Efficient spectrum sensing implementation based on energy-to-minimum eigenvalue ratio

Abstract

The present application relates to a high-efficiency spectrum sensing implementation method based on the ratio of energy and minimum eigenvalue, and a method for fast calculating sensing decision threshold based on cubic spline interpolation of natural boundary condition: first, sampling M receiving signals of N antennas successively to calculate sampling covariance matrix R x (N); then, calculating the minimum eigenvalue λ of the sampling covariance matrix by using inverse iteration method based on initial value estimation, and calculating sensing decision quantity t=tr(R x (N)) / λ, wherein tr(R x (N)) is the energy of the receiving signal; second, calculating sensing decision threshold γ by using the method of cubic spline interpolation of natural boundary condition; finally, making sensing decision: when t>γ, it is determined that the primary user signal exists, and when t<γ, it is determined that the primary user signal does not exist. The method has the advantages of high efficiency in calculation, easy hardware implementation and reliable sensing result, and is suitable for the primary user signal detection problem with high real-time requirement in cognitive radio system.

Description

Technical Field

[0001] This invention relates to an efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue, belonging to the field of cognitive radio in wireless communication technology. Background Technology

[0002] The spectrum sensing algorithm based on the ratio of energy to the minimum eigenvalue is an important primary user signal detection algorithm in cognitive radio. Its detection process does not rely on prior information such as the primary user signal, wireless channel, and noise variance, exhibiting fully blind detection characteristics and wide applicability. This algorithm constructs a statistical decision quantity using the ratio of the received signal energy to the minimum eigenvalue of the sampling covariance matrix. Its theoretical decision threshold involves calculating the Tracy-Widom inverse cumulative distribution function. Since calculating the minimum eigenvalue involves decomposing the received signal sampling covariance matrix, the complexity of solving the minimum eigenvalue using traditional methods is the cube of the received signal dimension. In this case, the computational complexity of the algorithm will significantly increase with the number of receiving antennas, the number of cooperating nodes, and the oversampling rate. Simultaneously, the calculation of the Tracy-Widom inverse cumulative distribution function cannot be simply solved using a closed-form expression; it requires table lookup methods or complex numerical calculations to obtain the decision threshold value corresponding to the false alarm probability of a specified target. Under conditions of limited computational and storage resources, the real-time requirements of spectrum sensing are difficult to meet. Under these circumstances, how to effectively improve the computational efficiency of spectrum sensing algorithms based on the ratio of energy to minimum eigenvalue is of significant research value. Summary of the Invention

[0003] Technical Problem: This invention proposes an efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue. This method offers advantages such as high computational efficiency, ease of hardware implementation, and reliable sensing results, making it highly valuable for real-time primary user signal detection in cognitive radio systems.

[0004] Technical Solution: The efficient spectrum sensing implementation method based on the ratio of energy to minimum eigenvalue proposed in this invention utilizes an inverse iterative method based on initial value estimation of the minimum eigenvalue to solve for the minimum eigenvalue of the received signal sampling covariance matrix, thereby accelerating convergence and improving computational accuracy. It simplifies the calculation of the sensing decision threshold using a cubic spline interpolation method based on free boundary conditions: First, the received signal from multiple antennas is sampled N times consecutively, and the received signal sampling covariance matrix is ​​calculated. Second, the minimum eigenvalue of the sampling covariance matrix is ​​calculated using an inverse iterative method based on initial value estimation, and this is used to construct the sensing decision quantity. Third, the sensing decision threshold is calculated using a cubic spline interpolation method based on free boundary conditions. Finally, a sensing decision is made: when the sensing decision quantity is greater than the threshold, the primary user signal is determined to exist; when the sensing decision quantity is less than the threshold, the primary user signal is determined to not exist.

[0005] The specific steps of this method are as follows:

[0006] Step 1. Sample the signals on the M receiving antennas at time n to obtain an M×1 dimensional received signal vector x(n) = [x1(n), x2(n), ..., x...]. M (n)] T The superscript "T" indicates the matrix transpose operator; after sampling N times consecutively, N received signal vectors are obtained: x(1), x(2), ..., x(N), from which the sampling covariance matrix of the received signal is calculated.

[0007] Step 2. Calculate the minimum eigenvalue λ of the sampling covariance matrix using the inverse iterative method based on the initial value estimation of the minimum eigenvalue, and calculate the perceptual decision quantity t = tr(R). x (N)) / λ, where tr(R) x (N) represents the received signal energy;

[0008] Step 3. Calculate the sensing decision threshold using a cubic spline interpolation method based on free boundary conditions. Among them, P f Let ψ(1-P) be the false alarm probability of the target. f (This is about 1-P) f A cubic spline interpolation polynomial based on natural boundary conditions;

[0009] Step 4. Perform a perception decision: If the perception decision quantity t is greater than the perception decision threshold γ, the primary user signal is determined to exist; otherwise, the primary user signal is determined not to exist.

[0010] in,

[0011] The specific steps for calculating the minimum eigenvalue of the sampling covariance matrix using the inverse iterative method based on initial value estimation, as described in step 2, are as follows:

[0012] Step 2.1. Initialize M-dimensional non-zero vectors Set the iteration precision error and the maximum number of iterations K;

[0013] Step 2.2. For matrix A x (N)=R x (N)-λ * I is decomposed into triangular components, i.e., A x (N) = LU. Where L represents A. x (N) is a lower triangular matrix; U represents A x The upper triangular matrix of (N); minimum eigenvalue estimate Where a represents R x The sum of squares of all elements in (N), where b represents R.x (N) The square of the trace.

[0014] Step 2.3. Set k = 1, in, Represents an approximate eigenvector;

[0015] Step 2.4. abs means taking the absolute value of all elements in the vector, and max means selecting the maximum value of all elements in the vector;

[0016] Step 2.5.

[0017] Step 2.6. When k≤K, execute steps 2.7-2.12;

[0018] Step 2.7. Utilize Obtain vector in, This represents a temporary vector introduced during the calculation process;

[0019] Step 2.8. Utilize Obtain vector in, This represents a temporary vector introduced during the calculation process;

[0020] Step 2.9.

[0021] Step 2.10. in, Indicates taking a vector The value corresponding to the element with the largest absolute value;

[0022] Step 2.11. If ERR < error, then Output the minimum eigenvalue and end the calculation;

[0023] Step 2.12. k = k + 1;

[0024] Step 2.13. When k = K + 1, output the minimum eigenvalue of the sampling covariance matrix.

[0025] In step 3, the cubic spline interpolation polynomial ψ(x) = ax based on free boundary conditions for ψ(x) is... 3 +bx 2 The range of values ​​for +cx+d and the corresponding coefficients are shown in Table 2.

[0026] Table 2 Value Range and Interpolation Coefficients

[0027]

[0028]

[0029] Beneficial effects: The beneficial effects of this invention are mainly reflected in the following two aspects:

[0030] 1. The present invention proposes an efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue. This method uses an inverse iterative method based on initial value estimation to calculate the minimum eigenvalue of the sampling covariance matrix. Compared with the classic inverse power method, it has the advantages of fast convergence speed and accurate calculation results. At the same time, this method is easy to implement in engineering.

[0031] 2. The efficient spectrum sensing implementation method based on the ratio of energy to minimum eigenvalue proposed in this invention calculates the sensing decision threshold based on the cubic spline interpolation method under natural boundary conditions. It can determine the theoretical decision threshold corresponding to a given false alarm probability of a target in real time, which is easy to implement in hardware and has low computational complexity. Attached Figure Description

[0032] Figure 1 A flowchart of an efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue;

[0033] Figure 2 This is a flowchart for calculating the minimum eigenvalue of the sampling covariance matrix using the inverse iterative method based on the initial estimate. Detailed Implementation

[0034] All symbol annotations

[0035]

[0036]

[0037] This invention proposes an efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue. This method utilizes an inverse iterative method based on initial value estimation of the minimum eigenvalue to solve for the minimum eigenvalue of the received signal sampling covariance matrix, thereby accelerating convergence and improving computational accuracy. It simplifies the calculation of the sensing decision threshold using a cubic spline interpolation method based on free boundary conditions: First, the received signal from multiple antennas is sampled N times consecutively, and the received signal sampling covariance matrix is ​​calculated. Second, the minimum eigenvalue of the sampling covariance matrix is ​​calculated using an inverse iterative method based on initial value estimation, and this is used to construct the sensing decision quantity. Third, the sensing decision threshold is calculated using a cubic spline interpolation method based on free boundary conditions. Finally, a sensing decision is made: when the sensing decision quantity is greater than the threshold, the primary user signal is determined to exist; when the sensing decision quantity is less than the threshold, the primary user signal is determined to not exist.

[0038] The following section provides a detailed description of an efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue proposed in this invention.

[0039] (I) Mathematical Model

[0040] Assume the cognitive receiver is configured with M antennas. At time n, signals from the 1st to the Mth receiving antennas are sampled, resulting in an M×1 dimensional received signal data vector x(n) = [x1(n), x2(n), ..., x...]. M (n)] T The actual received signal is the superposition of the primary user signal and the noise signal. Therefore, the received signal vector can be expressed as x(n) = s(n) + η(n), where s(n) and η(n) represent the M×1-dimensional primary user signal vector and the M×1-dimensional additive white Gaussian noise vector received after channel attenuation, respectively.

[0041] Let H0 represent the absence of the primary user signal and H1 represent its presence. The primary user signal is determined by performing N sampling operations on multiple antennas and analyzing the obtained data. Mathematically, this problem can be represented by the following binary hypothesis testing model.

[0042]

[0043] (II) Implementation Methods

[0044] Calculate the sampling covariance matrix based on the N received signal vectors obtained from sampling:

[0045]

[0046] In an additive white Gaussian noise channel, the received signals from multiple antennas are independent and identically distributed Gaussian random vectors in state H0, while in state H1, the received signals exhibit correlation due to the interaction of the primary user signal and the channel. The fully blind spectrum sensing algorithm based on the ratio of energy to the minimum eigenvalue of the sampling covariance matrix utilizes this characteristic, demonstrating excellent sensing performance in the detection of correlated signals.

[0047] Existing algorithms using the inverse power method to calculate the minimum eigenvalue of the received signal sampling covariance matrix suffer from slow convergence. Therefore, this invention first performs an initial tight estimate of the minimum eigenvalue of the received signal covariance matrix, and then uses an inverse iterative method to calculate the accurate estimate of the minimum eigenvalue of the sampling covariance matrix. Since the minimum eigenvalue estimation method provides a relatively accurate initial estimate beforehand, it effectively reduces the number of iterations in subsequent estimations and ultimately improves the estimation accuracy of the minimum eigenvalue. On the other hand, calculating the decision threshold corresponding to the false alarm probability of a given target involves calculating the inverse function of the Tracy-Widom cumulative distribution function. In fact, due to the inherent complexity of the Tracy-Widom cumulative distribution function definition, solving its inverse function is extremely difficult, and currently there is no closed-form solution or other effective calculation method. Therefore, two methods are generally used to address this: First, using dedicated software to calculate the quantiles corresponding to the false alarm probabilities of commonly used targets, and then directly calling these values ​​during decision-making by storing and looking up a table. This method requires a large amount of storage resources to store the data table and cannot obtain the quantile values ​​corresponding to the false alarm probabilities of arbitrarily consecutive targets. Secondly, the Monte Carlo method is used to obtain the decision threshold. However, this method requires a significant amount of numerical simulation time to obtain accurate decision threshold values, and when system parameters change, new simulations are needed to obtain new corresponding threshold values, resulting in poor applicability. To address this issue, this invention, based on the principle of cubic spline interpolation under free boundary conditions, utilizes finite discrete points to obtain a high-precision cubic polynomial expression for the Tracy-Widom inverse cumulative distribution function, thereby deriving a simple explicit expression for the decision threshold of the spectrum sensing algorithm based on the ratio of energy to the minimum eigenvalue. Experimental results show that the cubic spline interpolation method based on free boundary conditions is simple, has high computational accuracy, and the interpolated curve is continuous. Using this interpolation expression, the corresponding sensing decision threshold can be conveniently determined based on a given false alarm probability of the target, making it suitable for the rapid and accurate solution of the sensing decision threshold during primary user signal detection in cognitive radio systems.

[0048] (III) Specific Implementation Steps

[0049] Based on the above analysis and flowchart, the implementation steps of the efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue involved in this invention will be further explained:

[0050] (a) Sample the received signals on the M antennas at time n to obtain an M×1 dimensional received signal data vector x(n) = [x1(n), x2(n), ..., x...]. M (n)] TN consecutive samplings are performed to obtain N received signal vectors: x(1), x(2), ..., x(N). Based on these, the received signal sampling covariance matrix is ​​calculated.

[0051] (b) Calculate the minimum eigenvalue λ of the sampling covariance matrix using the inverse iterative method based on initial value estimation, and calculate the perceptual decision quantity t = tr(R). x (N)) / λ, where tr(R) x (N) represents the received signal energy;

[0052] (c) Calculate the sensing decision threshold corresponding to the false alarm probability of a given target using a cubic spline interpolation expression based on free boundary conditions. Among them, P f Let ψ(1-P) be the false alarm probability of the target. f (This is about 1-P) f A cubic spline interpolation polynomial based on natural boundary conditions;

[0053] (d) Perform perception decision: If the perception decision quantity t is greater than the perception decision threshold γ, determine that the main user signal exists; if the perception decision quantity t is less than the perception decision threshold γ, determine that the main user signal does not exist.

[0054] The inverse iterative calculation steps in step (b) based on the initial value estimation of the minimum eigenvalue are as follows:

[0055] Step 1: Initialize M-dimensional non-zero vectors Set the iteration precision error and the maximum number of iterations K;

[0056] Step 2, for matrix A x (N)=R x (N)-λ * I is decomposed into triangular components, i.e., A x (N) = LU. Where L represents A. x (N) is a lower triangular matrix; U represents A x The upper triangular matrix of (N); minimum eigenvalue estimate Where a represents R x The sum of squares of all elements in (N), where b represents R. x (N) The square of the trace.

[0057] Step 3: Set k = 1. in, Represents an approximate eigenvector;

[0058] Step 4 abs means taking the absolute value of all elements in the vector, and max means selecting the maximum value of all elements in the vector;

[0059] Step 5

[0060] Step 6: When k≤K, execute steps 7-12;

[0061] Step 7, utilize Seek in, This represents a temporary vector introduced during the calculation process;

[0062] Step 8, utilize Seek in, This represents a temporary vector introduced during the calculation process;

[0063] Step 9

[0064] Step 10 in, Indicates taking a vector

[0065] The value corresponding to the element with the largest absolute value;

[0066] Step 11: If ERR < error, then Output the minimum eigenvalue and end the calculation;

[0067] Step 12, k = k + 1;

[0068] Step 13: When k = K + 1, output the minimum eigenvalue of the sampling covariance matrix.

[0069] In step (c), the cubic spline interpolation polynomial ψ(x) = ax based on free boundary conditions for ψ(x) 3 +bx 2 The range of values ​​for +cx+d and the corresponding coefficients are shown in Table 3:

[0070] Table 3 Value Range and Interpolation Coefficients

[0071]

[0072]

Claims

1. A highly efficient method for spectrum sensing based on the ratio of energy to minimum eigenvalue, characterized in that... This method utilizes an inverse iterative method based on initial value estimation to efficiently solve for the minimum eigenvalue of the received signal sampling covariance matrix, and simplifies the calculation of the sensing decision threshold using a cubic spline interpolation method based on natural boundary conditions: First, for the continuous multi-antenna received signal... After each sampling, the sampling covariance matrix of the received signal is calculated. Secondly, using the initial value estimate based on the minimum eigenvalue. The inverse iterative method is used to calculate the minimum eigenvalue of the sampling covariance matrix, and this eigenvalue is used to calculate the perceptual decision value. express traces, Indicates the number of antennas. express The sum of squares of all elements in the set. express The square of the trace; then, the perceptual decision threshold is calculated using a cubic spline interpolation method based on natural boundary conditions. ,in, This represents the probability of a false alarm for the target. Indicates about The cubic spline interpolation polynomial based on natural boundary conditions is used; finally, a sensing decision is made: when the sensing decision is greater than the threshold, the main user signal is determined to exist; when the sensing decision is less than the threshold, the main user signal is determined to not exist.

2. The efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue as described in claim 1, characterized in that... The specific steps of this method are as follows: Step 1. At time right Signal sampling on the root receiving antenna is obtained 3D received signal vector The superscript " " represents the matrix transpose operator; Continuous sampling Next, get Each received signal vector: from which the sampling covariance matrix of the received signal is calculated. ; Step 2. Calculate the minimum eigenvalue of the sampling covariance matrix using the inverse iterative method based on initial value estimation. And calculate the perceptual decision quantity. , Step 3. Calculate the sensing decision threshold using a cubic spline interpolation method based on natural boundary conditions. ,in, The probability of a false alarm for the target. It is about A cubic spline interpolation polynomial based on natural boundary conditions; Step 4. Make a perceptual decision: If the perceptual decision quantity... Greater than the perception decision threshold If the primary user signal is not present, it is determined that the primary user signal exists; otherwise, it is determined that the primary user signal does not exist.

3. The efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue as described in claim 2, characterized in that... The specific steps for calculating the minimum eigenvalue of the sampling covariance matrix using the inverse iterative method based on initial value estimation, as described in step 2, are as follows: Step 2.

1. Initialization 2D nonzero vector Set iteration precision and maximum number of iterations ; Step 2.

2. For the matrix Perform triangular decomposition into ,in, express The lower triangular matrix, express The upper triangular matrix; the initial estimate of the minimum eigenvalue. ,in, express The sum of squares of all elements in the set. express The square of the trace; Step 2.

3. Set , ,in, Represents an approximate eigenvector; Step 2.

4. , This means taking the absolute value of all elements of the vector. This indicates selecting the maximum value among all elements in the vector; Step 2.

5. ; Step 2.

6. When Proceed to steps 2.7-2.12; Step 2.

7. Utilize Obtain vector ,in, This represents a temporary vector introduced during the calculation process; Step 2.

8. Utilize Obtain vector ,in, This represents a temporary vector introduced during the calculation process; Step 2.

9. ; Step 2.

10. Indicates taking a vector The value corresponding to the element with the largest absolute value; Step 2.

11. If ,but Output the minimum eigenvalue and end the calculation; Step 2.

12. ; Step 2.

13. When Output the minimum eigenvalue of the sampling covariance matrix. .

4. The efficient spectrum sensing method based on the ratio of energy to minimum eigenvalue as described in claim 2, characterized in that... In step 3 regarding cubic spline interpolation polynomial based on free boundary conditions The range of values ​​and corresponding coefficients are shown in Table 1: Table 1. Range of values ​​and interpolation coefficients 。

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