A Spectrum Sensing Method Based on the Distance of Signal Covariance Matrices

Abstract

The present invention discloses a spectrum sensing method based on the distance of signal covariance matrices, which includes performing short-time Fourier transform on the received signal, segmenting the signal in the time domain by using a window function, then performing Fourier transform on each sub-band signal to obtain a plurality of two-dimensional matrices regarding time and frequency, jointly constructing a new matrix from the amplitude vectors of these matrices at the same frequency, and obtaining its covariance matrix to get N signal covariance matrices, collecting pure noise signals as reference signals, performing the same processing on the noise signals to obtain N reference matrices, respectively calculating the Riemannian distances between these N pairs of signal covariance matrices and reference matrices, and obtaining the sum of the N Riemannian distances, using the sum of the Riemannian distances as a detection statistic to compare with a threshold, and making a final decision, which improves the detection accuracy of weak signals and reduces the influence of noise uncertainty.

Description

Technical Field

[0001] The present invention relates to the technical field of spectrum sensing, and particularly to a spectrum sensing method based on the distance of signal covariance matrix. Background Technique

[0002] The rapid development of wireless communication technology has led to a sharp increase in the demand for spectrum resources. However, the utilization rate of existing spectrum allocation strategies is relatively low. To solve the problem of spectrum resource shortage, cognitive radio technology has been proposed. The core idea of cognitive radio is to achieve dynamic spectrum allocation and spectrum sharing through the system's spectrum sensing and intelligent learning capabilities.

[0003] Traditional spectrum detection methods include energy detection, matched filter detection, and cyclostationary feature detection. The energy detection method obtains the sensing decision by calculating the energy of the signal and comparing it with a threshold. The energy detection method is widely used because of its easy implementation, but it is very sensitive to noise uncertainty. Matched filter detection achieves coherent detection by maximizing the signal-to-noise ratio, but requires information about the primary signal. Cyclostationary feature detection distinguishes signals and noise by analyzing the spectral correlation function of the signal. Although the detection accuracy is high, the calculation is complex.

[0004] Spectrum sensing can be regarded as a signal detection problem. By analyzing the probability distribution of the detection data, the presence of the primary signal can be determined. Information geometry is a new theoretical system that uses modern differential geometry methods to study problems in the fields of Riemannian manifold statistics and information. Information geometry was proposed by statisticians in 1945. Rao proposed using the Fisher information matrix as a Riemannian metric to study probability models. Then Amari introduced the concept of dual connection in information geometry and conducted a large number of studies. Currently, the information geometry theory has been widely applied in research fields such as signal classification, machine learning, and radar signal processing. In the context of information geometry, the spectrum sensing problem can be transformed into a geometric problem on a manifold, and the properties of the probability distribution function cluster can be analyzed using geometric methods. Lu et al. proposed a broadband spectrum sensing algorithm based on Riemannian distance and Riemannian mean, and then derived the decision threshold using the moment matching method. The geometric method does not need to consider the statistical characteristics of noise and the number of primary signals. Compared with traditional detection algorithms, the detection accuracy has indeed been improved. Chen et al. proposed a constant false alarm probability detector and a distance detector based on information geometry, using geodesic and symmetric Kullback-Leibler divergence to measure the distance on the manifold respectively. The distance detector has high detection accuracy, but requires prior information about the primary signal. Zhang et al. adopted a data fusion scheme based on Riemannian mean shift to eliminate abnormal data in the SU, and proposed a particle swarm optimization algorithm based on Riemannian distance to train the classifier on the manifold. This algorithm can be directly used on the manifold and effectively improves the sensing performance.

[0005] Although the above algorithm improves the accuracy of spectrum sensing to a certain extent, there are still problems such as being greatly affected by noise uncertainty and having low detection accuracy under low signal-to-noise ratio. Summary of the Invention

[0006] The present invention provides a spectrum sensing method based on the distance of signal covariance matrices, which solves the problems that spectrum sensing is greatly affected by noise uncertainty and has low detection accuracy under low signal-to-noise ratio.

[0007] To achieve the above object, the present invention provides the following technical solution: A spectrum sensing method based on the distance of signal covariance matrices, comprising the following steps:

[0008] Step 1: Process the signal received by the cognitive radio network model using short-time Fourier transform; segment the input signal x(t) using the window function w(t):

[0009] y(t) = x(t)w(t - τ)

[0010] And perform Fourier transform on it:

[0011]

[0012] By moving the window function, obtain the spectrum results of all segments from τ0 to τ l For discrete signals, X(ω, τ) corresponds to a two-dimensional matrix, that is, obtain l two-dimensional matrices X(ω, τ);

[0013] Step 2: The amplitudes at the same frequency of the above l matrices, that is, the ω-th row of each matrix, form a new frequency matrix:

[0014]

[0015] And calculate its covariance matrix R ω ;

[0016] Step 3: Collect pure noise signals as reference signals, and use the same processing method as in Step 2 for the reference signals to obtain N reference matrices R nω ;

[0017] Step 4: Calculate the Riemannian distances between N pairs of covariance matrices R ω and the reference matrix R nω respectively;

[0018] Step 5: Add up the sums of the Riemannian distances obtained by K cognitive users to get the final distance D, use it as the detection statistic and compare it with the threshold γ to make a final decision.

[0019] Preferably, in the cognitive radio network model, each cognitive user sends its local sensing result to the fusion center, and the fusion center makes a final decision according to the corresponding decision rule.

[0020] Preferably, assume that there is only one primary user and K cognitive users in the cognitive radio network model, and the sensing result is represented by the following binary hypothesis model:

[0021]

[0022] where h(m) is the channel gain, s(m) is the signal transmitted by the primary user, ω(m) is the independent and identically distributed Gaussian white noise, H0 represents the absence of the primary user and the channel is idle, and H1 represents the presence of the primary user and the channel is occupied.

[0023] Preferably, in step 4, under the assumptions of H0 and H1, the covariance matrices of the signals are respectively mapped to two points on the manifold. For two points R ω and R nω on the manifold, the Riemannian distance between them is calculated by using the following formula:

[0024]

[0025] Using the above formula, the Riemannian distance d between the signal covariance matrix of each sub-band and the reference matrix is obtained n and the sum of the Riemannian distances of each sub-band is calculated as d = ∑d n .

[0026] Preferably, in step 5, the formula for the final decision is:

[0027]

[0028] Compared with the prior art, the beneficial effects of the present invention are:

[0029] 1. In the present invention, according to the different characteristics of the signal at different frequencies, the short-time Fourier transform is used to segment the signal in the time domain, and the signals in different frequency bands are processed separately, which not only increases the amount of secondary data but also suppresses the out-of-band noise interference, thereby effectively improving the detection probability.

[0030] 2. In the present invention, the received signal is subjected to short-time Fourier transform. The signal is segmented in the time domain by using a window function, and then the Fourier transform is performed on each sub-band signal to obtain a plurality of two-dimensional matrices regarding time and frequency. The amplitude vectors of these matrices at the same frequency are jointly formed into a new matrix, and its covariance matrix is calculated, thus obtaining N signal covariance matrices. A pure noise signal is collected as a reference signal, and the same processing is performed on the noise signal to obtain N reference matrices. The Riemannian distances between these N pairs of signal covariance matrices and reference matrices are calculated respectively, and the sum of the N Riemannian distances is obtained. The sum of the Riemannian distances is used as a detection statistic to be compared with a threshold to make a final decision, which improves the detection accuracy of weak signals and reduces the influence of noise uncertainty. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings are used to provide further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention, but do not constitute a limitation to the present invention.

[0032] In the drawings:

[0033] Figure 1 is the CR network model diagram of the present invention;

[0034] Figure 2 is the comparison diagram of the ROC curves between the algorithm proposed by the present invention and the traditional algorithm;

[0035] Figure 3 is the comparison diagram of the SNR-Pd curves between the algorithm proposed by the present invention and the traditional algorithm. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] The following describes the preferred embodiments of the present invention with reference to the drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0037] Embodiment: As Figure 1 shown, a spectrum sensing method based on the distance of signal covariance matrices includes the following steps:

[0038] In the cognitive radio network model, each cognitive user sends its local sensing result to the fusion center, and the fusion center makes a final decision according to the corresponding decision rule. Assuming that there is only one primary user and K cognitive users in the cognitive radio network model, the sensing result is represented by the following binary hypothesis model:

[0039]

[0040] where h(m) is the channel gain, s(m) is the signal transmitted by the primary user, ω(m) is independent and identically distributed Gaussian white noise, H0 indicates the absence of the primary user and the channel is idle, and H1 indicates the presence of the primary user and the channel is occupied;

[0041] Step 1: Process the signal received by the cognitive radio network model using the short-time Fourier transform; segment the input signal x(t) using the window function w(t):

[0042] y(t) = x(t)w(t - τ)

[0043] And perform the Fourier transform on it:

[0044]

[0045] By moving the window function, obtain the spectral results of all segments from τ0 to τ l For the discrete signal, X(ω, τ) corresponds to a two-dimensional matrix, that is, obtain l two-dimensional matrices X(ω, τ);

[0046] Step 2: The amplitudes at the same frequency of the above l matrices, that is, the ω-th row of each matrix, form a new frequency matrix:

[0047]

[0048] And calculate its covariance matrix R ω ;

[0049] Step 3: Collect the pure noise signal as the reference signal, and use the same processing method as in Step 2 for the reference signal to obtain N reference matrices R nω ;

[0050] Step 4: Calculate the Riemannian distances between N pairs of covariance matrices R ω and the reference matrix R nω respectively; under the assumptions of H0 and H1, the covariance matrices of the signals are respectively mapped to two points on the manifold. For two points R ω and R nω on the manifold, calculate the Riemannian distance between them using the following formula:

[0051]

[0052] Using the above formula, find the Riemannian distance d between the signal covariance matrix and the reference matrix of each sub-band n And calculate the sum of the Riemannian distances of each sub-band d = ∑d n ;

[0053] Step 5: Add up the sum of the Riemannian distances obtained by K cognitive users to get the final distance D, which is used as the detection statistic and compared with the threshold γ to make a final decision. The formula is as follows:

[0054]

[0055] where, as Figure 2 shown in the comparison graph of the ROC curves between the proposed algorithm and the traditional algorithm and Figure 3 the comparison graph of the SNR-Pd curves between the proposed algorithm and the traditional algorithm, according to the different characteristics of the signal at different frequencies, the short-time Fourier transform is used to segment the signal in the time domain, and the signals in different frequency bands are processed separately, which not only increases the amount of secondary data, but also suppresses the out-of-band noise interference, thereby effectively improving the detection probability, improving the accuracy of spectrum sensing, being less affected by noise uncertainty, and improving the detection accuracy at low signal-to-noise ratios.

[0056] Finally, it should be noted that the above are only the preferred examples of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A spectrum sensing method based on the distance of signal covariance matrices, characterized in that, Including the following steps: Step 1: Process the signals received by the cognitive radio network model using the short-time Fourier transform; segment the input signal x(t) using the window function w(t): y(t) = x(t)w(t - τ) And perform Fourier transform on it: By means of a moving window function, the spectral results of all segments from τ0 to τ l are obtained. For a discrete signal, X(ω, τ) corresponds to a two-dimensional matrix, that is, l two-dimensional matrices X(ω, τ) are obtained; Step 2: The amplitudes at the same frequency of the above l matrices, that is, the ω-th row of each matrix, form a new frequency matrix: and calculate its covariance matrix R ω ; Step 3: Collect pure noise signals as reference signals, and perform the same processing on the reference signals as in Step 2 to obtain N reference matrices R nω ; Step 4: Calculate the Riemannian distances between N covariance matrices R ω and the reference matrix R nω respectively; Step 5: Add up the sum of the Riemannian distances obtained by K cognitive users to get the final distance D, use it as the detection statistic and compare it with the threshold γ to make a final decision; In step 4, under the assumptions of H0 and H1, where H0 represents that the primary user does not exist and the channel is idle, and H1 represents that the primary user exists and the channel is occupied, the covariance matrices of the signals are respectively mapped to two points on the manifold. For two points R ω and R nω on the manifold, the Riemannian distance between them is calculated by using the following formula: Using the above formula, calculate the Riemannian distance d between the signal covariance matrix and the reference matrix for each sub-band n And calculate the sum of the Riemannian distances for each sub-band: d = ∑d n .

2. The spectrum sensing method based on the distance of signal covariance matrix according to claim 1, wherein: The cognitive radio network model sends its local sensing results to the fusion center through each cognitive user, and the fusion center makes a final decision according to the corresponding decision rules.

3. A spectrum sensing method based on the distance of signal covariance matrix according to claim 2, characterized in that: Assume that there is only one primary user and K cognitive users in the cognitive radio network model, and the sensing result is represented by the following binary hypothesis model: Where h(m) is the channel gain, s(m) is the signal transmitted by the primary user, and ω(m) is independent and identically distributed Gaussian white noise.

4. A spectrum sensing method based on the distance of signal covariance matrix according to claim 1, characterized in that: In the above Step 5, the formula for the final decision is:

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