A sensor layout method for regional restricted spectrum map construction

Abstract

This invention claims protection for a sensor layout method for constructing a regionally constrained spectrum map, comprising the following steps: S1: Discretizing the region corresponding to the spectrum map; S2: Within the unconstrained region, calculating the l2 norm of each column of the channel matrix and selecting the point with the largest value as the first sampling point; S3: Based on compressed sensing correlation constraints, and considering the minimum global correlation between the sampling matrix and the channel matrix, using a greedy algorithm to select sampling points within the unconstrained region; S4: Further deriving the algorithm to simplify the greedy algorithm's computation. This invention treats the spectrum map construction process as a compressed sensing problem. Utilizing the special characteristics of the sampling matrix, the algorithm is derived from the correlation constraints of compressed sensing to optimize sensor layout, simplifying the sampling optimization algorithm and effectively improving the accuracy of the constructed spectrum map.

Description

Technical Field

[0001] This invention belongs to the field of radio monitoring technology and relates to a sensor layout method for constructing regionally restricted spectrum maps. Background Technology

[0002] Spectrum resources play a crucial role in driving social progress and ensuring national security. However, with the increasingly acute contradiction between spectrum demand and supply, the scarcity of spectrum resources has become one of the most pressing challenges in the field of wireless communication. Electromagnetic spectrum mapping, as an important tool, can intuitively display spectrum information of a target area, including key data such as frequency, time, received signal strength, and radiation source location, providing strong support for spectrum resource management and utilization. The introduction of electromagnetic spectrum mapping allows for a direct understanding of the spectrum usage status and trends of a target area. This technology is expected to play a vital role in multiple fields such as wireless communication, radar detection, radiation source location, detection of illegal radiation sources, and spectrum resource scheduling, making significant contributions to the rational allocation and efficient utilization of spectrum resources.

[0003] The core of constructing an electromagnetic spectrum map lies in using sensors to sample the target scene and acquire spectrum data. However, the sampling process faces challenges such as limited sampling area, a limited number of sampling points, and limited sampling time. Furthermore, experiments have verified that the accuracy of spectrum map reconstruction depends not only on the number of sampling points but also on their location. Therefore, by deeply studying and fully utilizing the inherent characteristics of the spatial spectrum, and accurately selecting the optimal sensor placement for sampling in scenarios with limited sampling areas, accurate spectrum maps can be successfully constructed even with relatively low data requirements. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a sensor layout method for constructing regionally limited spectrum maps. This method optimizes the sampling matrix based on the idea of ​​reconstructing spectrum environment maps using compressed sensing, obtaining the optimal sensor locations even with limited sampling areas. Through this method, the invention can determine the minimum number of sampling nodes and their optimal locations, thereby minimizing node usage while ensuring optimal mapping performance. This not only improves the efficiency and accuracy of spectrum map mapping but also helps reduce system costs and promotes the rational utilization and management of electromagnetic spectrum resources.

[0005] 1. A sensor deployment method for constructing region-constrained spectrum maps, characterized by comprising the following steps:

[0006] S1: Discretize the regions corresponding to the spectrum map;

[0007] S2: Within the unrestricted region, calculate the value of each column of the channel matrix. Norm, select the point with the largest norm as the first sampling point;

[0008] S3: Based on the correlation constraints of compressed sensing, from the perspective of minimizing the global correlation between the sampling matrix and the channel matrix, a greedy algorithm is used to select sampling points in the unrestricted region.

[0009] S4: Further derive the algorithm and simplify the greedy algorithm operation.

[0010] 2. The method according to claim 1, wherein step S1 specifically includes:

[0011] The region corresponding to the spectrum map is divided into N = N proportionally. x ×N y N square grids, where N x N represents the number of grid cells divided along the x-axis. y Let N represent the number of grid cells divided along the y-axis, and N be the total number of grid cells. Then the set of all discrete points can be represented as: U = {u1, u2, ... u...} N Assuming there are L restricted regions, the discrete points representing the restricted locations are as follows: Therefore, the set of discrete points in the unrestricted region is C. V U, meaning U and V are complementary sets, means that data in any region of the spectrum map can be mapped one-to-one with a two-dimensional data matrix composed of grids.

[0012] 3. The method according to claim 1, wherein step S2 specifically includes:

[0013] S2.1: As shown in the channel propagation model, the received signal strength at each grid point within the target area is generated by the linear superposition of the path losses from each radiation source. Furthermore, the number of radiation sources within the target area is sparse compared to the total number of grid points N. The corresponding radiation source location vector is:

[0014]

[0015] in Represents grid point u i The power of the radiation source exists at a certain point, and the sparsity of the radiation source vector is: K = ||x||0;

[0016] S2.2 Considering that path loss in signal transmission is distance-dependent, the path loss function between any two grid points is expressed as:

[0017]

[0018] Where: d0 is the reference distance. When the distance between the radiation source and the sensor is less than the reference distance, the effect of path loss is not considered. η is the path loss factor. Then the channel matrix for the entire region is:

[0019]

[0020] Its sampling matrix can be represented as:

[0021] Φ=[φ1,φ1,…,φ M ] T ,

[0022] in There is one and only one non-zero element And the position u selected by the i-th sensor j ∈C V U;

[0023] Therefore, the problem of spectrum map reconstruction can be viewed as a compressed sensing problem:

[0024] y=ΦΨx

[0025] That is, the process of reconstructing the radiation source vector x from known sampled data: y, sampling matrix Φ, and channel matrix Ψ;

[0026] S2.3 optimizes the sampling matrix by maximizing the matrix determinant. Within the unrestricted region, the point with the largest column 2 norm in the channel matrix is ​​selected as the first sampling point.

[0027]

[0028] 4. The method according to claim 1, wherein step S3 specifically includes:

[0029] S4.1: Existing research shows that the lower the correlation between the channel matrix Ψ and the sampling matrix Φ, the better the compressed sensing reconstruction effect. The correlation is defined by the following formula:

[0030]

[0031] Where: Definition After normalizing the matrix columns, S = ΦΨ is the perception matrix. Normalize each column vector of S, s i and Representing matrices S and respectively The i-th column vector;

[0032] However, the drawback of the above method is that it mainly focuses on describing local correlations: for example, even In a matrix where only two columns have large inner products, while the inner products of the other columns are all small, this can lead to a higher local correlation coefficient, but the actual performance of the sampling matrix may not be significantly affected, and it can still maintain relatively good performance. Conversely, another situation is... If the inner product of any two columns in the matrix is ​​close and small, although the local correlation may appear low, the overall correlation coefficient could be high. In this case, the performance of the sampling matrix may not be good. Therefore, global correlation characteristics should be considered when evaluating the performance of the sampling matrix to obtain more accurate evaluation results. Moreover, since the perceptual matrix has undergone column normalization, the autocorrelation coefficient of each column is 1. This means that the autocorrelation result will not have a substantial impact on the final solution. Therefore, the global correlation can be expressed as:

[0033]

[0034] Let Gram matrix Then μ all =sum(G), where sum(·) represents the sum of all elements in the matrix; the objective is transformed into: selecting a suitable sampling matrix Φ that minimizes its global correlation with the channel matrix Ψ. Therefore, minimizing... The sampling location is solved as a greedy optimization process.

[0035]

[0036] st |Ω|=m

[0037] In each iteration, the greedy algorithm selects a sampling position and combines it with previously sampled positions to minimize the correlation, as shown in the following equation:

[0038]

[0039] Repeat until M sampling points are determined. This represents the sampling matrix after i-1 iterations.

[0040] 5. The method according to claim 1, wherein step S4 specifically includes:

[0041] definition Where B is the column number of A, and (x, x) represents its diagonal element. Then, the column normalization of any matrix D is as follows: Simplify the above calculation process:

[0042]

[0043] in:

[0044]

[0045] And because: and Transpose matrices:

[0046]

[0047] in:

[0048]

[0049] From the above formula, we can derive the following: All parameters in this section are known and only need to be calculated once per iteration. Some parts need to participate in the iterative optimization process, which simplifies the calculation process.

[0050] Beneficial effects

[0051] 1) This method optimizes the measurement matrix based on the idea of ​​reconstructing a spectral environment map using compressed sensing, thereby obtaining the optimal sensor location when the sampling area is limited. Through this method, the present invention can determine the minimum number of sampling nodes and their optimal locations, thus ensuring optimal mapping performance while minimizing sensor usage.

[0052] 2) The sensor layout optimization scheme proposed in this method minimizes the global correlation between the sampling matrix and the channel matrix. The sensor location is selected by a greedy matching position optimization algorithm, and the calculation process is further simplified through formula derivation. Attached Figure Description

[0053] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0054] Figure 1 This is a flowchart of a sensor layout method for constructing a region-constrained spectrum map according to the present invention.

[0055] Figure 2 This is a model diagram of a sensor layout method for constructing regionally restricted spectrum maps according to the present invention. Detailed Implementation

[0056] Example 1

[0057] To make the steps of the present invention more detailed and clear, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0058] like Figure 1 The diagram shown is a flowchart of a sensor layout method for constructing a region-constrained spectrum map according to the present invention.

[0059] In step S1, the region corresponding to the spectrum map is discretized: the region corresponding to the spectrum map is divided into N = N according to the ratio. x ×N y N square grids, where N x N represents the number of grid cells divided along the x-axis. y Let N represent the number of grid cells divided along the y-axis, and N be the total number of grid cells. Then the set of all discrete points can be represented as: U = {u1, u2, ... u...} N Assuming there are L restricted regions, the discrete points representing the restricted locations are as follows: Therefore, the set of discrete points in the unrestricted region is C. V U, meaning U and V are complementary sets, means that data in any region of the spectrum map can be mapped one-to-one with a two-dimensional data matrix composed of grids.

[0060] In step S2, within the unrestricted area, the point with the largest column 2 norm in the channel matrix is ​​selected as the first sampling point. According to the channel propagation model, the received signal intensity at each grid point within the target area is generated by the linear superposition of path losses from different radiation sources. Furthermore, within the target area, the number of radiation sources is sparse compared to the total number of grid points N. The corresponding radiation source location vector is:

[0061]

[0062] Where p ui Represents grid point u i The power of the radiation source exists at a certain point, and the sparsity of the radiation source vector is: K = ||x||0;

[0063] S2.2 Considering that path loss in signal transmission is distance-dependent, the path loss function between any two grid points is expressed as:

[0064]

[0065] Where: d0 is the reference distance. When the distance between the radiation source and the sensor is less than the reference distance, the effect of path loss is not considered. η is the path loss factor. Then the channel matrix for the entire region is:

[0066]

[0067] Its sampling matrix can be represented as: Φ=[φ1,φ1,…,φ M ] T ,

[0068] in There is one and only one non-zero element And the position u selected by the i-th sensor j ∈C V U; Therefore, the problem of spectrum map reconstruction can be regarded as a compressed sensing problem: y = ΦΨx; that is, the process of reconstructing the radiation source vector x given the sampled data: y, the sampling matrix Φ, and the channel matrix Ψ;

[0069] S2.3 optimizes the sampling matrix by maximizing the matrix determinant. Within the unrestricted region, the point with the largest column 2 norm in the channel matrix is ​​selected as the first sampling point.

[0070]

[0071] In step S3, based on the correlation constraints of compressed sensing, and starting from the perspective of minimizing the correlation between the sampling matrix and the channel matrix, a greedy algorithm is used to select sampling points within the unrestricted region. Further derivation of the algorithm simplifies the calculation: Existing research shows that the lower the correlation between the channel matrix Ψ and the sampling matrix Φ, the better the compressed sensing reconstruction effect. The correlation is defined using the following formula:

[0072]

[0073] Where: Definition After normalizing the matrix columns, S = ΦΨ is the perception matrix. Normalize each column vector of S, s i and Representing matrices S and respectively The i-th column vector;

[0074] However, the drawback of the above method is that it mainly focuses on describing local correlations: for example, even In a matrix where only two columns have large inner products, while the inner products of the other columns are all small, this can lead to a higher local correlation coefficient, but the actual performance of the sampling matrix may not be significantly affected, and it can still maintain relatively good performance. Conversely, another situation is... If the inner product of any two columns in the matrix is ​​close and small, although the local correlation may appear low, the overall correlation coefficient could be high. In this case, the performance of the sampling matrix may not be good. Therefore, global correlation characteristics should be considered when evaluating the performance of the sampling matrix to obtain more accurate evaluation results. Moreover, since the perceptual matrix has undergone column normalization, the autocorrelation coefficient of each column is 1. This means that the autocorrelation result will not have a substantial impact on the final solution. Therefore, the global correlation can be expressed as:

[0075]

[0076] Let Gram matrix Then μall =sum(G), where sum(·) represents the sum of all elements in the matrix; the objective is transformed into: selecting a suitable sampling matrix Φ that minimizes its global correlation with the channel matrix Ψ. Therefore, minimizing... The sampling location is solved as a greedy optimization process.

[0077]

[0078] In each iteration, the greedy algorithm selects a sampling position and combines it with previously sampled positions to minimize the correlation, as shown in the following equation:

[0079]

[0080] Repeat until M sampling points are determined. This represents the sampling matrix after i-1 iterations. In step S4, the algorithm is further derived, simplifying the greedy algorithm's computation. Definition Where B is the column number of A, and (x, x) represents its diagonal element. Then, the column normalization of any matrix D is as follows: Simplify the above calculation process:

[0081]

[0082] in: And because: and Transpose matrices:

[0083]

[0084] in:

[0085] From the above formula, we can derive the following: All parameters in this section are known and only need to be calculated once per iteration. Some parts need to participate in the iterative optimization process, which simplifies the calculation process.

[0086] Example 2

[0087] This embodiment implements a sensor layout method for constructing regionally restricted spectrum maps. This embodiment is a description of Embodiment 1.

[0088] As attached Figure 2 This embodiment presents a sensor layout method for constructing a regionally restricted spectrum map. Given the sampled signal, sampling matrix, and channel matrix, the location and power of the radiation source are obtained through a compressed sensing reconstruction algorithm, and then multiplied with the channel matrix to construct a spectrum map through full spatial sampling.

[0089] As attached Figure 1 As shown in the figure, this embodiment presents a sensor layout method for constructing regionally limited spectrum maps, which achieves the purpose of sensor layout optimization by optimizing the correlation between the sampling matrix and the channel matrix.

[0090] When constructing a spectrum map for a spatial area of ​​32m×32m, where the restricted area is 4m≤X≤6m and 4m≤Y≤6m, the specific steps of the sensor layout optimization algorithm in this embodiment are as follows:

[0091] 1) Divide the spatial region of 32m×32m into 1024 grid points of 1m×1m each and number them 1, ..., 1024, recording them in U. Record the grid of the restricted area in V.

[0092] 2) Substitute the reference distance d0 = 1 and the path loss factor η = 2 into formulas ② and ③ to obtain the channel matrix Ψ. Then, using formula ④, obtain the position of the first sampling point in the unrestricted area.

[0093] 3) Using a greedy algorithm, sampling points are selected one by one for formula ⑧. To simplify the calculation process, formula ⑩ is derived for solving. After iteration, the sampling matrix Φ is finally obtained. This completes the sensor layout optimization when constructing a spectrum map under region constraints.

Claims

1. A sensor deployment method for constructing region-constrained spectrum maps, characterized in that, Includes the following steps: S1: Discretize the region corresponding to the spectrum map: Divide the region corresponding to the spectrum map into segments according to the specified proportions. A square grid, in which express Similarly, the number of grids divided along the axis. express The number of grid cells divided along the axis. Let be the total number of grid points. Then the set of all discrete points can be represented as: Assuming there is A restricted region, whose discrete points at the restricted locations are represented as follows: Then the set of discrete points in the unrestricted region is ,Right now and They are complementary sets; data in any region of the spectrum map can be mapped one-to-one with a two-dimensional data matrix composed of grids. ; S2: Within the unrestricted region, calculate the value of each column of the channel matrix. Norm, select the point with the largest norm as the first sampling point: S2.1: According to the channel propagation model, the received signal strength at each grid point within the target area is generated by the linear superposition of the path losses of each radiation source. Simultaneously, within the target area, the number of radiation sources and the total number of grid points... Since the data is sparse, the corresponding radiation source location vector is: in Represents grid points The power of the radiation source exists at a certain location, and the sparsity of the radiation source vector is: ; S2.2: Considering that path loss in signal transmission is distance-dependent, the path loss function between any two grid points is expressed as: in, This is a reference distance; when the distance between the radiation source and the sensor is less than the reference distance, the effect of path loss is not considered. Let be the path loss factor, then the channel matrix for the entire region is: Its sampling matrix can be represented as: in There is one and only one non-zero element. And the first The location selected by the sensor ; Therefore, the problem of spectrum map reconstruction is a compressed sensing problem: That is, known sampling data Sampling matrix and channel matrix Reconstruct the radiation source vector The process; S2.3: From the perspective of optimizing the sampling matrix by maximizing the matrix determinant, within the unrestricted region, the point with the largest column 2 norm in the channel matrix is ​​selected as the first sampling point: ； S3: From the perspective of minimizing the global correlation between the sampling matrix and the channel matrix, a greedy algorithm is used to select sampling points within the unrestricted region. In each iteration, the greedy algorithm selects a sampling position and combines it with previously sampled positions to minimize the correlation. Repeat until determined One sampling point, Indicates the process The sampling matrix after the next iteration; The greedy algorithm in step S3 is a simplified greedy algorithm, which is as follows: definition ,in for The number of columns, Let the diagonal elements be denoted as , then any matrix column units ; in, ; and Given that they are transposes of each other, we have: in, , As a fixed pre-computation term, it only needs to be calculated once in each iteration; For dynamic iteration terms, This is the vector of candidate sampling points to be traversed in this iteration; the candidate points are changed in each iteration. At that time, only recalculation is required. Then, after the iteration is complete... With fixed pre-calculation items Add them together to get Substitute this into the formula for minimum correlation; S4: Deploy sensors according to the selected sampling point locations, and construct a spectrum map of the region using the spectrum data collected by the sensors.

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