Cooperative spectrum sensing algorithm based on D-S evidence theory

Abstract

The invention provides a cooperative spectrum sensing method based on a D-S evidence theory. The cooperative spectrum sensing method comprises the following steps: building a cooperative spectrum sensing model; calculating a power spectral density curve of the secondary user SU under noise and signal conditions; calculating a cross correlation coefficient between the two secondary users, and converting the cross correlation coefficient into a conversion value beta ij; deducing Rayleigh distribution of which the modulus value of the cross correlation coefficient of the noise obeys the variance of 1, and solving the maximum value point of the Rayleigh distribution; calculating the distance between the beta ij mean value of each secondary user SU and the maximum value point of Rayleigh distribution according to the Euclidean distance, taking the distance as the fusion weight of each SU, solving each basic quality function of the D-S evidence theory through a power spectral density curve, fusing the basic quality functions of a plurality of secondary users, and solving the real-time average likelihood ratio of the multiple users; and comparing the real-time average likelihood ratios of the multiple users with an average likelihood threshold, and judging that a signal exists in the frequency spectrum of the main user. The method is better in detection performance and higher in reliability.

Description

Technical Field

[0001] The present invention relates to the field of cognitive radio, and in particular to a cooperative spectrum sensing method based on D-S evidence theory. Background Art

[0002] At present, maritime communication is compliance communication, and compliance communication performs data transmission through specified frequency bands. Since the maritime communication frequency band (VHF frequency band) is busy and limited, it is impossible to provide spectrum resources for more service expansion and new technology expansion verification. Since the maritime scenario is not as complex as the terrestrial scenario, there is more potential for available spectrum resources at sea compared to land. Without affecting the used frequency bands, cognitive radio can provide more spectrum resources for different types of services and promote the development and verification of new technologies.

[0003] The concept of cognitive radio (CR) was first proposed by Dr. Mitola and Professor Maguire in 1999 [1] , and its core idea is to achieve dynamic allocation of spectrum through spectrum sensing and intelligent decision-making. The technologies of cognitive radio mainly include spectrum sensing, spectrum decision, spectrum sharing, and spectrum management. Among them, spectrum sensing is the key technology, and using this technology, the spectrum can be detected to determine whether there is a primary user (PU) in the target frequency band.

[0004] Traditional spectrum sensing technology is that a single secondary user uses classical sensing algorithms for sensing. However, single-node spectrum sensing is extremely vulnerable to effects such as shadowing and multipath fading, which can cause unreliable sensing data and a significant decline in detection performance. To further improve the accuracy of sensing and make up for the deficiencies of single-node spectrum sensing technology, cooperative spectrum sensing technology (CSS) was born. CSS technology actually enables multiple secondary users to perform spectrum sensing on the communication target to be detected. Each sensing node takes advantage of its own electromagnetic environment to maximize advantages and avoid disadvantages, and fuses the sensing information of each sensing node, integrates it into the final result for decision-making processing, thereby improving the detection performance of spectrum sensing technology. Therefore, to obtain reliable detection results using cooperative spectrum sensing, the core technology is information fusion technology. However, using traditional fusion methods will also fuse uncertain sensing information, which will also lead to great uncertainty in the final fusion result and affect the credibility of the final sensing result. Therefore, to ensure the reliability and accuracy of cooperative spectrum sensing results, essentially, it is necessary to solve the problem of fusing uncertain information.

[0005] Currently, the main processing methods for uncertain information fusion mainly include: The Bayesian inference algorithm is simple, but has high requirements for prior information; The fuzzy set theory cannot describe the situation where two events have an intersection rather than being consistent, and generally reduces the accuracy of the result; Although neural networks have the ability of generalization and non-linear mapping and can play a predictive role for uncertain information. However, they are highly complex to apply and require high costs; Although genetic algorithms have self-learning ability and the algorithm itself can use the fuzzy adaptive method to solve problems, the algorithm complexity is high; Visual image fusion has good effects but has high requirements for hardware; The unscented Kalman filter can only accurately estimate linear process models and measurement models; The evidence theory converts uncertain information into a basic probability assignment (BPA) function through a function transformation, which can intuitively reflect uncertainty, and the greatest advantage is that it requires less prior information. Therefore, for the problem of uncertain information fusion, the evidence theory has great research space and application prospects. Therefore, scholars are increasingly concerned about the data fusion of multiple secondary users and how to fuse to obtain the best sensing results. Summary of the Invention

[0006] To solve the above problems, the technical solution adopted by the present invention is: A cooperative spectrum sensing method based on D-S evidence theory, including the following steps:

[0007] S1. Based on the fixed transmission power of the primary user (PU), calculate the received power of the secondary user (SU) at different distances from the PU through the Friis transmission formula, and build a cooperative spectrum sensing model;

[0008] S2. Calculate the power spectral density curves of the secondary user (SU) in the presence of noise and signals;

[0009] S3. Calculate the cross-correlation coefficient between two secondary users and obtain the transformed value β according to the T transform ij ;

[0010] S4. Deduce that the modulus of the cross-correlation coefficient of complex noise follows a Rayleigh distribution with a variance of 1, and find the maximum point of the Rayleigh distribution;

[0011] S5. Calculate the distance between the mean value of the transformed value β of each secondary user (SU) and the maximum point of the Rayleigh distribution according to the Euclidean distance, and use it as the fusion weight of each secondary user (SU). Obtain each basic mass function of the D-S evidence theory through the power spectral density curve, and fuse the basic mass functions of multiple secondary users to calculate the real-time average likelihood ratio of multiple users; ij ;

[0012] S6. Compare the real-time average likelihood ratio of multiple users with the average likelihood threshold respectively. When the real-time average likelihood ratio of M users is greater than the average likelihood threshold, it is determined that there is a signal in the primary user spectrum.

[0013] Further, the expression of the Friis transmission formula is:

[0014]

[0015] where P t represents the transmission power, P r (d) represents the signal power received by the secondary user, G t is the transmitting antenna gain, G r is the receiving antenna gain, L is the system loss coefficient independent of propagation, and λ represents the wavelength.

[0016] Further, the cooperative spectrum sensing model is expressed as:

[0017]

[0018] where: H0 and H1 respectively represent the absence and presence of signals in the primary user, w(n) represents noise, s(n) represents the transmitted signal with a transmission power of P t , the signal x(n) received by the secondary user with a received power of P r .

[0019] Further, the formula for calculating the power spectral density curve of the secondary user SU in the presence of noise and signals is as follows:

[0020]

[0021] Assume that the signal received by the secondary user is a circularly symmetric complex Gaussian random variable with a mean of 0 and a variance of and the noise is also a circularly symmetric complex Gaussian random variable with a mean of 0 and a variance of .

[0022] Where: and represent the energies of the noise and the signal received at the sampling point n respectively, and N(·) represents the normal distribution.

[0023] Further, the calculation formula for the cross-correlation coefficient between two secondary users is as follows:

[0024] When calculating the cross-correlation coefficient between two SUs, the cross-correlation coefficient of the signals received by the i-th antenna and the j-th antenna is:

[0025]

[0026] Where: i and j represent different secondary users, x i (n) represents the n-th sampling point of the i-th secondary user, and x j (n) represents the n-th sampling point of the j-th secondary user. The number of sampling points is k.

[0027] The transformation of the cross-correlation coefficient into the mean β ij is performed using the following formula:

[0028]

[0029] Further, the modulus of the complex noise correlation coefficient follows a Rayleigh distribution with a variance of 1, that is:

[0030] comβ ij > 0 and maxβ ij = 1.

[0031] Further, the distance d between the β ij mean of each SU calculated according to the Euclidean distance and maxβ ij is calculated using the following formula:

[0032]

[0033] The method for obtaining the basic probability assignment function of each secondary user by D-S evidence theory through the power spectral density curve is as follows:

[0034]

[0035]

[0036]

[0037] Where: m i (H0) represents the BPA value of the i-th secondary user being judged as "only noise" (H0), and m(H0) represents the BPA value of being judged as H0 after fusion; m i (H1) represents the BPA value of the i-th secondary user being judged as "primary user present" H1, and m(H1) represents the BPA value of being judged as H1 after fusion; K is the degree of conflict between evidence values.

[0038] Furthermore, the determination process of the average likelihood threshold is as follows:

[0039] When the false alarm probability is constrained, the received energy of a single secondary user is:

[0040]

[0041] Threshold The intersection value with the noise probability density curve of the i-th secondary user:

[0042]

[0043] Threshold The intersection value with the signal probability density curve of the i-th secondary user:

[0044]

[0045] Then the threshold The intersection value with the noise probability density curve of the i-th secondary user is f i (H0), and the intersection value with the signal probability density curve is f i (H1);

[0046] Therefore, the average likelihood threshold is expressed as:

[0047]

[0048] A spectrum sensing device based on covariance detection, comprising:

[0049] Building module: It is used to calculate the received power of secondary users (SUs) at different distances from the primary user (PU) based on the fixed transmit power of the PU and by using the Friis transmission formula, and to build a cooperative spectrum sensing model.

[0050] First calculation module: It is used to calculate the power spectral density curves of the SUs in the presence of noise and signals.

[0051] Second calculation module: It is used to calculate the cross-correlation coefficient between two SUs and obtain the transformed value β according to the T transformation. ij ;

[0052] Derivation module: It is used to derive that the modulus of the cross-correlation coefficient of complex noise follows a Rayleigh distribution with a variance of 1, and to find the maximum point of the Rayleigh distribution.

[0053] Fusion module: It is used to calculate the distance between the mean value of the transformed value β of each SU and the maximum point of the Rayleigh distribution according to the Euclidean distance, and use it as the fusion weight of each SU. Then, it calculates each basic mass function of the D-S evidence theory through the power spectral density curve, and fuses the basic mass functions of multiple SUs to obtain the real-time average likelihood ratio of multiple users. ij ; It compares the real-time average likelihood ratio of multiple users with the average likelihood threshold respectively. When the real-time average likelihood ratio of M users is greater than the average likelihood threshold, it is determined that there is a signal in the primary user spectrum.

[0054] Judgment module: It is used to compare the real-time average likelihood ratio of multiple users with the average likelihood threshold respectively. When the real-time average likelihood ratio of M users is greater than the average likelihood threshold, it is determined that there is a signal in the primary user spectrum.

[0055] Compared with the prior art, the present invention has the following advantages:

[0056] Through a cooperative spectrum sensing method based on the D-S evidence theory of the present invention, compared with the traditional D-S theory fusion algorithm, this algorithm improves the detection probability of the secondary user spectrum sensing by modifying the weight of the secondary user, has stronger reliability and adaptability, and has better robustness to noise. Compared with the traditional D-S evidence theory algorithm, the detection performance is improved in the same environment. The constructed SU weight optimization method makes full use of the correlation information of the SU received signal, has better robustness to noise, and improves the detection performance in a complex environment, has better practical value, significantly improves the detection performance, and has stronger reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0058] Figure 1 is the flow chart of the present application;

[0059] Figure 2 is the distribution diagram of the correlation coefficients of real noise and complex noise; where (a) is the cross-correlation coefficient of real noise, (b) is the cross-correlation coefficient of the real part of complex noise, (c) is the cross-correlation coefficient of the imaginary part of complex noise, and (d) is the cross-correlation coefficient.

[0060] Figure 3 is the comβ of 5 secondary users ij heat map of and comβ ij distance between the mean value and the maximum value of the noise correlation coefficient;

[0061] Figure 4 is the comβ of 5 secondary users ij mean value and maxβ ij distribution diagram of the distance between;

[0062] Figure 5 is the influence diagram of distance optimization on the basic probability assignment function of secondary users;

[0063] Figure 6 is the detection probability and false alarm probability diagram of the fusion method before and after weight optimization;

[0064] Figure 7 is the false alarm probability and detection probability diagram of different fusion methods;

[0065] Figure 8 is the comparison diagram of the signal-to-noise ratio wall between the D-S evidence theory and SUM under different noise uncertainties;

[0066] Figure 9 is the influence of the decision threshold on the detection probability under different signal-to-noise ratios. Detailed implementation manners

[0067] To enable those skilled in the art of this technology to better understand the solution of the present invention, we will describe the present invention more clearly and completely below.

[0068] Figure 1 is the flow chart of the present application;

[0069] A collaborative spectrum sensing method based on the D-S evidence theory includes the following steps:

[0070] S1. Based on the fact that the transmission power of the primary user PU remains fixed, calculate the received power of secondary users SU at different distances from the PU through the Friis transmission formula, and build a collaborative spectrum sensing model;

[0071] S2. Calculate the power spectral density curves of the secondary user SU in the presence of noise and signals;

[0072] S3. Calculate the cross-correlation coefficient between two secondary users and obtain the transformed value β according to the T transform ij ;

[0073] S4. Deduce that the modulus of the cross-correlation coefficient of complex noise follows a Rayleigh distribution with a variance of 1, and find the maximum point of the Rayleigh distribution

[0074] S5. Calculate β of each secondary user SU according to the Euclidean distance ij The distance between the mean value and the maximum point of the Rayleigh distribution is used as the fusion weight of each SU. Through the power spectral density curve, each basic mass function of D-S evidence theory is obtained, and the basic mass functions of multiple secondary users are fused to obtain the multi-user real-time average likelihood ratio

[0075] S6. Compare the multi-user real-time average likelihood ratio with the average likelihood threshold respectively. When there are M (5 ≤ M ≤ 10) users whose real-time average likelihood ratio is greater than the average likelihood threshold, it is determined that there is a signal in the primary user spectrum

[0076] The steps S1 / S2 / S3 / S4 / S5 / S6 are executed in sequence

[0077] 1) Under the condition that the transmission power of the primary user (PU) remains unchanged, calculate the received power of secondary users (SU) at different distances from the primary user through the Friis transmission formula; in this application, the transmitter is equal to the primary user, the transmitting antenna is the antenna of the primary user, the secondary user is equal to the receiver, and the receiving antenna is the antenna of this user

[0078] In free space, due to conditions such as isotropic radio wave propagation, zero conductivity, and an infinitely large space that is uniform and lossless, only fading caused by the increase in distance resulting in energy loss will occur. Therefore, in free space, the power between the primary user and the secondary user with a distance difference of d satisfies the well-known Friis transmission formula [2] , that is

[0079]

[0080] where P t represents the transmission power, P r (d) represents the signal power received by the receiving antenna, G t is the transmitting antenna gain, G r is the receiving antenna gain, L is the system loss coefficient independent of propagation (L ≥ 1), including the overall loss of various devices, and λ represents the wavelength

[0081] Assume that the primary user transmits a signal that is a complex circularly symmetric Gaussian random variable with a mean of 0 and a variance of , and the noise is also a complex circularly symmetric Gaussian random variable with a mean of 0 and a variance of Complex circularly symmetric Gaussian random variables. The transmitted signal and the noise are independent of each other. Therefore, the expressions for the noise and the transmitted signal are as follows:

[0082]

[0083]

[0084]

[0085]

[0086] Where, w i (n), w r (n) represent the real and imaginary parts of w(n) respectively., s r (n), s i (n) represent the real and imaginary parts of s(n) respectively.

[0087] Under the condition of zero mean, the power of the transmitted signal is equivalent to its variance It can be obtained that

[0088] s(n) ~ CN(0, P t )

[0089] Through the above derivation, the received power P of the secondary user r Can be obtained by the formula, and the power of the signal x(n) received by the secondary user is equivalent to its variance That is:

[0090]

[0091] Therefore, the cooperative spectrum sensing model of the secondary user is:

[0092]

[0093] Figure 1 Is the flowchart of the method of this application.

[0094] 2) Derive the power spectral density curves of the secondary user SU in the presence of noise and signal;

[0095] If the number of samples N is large enough (the number of sampling points N), then the energy is asymptotically Gaussian distributed. Therefore, the energy probability density curves of the noise and the signal with N points can be expressed as:

[0096]

[0097] 3) Calculate the cross-correlation coefficient (ρ ij ) between two secondary users SU and make an appropriate transformation of ρ ij into β ij;

[0098] Define the cross - correlation coefficient of the signals received by the i - th antenna and the j - th antenna as:

[0099]

[0100]

[0101] There are k sampling points. When the primary user (PU) signal does not exist, the signal received by the secondary user receiver is Gaussian white noise with a mean of 0 and a variance of . At this time, the signals received among secondary users are statistically independent of each other. In the Gaussian distribution, independence and uncorrelatedness are equivalent. Therefore, when the number of sampling points N approaches infinity, ρ ij = 0; when the primary user (PU) signal exists, there is a certain correlation among the signals received by secondary users due to the existence of the PU signal. At this time, as the signal - to - noise ratio increases, its correlation coefficient also increases (ρ ij is positively correlated). Therefore, when the number of sampling points N approaches infinity, ρ ij > 0, that is

[0102]

[0103] However, when H0 is true, ρ ij = 0 is the value obtained when the number of sampling points approaches infinity. However, in the actual spectrum sensing process, since the sensing time is limited, ρ ij can only be calculated through a finite number of sample points, that is, when H0 is true, ρ ij is approximately equal to 0. Therefore, there will also be a certain deviation between the actual value and the ideal value of ρ ij when H0 is true, that is to say ρ ij will not be exactly equal to 0, but follows a certain probability density function. When H0 is true and there are a finite number of sampling points, after making an appropriate transformation on ρ ij , it follows the Student's distribution with degrees of freedom N - 2, that is

[0104]

[0105] When the degrees of freedom N - 2 approach infinity, the Student's distribution can be approximated as the standard normal distribution. When N approaches infinity, then β ij follows the standard Gaussian distribution with a mean of 0 and a variance of 1. The probability density function of β ij when H0 is true can be expressed as:

[0106] Figure 2Distribution diagram of the correlation coefficient of real noise and complex noise, where (a) is the cross-correlation coefficient of real noise, (b) is the cross-correlation coefficient of the real part of complex noise, (c) is the cross-correlation coefficient of the imaginary part of complex noise, and (d) is the cross-correlation coefficient.

[0107] 4) Deduce that the modulus of the cross-correlation coefficient of the noise follows a Rayleigh distribution with a variance of 1, and find the maximum point of the Rayleigh distribution;

[0108] The above derivation is for the case where both the signal and the noise are real. However, in an actual communication system, the transmitted PU signal is generally complex. And this application assumes that the noise is a zero-mean circularly symmetric complex Gaussian noise, and the noise follows Therefore, the correlation coefficient of the covariance matrix of the complex noise is complex. Observing the characteristics of the complex correlation coefficient, the real part Reρ of the correlation coefficient of the complex noise ij and the imaginary part Imρ ij have the same distribution and are respectively equivalent to the correlation coefficient of the real noise expanded by times. And the complex correlation coefficient is more concentrated around the value of 0 compared to the real correlation coefficient. When a finite number of sampling points are collected under the condition of H0, after appropriate transformation of the real part Reρ ij and the imaginary part Imρ ij of the complex correlation coefficient, they are respectively denoted as Reβ ij and Imβ ij . It can be obtained that Reβ ij and Imβ ij follow the Student's distribution with degrees of freedom N - 2:

[0109]

[0110] When the degrees of freedom N - 2 tend to infinity, the Student's distribution can be approximated as the standard normal distribution. Therefore, when N tends to infinity, then Reβ ij and Imβ ij follow the standard Gaussian distribution with a mean of 0 and a variance of 1. Therefore, the probability density function of Reβ ij , Imβ ij under H0 can be expressed as:

[0111]

[0112]

[0113] Take the modulus of the complex correlation coefficient, that is

[0114]

[0115] Also, since Reβ ij , Imβ ijIt follows a standard normal distribution with a mean of 0 and a variance of 1. Therefore, the modulus of the complex noise correlation coefficient follows a Rayleigh distribution with a variance of 1, i.e.:

[0116]

[0117] The point with the maximum probability of the Rayleigh distribution with a variance of 1 is that the modulus of the correlation coefficient is 1. And the modulus of the correlation coefficient is distributed between 0 and 4.

[0118] Figure 3 For comβ of 5 secondary users ij Heat map of and comβ ij The distance between the mean and the maximum value of the noise correlation coefficient.

[0119] Figure 4 For comβ of 5 secondary users ij The mean of comβ and maxβ ij Distribution map of the distance between them.

[0120] 5) Calculate the β of each SU using the Euclidean distance ij The mean of comβ and maxβ ij The distance between them is used as the fusion weight of each SU, and D-S evidence theory is used for fusion;

[0121] Calculate the mean of the correlation coefficients between each secondary user and other secondary users, i.e.:

[0122]

[0123] According to the above, the maximum value of the Rayleigh distribution probability maxβ ij is that the correlation coefficient is 1. According to the differences in the sensing channels where the secondary users are located, the basic probability assignment function of each secondary user can be modified using the difference between the mean of the correlation coefficients between different secondary users and other secondary users and the maximum value of the noise correlation coefficient to reflect the influence of different secondary user channels on the sensing results. The Euclidean distance can accurately calculate the distance between the mean of each secondary user and maxβ ij between them. The Euclidean distance can be the true distance of a vector in Euclidean space and can be expressed as:

[0124]

[0125] When calculating the distance between the mean of the correlation coefficients of secondary users and the maximum value of the noise correlation coefficient using the Euclidean distance measure, the complexity is low and the calculation speed is fast, and the distance between the mean of the correlation coefficients of each secondary user and the maximum value of the noise correlation coefficient can be calculated quickly. Denote the distance between each secondary user and the maximum noise correlation coefficient as:

[0126] d1, d2, d3, d4,..., dM

[0127] Calculate the sum of the distances between all secondary users and the maximum correlation coefficient of noise, denoted as d:

[0128] d = d1 + d2 + d3 + d4 +... + d M

[0129] The larger the distance d, the greater the distance between the mean of the correlation coefficients of the secondary users and the maximum value of the correlation coefficient of noise. Then, the less the secondary users transmit noise, so the greater the probability that the secondary users transmit signals. The smaller the distance d, the smaller the distance between the mean of the correlation coefficients of the secondary users and the maximum value of the correlation coefficient of noise. Then, the more the secondary users transmit noise, so the greater the probability that the secondary users transmit noise.

[0130] Then, normalize the distance sum obtained for each secondary user to obtain the weight of the reliability of each secondary user, that is:

[0131]

[0132] As known from the previous section, the matrix of the basic probability assignment functions of M secondary users is:

[0133]

[0134] Modify the basic probability assignment function of each secondary user using the weight.

[0135]

[0136] Calculate the weighted average evidence as follows:

[0137]

[0138] Therefore, the basic mass function of the i-th secondary user is:

[0139]

[0140] Obtain the modified basic probability assignment functions of noise, signal, and uncertainty for different sensors. For D-S evidence theory fusion of different sensors, the fusion formula for multiple sensors is as follows:

[0141]

[0142] And, A i can be an element in the set {H0, H1, Ω}. Among them: m i (H0) represents the BPA value for the i-th secondary user being judged as "only noise" (H0), and m(H0) represents the BPA value for being judged as H0 after fusion; m i(H1) represents the BPA value of the i-th secondary user judging "primary user exists" as H1, and m(H1) represents the BPA value judged as H1 after fusion; K is the degree of conflict between evidence values.

[0143] Find the likelihood ratio of the basic mass function of the signal and noise:

[0144]

[0145] Figure 5 It is the influence diagram of distance optimization on the basic probability assignment function of secondary users.

[0146] Figure 6 It is the detection probability and false alarm probability diagram of the fusion method before and after weight optimization.

[0147] Figure 7 The false alarm probability and detection probability diagram of different fusion methods.

[0148] Figure 8 The comparison diagram of the signal-to-noise ratio wall between the D-S evidence theory and SUM under different noise uncertainties.

[0149] 6) Derive the construction method of the fusion decision threshold based on the average likelihood ratio;

[0150] According to the central limit theorem, the linear combination of the energies and noises of these secondary users will follow an approximate normal distribution. Specifically, since the noise is normally distributed and has the same statistical characteristics, the distribution of the total energy of M secondary users will be affected by the energy distributions of these individual users. Therefore, the energy distribution of M secondary users will approximately follow a new normal distribution, and its mean and variance will depend on the noise characteristics of each secondary user and their mutual relationships. Thus, the noise energy distribution of M secondary users follows:

[0151]

[0152] When the standard variances of the secondary users are known and determined, the expression of the false alarm probability of M secondary users:

[0153]

[0154] where Q(·) is the tail probability of the standard normal distribution. After deriving the expression of P fa , the threshold can be inversely deduced. When the false alarm probability is constrained, the expression of the obtained threshold η is:

[0155]

[0156] It can be seen from the above formula that the threshold η is related to the number of secondary users, the noise power of secondary users, and the pre-set false alarm probability.

[0157] Taking the mean of the threshold η, the mean represents the energy of the noise received by a single secondary user under the condition of a fixed false alarm probability. Therefore, the energy received by a single secondary user is:

[0158]

[0159] The process of taking the mean of the threshold η can effectively improve the accuracy and reliability of the system when making detection decisions. By combining the thresholds of multiple secondary users into a unified threshold, the probability of misjudgment of a single secondary user can be reduced to a certain extent, thereby increasing the detection probability of the entire system. The advantage of this method is that it can comprehensively consider the observation results of each secondary user, better resist noise or errors that may exist in a single user, and ensure that the overall decision-making process is more robust and efficient. Therefore, reasonably designing and calculating appropriate threshold values is crucial for improving the detection accuracy and optimizing the system performance.

[0160] According to the derived probability density curves of the energy spectra of each secondary user under H0 and H1, the threshold is intersected with the probability density curves of the energy spectra of each secondary user. In fact, it is to solve the intersection points of the threshold with the probability density function (PDF) curves of different secondary users under noise conditions and signal conditions.

[0161] The threshold The intersection value with the noise probability density curve of the i-th secondary user:

[0162]

[0163] The threshold The intersection value with the signal probability density curve of the i-th secondary user:

[0164]

[0165] Then the intersection value of the threshold with the noise probability density curve of the i-th secondary user is f i (H0), and the intersection value with the signal probability density curve is f i (H1).

[0166] First, according to the above formula, find the values corresponding to the intersections of the noise probability density curve and the signal probability density curve for each secondary user from secondary user 1 to secondary user M. These intersection values represent the probabilities of noise and signal for each secondary user when the received energy is the threshold η′. Next, calculate the ratio between the intersection values calculated for each secondary user. Then, to further fuse this information, we sum up the intersection ratios of all secondary users to obtain a total sum. Finally, by taking the mean of this total sum, we can obtain a new fusion threshold λ, which incorporates the contributions of all secondary users. This fusion threshold λ is an optimized threshold that can effectively improve the detection performance of the overall system because it takes into account the performance differences of each secondary user in different environments and fuses this information into a unified threshold value, thereby enhancing the robustness and precision of the system. Therefore, the threshold setting of the fusion decision threshold λ is as follows:

[0167]

[0168] The fusion decision rule is as follows:

[0169]

[0170] Figure 9 The influence of the decision threshold on the detection probability under different signal-to-noise ratios.

[0171] A spectrum sensing device based on covariance detection, comprising:

[0172] A building module: used to build a cooperative spectrum sensing model by calculating the received power of secondary users (SUs) at different distances from the primary user (PU) based on the fixed transmitted power of the primary user (PU) using the Friis transmission formula;

[0173] A first calculation module: used to calculate the power spectral density curves of the secondary user (SU) in the case of noise and signal;

[0174] A second calculation module: used to calculate the cross-correlation coefficient between two secondary users and obtain the transformed value β according to the T transformation ij ;

[0175] A derivation module: used to derive that the modulus of the cross-correlation coefficient of complex noise follows a Rayleigh distribution with a variance of 1 and find the maximum point of the Rayleigh distribution;

[0176] A fusion module: used to calculate the distance between the mean of the transformed value β of each secondary user (SU) and the maximum point of the Rayleigh distribution according to the Euclidean distance as the fusion weight of each SU, and obtain each basic mass function of the D-S evidence theory through the power spectral density curve, and fuse the basic mass functions of multiple secondary users to find the real-time average likelihood ratio of multiple users; ij and use it as the fusion weight for each SU, obtain each basic mass function of the D-S evidence theory through the power spectral density curve, fuse the basic mass functions of multiple secondary users, and find the real-time average likelihood ratio of multiple users;

[0177] Judgment module: used to compare the average likelihood ratios of multiple users in real time with the average likelihood threshold respectively. When the average likelihood ratios of M users in real time are greater than the average likelihood threshold, it is determined that there is a signal in the primary user spectrum.

[0178] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

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[0180] [2]FRANEK O.Phasor alternatives to Friis’transmission equation[J].IEEE Antennas and Wireless Propagation Letters,2017,17(1):90-93.

Claims

1. A collaborative spectrum sensing method based on D-S evidence theory, characterized in that, It includes the following steps: S1. Based on the fact that the transmission power of the primary user (PU) remains fixed, calculate the received power of secondary users (SUs) at different distances from the PU through the Friis transmission formula, and build a cooperative spectrum sensing model; S2. Calculate the power spectral density curves of the secondary user (SU) in the presence of noise and signals; S3. Calculate the cross-correlation coefficient between two secondary users and obtain the transformation value β according to the T transformation ij ; S4. Deduce that the modulus of the cross-correlation coefficient of complex noise follows a Rayleigh distribution with a variance of 1, and find the maximum point of the Rayleigh distribution; S5. Calculate the transformation value β of each secondary user SU according to the Euclidean distance ij The distance between the mean value and the maximum point of the Rayleigh distribution is used as the fusion weight of each secondary user SU. The basic mass function of D-S evidence theory is obtained through the power spectral density curve, and the basic mass functions of multiple secondary users are fused to obtain the average likelihood ratio of multiple users in real time; S6. Compare the real-time average likelihood ratios of multiple users with the average likelihood threshold respectively. When the real-time average likelihood ratios of M users are greater than the average likelihood threshold, it is determined that there is a signal in the primary user spectrum.

2. The collaborative spectrum sensing method based on the D-S evidence theory according to claim 1, characterized in that The expression of the Friis transmission formula is: Among them, P t represents the transmit power, and P r (d) represents the signal power received by the secondary user. G t is the transmit antenna gain, G r is the receive antenna gain, L is the system loss coefficient independent of propagation, and λ represents the wavelength.

3. A collaborative spectrum sensing method based on D-S evidence theory according to claim 1, characterized in that, The cooperative spectrum sensing model is expressed as: Where: H0 and H1 respectively represent the absence and presence of signals in the primary user, w(n) represents noise, s(n) represents the transmitted signal, and the transmission power is P t , the signal x(n) received by the secondary user, and the received power is P r .

4. A collaborative spectrum sensing method based on D-S evidence theory according to claim 1, characterized in that, The formula for calculating the power spectral density curves of the secondary user (SU) in the presence of noise and signals is as follows: Suppose the signal received by the secondary user is a circularly symmetric complex Gaussian random variable with a mean of 0 and a variance of , and the noise is also a circularly symmetric complex Gaussian random variable with a mean of 0 and a variance of . Wherein: and respectively represent the energies received by noise and signal when the number of sampling points is n, and N(·) represents the normal distribution.

5. A collaborative spectrum sensing method based on D-S evidence theory according to claim 1, characterized in that, The calculation formula for the cross-correlation coefficient between two secondary users is as follows: Calculate the cross-correlation coefficient between two SUs. The cross-correlation coefficient of the signals received by the i-th antenna and the j-th antenna is: where: i and j represent different secondary users, x i (n) represents the nth sampling point of the ith secondary user, x j (n) represents the nth sampling point of the jth secondary user. The number of sampling points is k. Transform the cross-correlation coefficient into the mean β ij , and the formula used is as follows:

6. A collaborative spectrum sensing method based on D-S evidence theory according to claim 1, characterized in that, The modulus of the complex noise correlation coefficient follows a Rayleigh distribution with a variance of 1, that is: comβ ij > 0 and maxβ ij = 1.

7. A collaborative spectrum sensing method based on D-S evidence theory according to claim 1, characterized in that The β of each SU calculated according to the Euclidean distance ij The mean value and maxβ ij The distance d between them is calculated using the following formula: The basic probability assignment function of each secondary user in the D-S evidence theory obtained through the power spectral density curve is as follows: where: m i (H0) represents the BPA value that the i-th secondary user judges as "only noise" (H0), and m(H0) represents the BPA value that is judged as H0 after fusion; m i (H1) represents the BPA value that the i-th secondary user judges as "primary user present" H1, and m(H1) represents the BPA value that is judged as H1 after fusion; K is the degree of conflict between the evidence values.

8. A collaborative spectrum sensing method based on D-S evidence theory according to claim 1, characterized in that, The determination process of the average likelihood threshold is as follows: Under the condition that the false alarm probability is constrained, the received energy of a single secondary user is obtained as follows: Threshold Intersection value with the noise probability density curve of the i-th secondary user: Threshold The intersection value with the signal probability density curve of the i-th secondary user: The threshold The intersection value with the noise probability density curve of the i-th secondary user is f i (H0), and the intersection value with the signal probability density curve is f i (H1); Therefore, the average likelihood threshold is expressed as:

9. A spectrum sensing device based on covariance detection, characterized in that, It includes: Building module: used to calculate the received power of secondary users (SUs) at different distances from the primary user (PU) through the Friis transmission formula based on the fact that the transmission power of the primary user (PU) remains fixed, and build a cooperative spectrum sensing model; First calculation module: used to calculate the power spectral density curves of the secondary user (SU) in the presence of noise and signals; The second calculation module: used to calculate the cross-correlation coefficient between two secondary users and obtain the transformation value β according to the T transformation ij ; Deduction module: used to deduce that the modulus of the cross-correlation coefficient of complex noise follows a Rayleigh distribution with a variance of 1, and find the maximum point of the Rayleigh distribution; Fusion module: used to calculate the transformation value β of each secondary user (SU) according to the Euclidean distance, and take the distance between the mean value of ij and the maximum value point of the Rayleigh distribution as the fusion weight of each SU. Calculate each basic mass function of the D-S evidence theory through the power spectral density curve, fuse the basic mass functions of multiple secondary users, and obtain the average likelihood ratio of multiple users in real time; ij ​ Judgment module: used to compare the real-time average likelihood ratios of multiple users with the average likelihood threshold respectively. When the real-time average likelihood ratios of M users are greater than the average likelihood threshold, it is determined that there is a signal in the primary user spectrum.

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