid point j, ζ i represents the coordinates of the grid point i;

[0018] S23, the source intensity model y=ΦFx in the three-dimensional space is recovered by compressed sensing, wherein F is the channel matrix, x is the source sparse vector, and Φ is the sampling matrix. The principal component analysis is adopted to perform dimension reduction processing on the non-restricted condition perception space channel matrix F, and the points represented by the columns with larger channel energy are selected as the pre-selected pre-sampling grid point set, and the sampling matrix Φ is obtained.

[0019] Preferably, the sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition comprises the following steps in step S23:

[0020] S231, for the column vector f of the channel matrix i , each column subtracts the mean value to obtain f' i , and the corresponding matrix F' = [f'1, f'2…f' n ] is obtained.

[0021] S232, singular value decomposition is performed on F', and the eigenvalues are sorted from large to small, and the eigenvalues correspond to their eigenvectors, so there are eigenvalues k1, k2…k n , and the corresponding eigenvectors w1, w2…w n .

[0022] S232, the eigenvectors corresponding to the largest m eigenvalues are reserved, and the original channel matrix F is multiplied to obtain a reduced dimension channel matrix

[0023] S232, select m channel energy points as the pre-sampling grid point set

[0024] Preferably, the sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition comprises the following steps in step S23:

[0025] S31, there are sampling limited grid points in the actual three-dimensional space, and the corresponding limited sampling grid point set is G = {g1, g2…g o}, and the optional sampling grid point set is P = full_point-{G};

[0026] S32, the sampling matrix obtained in step S23 is , wherein m is the number of pre-sampling grid points, and the elements in the sampling matrix correspond to the sampling receiver placement positions, that is, the elements in the sampling matrix Φ are 0 or 1, and the grid points with a value of 1 are sampling receiver placement points.

[0027] S33, by using the simulated annealing algorithm, the pre-sampling grid point set is processed, and the limited sampling grid point is replaced by the optional sampling grid point for sampling, and the optimization model is: Wherein A=ΦF, the simulated annealing algorithm minimizes the norm value in the optimization model by sampling the matrix Φ, each kind of sampling receiver placement scheme is placed as an annealing algorithm solution, the optional sampling grid points in the annealing algorithm solution are reserved, the new optional sampling grid points are selected each time iteration, and the new annealing algorithm solution is composed of the new optional sampling grid points and the reserved optional sampling grid points, the optimization model corresponding to the new annealing algorithm solution is solved, and the optimization model corresponding to the previous annealing algorithm solution is compared, and finally the optimal annealing algorithm solution is obtained after multiple iterations and annealing, that is, the sampling grid point set not including the limited sampling grid points.

[0028] Preferably, the above-mentioned sampling point selection method for constructing a three-dimensional spectrum map under a constraint condition, the step S33:

[0029] The input of the simulated annealing algorithm: the reserved optional sampling grid point set and Λ, the number of optional sampling grid points to be optimized h, the optional sampling grid point set P, the channel matrix F, the initial annealing temperature T0, the termination temperature T end , the cooling rate β, the number of temperature iterations N, and the cost function is

[0030] The output of the simulated annealing algorithm: the sampling matrix Φ;

[0031] The specific steps are as follows:

[0032] S331, when T>T end , iteration, N times of temperature iteration each time, h optional sampling grid points are randomly generated from the optional sampling grid point set P each time, and the corresponding Φ i is calculated. i A i =Φ i F, and C(A i ) is calculated.

[0033] S332, if C(A i )-C best <0, otherwise q=random(0,1); if q i <0, best ,

[0034] S333, T=T×β, jump to execute S331;

[0035] S334, when T<=T end , stop iteration, and the corresponding sampling matrix Φ is obtained according to Λ best and .

[0036] Preferably, the annealing initial temperature T0=100, the termination temperature T end =1×e -5 , the cooling rate β=0.98, and the number of iterations at each temperature is 1000.

[0037] Preferably, the restriction condition refers to a situation where the sampling environment is limited to a space with a low vertical height.

[0038] The sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition has the following beneficial effects: when constructing a three-dimensional radio environment map, if the sampling environment is limited and high-altitude sampling is not possible, the compressed sensing is applied to the construction of the three-dimensional spectrum map, the sampling point selection is guided by the RIP criterion (also known as: Restricted Isometry Property, RIP) in the compressed sensing, a principal component analysis channel matrix preprocessing is adopted, and the simulated annealing algorithm is used to select the sampling point, so that the performance similar to that in the non-restriction condition can be achieved by sampling at a low vertical height, and the accuracy of constructing the spectrum map under the sampling restriction condition is effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 FIG. 1 is a conceptual diagram of a sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition.

[0040] Figure 2 FIG. 2 is a flowchart of a sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition.

[0041] Figure 3 FIG. 3 is a three-dimensional spectrum map construction model diagram of a sampling point selection method for constructing a three-dimensional spectrum map under a restriction condition. DETAILED DESCRIPTION

[0042] The features and exemplary embodiments of various aspects of the present application will be described in detail below. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one of ordinary skill in the art that the present application can be practiced without some or all of these specific details. The description of the embodiments is merely intended to provide a better understanding of the present application by showing examples of the present application. The present application is in no way limited to any specific configuration and algorithm set forth below, but covers any modification, replacement, and improvement of elements, components, and algorithms without departing from the concept of the present application. In the accompanying drawings and the following description, well-known structures and techniques are not shown in order to avoid unnecessary obscuring of the present application.

[0043] Example 1

[0044] This embodiment implements a method for selecting sampling points when constructing a three-dimensional spectrum map under constraints.

[0045] Traditional sampling point selection algorithms for constructing 3D spectrum maps under constraints require sampling at different vertical heights when using compressed sensing to recover the 3D spectrum map. This embodiment solves the problem of low map recovery accuracy when environmental constraints limit sampling to a lower vertical height.

[0046] This embodiment presents a sampling point selection method for constructing a 3D spectrum map under constraints. Specifically, it proposes a sampling receiver placement algorithm under constraints for 3D spectrum construction. This embodiment implements a sampling point selection method for constructing a 3D spectrum map under constraints, applying compressed sensing to the 3D spectrum map construction. It utilizes the RIP criterion in compressed sensing to guide sampling point selection, employs a channel matrix preprocessing method based on principal component analysis, and uses a simulated annealing algorithm to select sampling points, effectively improving the accuracy of spectrum map construction under sampling-constrained conditions.

[0047] Figure 1 This is a conceptual diagram of a sampling point selection method for constructing a 3D spectrum map under constrained conditions. (See attached diagram.) Figure 1 As shown in this embodiment, a sampling point selection method is proposed for constructing a three-dimensional spectrum map under constraints. The main idea is to explore the sparsity of signal sources in three-dimensional space and construct a spectrum map through compressed sensing and a channel propagation model in space. Therefore, the placement of the sampling receiver can be guided by the construction principle of the sensing matrix in compressed sensing technology. In this embodiment, the channel matrix is ​​preprocessed and points are selected through principal component analysis, and then the restricted points are further optimized through simulated annealing algorithm to obtain the sampling set.

[0048] Figure 2 This is a flowchart illustrating a method for selecting sampling points when constructing a 3D spectral map under constraints. (See attached flowchart.) Figure 2 As shown in the figure, this embodiment provides a method for selecting sampling points when constructing a three-dimensional spectrum map under constraints, including the following steps:

[0049] Step 1: Divide the 3D space XYZ to be recovered, with corresponding lengths N1, N2, and N3, into n = N1 × N2 × N3 grid points, and label each point 1...n. The spectral energy of each grid point in the space is generated by the linear superposition of energy from different sources after path loss. Then, noise is added. According to the definition of sparsity, the number of sources is sparse compared to the total number of grid points in the space, resulting in a sparse vector. Each element x i for:

[0050]

[0051] wherein is the point x i source power size at point x.

[0052] Step 2: Figure 3 is a sampling point selection method for constructing a three-dimensional spectrum map under a limited condition. As shown in the accompanying Figure 3 , the embodiment is a sampling point selection method for constructing a three-dimensional spectrum map under a limited condition. Since the path loss is related to the distance, the channel f ij between point i and point j can be obtained as:

[0053]

[0054]

[0055] wherein, a represents the path loss index, d ij represents the distance between point i and point j, and ζ i represents the point i coordinate. Accordingly, the embodiment can obtain the channel matrix F:

[0056]

[0057] The embodiment hopes to sample from space to reconstruct a sparse vector x, and accordingly there is a sampling matrix wherein m is the number of sampling points, and the elements φ ij in the corresponding matrix are:

[0058]

[0059] Therefore, the general model for recovering the source intensity in a three-dimensional space through compressed sensing is:

[0060] y = ΦFx (6)

[0061] Step 3: Perform dimension reduction processing on the channel matrix F through principal component analysis, and select the points represented by the columns with larger channel energy as pre-selected sampling points.

[0062] a. For the column vectors f i of the channel matrix, each column is subtracted by the mean value to obtain f' i , and the corresponding matrix F' = [f'1, f'2…f' n ] is obtained.

[0063] b. Singular value decomposition is performed on F', and the eigenvalues are sorted from large to small. The eigenvalues correspond to their eigenvectors, so there are eigenvalues k1, k2…k n , and the corresponding eigenvectors ω1, ω2…ω n .

[0064] c. Keep the eigenvectors corresponding to the largest m eigenvalues, multiply them with the original channel matrix F to get the reduced dimension channel matrix F new .

[0065]

[0066] d. Select the m points with the largest channel energy as the pre-sampling points.

[0067]

[0068] Step 4: There are sampling-restricted points in the actual space, such as geographical locations that do not allow sampling. The restricted sampling point set is (9), and the optional point set is (10). This embodiment processes the pre-sampling points using the simulated annealing algorithm and finds alternative points for the existing sampling points to optimize the model:

[0069] G = {g1, g2…g o} (9)

[0070] P = full_point - {G} (10)

[0071]

[0072] where A = ΦF. When the three-dimensional mesh model is successfully divided, the channel matrix F is constant. Therefore, the simulated annealing algorithm minimizes the norm value in equation (11) by designing the sampling matrix Φ. Unlike other optimization of sampling matrices, the sampling matrix in this embodiment corresponds to the placement of the sampling receiver, i.e., the elements in Φ can only be 0 or 1, and the points with a value of 1 are the sampling receiver placement points. Therefore, this embodiment corresponds each sampling receiver placement scheme to a solution in the annealing algorithm, retains the pre-sampling points, and selects new sampling points and retained points to form a new solution at each iteration. The corresponding equation (11) is solved and compared with the previous iteration. After multiple iterations and annealing, the optimal solution is obtained. The specific steps are as follows:

[0073] Simulated annealing algorithm, input: selected point set Λ, number of points to be optimized h, set of available points P, channel matrix F, initial annealing temperature T0, termination temperature T end , cooling rate β, and number of iterations N at each temperature.

[0074] Output: measurement matrix Φ.

[0075] The specific process is as follows:

[0076] 1. When T > T end , iterate, and iterate N times at each temperature;

[0077] Generate h points from the set of available points P at each iteration, and generate the corresponding Calculate the corresponding Φ i A i =Φ i F, and calculate C(A) i );

[0078] If C(A) i )-C best <0,

[0079] Otherwise, let q = random(0,1);

[0080] If q < exp[-(C(A) i )-C best ) / T],

[0081] 2. T = T × β;

[0082] 3. According to Λ best The corresponding Φ is obtained from equation (5).

[0083] Compared with existing technologies, when constructing a three-dimensional radio environment map, and when sampling is restricted and high-altitude sampling is not possible, the algorithm in this embodiment can achieve performance similar to that under unrestricted conditions by sampling at points with lower vertical heights.

[0084] Example 2

[0085] This embodiment implements a method for selecting sampling points when constructing a three-dimensional spectrum map under constraints. This embodiment is a specific implementation based on Embodiment 1.

[0086] Compressed sensing aims to reconstruct the original signal with high precision under Nyquist sampling conditions. (See attached image.) Figure 3 As shown in this embodiment, a sampling point selection method is used when constructing a three-dimensional spectrum map under constraints. When constructing a three-dimensional spectrum map, the signal source strength is reconstructed by sampling in space, and then the spectrum map is constructed through a channel propagation model.

[0087] As attached Figure 2 As shown in this embodiment, a sampling point selection method for constructing a three-dimensional spectrum map under constraints mainly guides the sampling point selection by constructing the sensing matrix in compressed sensing. When constructing a spectrum map of three-dimensional space XYZ corresponding to 10m, 10m, and 3m regions, the specific steps of the sampling point selection algorithm under constraints in this embodiment are as follows:

[0088] ① Divide the three-dimensional space XYZ into 300 grid points of 1m*1m*1m, with corresponding numbers 1.....300.

[0089] (2) and the channel matrix F is obtained.

[0090] (3) Principal component analysis is performed on the channel matrix F to obtain the reduced dimension channel matrix by formula (7), and then the pre-sampling point set A is obtained by selecting the points with larger channel energy by formula (8).

[0091] (4) According to the limited sampling set, the part with z>2 cannot be sampled in this embodiment, that is, when the sampling point number is greater than 200, it cannot be sampled, and the points with number greater than 200 in the set A need to be re-optimized by the simulated annealing algorithm.

[0092] (5) Therefore, the points with number less than 200 in the pre-sampling set are retained in this embodiment, and the input parameters are T0=100; the termination temperature T end =1×e -5 ; the annealing coefficient β=0.98; the iteration number is 1000, the cost function is formula (11), the steps are as described in embodiment 1, the annealing algorithm is started to solve, and finally the sampling matrix Φ is output.

[0093] Those skilled in the art can understand that all or part of the steps of the above embodiments can be completed by hardware, or by program to instruct related hardware to complete, and the program can be stored in a computer readable storage medium, wherein the storage medium can be a magnetic disc, an optical disc, a read-only memory (ROM) or a random access memory (RAM) and the like.

[0094] The above is only the preferred embodiment of the present application, and it should be pointed out that those skilled in the art can make several improvements and supplements without departing from the principles of the present application, and these improvements and supplements should also be regarded as the protection scope of the present application.

Claims

1. A method for selecting sampling points when constructing a three-dimensional spectrum map under constrained conditions, characterized in that... Includes the following steps: S1. Divide the three-dimensional space corresponding to the three-dimensional spectrum map into equal grid points and number them to construct a perception space under unrestricted conditions. S2. Using the RIP criterion in compressed sensing to guide the selection of sampling grid points in the sensing space under unrestricted conditions, principal component analysis is performed on the channel matrix of the sensing space under unrestricted conditions to preprocess the pre-sampling grid point set. S3. Based on the constraints, the grid points are divided into a set of restricted sampling grid points and a set of optional sampling grid points. The restricted sampling grid points in the pre-sampled grid point set are further optimized by the simulated annealing algorithm to obtain the set of optional sampling grid points. Step S1: The three-dimensional spectrum map to be restored corresponds to the three-dimensional space. The lengths corresponding to the three dimensions are respectively , , Divided into There are 10 grid points, and each grid point is labeled. ; Step S2 specifically includes the following steps: S21. Under unrestricted conditions, the spectral energy of each grid point in the sensing space is generated by the linear superposition of the energies of different information sources after path loss. The number of information sources is sparse relative to the total number of grid points, and the corresponding information source sparse vector... Each source sparse vector element for: ,in For grid points Power level of the signal source; S22. Since path loss is related to distance, grid points can be obtained. With grid points Channel between for: Under unrestricted conditions, the sensing space channel matrix F is: ,in, , Represents the road damage index. Representing grid points With grid points The distance between them Representing grid points coordinate; S23. Recovering the source strength model in three-dimensional space using compressed sensing. Where F is the channel matrix, x is the sparse vector of the information source, and Φ is the sampling matrix. Principal component analysis is used to reduce the dimensionality of the sensing space channel matrix F under unrestricted conditions, and the points represented by the columns with larger channel energy are selected as the pre-selected set of pre-sampled grid points to obtain the sampling matrix Φ. Step S23 specifically includes the following steps: S231, For the column vectors of the channel matrix Subtract the mean from each column to get The corresponding matrix is ​​obtained. ; S232, to Perform singular value decomposition and sort its eigenvalues ​​from largest to smallest. Each eigenvalue corresponds to its eigenvector. Then, we have the eigenvalues... The corresponding feature vector ; S233. Retain the eigenvectors corresponding to its largest m eigenvalues, multiply them by the channel matrix F, and obtain the dimension-reduced channel matrix. ; S234. Select m points with high channel energy as the presampling grid point set. ; Step S3 specifically includes the following steps: S31. In actual three-dimensional space, there exist grid points with limited sampling, and correspondingly, there is a set of grid points with limited sampling. Optional sampling grid point set ; S32, S23 obtained sampling matrix ,in, The number of presampled grid points, and the elements in the sampling matrix. This corresponds to the placement location of the sampling receiver, i.e., the elements in the sampling matrix Φ are 0 or 1, where the grid points with a value of 1 are the placement points of the sampling receiver; S33. Using simulated annealing algorithm, the pre-sampled grid point set is processed, and alternative optional sampling grid points are found for the restricted sampling grid points. The optimized model is as follows: Where A=ΦF, the simulated annealing algorithm minimizes the norm value in the optimization model through the sampling matrix Φ, and assigns each sampling receiver placement scheme to an annealing algorithm solution. The optional sampling grid points in the annealing algorithm solution are retained. In each iteration, new optional sampling grid points are selected and combined with the retained optional sampling grid points to form a new annealing algorithm solution. The optimization model corresponding to the new annealing algorithm solution is calculated and compared with the optimization model corresponding to the previous annealing algorithm solution. Finally, after multiple iterations and annealing, the optimal annealing algorithm solution is obtained, which is the set of sampling grid points that does not include the restricted sampling grid points.

2. The sampling point selection method for constructing a three-dimensional spectrum map under constrained conditions according to claim 1, characterized in that... Step S33: The inputs to the simulated annealing algorithm are: the set of available sampling grid points and Λ, the number of available sampling grid points h to be optimized, the set of available sampling grid points P, the channel matrix F, and the initial annealing temperature. Termination temperature Cooling rate For each temperature, the number of iterations is N, and the cost function is... ; The output of the simulated annealing algorithm is: the sampling matrix Φ; The specific steps are as follows: S331, when The process iterates N times for each temperature. In each iteration, h optional sampling grid points are randomly generated from the set of optional sampling grid points P, and the corresponding... Calculate the corresponding , and calculate ; S332, if , Otherwise, let q = random(0,1); if , ; S333, Order Jump to execute S331; S334, when Stop iteration when, according to and The corresponding sampling matrix Φ is obtained.

3. The sampling point selection method for constructing a three-dimensional spectrum map under constrained conditions according to claim 2, characterized in that: Initial annealing temperature Termination temperature Cooling rate Each temperature iteration is performed 1000 times.

4. A method for selecting sampling points when constructing a three-dimensional spectrum map under constrained conditions according to any one of claims 1 to 3, characterized in that: The aforementioned limitation means that sampling can only be performed in spaces with a vertical height below a preset threshold when environmental constraints exist.

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