A joint spatio-temporal opportunity detection method based on graph learning

Abstract

The present invention discloses a joint space-time opportunity detection method based on graph learning, which forms an average power data matrix from the average power of all samples obtained by equally spaced sampling of received signals received through various channels by each secondary user in multiple historical perception time slots; takes the average power data matrix as input, constructs a target optimization problem of robust graph learning, and converts it into an augmented Lagrangian function after adding auxiliary variables; optimizes each variable in the augmented Lagrangian function, and then calculates the normalized weight value between each secondary user and each of its neighbors and its own normalized weight value, thereby calculating the test statistic of each secondary user detecting each channel in the current perception time slot, compares the test statistic with a preset threshold, and determines whether the secondary user can access the channel in the current perception time slot; the advantage is that it can accurately detect spectrum holes in time and space in real complex scenarios at the same time.

Description

Technical Field

[0001] The present invention relates to a cognitive radio technology, and in particular to a joint space-time opportunity detection method based on graph learning, which first captures the correlation between secondary users through graph learning, and then uses weighted fusion of data on local secondary users to determine whether the secondary users have spatial or temporal access opportunities. Background Art

[0002] As the surge in the number of 5G users leads to an explosive growth in business volume, limited spectrum resources will restrict the application and popularization of 5G communications. At present, my country adopts a fixed spectrum allocation management mechanism. Each authorized user (i.e., primary user) is assigned a fixed channel, and unauthorized users are not allowed to use the channels originally allocated to authorized users. The fixed spectrum allocation strategy will lead to low spectrum resource utilization. Cognitive radio technology is recognized as a promising technology to improve the utilization of spectrum resources. It allows unauthorized users to opportunistically use the channels originally allocated to authorized users without interfering with the communication of authorized users. As a key functional module in cognitive radio technology, spectrum sensing aims to efficiently and accurately detect spectrum holes in multiple dimensions (including spatial spectrum holes, temporal spectrum holes, etc.), so as to improve the utilization of spectrum resources while avoiding unacceptable interference caused by unauthorized users to authorized users.

[0003] Many existing spectrum sensing methods often only consider spectrum holes in time or spectrum holes in space. Detection of spectrum holes in time is proposed in a spectrum homogeneous environment, where the spectrum homogeneous environment means that secondary users in different geographical locations have the same degree of access opportunities. Detection of spectrum holes in time is equivalent to detecting whether the primary user signal exists in time. Compared with non-cooperative spectrum sensing schemes, cooperative spectrum sensing schemes can better solve problems such as hidden terminals, thereby effectively improving the accuracy of spectrum hole detection in time. Detection of spectrum holes in space is proposed in a spectrum heterogeneous environment, where the spectrum heterogeneous environment means that secondary users in different geographical locations have different degrees of access opportunities. Detection of spectrum holes in space is often understood as judging whether the secondary user is within the propagation range of the primary user. However, in many actual scenarios, there are often both spatial spectrum holes and temporal spectrum holes. We need to detect both spatial and temporal spectrum holes in a spectrum heterogeneous environment (joint space-time opportunity detection). At present, the spectrum sensing schemes proposed for joint space-time opportunity detection mainly include traditional non-cooperative spectrum sensing schemes, global cooperative spectrum sensing schemes (such as maximum ratio fusion schemes, equal gain fusion schemes, etc.), and local cooperative schemes based on spatial correlation. The performance of the above three methods needs to be improved, especially in urban scenes with dense buildings. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a joint space-time opportunity detection method based on graph learning in spectrally heterogeneous cognitive radio networks, which can accurately detect spectrum holes in time and space in real complex scenarios.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a joint space-time opportunity detection method based on graph learning, characterized by comprising the following steps:

[0006] Step 1: In the cognitive radio system, it is assumed that there is a primary user and N secondary users; and it is assumed that in each sensing time slot, each secondary user performs equal-interval sampling on the received signals received through K channels, and each secondary user performs equal-interval sampling on the received signals received through one channel to obtain a total of G samples, and the g-th sample obtained by the i-th secondary user performing equal-interval sampling on the received signals received through the k-th channel is recorded as r k,i (g); wherein N, K, G, i, k, and g are all positive integers, N>1, K≥1, G>1, and the initial values ​​of i, k, and g are all 1, 1≤i≤N, 1≤k≤K, and 1≤g≤G;

[0007] Step 2: Target T num sensing time slots, T num The sensing time slots are taken as historical sensing time slots, and the average power of all samples obtained by each secondary user sampling the received signal received through each channel at equal intervals in each historical sensing time slot is calculated. The average power of all samples obtained by the i-th secondary user sampling the received signal received through the k-th channel at equal intervals in the t-th historical sensing time slot is recorded as Among them, T num , t are both positive integers, T num ≥50, 1≤t≤T num , the symbol “||” is the modulus operator for complex numbers;

[0008] Step 3: All the average powers calculated in step 2 form an average power data matrix, recorded as in, The dimension is (K×T num )×N;

[0009] Step 4: As input, we construct a robust graph learning optimization problem, which is described as:

[0010]

[0011] Among them, P represents low-rank data, and the dimension of P is (K×T num)×N, E represents random noise data, and the dimension of E is (K×T num )×N, S represents the neighbor probability matrix, the dimension of S is N×N, and the element in the i-th row and j-th column of S is s i,j ,s i,j represents the probability that the jth secondary user is selected as the neighbor of the ith secondary user, 0≤s i,j ≤1, L represents the graph Laplacian matrix, The dimension of S1 is N×1, II represents an all-one column vector, 1≤j≤N, min() represents the minimum function, Tr() represents the trace function, the superscript “T” represents the transpose of a vector or matrix, “st” represents “subject to…”, and the symbol “|||| * " is the symbol for the nuclear norm, and the symbol "|| || F " is the Frobenius norm, α, β, γ are all hyperparameters, α>0, β>0, γ>0;

[0012] Step 5: Add an auxiliary variable Z to the description of the target optimization problem of robust graph learning, and let Z = P, and obtain the target optimization problem of robust graph learning with auxiliary variables, which is described as:

[0013]

[0014] Step 6: Convert the description of the objective optimization problem of robust graph learning with auxiliary variables into an augmented Lagrangian function, which is described as:

[0015]

[0016] in, represents the augmented Lagrangian function representation, Y1 and Y2 are both Lagrangian multipliers, and the dimensions of Y1 and Y2 are both (K×T num )×N, the symbol “<>” is the inner product calculation symbol, ρ1 and ρ2 are both constant parameters, ρ1>0, ρ2>0;

[0017] Step 7: Use the alternating direction multiplier method to optimize each variable in the augmented Lagrangian function to obtain the optimized value of each variable. The optimized values ​​of P, E, S, Z, Y1, and Y2 are recorded as P best 、E best , S best , Z best , Y 1,best , Y 2,best ; Then calculate the optimal value of L, recorded as L best ,

[0018] Step 8: Let L best =DW; then solve for Lbest =DW to get the value of W, recorded as Where D represents the degree matrix, D is a diagonal matrix of dimension N×N, and the element in the i-th row and i-th column of D is d i,i , W represents the weight matrix, the dimension of W is N×N, w i,j represents the element in the i-th row and j-th column of W;

[0019] Step 9: According to All elements in determine all neighbors of each secondary user. The process of determining all neighbors of the i-th secondary user is: The element in row i and column j of represents the weight between the ith secondary user and the jth secondary user. If If φ is not equal to 0, the i-th secondary user and the j-th secondary user are considered to be neighbors. Then the normalized weight value between each secondary user and each of its neighbors is calculated, and the normalized weight value between the i-th secondary user and its n-th neighbor is recorded as φ i,column(n) , And calculate the normalized weight value of each secondary user, and record the normalized weight value of the i-th secondary user as φ i,i , Among them, 1≤n≤Num i , Num i Indicates the number of neighbors of the ith secondary user, Num i ≥1, column(n) means taking the nth neighbor of the ith secondary user in The column number in express The element in row i and column(n) of represents the weight of the data of the ith secondary user when it is merged with all its neighbors,

[0020] Step 10: According to the normalized weight values ​​between each secondary user and all its neighbors and the normalized weight value of each secondary user itself, the test statistic of each secondary user detecting each channel in the current sensing time slot is calculated, and the test statistic of the i-th secondary user detecting the k-th channel in the current sensing time slot is recorded as ζ k,i , Then, by comparing the test statistics of each secondary user detecting each channel in the current sensing time slot with the preset threshold for detecting the channel, it is determined whether the secondary user can access the channel in the current sensing time slot. When the i-th secondary user detects the k-th channel in the current sensing time slot, when ζ k,i Greater than the preset threshold λ for detecting the kth channel kWhen ζ , it is considered that the i-th secondary user can access the k-th channel in the current sensing time slot; k,i Less than or equal to the preset threshold λ for detecting the kth channel k , it is considered that the i-th secondary user cannot access the k-th channel in the current sensing time slot; where x k,i represents the average power of all samples obtained by equally spaced sampling of the received signal received through the kth channel by the i-th secondary user in the current sensing time slot, x k,column(n) represents the average power of all samples obtained by equally spaced sampling of the received signal received through the kth channel by the column(n)th secondary user in the current sensing time slot, λ k The value of is determined according to the false alarm probability, which is greater than 0 and less than or equal to 0.1.

[0021] In the step 3, The acquisition process is:

[0022] Step 3_1: Let X i represents the matrix consisting of all average powers corresponding to the i-th secondary user, Among them, X i The dimension is K×T num , the symbol “[]” represents a vector or matrix. The dimensions of are all K×1, represents a column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the t-th historical sensing time slot, represents the average power of all samples obtained by equally sampling the received signal received through the first channel by the i-th secondary user in the t-th historical sensing time slot, represents the average power of all samples obtained by equally sampling the received signal received through the second channel by the i-th secondary user in the t-th historical sensing time slot, represents the average power of all samples obtained by equally spaced sampling of the received signal received through the Kth channel by the i-th secondary user in the t-th historical sensing time slot, represents a column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the first historical sensing time slot, represents a column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the second historical sensing time slot, Indicates that by the T numA column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the historical sensing time slot, where the superscript "T" represents the transpose of a vector or matrix;

[0023] Step 3_2: Place the X i Converted into a column vector, denoted as in, The dimension is (K×T num )×1, represents the average power of all samples obtained by equally sampling the received signal received through the first channel by the i-th secondary user in the first historical sensing time slot, represents the average power of all samples obtained by equally spaced sampling of the received signal received through the Kth channel by the i-th secondary user in the first historical sensing time slot, Indicates that in the T num The average power of all samples obtained by equally sampling the received signal received through the first channel by the i-th secondary user in the historical sensing time slot, Indicates that in the T num The average power of all samples obtained by equally spaced sampling of the received signal received through the Kth channel by the i-th secondary user in the history sensing time slot;

[0024] Step 3_3: Order in, Represents the column vector converted from the matrix consisting of all average powers corresponding to the first secondary user, Represents the column vector converted from the matrix consisting of all average powers corresponding to the second secondary user, Represents the column vector of the matrix consisting of all average powers corresponding to the Nth secondary user, The dimensions are (K×T num )×1.

[0025] The specific process of step 7 is as follows:

[0026] Step 7_1: Set the initial value of Z to Set the initial values ​​of E, Y1, and Y2 to 0; let m represent the number of iterations, and the initial value of m is 1; introduce parameter ρ, and let ρ=ρ1=ρ2;

[0027] Step 7_2: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable P. The problem of optimizing P at the mth iteration is described as: Then solve Get the value of P at the mth iteration, denoted as P (m) , Among them, H (m-1) is the introduced intermediate variable, H (m-1) The dimension is (K×T num )×N, when m=1, Z (m-1) That is Z (0) , That is, the initial value of Z is When m≠1, Z (m-1) represents the value of Z at the m-1th iteration. When m=1, E (m-1) That is E (0) , E (0) =0, that is, the initial value of E is 0. When m≠1, E (m-1) Indicates the value of E at the m-1th iteration, when m = 1 That is That is, the initial value of Y1 is 0, when m≠1 Indicates the value of Y1 at the m-1th iteration. When m=1 That is That is, the initial value of Y2 is 0, when m≠1 represents the value of Y2 at the m-1th iteration, and U represents H (m-1) The left singular vector matrix obtained after singular value decomposition, the dimension of U is (K×T num )×Q, V represents H (m-1) The right singular vector matrix obtained after singular value decomposition, the dimension of V is N×Q, diag() is the function to obtain the diagonal matrix, Indicates The elements in are diagonal matrices consisting of diagonal elements, The dimension is Q×Q, The qth element in is max() is the maximum value function, abs() is the absolute value function, sgn() is the sign function, Q represents H (m-1) rank, 1≤q≤Q,σ q represents the qth element in σ, and the diagonal matrix diag(σ) formed by the elements in σ as diagonal elements is H (m-1) The singular value matrix obtained after singular value decomposition, diag(σ), has a dimension of Q×Q;

[0028] Step 7_3: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable E. The problem of optimizing E at the mth iteration is described as: Then solve Get the value of E at the mth iteration, denoted as E (m) ,

[0029] Step 7_4: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable S. The problem of optimizing S at the mth iteration is described as: Then the description of the problem of optimizing S for the mth iteration is transformed into an unconstrained Lagrangian function, which is described as: Solve again Get the value of S at the mth iteration, denoted as S (m) , S (m) The element in row i and column j of Among them, the symbol “< >” is the inner product calculation symbol, μ and ξ are Lagrange multipliers, the dimension of μ is N×1, the dimension of ξ is N×N, max() is the maximum value function, μ i represents the i-th element in μ, is the introduced intermediate variable, The symbol “|| ||2” is the L2 norm symbol. Represents Z (m-1) The i-th column vector in Represents Z (m-1) The j-th column vector in The dimension is (K×T num )×1;

[0030] Step 7_5: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable Z. The problem of optimizing Z at the mth iteration is described as: Then solve Get the value of Z at the mth iteration, denoted as Z (m) , in, I represents the identity matrix with dimension N×N;

[0031] Step 7_6: Calculate the value of Y1 at the mth iteration and the value of Y2 at the mth iteration, which are recorded as and

[0032] Step 7_7: Judgement And |P (m) -Z (m) |≤10 -4 Is it true? If so, the iteration process ends and the optimized values ​​of P, E, S, Z, Y1, and Y2 are obtained, which are recorded as P best 、E best , S best , Z best , Y 1,best , Y 2,best , P best =P(m) , E best =E (m) , S best =S (m) , Z best =Z (m) , Otherwise, let m=m+1, and then return to step 7_2 to continue execution; where the "=" in m=m+1 is an assignment symbol.

[0033] Compared with the prior art, the advantages of the present invention are:

[0034] 1) The method of the present invention utilizes the characteristics that secondary users with strong correlation have similar access opportunities and that fusing the data between secondary users with strong correlation can improve the performance of joint space-time opportunity detection. The correlation information between secondary users is well captured through a graph learning method, and then the weight information obtained by adaptive learning is normalized and used as the weight for weighted fusion between secondary user data, thereby obtaining a test statistic. The obtained test statistic enables the method of the present invention to accurately determine whether a secondary user has an opportunity to access the channel.

[0035] 2) The method of the present invention is a data-driven method, so the location information of the secondary user is not required, which is conducive to protecting the location information of the secondary user and ensuring the security and privacy of the secondary user.

[0036] 3) The method of the present invention is suitable for complex urban scenarios. In complex urban scenarios, secondary users with similar geographical locations are likely to have different access opportunities due to building obstructions. Since the method of the present invention is a data-driven method, the performance is hardly affected. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flowchart of the overall implementation process of the method of the present invention;

[0038] Figure 2 The following is a curve comparison of the correct detection probability versus signal-to-noise ratio using the method of the present invention, the traditional non-cooperative method, the traditional cooperative method, and the method based on spatial correlation in the first channel (carrier frequency is 2412 MHz, transmission power is 30 dBm);

[0039] Figure 3 The graph is a curve comparison of the global detection probability versus the global false alarm probability using the method of the present invention, the traditional non-cooperative method, the traditional cooperative method, and the method based on spatial correlation in the first channel (carrier frequency is 2412 MHz, transmission power is 30 dBm). DETAILED DESCRIPTION

[0040] The present invention is further described in detail below with reference to the accompanying drawings.

[0041] The present invention proposes a joint space-time opportunity detection method based on graph learning, and its overall implementation flow chart is as follows: Figure 1 As shown, it includes the following steps:

[0042] Step 1: In the cognitive radio system, it is assumed that there is a primary user and N secondary users; and it is assumed that in each sensing time slot, each secondary user performs equal-interval sampling on the received signals received through K channels, and each secondary user performs equal-interval sampling on the received signals received through one channel to obtain a total of G samples, and the g-th sample obtained by the i-th secondary user performing equal-interval sampling on the received signals received through the k-th channel is recorded as r k,i (g); wherein N, K, G, i, k, and g are all positive integers, N>1, and the value of N in the actual environment is related to the range of the secondary user layout scene, requiring that the secondary users should not be too densely arranged, such as: the scene size is 1421 meters × 1345 meters, and the average distribution density of secondary users is 0.0015 per square meter, K≥1, and in this embodiment, K=10, G>1, and the value of G is determined by the sampling frequency, and the higher the sampling frequency, the higher the accuracy, and the higher the calculation complexity. Therefore, in actual applications, the sampling frequency can be determined by compromising the accuracy and calculation complexity. The initial values ​​of i, k, and g are all 1, 1≤i≤N, 1≤k≤K, and 1≤g≤G.

[0043] Step 2: Target T num sensing time slots, T num The sensing time slots are taken as historical sensing time slots, and the average power of all samples obtained by each secondary user sampling the received signal received through each channel at equal intervals in each historical sensing time slot is calculated. The average power of all samples obtained by the i-th secondary user sampling the received signal received through the k-th channel at equal intervals in the t-th historical sensing time slot is recorded as Among them, T num , t are both positive integers, T num ≥50, in this embodiment, T num =100, 1≤t≤T num , the symbol “||” is the modulus operator for complex numbers; here, T num The sensing time slots can be continuous or discontinuous.

[0044] Step 3: All the average powers calculated in step 2 form an average power data matrix, recorded as in, The dimension is (K×T num )×N.

[0045] In this embodiment, in step 3, The acquisition process is:

[0046] Step 3_1: Let X i represents the matrix consisting of all average powers corresponding to the i-th secondary user, Among them, X i The dimension is K×T num , the symbol “[]” represents a vector or matrix. The dimensions of are all K×1, represents a column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the t-th historical sensing time slot, represents the average power of all samples obtained by equally sampling the received signal received through the first channel by the i-th secondary user in the t-th historical sensing time slot, represents the average power of all samples obtained by equally sampling the received signal received through the second channel by the i-th secondary user in the t-th historical sensing time slot, represents the average power of all samples obtained by equally spaced sampling of the received signal received through the Kth channel by the i-th secondary user in the t-th historical sensing time slot, represents a column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the first historical sensing time slot, represents a column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the second historical sensing time slot, Indicates that by the T num The column vector is composed of the average power of all samples obtained by the i-th secondary user in the historical sensing time slot by sampling the received signal received through each channel at equal intervals, The respective expressions can be expressed by OK, the superscript "T" indicates the transpose of a vector or matrix.

[0047] Step 3_2: Place the X i Converted into a column vector, denoted as in, The dimension is (K×T num )×1, represents the average power of all samples obtained by equally sampling the received signal received through the first channel by the i-th secondary user in the first historical sensing time slot, represents the average power of all samples obtained by equally spaced sampling of the received signal received through the Kth channel by the i-th secondary user in the first historical sensing time slot, Indicates that in the T num The average power of all samples obtained by equally sampling the received signal received through the first channel by the i-th secondary user in the historical sensing time slot, Indicates that in the T num The average power of all samples obtained by equally spaced sampling of the received signal received through the Kth channel by the i-th secondary user in the history sensing time slot.

[0048] Step 3_3: Order in, Represents the column vector converted from the matrix consisting of all average powers corresponding to the first secondary user, Represents the column vector converted from the matrix consisting of all average powers corresponding to the second secondary user, Represents the column vector of the matrix consisting of all average powers corresponding to the Nth secondary user, The dimensions are (K×T num )×1.

[0049] Step 4: As input, we construct a robust graph learning optimization problem, which is described as:

[0050]

[0051] Among them, P represents low-rank data (clean data), and the dimension of P is (K×T num )×N, E represents random noise data, and the dimension of E is (K×T num )×N, S represents the neighbor probability matrix, the dimension of S is N×N, and the element in the i-th row and j-th column of S is s i,j ,s i,j represents the probability that the jth secondary user is selected as the neighbor of the ith secondary user, 0≤s i,j ≤1, L represents the graph Laplacian matrix, The dimension of S1 is N×1, II represents an all-one column vector, 1≤j≤N, min() represents the minimum function, Tr() represents the trace function, the superscript “T” represents the transpose of a vector or matrix, “st” represents “subject to…”, and the symbol “|| || * " is the symbol for the nuclear norm, and the symbol "|| || F " is the Frobenius norm (Fibonacci norm), α, β, and γ are all hyperparameters, α>0, β>0, γ>0, and in this embodiment, α, β, and γ are all set to 0.1.

[0052] Step 5: Add an auxiliary variable Z to the description of the target optimization problem of robust graph learning, and let Z = P, and obtain the target optimization problem of robust graph learning with auxiliary variables, which is described as:

[0053]

[0054] Step 6: Convert the description of the objective optimization problem of robust graph learning with auxiliary variables into an augmented Lagrangian function, which is described as:

[0055]

[0056] in, represents the augmented Lagrangian function representation, Y1 and Y2 are both Lagrangian multipliers, and the dimensions of Y1 and Y2 are both (K×T num )×N, the symbol “<>” is the inner product calculation symbol, ρ1 and ρ2 are both constant parameters, ρ1>0, ρ2>0, and in this embodiment, ρ1 and ρ2 are both taken as 0.1.

[0057] Step 7: Use the alternating direction multiplier method (ADMM) to optimize each variable in the augmented Lagrangian function to obtain the optimized value of each variable. The optimized values ​​of P, E, S, Z, Y1, and Y2 are recorded as P best 、E best , S best , Z best , Y 1,best , Y 2,best ; Then calculate the optimal value of L, recorded as L best ,

[0058] In this embodiment, the specific process of step 7 is:

[0059] Step 7_1: Set the initial value of Z to Set the initial values ​​of E, Y1, and Y2 to 0; let m represent the number of iterations, and the initial value of m is 1; introduce the parameter ρ, and let ρ=ρ1=ρ2.

[0060] Step 7_2: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable P. The problem of optimizing P at the mth iteration is described as: Then solve Get the value of P at the mth iteration, denoted as P (m) , Among them, H (m-1) is the introduced intermediate variable, H (m-1) The dimension is (K×T num )×N, when m=1, Z(m-1) That is Z (0) , That is, the initial value of Z is When m≠1, Z (m-1) represents the value of Z at the m-1th iteration. When m=1, E (m-1) That is E (0) , E (0) =0, that is, the initial value of E is 0. When m≠1, E (m-1) Indicates the value of E at the m-1th iteration, when m = 1 That is That is, the initial value of Y1 is 0, when m≠1 Indicates the value of Y1 at the m-1th iteration. When m=1 That is That is, the initial value of Y2 is 0, when m≠1 represents the value of Y2 at the m-1th iteration, and U represents H (m-1) The left singular vector matrix obtained after singular value decomposition (SVD) has a dimension of (K×T num )×Q, V represents H (m-1) The right singular vector matrix obtained after singular value decomposition (SVD), the dimension of V is N×Q, diag() is the function to obtain the diagonal matrix, Indicates The elements in are diagonal matrices consisting of diagonal elements, The dimension is Q×Q, The qth element in is max() is the maximum value function, abs() is the absolute value function, sgn() is the sign function, when σ q >0 when sgn(σ q ) is 1, when σ q ≤0 when sgn(σ q ) is -1, Q represents H (m-1) rank, 1≤q≤Q,σ q represents the qth element in σ, and the diagonal matrix diag(σ) formed by the elements in σ as diagonal elements is H (m-1) The singular value matrix obtained after singular value decomposition (SVD), diag(σ) has dimensions Q×Q, H (m-1) After singular value decomposition (SVD), it is Udiag(σ)V T .

[0061] Step 7_3: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable E. The problem of optimizing E at the mth iteration is described as: Then solve Get the value of E at the mth iteration, denoted as E (m) ,

[0062] Step 7_4: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable S. The problem of optimizing S at the mth iteration is described as: Then the description of the problem of optimizing S for the mth iteration is transformed into an unconstrained Lagrangian function, which is described as: Solve again Get the value of S at the mth iteration, denoted as S (m) , S (m) The element in row i and column j of Among them, the symbol “<>” is the inner product calculation symbol, μ and ξ are Lagrange multipliers, the dimension of μ is N×1, the dimension of ξ is N×N, max() is the maximum value function, μ i represents the i-th element in μ, is the introduced intermediate variable, The symbol “|| ||2” is the L2 norm symbol. Represents Z (m-1) The i-th column vector in Represents Z (m-1) The j-th column vector in The dimension is (K×T num )×1.

[0063] Step 7_5: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable Z. The problem of optimizing Z at the mth iteration is described as: Then solve Get the value of Z at the mth iteration, denoted as Z (m) , in, I represents the identity matrix of dimension N×N.

[0064] Step 7_6: Calculate the value of Y1 at the mth iteration and the value of Y2 at the mth iteration, which are recorded as and

[0065] Step 7_7: Judgement And |P (m) -Z (m) |≤10 -4 Is it true? If so, the iteration process ends and the optimized values ​​of P, E, S, Z, Y1, and Y2 are obtained, which are recorded as P best 、E best , S best, Z best , Y 1,best , Y 2,best , P best =P (m) , E best =E (m) , S best =S (m) , Z best =Z (m) , Otherwise, let m=m+1, and then return to step 7_2 to continue execution; where the "=" in m=m+1 is an assignment symbol.

[0066] Step 8: Let L best =DW; then solve for L best =DW to get the value of W, recorded as Where D represents the degree matrix, D is a diagonal matrix of dimension N×N, and the element in the i-th row and i-th column of D (i.e., the element on the diagonal) is d i,i , W represents the weight matrix, the dimension of W is N×N, w i,j Represents the element in row i and column j in W.

[0067] Step 9: According to All elements in determine all neighbors of each secondary user. The process of determining all neighbors of the i-th secondary user is: The element in row i and column j of represents the weight between the ith secondary user and the jth secondary user. If If φ is not equal to 0, the i-th secondary user and the j-th secondary user are considered to be neighbors. Then the normalized weight value between each secondary user and each of its neighbors is calculated, and the normalized weight value between the i-th secondary user and its n-th neighbor is recorded as φ i,column(n) , And calculate the normalized weight value of each secondary user, and record the normalized weight value of the i-th secondary user as φ i,i , Among them, 1≤n≤Num i , Num i Indicates the number of neighbors of the ith secondary user, Num i ≥1, column(n) means taking the nth neighbor of the ith secondary user in The column number in express The element in row i and column(n) of represents the weight of the data of the ith secondary user when it is merged with all its neighbors,

[0068] Step 10: According to the normalized weight values ​​between each secondary user and all its neighbors and the normalized weight value of each secondary user itself, the test statistic of each secondary user detecting each channel in the current sensing time slot is calculated, and the test statistic of the i-th secondary user detecting the k-th channel in the current sensing time slot is recorded as ζ k,i , Then, by comparing the test statistics of each secondary user detecting each channel in the current sensing time slot with the preset threshold for detecting the channel, it is determined whether the secondary user can access the channel in the current sensing time slot. When the i-th secondary user detects the k-th channel in the current sensing time slot, when ζ k,i Greater than the preset threshold λ for detecting the kth channel k When ζ , it is considered that the i-th secondary user can access the k-th channel in the current sensing time slot; k,i Less than or equal to the preset threshold λ for detecting the kth channel k , it is considered that the i-th secondary user cannot access the k-th channel in the current sensing time slot; where x k,i represents the average power of all samples obtained by equally spaced sampling of the received signal received through the kth channel by the i-th secondary user in the current sensing time slot, x k,column(n) represents the average power of all samples obtained by equally spaced sampling of the received signal received through the kth channel by the column(n)th secondary user in the current sensing time slot, λ k The value of is determined according to the false alarm probability, which is greater than 0 and less than or equal to 0.1.

[0069] The feasibility and effectiveness of the method of the present invention are further illustrated by the following simulation.

[0070] In the simulation, the number of historical sensing time slots T is taken num =100, the scene size is 1421 meters × 1345 meters, the average distribution density of secondary users is 0.0015 per square meter, the number of channels K = 10, among which the transmission power of 5 channels is 30 dBm, the transmission power of the other 5 channels is 25 dBm, the noise power is -75 dBm, the transmission boundary is set to -12 dB, the signal-to-noise ratio varies from -20 dB to 0 dB, and the false alarm probability in time is set to 0.1.

[0071] In the simulation, the methods used for performance comparison include traditional non-cooperative methods, traditional cooperative methods, and spatial correlation-based methods (cited from the literature "Q.Wu, G.Ding, J.Wang and Y.Yao,"Spatial-TemporalOpportunity Detection for Spectrum-Heterogeneous Cognitive Radio Networks:Two-Dimensional Sensing," in IEEE Transactions on Wireless Communications).

[0072] Figure 2 A curve comparison of the correct detection probability versus signal-to-noise ratio in the first channel (carrier frequency is 2412MHz, transmission power is 30dBm) using the method of the present invention, the traditional non-cooperative method, the traditional cooperative method, and the method based on spatial correlation is given. Figure 2 It can be seen that from the perspective of secondary users, the method of the present invention can not only improve the detection probability in time but also reduce the false alarm power in space, thereby achieving the best overall performance. The main defect of the traditional non-cooperative method is that it cannot accurately detect the spectrum hole in time. The traditional cooperative method broadcasts the test statistic constructed after cooperation to each secondary user and uses it as the test statistic of each secondary user. When the primary user transmits a signal in the channel, the secondary users outside the transmission range will always be judged as inaccessible, which will lose a large number of spatial access opportunities, thus greatly increasing the false alarm probability in space. Considering that the access opportunities of secondary users with similar geographical locations in actual scenarios are less similar, the performance of the method of the present invention will decline. When SNR=-16.5dB, the correct detection probability of secondary users using the method of the present invention exceeds 96%, and the correct detection probability of secondary users using the spatial correlation method is 83.5%; when SNR=-8.5dB, the correct detection probability of secondary users using the method of the present invention exceeds 99%, and the correct detection probability of secondary users using the traditional non-cooperative method is 82.7%. It can be seen that the method of the present invention can not only correctly detect spectrum holes in time, but also effectively reduce the false alarm probability in space, thereby achieving the best overall performance.

[0073] Figure 3 A curve comparison of the global detection probability versus the global false alarm probability in the first channel (carrier frequency is 2412MHz, transmission power is 30dBm) using the method of the present invention, the traditional non-cooperative method, the traditional cooperative method, and the spatial correlation method is given. Figure 3It can be seen that when the global false alarm probability is 0.05, the global detection probability of the method of the present invention reaches 95.3%, the global detection probability based on the spatial correlation method is 81.5%, and the global detection probability of the traditional non-collaborative method is only 64.4%. The method of the present invention is superior to other methods.

[0074] In the above, the false alarm probability in time indicates the probability that the primary user signal actually exists but is judged as not existing; the global false alarm probability indicates the probability that the secondary user actually has an access opportunity in time or space but is judged as inaccessible; the global detection probability indicates the probability that the secondary user is actually inaccessible and is correctly judged as inaccessible; the correct detection probability indicates the probability that the secondary user correctly detects whether there is an access opportunity in space or time.

Claims

1. A joint spatiotemporal opportunity detection method based on graph learning, characterized in that The following steps are involved: Step 1: Assume that there is one primary user and N secondary users in the cognitive radio system; It is assumed that in each sensing time slot, each secondary user performs equal-interval sampling on the received signals received through K channels, and each secondary user performs equal-interval sampling on the received signals received through one channel to obtain a total of G samples. The g-th sample obtained by the i-th secondary user performing equal-interval sampling on the received signals received through the k-th channel is recorded as r k,i (g); wherein N, K, G, i, k, and g are all positive integers, N>1, K≥1, G>1, and the initial values ​​of i, k, and g are all 1, 1≤i≤N, 1≤k≤K, and 1≤g≤G; Step 2: Target T num sensing time slots, T num The sensing time slots are taken as historical sensing time slots, and the average power of all samples obtained by each secondary user sampling the received signal received through each channel at equal intervals in each historical sensing time slot is calculated. The average power of all samples obtained by the i-th secondary user sampling the received signal received through the k-th channel at equal intervals in the t-th historical sensing time slot is recorded as Among them, T num , t are both positive integers, T num ≥50, 1≤t≤T num , the symbol "||" is the modulus operator for complex numbers; Step 3: All the average powers calculated in step 2 form an average power data matrix, recorded as in, The dimension is (K×T num )×N; Step 4: As input, we construct a robust graph learning optimization problem, which is described as: Among them, P represents low-rank data, and the dimension of P is (K×T num )×N, E represents random noise data, and the dimension of E is (K×T num )×N, S represents the neighbor probability matrix, the dimension of S is N×N, and the element in the i-th row and j-th column of S is s i,j ,s i,j represents the probability that the jth secondary user is selected as the neighbor of the ith secondary user, 0≤s i,j ≤1, L represents the graph Laplacian matrix, The dimension of S1 is N×1, Ⅱ represents a full 1 column vector, 1≤j≤N, min() represents the minimum function, Tr() represents the trace function, and the superscript " T " indicates the transpose of a vector or matrix, "st" means "subject to...", and the symbol "|| || * " is the symbol for the nuclear norm, and the symbol "|| || F " is the Frobenius norm, α, β, γ are all hyperparameters, α>0, β>0, γ>0; Step 5: Add an auxiliary variable Z to the description of the target optimization problem of robust graph learning, and let Z = P, and obtain the target optimization problem of robust graph learning with auxiliary variables, which is described as: Step 6: Convert the description of the objective optimization problem of robust graph learning with auxiliary variables into an augmented Lagrangian function, which is described as: in, represents the augmented Lagrangian function representation, Y1 and Y2 are both Lagrangian multipliers, and the dimensions of Y1 and Y2 are both (K×T num )×N, the symbol "<>" is the inner product calculation symbol, ρ1 and ρ2 are both constant parameters, ρ1>0, ρ2>0; Step 7: Use the alternating direction multiplier method to optimize each variable in the augmented Lagrangian function to obtain the optimized value of each variable. The optimized values ​​of P, E, S, Z, Y1, and Y2 are recorded as P best 、E best , S best , Z best , Y 1,best , Y 2,best ; Then calculate the optimal value of L, recorded as L best , Step 8: Let L best =DW; then solve for L best =DW to get the value of W, recorded as Where D represents the degree matrix, D is a diagonal matrix of dimension N×N, and the element in the i-th row and i-th column of D is d i,i , W represents the weight matrix, the dimension of W is N×N, w i,j represents the element in the i-th row and j-th column of W; Step 9: According to All elements in determine all neighbors of each secondary user. The process of determining all neighbors of the i-th secondary user is: The element in row i and column j of represents the weight between the ith secondary user and the jth secondary user. If If φ is not equal to 0, the i-th secondary user and the j-th secondary user are considered to be neighbors. Then the normalized weight value between each secondary user and each of its neighbors is calculated, and the normalized weight value between the i-th secondary user and its n-th neighbor is recorded as φ i,column(n) , And calculate the normalized weight value of each secondary user, and record the normalized weight value of the i-th secondary user as φ i,i , Among them, 1≤n≤Num i , Num i Indicates the number of neighbors of the ith secondary user, Num i ≥1, column(n) means taking the nth neighbor of the ith secondary user in The column number in express The element in row i and column(n) of represents the weight of the data of the ith secondary user when it is merged with all its neighbors, Step 10: According to the normalized weight values ​​between each secondary user and all its neighbors and the normalized weight value of each secondary user itself, the test statistic of each secondary user detecting each channel in the current sensing time slot is calculated, and the test statistic of the i-th secondary user detecting the k-th channel in the current sensing time slot is recorded as ζ k,i , Then, by comparing the test statistics of each secondary user detecting each channel in the current sensing time slot with the preset threshold for detecting the channel, it is determined whether the secondary user can access the channel in the current sensing time slot. When the i-th secondary user detects the k-th channel in the current sensing time slot, when ζ k,i Greater than the preset threshold λ for detecting the kth channel k When ζ , it is considered that the i-th secondary user can access the k-th channel in the current sensing time slot; k,i Less than or equal to the preset threshold λ for detecting the kth channel k , it is considered that the i-th secondary user cannot access the k-th channel in the current sensing time slot; where x k,i represents the average power of all samples obtained by equally spaced sampling of the received signal received through the kth channel by the i-th secondary user in the current sensing time slot, x k,column(n) represents the average power of all samples obtained by equally spaced sampling of the received signal received through the kth channel by the column(n)th secondary user in the current sensing time slot, λ k The value of is determined according to the false alarm probability, which is greater than 0 and less than or equal to 0.

1.

2. According to claim 1, a joint space-time opportunity detection method based on graph learning is characterized in that In the step 3, The acquisition process is: Step 3_1: Let X i represents the matrix consisting of all average powers corresponding to the i-th secondary user, Among them, X i The dimension is K×T num , the symbol "[]" represents a vector or matrix. The dimensions of are all K×1, represents a column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the t-th historical sensing time slot, represents the average power of all samples obtained by equally sampling the received signal received through the first channel by the i-th secondary user in the t-th historical sensing time slot, represents the average power of all samples obtained by equally sampling the received signal received through the second channel by the i-th secondary user in the t-th historical sensing time slot, represents the average power of all samples obtained by equally spaced sampling of the received signal received through the Kth channel by the i-th secondary user in the t-th historical sensing time slot, represents a column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the first historical sensing time slot, represents a column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the second historical sensing time slot, Indicates that by the T num A column vector consisting of the average power of all samples obtained by equally spaced sampling of the received signal received through each channel by the i-th secondary user in the historical sensing time slot, where the superscript "T" represents the transpose of a vector or matrix; Step 3_2: Place the X i Converted into a column vector, denoted as in, The dimension is (K×T num )×1, represents the average power of all samples obtained by equally sampling the received signal received through the first channel by the i-th secondary user in the first historical sensing time slot, represents the average power of all samples obtained by equally spaced sampling of the received signal received through the Kth channel by the i-th secondary user in the first historical sensing time slot, Indicates that in the T num The average power of all samples obtained by equally sampling the received signal received through the first channel by the i-th secondary user in the historical sensing time slot, Indicates that in the T num The average power of all samples obtained by equally spaced sampling of the received signal received through the Kth channel by the i-th secondary user in the history sensing time slot; Step 3_3: Order in, Represents the column vector converted from the matrix consisting of all average powers corresponding to the first secondary user, Represents the column vector converted from the matrix consisting of all average powers corresponding to the second secondary user, Represents the column vector of the matrix consisting of all average powers corresponding to the Nth secondary user, The dimensions are (K×T num )×1.

3. A method for joint space-time opportunity detection based on graph learning according to claim 1 or 2, characterized in that The specific process of step 7 is as follows: Step 7_1: Set the initial value of Z to Set the initial values ​​of E, Y1, and Y2 to 0; let m represent the number of iterations, and the initial value of m is 1; introduce parameter ρ, and let ρ=ρ1=ρ2; Step 7_2: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable P. The problem of optimizing P at the mth iteration is described as: Then solve Get the value of P at the mth iteration, denoted as P (m) , Among them, H (m-1) is the introduced intermediate variable, H (m-1) The dimension is (K×T num )×N, when m=1, Z (m-1) That is Z (0) , That is, the initial value of Z is When m≠1, Z (m-1) represents the value of Z at the m-1th iteration. When m=1, E (m-1) That is E (0) , E (0) =0, that is, the initial value of E is 0. When m≠1, E (m-1) Indicates the value of E at the m-1th iteration, when m = 1 That is That is, the initial value of Y1 is 0, when m≠1 Indicates the value of Y1 at the m-1th iteration. When m=1 That is That is, the initial value of Y2 is 0, when m≠1 represents the value of Y2 at the m-1th iteration, and U represents H (m-1) The left singular vector matrix obtained after singular value decomposition, the dimension of U is (K×T num )×Q, V represents H (m-1) The right singular vector matrix obtained after singular value decomposition, the dimension of V is N×Q, diag() is the function to obtain the diagonal matrix, Indicates The elements in are diagonal matrices consisting of diagonal elements, The dimension is Q×Q, The qth element in is max() is the maximum value function, abs() is the absolute value function, sgn() is the sign function, Q represents H (m-1) rank, 1≤q≤Q,σ q represents the qth element in σ, and the diagonal matrix diag(σ) formed by the elements in σ as diagonal elements is H (m-1) The singular value matrix obtained after singular value decomposition, diag(σ), has a dimension of Q×Q; Step 7_3: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable E. The problem of optimizing E at the mth iteration is described as: Then solve Get the value of E at the mth iteration, denoted as E (m) , Step 7_4: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable S. The problem of optimizing S at the mth iteration is described as: Then the description of the problem of optimizing S for the mth iteration is transformed into an unconstrained Lagrangian function, which is described as: Solve again Get the value of S at the mth iteration, denoted as S (m) , S (m) The element in row i and column j of Among them, the symbol "<>" is the inner product calculation symbol, μ and ξ are Lagrange multipliers, the dimension of μ is N×1, the dimension of ξ is N×N, max() is the maximum value function, μ i represents the i-th element in μ, is the introduced intermediate variable, The symbol "|| ||2" is the L2 norm symbol. Represents Z (m-1) The i-th column vector in Represents Z (m-1) The j-th column vector in The dimension is (K×T num )×1; Step 7_5: At the mth iteration, fix the other variables in the description of the augmented Lagrangian function and optimize only the variable Z. The problem of optimizing Z at the mth iteration is described as: Then solve Get the value of Z at the mth iteration, denoted as Z (m) , in, I represents the identity matrix with dimension N×N; Step 7_6: Calculate the value of Y1 at the mth iteration and the value of Y2 at the mth iteration, which are recorded as and Step 7_7: Judgement And |P (m) -Z (m) |≤10 -4 Is it true? If so, the iteration process ends and the optimized values ​​of P, E, S, Z, Y1, and Y2 are obtained, which are recorded as P best 、E best , S best , Z best , Y 1,best , Y 2,best , P best =P (m) , E best =E (m) , S best =S (m) , Z best =Z (m) , Otherwise, let m=m+1, and then return to step 7_2 to continue execution; wherein, the "=" in m=m+1 is an assignment symbol.

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