Spectrum sensing method based on non-circular signal spatial spectrum

Abstract

The invention discloses a spectrum sensing method based on a non-circular signal spatial spectrum, namely, maximum-minimum non-circular signal spatial spectrum detection (maximum-minimum non-circular signal NC signals, NC-MMSS), and relates to a spectrum sensing method based on a non-circular signal spatial spectrum. The method comprises the following steps: firstly, improving a signal spatial spectrum by using complementary covariance information of a non-circular signal to obtain a non-circular signal spatial spectrum; and then, setting the test statistics as the ratio of the maximum value to the minimum value of the non-circular signal spatial frequency spectrum, and comparing the test statistics with a set threshold value to obtain a judgment result. If it is judged that the main user signal exists, the estimated value of the incoming angle of the main user signal needs to be output. By considering the complementary covariance information of the non-circular signal, the method provided by the invention has better detection performance, and can provide more accurate incoming angle information for spectrum access.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and more specifically, to a spectrum sensing method based on a non-circular signal spatial spectrum. Background Art

[0002] In recent years, with the rapid growth of wireless communication services, the demand for higher data transmission rates in wireless communication has continued to grow, and more and more spectrum resources have been occupied. However, the traditional spectrum allocation strategy is static and the spectrum utilization rate is low. In order to improve spectrum utilization, Joseph Mitola proposed cognitive radio technology. In cognitive radio, secondary users can opportunistically use the authorized spectrum of the primary user for data transmission when the primary user is idle, which can effectively improve spectrum utilization. Spectrum sensing is one of the key technologies of cognitive radio. It is mainly responsible for detecting whether there are spectrum holes, that is, whether the primary user is occupying the authorized spectrum.

[0003] Classic spectrum sensing methods mainly include energy detection (ED), covariance absolute value detection (CAV), and α-combinatorial spectrum sensing algorithm based on the maximum, arithmetic mean and geometric mean of the eigenvalues ​​(α-ME-AM-GM), etc. The above methods all use the time domain characteristics or frequency domain characteristics of the received signal to achieve detection, while ignoring the spatial domain characteristics of the received signal.

[0004] At present, scholars have proposed a variety of spectrum sensing algorithms that use the spatial spectrum characteristics of the received signal in the spatial domain to detect spectrum holes, such as central-symmetry-based feature detection (CSFD), maximum-minimum delay-sum ratio detection (MMDS), and detectors based on superposition of spatial spectrum. However, the above methods only use the standard covariance information of the received signal, while ignoring the possible non-circular statistical characteristics of the signal. Non-circular signals are very common in modern communication systems, such as binary phase shift keying signals, M-ary amplitude shift keying signals, pulse amplitude modulation signals, etc. These non-circular signals contain not only standard covariance information, but also additional complementary covariance information. The complementary covariance information of non-circular signals can be used to improve the spatial spectrum of the signal, thereby further improving the performance of spectrum sensing methods based on spatial spectrum. Summary of the invention

[0005] The present invention provides a spectrum sensing method based on non-circular signal spatial spectrum, which effectively improves the performance of spectrum sensing by making full use of complementary covariance information of non-circular signals.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A spectrum sensing method based on the spatial spectrum of non-circular signals is the maximum-minimum spatial spectrum of the NC signals (NC-MMSS). Figure 1 As shown, the following steps are included:

[0008] S1: M-element uniform linear array acquires received data;

[0009] S2: conjugate the received data of the uniform linear array and combine it with the original data to obtain the extended received data;

[0010] S3: Calculate the sample covariance matrix based on the extended received data;

[0011] S4: Calculate the non-circular signal spatial spectrum according to the sample covariance matrix;

[0012] S5: construct the test statistic T using the non-circular signal spatial spectrum and solve the threshold γ;

[0013] S6: If T>γ, determine that the primary user signal exists and output the estimated signal direction angle If T≤γ, it is determined that the primary user signal does not exist.

[0014] Preferably, in step S1, the array element spacing of the M-element uniform linear array is d, and d is set as a half wavelength of the primary user signal, specifically:

[0015] d = λ / 2

[0016] Where λ is the wavelength of the primary user signal.

[0017] Preferably, the received data described in step S1 specifically includes:

[0018]

[0019] In the formula, x(k)=[x1(k),x2(k),…,x M (k)] T is the received data of the uniform linear array, and its standard covariance matrix is ​​R x =E[x(k)x H (k)], the complementary covariance matrix is ​​C x=E[x(k)x T (k)],x1(k),x2(k),…,x M (k) represents the kth received data of the 1st array element to the Mth array element. n(k)=[n1(k),n2(k),…,n M (k)] T is a circularly symmetric complex Gaussian white noise vector. s(k) is the primary user signal, which is a strictly non-circular signal. K is the total number of samples of received data, and h is the channel attenuation coefficient. H0 represents the case where the primary user signal does not exist, and H1 represents the case where the primary user signal exists. represents the steering vector, and θ0 is the direction angle of the main user signal.

[0020] Preferably, the extended received data described in step S2 is specifically:

[0021] y(k)=[x T (k),x H (k)] T

[0022] Where y(k) is the extended received data.

[0023] Preferably, in step S3, the sample covariance matrix is ​​calculated according to the extended received data, specifically:

[0024]

[0025] In the formula, is the sample covariance matrix of the extended received data, which contains the standard covariance information and complementary covariance information of the received data x(k).

[0026] Preferably, the non-circular signal spatial spectrum in step S4 is specifically:

[0027]

[0028] In the formula, represents the spatial spectrum of non-circular signal, is the extended steering vector, and its expression is:

[0029]

[0030] In the formula, is the steering vector. Define the angle search area as The number of search angles in the two dimensions is I and J respectively. Compared with the spatial spectrum P obtained by the conventional beamforming (CBF) algorithm CBF (θ i )=a H(θ i )R x a(θ i ), the non-circular signal spatial spectrum is improved by using the complementary covariance information of the non-circular signal. The signal-to-noise ratio in the direction of the primary user signal's coming angle is improved by 3 dB, which is beneficial for detecting the primary user signal from the noise.

[0031] Preferably, in step S5, the non-circular signal spatial spectrum is used Construct the test statistic, specifically:

[0032]

[0033] In the formula, T is the test statistic.

[0034] Preferably, the method for solving the threshold value γ in step S5 is specifically as follows:

[0035] In the case of H0, that is, when only noise exists, Rayleigh Ritz theorem gives in The sample covariance matrix representing the extended received data The maximum eigenvalue of; when the sampling number K is large enough, Approaching in represents the noise power. Therefore, when the number of samples K is large enough, it can be considered that The false alarm probability In cognitive radio systems, it is usually required that the actual value of the false alarm probability is less than or equal to its theoretical value. Therefore, we can is considered as an approximation of the false alarm probability. In the case of H0, is a Wishart random matrix, according to its largest eigenvalue The asymptotic distribution of is a 2nd-order Tracy-Wisdom distribution. Therefore, the false alarm probability P fa The theoretical expression of can be approximated as:

[0036]

[0037] In the formula, F2(·) is the cumulative distribution function of Tracy-Wisdom2-order distribution. fa The expression of the threshold γ is obtained as:

[0038]

[0039] In the formula, It is the inverse of the cumulative distribution function of the Tracy-Wisdom2nd order distribution.

[0040] Preferably, in step S6, when it is determined that the primary user signal exists, the output signal arrival angle estimation value is:

[0041]

[0042] In the formula, is the estimated value of the main user signal coming angle.

[0043] Preferably, the spectrum sensing method based on the non-circular signal spatial spectrum proposed in steps S1 to S6 has a detection probability P d The theoretical expression of can be approximated as:

[0044]

[0045] In the formula, is the cumulative distribution function of the chi-square distribution with parameter 2MK, is the estimated value of the power of the primary user signal s(k).

[0046] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0047] The present invention proposes a spectrum sensing method based on non-circular signal spatial spectrum, namely, maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS). First, the signal spatial spectrum is improved by using the complementary covariance information of the non-circular signal to obtain the non-circular signal spatial spectrum, which is conducive to detecting the main user signal from the noise. Then the test statistic is set to the ratio of the maximum value to the minimum value of the non-circular signal spatial spectrum, and compared with the set threshold to obtain the judgment result. If it is judged that the main user signal exists, it is also necessary to output the estimated value of the main user signal coming angle. Compared with the existing covariance absolute value detection (CAV), center-symmetric feature detection (CSFD), maximum-minimum delay sum spectrum ratio detection (MMDS), detector based on superposition spatial spectrum and other methods, the method proposed in the present invention has better detection performance and can provide more accurate coming angle information for spectrum access. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 The present invention is a schematic diagram of the process of the method.

[0049] Figure 2Schematic diagram of the detection probability changes of the maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS) and covariance absolute value detection (CAV) proposed in the present invention, the α-fusion spectrum sensing algorithm based on eigenvalue maximum value-arithmetic mean value-geometric mean value (α-ME-AM-GM), the feature detection based on central symmetry (CSFD), the maximum-minimum delayed sum spectrum ratio detection (MMDS) and the detector based on superposition spatial spectrum under different signal-to-noise ratios.

[0050] Figure 3 It is a schematic diagram of the detection probability changes of the maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS) and covariance absolute value detection (CAV) proposed in the present invention, the α-fusion spectrum sensing algorithm based on eigenvalue maximum value-arithmetic mean value-geometric mean value (α-ME-AM-GM), the feature detection based on central symmetry (CSFD), the maximum-minimum delay sum spectrum ratio detection (MMDS) and the detector based on the superposition spatial spectrum under different false alarm probabilities.

[0051] Figure 4 is the detection probability P of the maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS) proposed in the present invention under different signal-to-noise ratios d and false alarm probability P fa Schematic diagram of the change of theoretical value and simulation value, where (a) is the detection probability P d Schematic diagram of the change of theoretical value and simulation value with different signal-to-noise ratio; (b) is the false alarm probability P fa Schematic diagram of the change of theoretical value and simulation value with different signal-to-noise ratios.

[0052] Figure 5 Schematic diagram of the change in root mean square error of the main user signal coming angle estimation of the maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS) proposed in the present invention and the central symmetric feature detection (CSFD), the maximum-minimum delayed sum spectrum ratio detection (MMDS) and the detector based on the superposition spatial spectrum under different signal-to-noise ratios. DETAILED DESCRIPTION

[0053] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0054] 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;

[0055] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0056] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0057] Example 1

[0058] A spectrum sensing method based on non-circular signal spatial spectrum, namely maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS), is proposed. Figure 1 As shown, the following steps are included:

[0059] S1: M-element uniform linear array obtains received data x(k);

[0060] S2: Take the conjugate of the received data of the uniform linear array and combine it with the original data to obtain the extended received data y(k)=[x T (k),x H (k)] T ;

[0061] S3: Calculate the sample covariance matrix based on the extended received data

[0062] S4: Calculate the non-circular signal spatial spectrum based on the sample covariance matrix in is the extended steering vector, is the guiding vector;

[0063] S5: Using the spatial spectrum of non-circular signals Constructing the test statistic Setting the Threshold in in is the inverse function of the cumulative distribution function of the Tracy-Wisdom2nd order distribution, P fa is the pre-set false alarm probability;

[0064] S6: If T>γ, determine that the primary user signal exists and output the estimated signal direction angle If T≤γ, it is determined that the primary user signal does not exist.

[0065] This embodiment provides a spectrum sensing method based on non-circular signal spatial spectrum, namely, maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS). The proposed method uses the complementary covariance information of the non-circular signal to obtain an improved non-circular signal spatial spectrum, which is conducive to detecting the main user signal from the noise. At the same time, the difference between the ratio of the maximum value and the minimum value of the non-circular signal spatial spectrum in the presence and absence of the main user signal is used for detection. Compared with other methods, the method proposed in the present invention has better detection performance and can provide more accurate angle of arrival information for spectrum access.

[0066] Example 2

[0067] This embodiment provides a simulation embodiment of embodiment 1. In the specific implementation process, the simulation parameters are set as follows: the main user signal is set to a BPSK signal, the signal carrier frequency is 10 MHz, the signal direction angle is 30°, and the electromagnetic wave propagation speed is 3×10 8 m / s, the sampling frequency is 100MHz, and the number of samples for a single detection is 1000; the number of array elements of the uniform linear array of the secondary user is 16, and the array element spacing is 1.5m; the channel model is set to Rayleigh fading channel; the noise type is complex Gaussian white noise; the simulation is based on 20,000 Monte Carlo experiments, in which the presence of the primary user signal and only noise appear randomly, and the prior probability of both situations is 0.5.

[0068] The maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS) proposed in Example 1 is compared with the covariance absolute value detection (CAV), the α-ME-AM-GM based on the maximum-arithmetic mean-geometric mean of the eigenvalue, the central symmetric feature detection (CSFD), the maximum-minimum delay sum spectrum ratio detection (MMDS) and the detector based on the superposition spatial spectrum under different signal-to-noise ratios. The false alarm probability is set to 0.01. Figure 2 As shown, the NC-MMSS curve corresponds to the new method proposed in the present invention, the CAV curve corresponds to the covariance absolute value detection method, the α-ME-AM-GM curve corresponds to the α fusion spectrum sensing algorithm based on the maximum eigenvalue-arithmetic mean-geometric mean, the CSFD curve corresponds to the feature detection method based on central symmetry, the MMDS curve corresponds to the maximum-minimum delay addition spectrum ratio detection method, and the Alg. [9] curve corresponds to the detector based on the superposition spatial spectrum. The NC-MMSS method proposed in Example 1 is superior to other methods. When the detection probability is 90%, the NC-MMSS method proposed in Example 1 obtains a gain of at least 1.5 dB compared with other methods. It is worth noting that in the range of signal-to-noise ratio from -24 dB to -23 dB, the detection probability of the Alg. [9] method is slightly higher. This is because the false alarm probability of this method is much greater than the false alarm probability of the NC-MMSS method.

[0069] The above examples show that, compared with other methods, the method described in Example 1 can achieve better detection performance under different signal-to-noise ratios.

[0070] On the basis of the above embodiments, the maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS), covariance absolute value detection (CAV), α-ME-AM-GM based on eigenvalue maximum value-arithmetic mean value-geometric mean value, feature detection based on center symmetry (CSFD), maximum-minimum delay sum spectrum ratio detection (MMDS) and detection probability curves of the detector based on superposition spatial spectrum under different false alarm probabilities mentioned in Example 1 are plotted, that is, the ROC curve is plotted. Specifically, the signal-to-noise ratio is set to -19dB, and 12 preset false alarm probabilities are selected as 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1 respectively. The settings of other parameters are the same as those in the above embodiments. Figure 3 As shown, the NC-MMSS curve corresponds to the new method proposed in the present invention, the CAV curve corresponds to the covariance absolute value detection method, the α-ME-AM-GM curve corresponds to the α fusion spectrum sensing algorithm based on the maximum eigenvalue-arithmetic mean-geometric mean, the CSFD curve corresponds to the feature detection method based on central symmetry, the MMDS curve corresponds to the maximum-minimum delay addition spectrum ratio detection method, and the Alg. [9] curve corresponds to the detector based on the superposition spatial spectrum. The detection probability of the above methods increases with the increase of the false alarm probability. Under the same false alarm probability, the detection probability of the NC-MMSS method proposed in the present invention is significantly higher.

[0071] The above embodiments show that under low signal-to-noise ratio and different false alarm probabilities, the method described in Embodiment 1 can achieve a higher detection probability, which further verifies the superiority of the detection performance of the proposed method.

[0072] Then, the detection probability P of the maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS) proposed in Example 1 under different signal-to-noise ratios is compared. d and false alarm probability P fa Theoretical and simulation values ​​of the false alarm probability P fa Set to 0.01. Figure 4 As shown in (a), the detection probability P d The simulation value of is significantly larger than its theoretical value, which is reasonable because cognitive radio systems usually require the detection probability P d The actual value of is greater than or equal to its theoretical value. Figure 4 As shown in (b), the false alarm probability P fa The simulation value of is less than its theoretical setting of 0.01, which is reasonable because cognitive radio systems usually require a false alarm probability P fa The actual value of is less than or equal to its theoretical value.

[0073] Finally, the angle of arrival estimation performance of the maximum-minimum non-circular signal spatial spectrum detection (NC-MMSS) proposed in Example 1 is compared with that of the center-symmetric feature detection (CSFD), the maximum-minimum delay-sum spectrum ratio detection (MMDS) and the detector based on the superposition spatial spectrum. The simulation setting is the same as that of the above embodiment, and the root mean square error between the true value and the estimated value of the main user signal angle of arrival is used as the measurement indicator. Figure 5 As shown in the figure, the NC-MMSS curve corresponds to the new method proposed in the present invention, the CSFD curve corresponds to the feature detection method based on centrosymmetry, the MMDS curve corresponds to the maximum-minimum delay addition spectrum ratio detection method, and the Alg. [9] curve corresponds to the detector based on superposition spatial spectrum. The root mean square error of the angle estimation of the above methods decreases with the increase of the signal-to-noise ratio. Under low signal-to-noise ratio, the root mean square error of the angle estimation of the NC-MMSS method described in Example 1 is significantly lower.

[0074] The above embodiments show that under low signal-to-noise ratio, the method described in Embodiment 1 can achieve better arrival angle estimation performance while ensuring a higher detection probability.

[0075] The same or similar reference numerals correspond to the same or similar components;

[0076] 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;

[0077] 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 spectrum sensing method based on non-circular signal spatial spectrum, characterized in that: The following steps are involved: S1: M-element uniform linear array acquires received data; S2: conjugate the received data of the uniform linear array and combine it with the original data to obtain the extended received data; S3: Calculate the sample covariance matrix based on the extended received data; S4: Calculate the non-circular signal spatial spectrum according to the sample covariance matrix; S5: construct the test statistic T using the non-circular signal spatial spectrum and solve the threshold γ; S6: If T>γ, determine that the primary user signal exists and output the estimated signal direction angle If T≤γ, it is determined that the primary user signal does not exist.

2. The spectrum sensing method based on non-circular signal spatial spectrum according to claim 1, characterized in that: In step S1, the array element spacing d of the M-element uniform linear array is set to half the wavelength of the primary user signal, and the received data in step S1 is specifically: In the formula, x(k)=[x1(k),x2(k),…,x M (k)] T is the received data of the uniform linear array, and its standard covariance matrix is ​​R x =E[x(k)x H (k)], the complementary covariance matrix is ​​C x =E[x(k)x T (k)],x1(k),x2(k),…,x M (k) represents the kth received data of the 1st array element to the Mth array element. n(k)=[n1(k),n2(k),…,n M (k)] T is a circularly symmetric complex Gaussian white noise vector. s(k) is the primary user signal, which is a strictly non-circular signal. K is the total number of samples of received data, and h is the channel attenuation coefficient. H0 represents the case where the primary user signal does not exist, and H1 represents the case where the primary user signal exists. a(θ0)= represents the steering vector, and θ0 is the direction angle of the main user signal.

3. The spectrum sensing method based on non-circular signal spatial spectrum according to claim 2, characterized in that: The extended received data described in step S2 is specifically: y(k)=[x T (k),x H (k)] T Where y(k) is the extended received data.

4. The spectrum sensing method based on non-circular signal spatial spectrum according to claim 3, characterized in that: In step S3, the sample covariance matrix is ​​calculated according to the extended received data, specifically: In the formula, is the sample covariance matrix of the extended received data, which contains the standard covariance information and complementary covariance information of the received data x(k).

5. The spectrum sensing method based on non-circular signal spatial spectrum according to claim 4, characterized in that: The non-circular signal spatial spectrum in step S4 Specifically: In the formula, represents the spatial spectrum of non-circular signal, is the extended steering vector, and its expression is: In the formula, is the steering vector. Define the angle search area as The number of search angles in the two dimensions is I and J respectively. Compared with the spatial spectrum P obtained by the conventional beamforming (CBF) algorithm CBF (θ i )=a H (θ i )R x a(θ i ), the non-circular signal spatial spectrum is improved by using the complementary covariance information of the non-circular signal. The signal-to-noise ratio in the direction of the primary user signal's coming angle is improved by 3 dB, which is beneficial for detecting the primary user signal from the noise.

6. The spectrum sensing method based on non-circular signal spatial spectrum according to claim 5, characterized in that: In step S5, the non-circular signal spatial spectrum is used Construct the test statistic, specifically: In the formula, T is the test statistic.

7. The spectrum sensing method based on non-circular signal spatial spectrum according to claim 6, characterized in that: The method for solving the threshold value γ in step S5 is specifically as follows: In the case of H0, that is, when only noise exists, Rayleigh Ritz theorem gives in The sample covariance matrix representing the extended received data The maximum eigenvalue of When the number of samples K is large enough, Approaching in represents the noise power. Therefore, when the number of samples K is large enough, it can be considered that The false alarm probability In cognitive radio systems, it is usually required that the actual value of the false alarm probability is less than or equal to its theoretical value. Therefore, we can is considered as an approximation of the false alarm probability. In the case of H0, is a Wishart random matrix, according to its largest eigenvalue The asymptotic distribution of is a 2nd-order Tracy-Wisdom distribution. Therefore, the false alarm probability P fa The theoretical expression of can be approximated as: In the formula, F2(·) is the cumulative distribution function of Tracy-Wisdom2-order distribution. f The expression of the threshold γ is obtained by a: In the formula, It is the inverse of the cumulative distribution function of the Tracy-Wisdom2nd order distribution.

8. The spectrum sensing method based on non-circular signal spatial spectrum according to claim 7, characterized in that: In step S6, when it is determined that the primary user signal exists, the output signal direction angle estimation value is: In the formula, is the estimated value of the main user signal coming angle.

9. Preferably, the spectrum sensing method based on non-circular signal spatial spectrum according to claim 8 is characterized in that: Its detection probability P d The theoretical expression of can be approximated as: In the formula, is the cumulative distribution function of the chi-square distribution with parameter 2MK, is the estimated value of the power of the primary user signal s(k).

Images