CN108900267B - Single-side right-tail goodness-of-fit inspection spectrum sensing method and device based on characteristic values - Google Patents
Single-side right-tail goodness-of-fit inspection spectrum sensing method and device based on characteristic values Download PDFInfo
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Abstract
The invention provides a single-side right-tail goodness-of-fit test spectrum sensing method and device based on characteristic values, and aims to solve the technical problem of low detection probability in the prior art. The implementation steps comprise: the signal receiving and sampling module and the received signal segmenting module receive and sample authorized user signals and then segment the signals, the covariance matrix of each segment of signals is calculated by the covariance calculation module, then the eigenvalue decomposition module performs eigenvalue decomposition on the covariance matrix of each segment of signals and calculates the ratio of the maximum eigenvalue to the trace mean value, the fitting object calculation module calculates the fitting object of each segment, and finally the fitting goodness inspection module calculates inspection statistics and judges whether authorized users exist or not to finish spectrum sensing. The invention effectively improves the detection probability on the premise of ensuring the stability, and can be used for detecting the idle frequency spectrum by an unauthorized user in a cognitive radio system.
Description
Technical Field
The invention belongs to the technical field of communication, relates to a spectrum sensing method and a spectrum sensing device, and particularly relates to a spectrum sensing method and a spectrum sensing device based on single-side right-tail goodness-of-fit test of a covariance matrix eigenvalue of a received signal, which can be used for detecting an idle spectrum by an unauthorized user in a cognitive radio system.
Background content
The spectrum sensing is a key link of the cognitive radio technology, unauthorized users in the cognitive radio system automatically sense the use condition of surrounding spectrum through the spectrum sensing technology, idle spectrum resources are utilized on the premise of not interfering normal communication of authorized users, the spectrum sensing technology is applied, dynamic management of the spectrum resources is realized, the spectrum utilization rate is improved, powerful technical support is provided for relieving the problem of insufficient spectrum resources, and the reliable spectrum sensing technology can ensure efficient operation of the whole cognitive radio system.
The existing spectrum sensing methods are mainly divided into a spectrum sensing method based on energy detection, a spectrum sensing method based on matched filter detection, a spectrum sensing method based on cyclic characteristic detection, a spectrum sensing method based on goodness-of-fit detection, a spectrum sensing method based on random matrix theory and the like. The spectrum sensing method based on energy detection is low in complexity and is easily influenced by noise uncertainty; the spectrum sensing method based on the matched filter detection has excellent performance, but needs to send the prior information of signals; the spectrum sensing method based on the cyclic feature detection has high precision, needs larger data volume, has high calculation complexity and is limited in practical application; the spectrum sensing method based on goodness-of-fit detection does not need any prior information of a sending signal, constructs statistic according to the empirical distribution number of a receiving signal, and converts spectrum sensing into a goodness-of-fit detection problem, but most of the existing goodness-of-fit detection is based on chi-square distribution and is easily influenced by noise uncertainty.
A sensing method Based on random matrix theory includes sampling received signals, storing sampled discrete signals into matrix, calculating covariance matrix of received Signal matrix, decomposing characteristic value, utilizing structure of characteristic value to calculate test statistic and sensing, said method is not affected by Noise uncertainty and has stable detection Performance, in Nadler B, Penna F, Garello R2011 IEEE International Conference on communication Nadler, 2011:1-5, published Performance of basic-Based Signal Detectors with Known and Unknown Noise Level, said method uses multiple antennas to receive and sample authorized user signals, storing discrete sampling point into matrix to obtain received Signal matrix, then solving covariance matrix of received Signal matrix, and finally, comparing the test statistic with a threshold, judging whether authorized users exist or not, and obtaining a spectrum sensing result. The method calculates the test statistic by receiving the eigenvalue of the signal covariance matrix, is not influenced by noise uncertainty, has stable detection performance, but has the defect of low detection probability due to underutilization of the information of eigenvalue distribution.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a frequency spectrum sensing method and a frequency spectrum sensing device for testing the fitting goodness of a single-side right tail based on a characteristic value, which are used for solving the technical problem of low detection probability in the prior art.
The technical idea of the invention is as follows: the signal receiving and sampling module and the received signal segmenting module receive and sample authorized user signals and then segment the signals, the covariance calculation module calculates a covariance matrix of each segment of signals, the eigenvalue decomposition module performs eigenvalue decomposition on the covariance matrix of each segment of signals and calculates the ratio of the maximum eigenvalue to the trace mean value, then the fitting object module calculates the fitting object of each segment, and finally the fitting goodness inspection module calculates inspection statistics and judges whether the authorized user exists or not.
According to the technical thought, the technical scheme adopted for achieving the purpose of the invention is as follows:
a frequency spectrum sensing method based on feature value unilateral right tail goodness-of-fit test comprises the following steps:
(1) the signal receiving and sampling module samples the received authorized user signal:
the signal receiving and sampling module receives the complex signal of the authorized user and samples the complex signal to obtain a received signal Y with the size of r multiplied by N:
the number of sampling points is N, N is more than or equal to 1, N represents the nth sampling point, N is 1,2, the.
(2) The received signal segmentation module segments the received signal Y:
the received signal segmentation module divides the received signal Y into K sections of signal matrixes, the size of each section of signal matrix is r multiplied by m, m is the number of columns contained in each section of signal matrix, m is more than or equal to 1 and less than or equal to N, and the kth section of signal matrix YkThe expression of (a) is:
yk＝[Y((k-1)m+1),Y((k-1)m+2),...,Y(km)]
wherein K is 1, 2.., K;
(3) the covariance matrix calculation module calculates a signal matrix ykOf the covariance matrix Rk：
Wherein, E [. C]The indication is taken as to what is desired,
representing the Hermite transformation, RkThe size of (a) is r × r;
(4) the eigenvalue decomposition module calculates a covariance matrix RkThe ratio of the maximum eigenvalue to the trace mean of (c):
(4a) eigenvalue decomposition module pair covariance matrix RkDecomposing the eigenvalue to obtain P eigenvalues lambdapWherein P is 1,2,. cndot, P;
(4b) selecting lambda by eigenvalue decomposition modulepMedium maximum eigenvalue lambdakmaxWhile passing through λpCalculation of RkTrace mean tr of:
(4c) the eigenvalue decomposition module calculates the maximum eigenvalue lambdakmaxRatio U to trace mean trk：
(5) The fitting object calculation module calculates a signal matrix ykFitting object x ofk：
Wherein u is a central parameter,
epsilon is a scaling parameter that is,
(6) the test statistic construction module calculates a test statistic T:
test statistic construction Module calculates xkTheoretical distribution function F of0(x) At xkValue of F0(xk) And according to the one-sided right-tail fitting goodness test criterion, passing through F0(xk) Calculating a test statistic T:
wherein ln (·) represents a natural logarithmic function;
(7) the judgment module obtains a spectrum sensing result:
(7a) setting false alarm probability to Pf，0≤PfAnd (3) less than or equal to 1, calculating and judging whether a threshold eta of an authorized user exists:
η＝γ-1(Γ(K)(1-Pf),K)-K
wherein the content of the first and second substances,
for the lower incomplete gamma function, gamma (. cndot.) is complete gammaA ma function;
(7b) the judgment module judges whether T is larger than or equal to eta, if yes, an authorized user exists, and if not, the authorized user does not exist.
The utility model provides a spectrum sensing device of unilateral right tail goodness of fit inspection based on eigenvalue, includes signal reception sampling module, covariance matrix calculation module and eigenvalue decomposition module, wherein:
the signal receiving and sampling module is used for receiving and sampling an authorized user signal;
the covariance matrix calculation module is used for calculating a covariance matrix of a signal matrix generated by the received signal segmentation module;
the eigenvalue decomposition module is used for calculating the ratio of the maximum eigenvalue of the covariance matrix generated by the covariance matrix calculation module to the trace mean;
a received signal segmentation module is connected between the signal receiving sampling module and the covariance matrix calculation module and is used for segmenting the received signals obtained by the signal receiving sampling module;
the output end of the eigenvalue decomposition module is sequentially connected with a fitting object calculation module and a fitting goodness inspection module, wherein:
the fitting object calculation module is used for calculating the fitting object of each section of signal matrix according to the ratio of the maximum eigenvalue to the trace mean value calculated by the eigenvalue decomposition module;
and the goodness-of-fit inspection module is used for acquiring a spectrum sensing result according to the fitting object generated by the fitting object calculation module.
Above-mentioned spectral sensing device based on unilateral right tail goodness of fit inspection of eigenvalue, goodness of fit inspection module is including test statistics structure module and judgement module, wherein:
the test statistic construction module is used for constructing test statistic according to a unilateral right tail fitting goodness test criterion by utilizing the fitting object generated by the fitting object calculation module;
and the judging module is used for judging whether the authorized user exists according to the test statistic generated by the test statistic constructing module to obtain a spectrum sensing result.
Compared with the prior art, the invention has the following advantages:
the invention utilizes the characteristic value of the covariance matrix of the received signal without being influenced by noise uncertainty when calculating the fitting object, adopts the unilateral right-tail fitting goodness test criterion when calculating the test statistic, and utilizes the value of the theoretical distribution function of the fitting object at the fitting object, thereby avoiding the defect of insufficient utilization of characteristic value distribution information in the prior art.
Drawings
FIG. 1 is a flow chart of an implementation of the spectrum sensing method of the present invention;
FIG. 2 is a schematic structural diagram of a spectrum sensing apparatus according to the present invention;
FIG. 3 is a simulation comparison graph of the detection probability as a function of the signal to noise ratio of the present invention and the prior art;
FIG. 4 is a simulation comparison graph of the detection probability of the present invention and the prior art as a function of the number of sampling points.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the spectrum sensing method based on the one-sided right-tail goodness of fit test of the characteristic values includes the following steps:
step 1) a signal receiving and sampling module samples received authorized user signals:
the signal receiving and sampling module receives complex signals of authorized users by 16 receiving antennas to obtain high-frequency signals containing noise, the baseband signals containing Gaussian complex noise are obtained after down-conversion and demodulation processing, then the baseband signals are sampled, the number N of sampling points is 1000, the sampled discrete signals are stored in a matrix, and received signals Y are obtained:
y is a matrix of size 16 × 1000, Y (n) denotes the nth column of the received signal Y, n is 1, 2.., 16, and when there is no authorized user, Y includes only gaussian complex noise;
step 2) the received signal segmentation module segments the received signal Y:
the received signal segmentation module divides the received signal Y into 4 segments of signal matrixes, the size of each segment of signal matrix is 16 multiplied by 4, each segment of signal matrix comprises 250 columns, and then the kth segment of signal matrix YkThe expression of (a) is:
yk＝[Y(250(k-1)+1),Y(250(k-1)+2),...,Y(250k)]
where k is 1,2,3,4, and Y contains only gaussian complex noisekIs a gaussian random matrix;
step 3) the covariance matrix calculation module calculates the signal matrix ykOf the covariance matrix Rk：
Wherein, E [. C]The indication is taken as to what is desired,
representing the Hermite transformation, RkHas a size of 16 × 16, according to the random matrix theory, when y iskWhen it is a Gaussian random matrix, RkIs a Wishart matrix;
step 4) calculating a covariance matrix R by an eigenvalue decomposition modulekThe ratio of the maximum eigenvalue to the trace mean of (c):
step 4a) eigenvalue decomposition module pair covariance matrix RkDecomposing the eigenvalue to obtain 16 eigenvalues lambdapWherein p is 1, 2.., 16;
step 4b) selecting lambda by a characteristic value decomposition modulepMedium maximum eigenvalue lambdakmaxWhile passing through λpCalculation of RkTrace mean tr of:
step 4c) the eigenvalue decomposition module calculates the maximum eigenvalue lambdakmaxRatio U to trace mean trk：
Step 5) calculating a signal matrix y by a fitting object calculation modulekFitting object x ofk：
Wherein u is a central parameter,
epsilon is a scaling parameter that is,
when only Gaussian complex noise is present in the received signal, ykIs a Gaussian random matrix, RkIs the Wishart matrix, xkObeying a 2 nd order Tracy-Widom distribution, xkCumulative distribution function F0(x) The expression of (a) is:
wherein, FTW2(x) Is a Tracy-Widom cumulative distribution function, F "TW2(x) Is FTW2(x) 2 derivatives of;
step 6), calculating a test statistic T by a test statistic construction module:
test statistic construction Module calculates xkTheoretical distribution ofNumber F0(x) At xkValue of F0(xk) And according to the one-sided right-tail fitting goodness test criterion, passing through F0(xk) Calculating a test statistic T:
wherein ln (·) represents a natural logarithm function, the expression form of the Tracy-Widom distribution function mentioned in step 5) is complex, there is no closed expression, the cumulative distribution function expression is difficult to be solved, but a 2-order Tracy-Widom cumulative distribution function F is already solvedTW2(x) And its 2 nd derivative F "TW2(x) And tabulating to find F by looking up the tableTW2(x) At xkValue of (A), FTW2(x) Derivative of order 2F "TW2(x) At xkThe value of (b) is calculated as xkTheoretical distribution function F of0(x) At xkValue of F0(xk)。
Step 7), the judgment module obtains a spectrum sensing result:
step 7a) setting the false alarm probability to Pf，0≤PfAnd (3) less than or equal to 1, calculating and judging whether a threshold eta of an authorized user exists:
η＝γ-1(Γ(4)(1-Pf),4)-4
wherein the content of the first and second substances,
for the lower incomplete gamma function, Γ (·) is the complete gamma function;
step 7b) judging whether an authorized user exists by a judgment module:
if the test statistic T is larger than a preset threshold eta, judging as H1That is, the authorized user exists, if the test statistic T is less than the preset threshold eta, the judgment is madeH0I.e. the authorized user does not exist.
The technical effects of the invention are further explained by combining simulation experiments as follows:
1. simulation conditions are as follows: the operating system adopts Intel (R) core (TM) i5-4590 CPU @3.30GHz and 64-bit Windows, the simulation software adopts MATLAB R, and the simulation parameters are set as follows:
the number of transmitting antennas is 1, the number of receiving antennas is 16, the modulation mode of the authorized user signal is QPSK, the propagation channel is Rayleigh channel, and the given false alarm probability PfThe grouping number K is 4, and the influence of the signal-to-noise ratio and the sampling point number on the detection probability of the method and the method of Nadler B and the like under different grouping conditions is simulated and compared;
2. simulation content and result analysis:
referring to fig. 3, the signal-to-noise ratio is increased from-16 dB to 0dB, the detection probability of the method of the present invention is increased from 0.265 to 0.999, the detection probability of the spectral sensing method based on the eigenvalue of the covariance matrix of the received signal proposed by Nadler B et al is increased from 0.241 to 0.999, the detection probabilities of the two methods are close when the signal-to-noise ratio is increased from-2 dB to 0dB, and the detection probability of the method of the present invention is higher than that of the spectral sensing method based on the eigenvalue of the covariance matrix of the received signal proposed by Nadler B et al when the signal-to-noise ratio is less than-2 dB.
Referring to fig. 4, the number of sampling points is increased from 100 to 1000, the detection probability of the method of the present invention is increased from 0.708 to 0.885, and the detection probability of the spectral sensing method based on the eigenvalue of the covariance matrix of the received signal, which is proposed by Nadler B et al, is increased from 0.639 to 0.844, but the detection probability of the method of the present invention is higher than that of the spectral sensing method based on the eigenvalue of the covariance matrix of the received signal, which is proposed by Nadler B et al, under the same number of sampling points.
In summary, two results obtained from two simulation experiments show that, under the same conditions, compared with the spectrum sensing method based on the eigenvalue of the covariance matrix of the received signal, which is proposed by Nadler B et al, the method effectively improves the detection probability.
Claims (4)
1. A frequency spectrum sensing method based on feature value unilateral right tail goodness-of-fit test is characterized by comprising the following steps:
(1) the signal receiving and sampling module samples the received authorized user signal:
the signal receiving and sampling module receives the complex signal of the authorized user and samples the complex signal to obtain a received signal Y with the size of r multiplied by N:
the number of sampling points is N, N is more than or equal to 1, N represents the nth sampling point, N is 1,2, the.
(2) The received signal segmentation module segments the received signal Y:
the received signal segmentation module divides the received signal Y into K sections of signal matrixes, the size of each section of signal matrix is r multiplied by m, m is the number of columns contained in each section of signal matrix, m is more than or equal to 1 and less than or equal to N, and the kth section of signal matrix YkThe expression of (a) is:
yk＝[Y((k-1)m+1),Y((k-1)m+2),...,Y(km)]
wherein K is 1, 2.., K;
(3) the covariance matrix calculation module calculates a signal matrix ykOf the covariance matrix Rk：
Wherein, E [. C]The indication is taken as to what is desired,
representing the Hermite transformation, RkThe size of (a) is r × r;
(4) the eigenvalue decomposition module calculates a covariance matrix RkThe ratio of the maximum eigenvalue to the trace mean of (c):
(4a) eigenvalue decomposition module pair covariance matrix RkDecomposing the eigenvalue to obtain P eigenvalues lambdapWherein P is 1,2,. cndot, P;
(4b) selecting lambda by eigenvalue decomposition modulepMedium maximum eigenvalue lambdakmaxWhile passing through λpCalculation of RkTrace mean tr of:
(4c) the eigenvalue decomposition module calculates the maximum eigenvalue lambdakmaxRatio U to trace mean trk：
(5) The fitting object calculation module calculates a signal matrix ykFitting object x ofk：
Wherein mu is a central parameter,
epsilon is a scaling parameter that is,
when only Gaussian complex noise is present in the received signal, ykIs a Gaussian random matrix, RkIs the Wishart matrix, xkObeying a 2 nd order Tracy-Widom distribution, xkCumulative distribution function F0(x) The expression of (a) is:
wherein, FTW2(x) Is a Tracy-Widom cumulative distribution function, F "TW2(x) Is FTW2(x) 2 derivatives of;
(6) the test statistic construction module calculates a test statistic T:
test statistic construction Module calculates xkTheoretical distribution function F of0(x) At xkValue of F0(xk) And according to the one-sided right-tail fitting goodness test criterion, passing through F0(xk) Calculating a test statistic T:
wherein ln (·) represents a natural logarithmic function;
(7) the judgment module obtains a spectrum sensing result:
(7a) setting false alarm probability to Pf，0≤PfAnd (3) less than or equal to 1, calculating and judging whether a threshold eta of an authorized user exists:
η＝γ-1(Γ(K)(1-Pf),K)-K
wherein the content of the first and second substances,
for the lower incomplete gamma function, Γ (·) is the complete gamma function;
(7b) the judgment module judges whether T is larger than or equal to eta, if yes, an authorized user exists, and if not, the authorized user does not exist.
2. The method for spectrum sensing based on eigenvalue one-sided right-tail goodness-of-fit test of claim 1, wherein the step (6) of calculating xkTheoretical distribution function F of0(x) At xkValue of F0(xk) The calculation formula is as follows:
wherein, FTW2(xk) Is a 2-order Tracy-Widom cumulative distribution function FTW2(x) Table of discrete values at xkValue of (a), F "TW2(xk) Is FTW2(x) Derivative of order 2F "TW2(x) Table of discrete values at xkThe value of (c) is r is the number of receiving antennas, m is the number of columns contained in each segment of matrix after the received signal is segmented, u is the center parameter, and epsilon is the scaling parameter.
3. The utility model provides a spectrum sensing device of unilateral right tail goodness of fit inspection based on eigenvalue, includes signal reception sampling module, covariance matrix calculation module and eigenvalue decomposition module, wherein:
the signal receiving and sampling module is used for receiving and sampling an authorized user signal;
the signal receiving and sampling module receives the complex signal of the authorized user and samples the complex signal to obtain a received signal Y with the size of r multiplied by N:
the number of sampling points is N, N is more than or equal to 1, N represents the nth sampling point, N is 1,2, the.
The covariance matrix calculation module is used for calculating a covariance matrix of a signal matrix generated by the received signal segmentation module;
the covariance matrix calculation module calculates a signal matrix ykOf the covariance matrix Rk：
Wherein, E [. C]The indication is taken as to what is desired,
representing the Hermite transformation, RkThe size of (a) is r × r;
the eigenvalue decomposition module is used for calculating the ratio of the maximum eigenvalue of the covariance matrix generated by the covariance matrix calculation module to the trace mean;
the method is characterized in that:
a received signal segmentation module is connected between the signal receiving sampling module and the covariance matrix calculation module and is used for segmenting the received signals obtained by the signal receiving sampling module;
the output end of the eigenvalue decomposition module is sequentially connected with a fitting object calculation module and a fitting goodness inspection module, wherein:
the fitting object calculation module is used for calculating the fitting object of each section of signal matrix according to the ratio of the maximum eigenvalue to the trace mean value calculated by the eigenvalue decomposition module;
and the goodness-of-fit inspection module is used for acquiring a spectrum sensing result according to the fitting object generated by the fitting object calculation module.
4. The apparatus for spectrum sensing based on eigenvalue one-sided right-tail goodness-of-fit test of claim 3, wherein the goodness-of-fit test module comprises a test statistic construction module and a decision module, wherein:
the test statistic construction module is used for constructing test statistic according to a unilateral right tail fitting goodness test criterion by utilizing the fitting object generated by the fitting object calculation module;
and the judging module is used for judging whether the authorized user exists according to the test statistic generated by the test statistic constructing module to obtain a spectrum sensing result.
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