A CAV spectrum sensing method based on generalized stochastic resonance

Abstract

The present invention discloses a CAV spectrum sensing method based on generalized stochastic resonance, which applies the generalized stochastic resonance theory to the CAV algorithm, and maximizes the difference of the probability density function of the test statistic by adding an appropriate DC component to the received signal, thereby improving the detection performance under low signal-to-noise ratio. Compared with the existing classic CAV detection algorithm and energy detection algorithm (ED), the scheme proposed by the present invention has a computational complexity comparable to that of the CAV algorithm, and the detection effect under different target signal parameters is better than that of the CAV algorithm and the ED algorithm, that is, without significantly increasing the computational complexity, the detection performance under low signal-to-noise ratio is better.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and more specifically, to a CAV spectrum sensing method based on generalized stochastic resonance. Background Art

[0002] Spectrum sensing, as a key technology in cognitive radio, has always been a hot research topic. Spectrum sensing technology can sense the available spectrum in the surrounding space, determine whether there is a primary user signal, find spectrum holes, and make full use of idle spectrum resources. It is a prerequisite for spectrum sharing and spectrum management in cognitive radio and plays an important role.

[0003] At present, the commonly used spectrum sensing methods include matched filter (MF), cyclostationary detection (CSD), energy detection (ED), covariance absolute value (CAV), etc. The MF algorithm is the best detection method under Gaussian background noise. It improves the detection performance by maximizing the output signal-to-noise ratio, but it requires knowing all the information of the signal, which is difficult to achieve in practice. The CSD algorithm uses the cyclostationary characteristics of the signal for detection and has good performance under low signal-to-noise ratio, but its extremely high computational complexity limits its application in practice. The ED algorithm is a very commonly used blind detection algorithm. It compares the energy of the received signal with the decision threshold to detect the presence or absence of the signal. Its performance is poor under low signal-to-noise ratio, and because it needs to accurately estimate the noise variance, it is easily affected by noise uncertainty. The CAV algorithm uses the characteristics of the covariance matrix of the received signal for detection. It has good performance when the signal autocorrelation is strong. In multi-antenna scenarios, since the received signals of each antenna have strong spatial correlation, the CAV algorithm can also be applied, but its performance under low signal-to-noise ratio is still not good enough.

[0004] Stochastic resonance (SR) is a concept proposed by Benzi et al. in 1981 when studying paleometeorological glaciers. Its basic principle is that in some nonlinear systems, an appropriate amount of noise can enhance the signal. In order to improve the performance of spectrum sensing algorithms under low signal-to-noise ratios, some scholars began to combine SR with spectrum sensing technology. Since SR has high requirements for hardware implementation, it is difficult to apply it in practice. Later, Chen et al. broadened the concept of SR and proposed generalized stochastic resonance, proving the benefits of noise for baseband signal detection in some nonlinear detectors. However, in actual combined applications, the specific form and optimal value of noise need to be further analyzed, and accurate theoretical analysis is required to maximize the performance improvement effect. Summary of the invention

[0005] The present invention provides a CAV spectrum sensing method based on generalized stochastic resonance, which maximizes the probability density function difference of the test statistic and improves the spectrum sensing performance under low signal-to-noise ratio.

[0006] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0007] A CAV spectrum sensing method based on generalized stochastic resonance comprises the following steps:

[0008] Utilize multiple antennas to receive signals;

[0009] According to the formula of false alarm probability and detection probability, the DC amplitude is taken as a variable, the false alarm probability is fixed, and the detection probability is maximized to obtain the optimal DC amplitude;

[0010] Calculate the decision threshold according to the obtained optimal DC amplitude;

[0011] A DC signal having an amplitude of the best DC amplitude obtained is added to the received signal of the multiple antennas to obtain a signal matrix, and a covariance matrix of the signal matrix is ​​calculated;

[0012] According to the covariance matrix, the test statistic is constructed using the CAV algorithm;

[0013] Compare the test statistic with the judgment threshold and output the judgment result.

[0014] Preferably, the received signal of the multiple antennas is specifically:

[0015] r(n)=[r1(n), r2(n),..., r L (n)] T , n = 0, 1, ..., N-1

[0016] r l (n) = s (n) + η l (n), l = 0, 1, ..., L

[0017] Where r(n) is the received signal of multiple antennas, r l (n) is the received signal of the lth antenna, l = 0, 1, ..., L is the antenna number, n = 0, 1, ..., N-1 is the sampling point number, s(n) is the target primary user signal, and has a mean of μ and a variance of A Gaussian random signal, η l (n) has zero mean and variance is Gaussian white noise.

[0018] Preferably, the method for solving the optimal DC amplitude is specifically:

[0019] Let the amplitude d of the DC signal be a variable, and add the DC signal with amplitude d to the received signal r l (n), and get the matrix X;

[0020] Solve for the covariance matrix R of matrix X x ;

[0021] According to the covariance matrix R x Calculate the test statistic and get the false alarm probability P fa and the detection probability P d ;

[0022] Fixed false alarm probability P fa , maximize the detection probability and obtain the optimal DC amplitude.

[0023] Preferably, a DC signal with an amplitude of d is added to the received signal r l (n), we get the matrix X, which is:

[0024] Add a DC signal with an amplitude of d to the received signal r l (n):

[0025] x l (n) = r l (n)+d

[0026] It is expressed in matrix form as:

[0027] X=[x(0),x(1),...,x(N-1)] T

[0028] x(n)=[x1(n),x2(n),...,x L (n)] T .

[0029] Preferably, the covariance matrix R of the matrix X is solved x , specifically:

[0030]

[0031] Preferably, according to the covariance matrix R x Calculate the test statistic, specifically:

[0032] Let r ij is the covariance matrix R x The element in the i-th row and j-th column of , then the test statistic T is:

[0033]

[0034] Preferably, the false alarm probability P is obtained fa and the detection probability P d , specifically:

[0035] make When the signal exists, for i≠j:

[0036]

[0037]

[0038]

[0039]

[0040] In the formula, is the expected sign, var(.) is the variance sign, Θ1 and Δ1 are used to represent r in the case of signal. ij The mean and variance var(r ij ), then r ij The absolute value of r ij | obeys a half-normal distribution, with a mean of μ r1 and variance They are:

[0041]

[0042]

[0043] in, Then T0 is the sum of several half-normal distribution variables, and its distribution is approximately Gaussian distribution The tail of , where:

[0044]

[0045]

[0046] When the signal does not exist, the mean μ and variance of the target signal is 0, substitute it into the above formula, and use Θ0 and Δ0 to represent the mean value in the absence of signal. and variance var(r ij ), we get:

[0047]

[0048]

[0049]

[0050] At this time, |r ij The mean μ of | r0 and variance They are:

[0051]

[0052]

[0053] Correspondingly, T0 follows a Gaussian distribution The tail of , where:

[0054]

[0055]

[0056] False alarm probability P fa and the detection probability P d for:

[0057]

[0058]

[0059] In the formula, H0 and H1 represent the two hypotheses of no signal and signal, respectively.

[0060] Preferably, the false alarm probability P is fixed fa , maximize the detection probability to obtain the optimal DC amplitude, specifically:

[0061] If the false alarm probability is fixed, the intermediate threshold is selected as:

[0062] γ0=μ0+Q -1 (P fa )σ0

[0063] The optimal DC signal amplitude d opt :

[0064]

[0065] The optimal amplitude d is obtained by numerical simulation. opt .

[0066] Preferably, the decision threshold is calculated according to the optimal DC amplitude obtained in step S2, specifically:

[0067] γ th =2γ0+1

[0068] In the formula, γ th The judgment threshold.

[0069] Preferably, the test statistic is compared with the judgment threshold, and the judgment result is output, specifically:

[0070] If the test statistic T>γ th , then it is determined that there is a target signal, if T<γ th, then it is determined that there is no target signal.

[0071] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0072] Compared with the existing classic CAV detection algorithm and energy detection algorithm (ED), the scheme proposed in the present invention has a computational complexity comparable to that of the CAV algorithm, and has better detection effects under different target signal parameters than the CAV algorithm and the ED algorithm, that is, without significantly increasing the computational complexity, the detection performance under low signal-to-noise ratio is better. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0074] Figure 2 It is a schematic diagram of the method framework of the present invention.

[0075] Figure 3 The following is a comparison chart of detection performances of the method of the present invention, the CAV algorithm, and the ED algorithm when μ=1 provided in the embodiment.

[0076] Figure 4 The following is a comparison chart of detection performances of the method of the present invention, the CAV algorithm, and the ED algorithm when μ=0.1 provided in the embodiment. DETAILED DESCRIPTION

[0077] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0078] In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product;

[0079] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0080] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0081] Example 1

[0082] This embodiment provides a CAV spectrum sensing method based on generalized stochastic resonance. Figure 1 and Figure 2 As shown, the following steps are included:

[0083] Utilize multiple antennas to receive signals;

[0084] According to the formula of false alarm probability and detection probability, the DC amplitude is taken as a variable, the false alarm probability is fixed, and the detection probability is maximized to obtain the optimal DC amplitude;

[0085] Calculate the decision threshold according to the obtained optimal DC amplitude;

[0086] A DC signal having an amplitude of the best DC amplitude obtained is added to the received signal of the multiple antennas to obtain a signal matrix, and a covariance matrix of the signal matrix is ​​calculated;

[0087] According to the covariance matrix, the test statistic is constructed using the CAV algorithm;

[0088] Compare the test statistic with the judgment threshold and output the judgment result.

[0089] This embodiment applies the generalized stochastic resonance theory to the CAV algorithm, and maximizes the difference in the probability density function of the test statistic by adding an appropriate DC component to the received signal, thereby improving the detection performance under low signal-to-noise ratio.

[0090] Example 2

[0091] This embodiment further discloses the following contents based on the embodiment 1:

[0092] The received signals of multiple antennas are as follows:

[0093] r(n)=[r1(n), r2(n),..., r L (n)] T , n = 0, 1, ..., N-1

[0094] r l (n) = s (n) + η l (n), l = 0, 1, ..., L

[0095] Where r(n) is the received signal of multiple antennas, r l (n) is the received signal of the lth antenna, l = 0, 1, ..., L is the antenna number, n = 0, 1, ..., N-1 is the sampling point number, s(n) is the target primary user signal, and has a mean of μ and a variance of A Gaussian random signal, η l (n) has zero mean and variance is Gaussian white noise.

[0096] The method for solving the optimal DC amplitude is as follows:

[0097] Let the amplitude d of the DC signal be a variable, and add the DC signal with amplitude d to the received signal r l (n), and get the matrix X;

[0098] Solve for the covariance matrix R of matrix X x ;

[0099] According to the covariance matrix R xCalculate the test statistic and get the false alarm probability P fa and the detection probability P d ;

[0100] Fixed false alarm probability P fa , and the optimal DC amplitude is obtained by maximizing the detection probability.

[0101] Add a DC signal with an amplitude of d to the received signal r l (n), we get the matrix X, which is:

[0102] Add a DC signal with an amplitude of d to the received signal r l (n):

[0103] x l (n) = r l (n)+d

[0104] It is expressed in matrix form as:

[0105] X=[x(0),x(1),...,x(N-1)] T

[0106] x(n)=[x1(n),x2(n),...,x L (n)] T .

[0107] Solve for the covariance matrix R of matrix X x , specifically:

[0108]

[0109] According to the covariance matrix R x Calculate the test statistic, specifically:

[0110] Let r ij is the covariance matrix R x The element in the i-th row and j-th column of , then the test statistic T is:

[0111]

[0112] Get the false alarm probability P fa and the detection probability P d , specifically:

[0113] make When the signal exists, for i≠j:

[0114]

[0115]

[0116]

[0117]

[0118] In the formula, is the expected sign, var(.) is the variance sign, and when N is large, the random variable r ii Its mean can be used Approximate replacement expression, Θ1 and Δ1 are used to represent r in the case of signal ij The mean and variance var(r ij ), then r ij The absolute value of r ij | obeys a half-normal distribution, with a mean of μ r1 and variance They are:

[0119]

[0120]

[0121] in, Then T0 is the sum of several half-normal distribution variables, and its distribution is approximately Gaussian distribution The tail of , where:

[0122]

[0123]

[0124] When the signal does not exist, the mean μ and variance of the target signal is 0, substitute it into the above formula, and use Θ0 and Δ0 to represent the mean value in the absence of signal. and variance var(r ij ), we get:

[0125]

[0126]

[0127]

[0128] At this time, |r ij The mean μ of | r0 and variance They are:

[0129]

[0130]

[0131] Correspondingly, T0 follows a Gaussian distribution The tail of , where:

[0132]

[0133]

[0134] False alarm probability P fa and the detection probability P d for:

[0135]

[0136]

[0137] In the formula, H0 and H1 represent the two hypotheses of no signal and signal, respectively.

[0138] Fixed false alarm probability P fa , maximize the detection probability to obtain the optimal DC amplitude, specifically:

[0139] If the false alarm probability is fixed, the intermediate threshold is selected as:

[0140] γ0=μ0+Q -1 (P fa )σ0

[0141] The optimal DC signal amplitude d opt :

[0142]

[0143] The optimal amplitude d is obtained by numerical simulation. opt , specifically: P d Treat it as a function of variable d, calculate all its values ​​within a given interval of independent variables, and finally return the value that makes P d The largest independent variable d.

[0144] Example 3

[0145] This embodiment further discloses the following contents based on Embodiment 1 and Embodiment 2:

[0146] According to the optimal DC amplitude obtained in step S2, the decision threshold is calculated, which is specifically:

[0147] γ th =2γ0+1

[0148] In the formula, γ th The judgment threshold.

[0149] The method of Example 2 is used to calculate the covariance matrix and test statistic after adding the optimal DC amplitude to the received signal.

[0150] Compare the test statistic with the judgment threshold and output the judgment result, specifically:

[0151] If the test statistic T>γ th , then it is determined that there is a target signal, if T<γ th , then it is determined that there is no target signal.

[0152] In a specific embodiment, the simulation parameters are set as follows: the parameter of the target signal is μ=1, The number of antennas is L = 3, the number of sampling points is N = 500, and the false alarm rate is P fa =0.1, the optimization interval of the DC signal amplitude d is [-10, 30], the interval is 0.1, and the number of Monte Carlo simulations is 10000.

[0153] The detection performance of the new method proposed in this invention is compared with that of the classic CAV algorithm and ED algorithm, as follows: Figure 3 As shown in the figure, GSRCAV corresponds to the new method of the present invention. For the detection of target signals with given parameters, when the mean value of the target signal is large, the detection probability of the CAV algorithm and the ED algorithm reaches 100% when the signal-to-noise ratio is -8dB, while the new method proposed in the present invention has reached 100% detection probability when the signal-to-noise ratio is -14dB, and at a signal-to-noise ratio of -30dB to -10dB, the new method proposed in the present invention is far superior to the classic CAV algorithm and ED algorithm, with a performance improvement of about 7 to 12dB, which verifies that the algorithm has good detection performance under low signal-to-noise ratio.

[0154] The above embodiments show that when the target detection signal is a Gaussian random signal with a large mean, the method of the present invention can achieve better spectrum perception effect under low signal-to-noise ratio, and the computational complexity is not significantly improved.

[0155] Based on the above embodiments, the detection performance of target signals with different parameters is verified. Specifically, in the process of setting the simulation parameters, the mean value of the modified target signal is μ=0.1, and other parameters remain unchanged. The detection performance of the new method proposed in the present invention is compared with that of the CAV algorithm and the ED algorithm, and the results are as follows:

[0156] like Figure 4As shown in the figure, GSRCAV corresponds to the new method of the present invention. When the mean value of the target signal is small, the detection performance of the CAV algorithm and the ED algorithm is basically unchanged compared to when the mean value of the target signal is large. The detection performance of the method proposed by the present invention is significantly reduced compared to when the mean value of the target signal is large. The detection probability is only 100% when the signal-to-noise ratio is -9dB, but the detection performance under low signal-to-noise ratio is still better than that of the CAV algorithm and the ED algorithm. Compared with the two classic algorithms, the detection performance of the new method proposed by the present invention is improved by about 1 to 3dB, which verifies that the algorithm has good detection performance under low signal-to-noise ratio.

[0157] The above embodiments show that when the mean value of the target signal is small, the method of the present invention can still achieve a good spectrum sensing effect, and the calculation complexity is not significantly increased.

[0158] The same or similar reference numerals correspond to the same or similar components;

[0159] The terms used in the drawings to describe positional relationships are only used for illustrative purposes and should not be construed as limiting this patent;

[0160] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A CAV spectrum sensing method based on generalized stochastic resonance, characterized in that: The following steps are involved: Utilize multiple antennas to receive signals; According to the formula of false alarm probability and detection probability, the DC amplitude is taken as a variable, the false alarm probability is fixed, and the detection probability is maximized to obtain the optimal DC amplitude; Calculate the decision threshold according to the obtained optimal DC amplitude; A DC signal having an amplitude of the best DC amplitude obtained is added to the received signal of the multiple antennas to obtain a signal matrix, and a covariance matrix of the signal matrix is ​​calculated; According to the covariance matrix, the test statistic is constructed using the CAV algorithm; Compare the test statistic with the judgment threshold and output the judgment result; The received signals of multiple antennas are as follows: r(n)=[r1(n),r2(n),…,r L (n)] T ,n=0,1,…,N-1 r l (n)=s(n)+η l (n),l=0,1,…,L Where r(n) is the received signal of multiple antennas, r l (n) is the received signal of the lth antenna, l = 0, 1, ..., L is the antenna number, n = 0, 1, ..., N-1 is the sampling point number, s(n) is the target primary user signal, which has a mean of μ and a variance of A Gaussian random signal, η l (n) has zero mean and variance is Gaussian white noise; The specific method for solving the optimal DC amplitude is: Let the amplitude d of the DC signal be a variable, and add the DC signal with amplitude d to the received signal r l (n), and get the matrix X; Solve for the covariance matrix R of matrix X x ; According to the covariance matrix R x Calculate the test statistic and get the false alarm probability P fa and the detection probability P d ; Fixed false alarm probability P fa , maximize the detection probability to obtain the optimal DC amplitude; Add a DC signal with an amplitude of d to the received signal r l (n), we get the matrix X, which is: Add a DC signal with an amplitude of d to the received signal r l (n): x l (n)=r l (n)+d It is expressed in matrix form as: X=[x(0),x(1),…,x(N-1)] T x(n)=[x1(n),x2(n),…,x L (n)] T Solve for the covariance matrix R of matrix X x , specifically: According to the covariance matrix R x Calculate the test statistic, specifically: Let r ij is the covariance matrix R x The element in the i-th row and j-th column of , then the test statistic T is: Get the false alarm probability P fa and the detection probability P d , specifically: make When the signal exists, for i≠j: In the formula, is the expected sign, var(.) is the variance sign, Θ1 and Δ1 are used to represent r in the case of signal. ij The mean and variance var(r ij ), then r ij The absolute value of |r ij |Follows a half-normal distribution with a mean of μ r1 and variance They are: in, Then T0 is the sum of several half-normal distribution variables, and its distribution is approximately Gaussian distribution The tail of , where: When the signal does not exist, the mean μ and variance of the target signal is 0, substitute it into the above formula, and use Θ0 and Δ0 to represent the mean value in the absence of signal. and variance var(r ij ), we get: At this time, |r ij The mean μ of | r0 and variance They are: Correspondingly, T0 follows a Gaussian distribution The tail of , where: False alarm probability P fa and the detection probability P d for: In the formula, H0 and H1 represent the two hypotheses of no signal and signal, respectively.

2. The CAV spectrum sensing method based on generalized stochastic resonance according to claim 1 is characterized in that: Fixed false alarm probability P fa , maximize the detection probability to obtain the optimal DC amplitude, specifically: If the false alarm probability is fixed, the intermediate threshold is selected as: γ0=μ0+Q -1 (P fa )σ0 The optimal DC signal amplitude d opt : The optimal amplitude d is obtained by numerical simulation. opt .

3. The CAV spectrum sensing method based on generalized stochastic resonance according to claim 1 or 2, characterized in that: According to the optimal DC amplitude obtained in step S2, the decision threshold is calculated, which is specifically: c th =2γ0+1 In the formula, γ th The judgment threshold.

4. The CAV spectrum sensing method based on generalized stochastic resonance according to claim 3 is characterized in that: Compare the test statistic with the judgment threshold and output the judgment result, specifically: If the test statistic T>γ th , then it is determined that there is a target signal, if T<γ th , then it is determined that there is no target signal.

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