CN109150339B - Frequency spectrum sensing method and system based on Rayleigh fading channel signal envelope - Google Patents

Frequency spectrum sensing method and system based on Rayleigh fading channel signal envelope Download PDF

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CN109150339B
CN109150339B CN201710512315.8A CN201710512315A CN109150339B CN 109150339 B CN109150339 B CN 109150339B CN 201710512315 A CN201710512315 A CN 201710512315A CN 109150339 B CN109150339 B CN 109150339B
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authorized user
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CN109150339A (en
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周义明
李英顺
刘建东
田小平
张世博
张莉
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Beijing Institute of Petrochemical Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
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    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/382—Monitoring; Testing of propagation channels for resource allocation, admission control or handover
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
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Abstract

The invention relates to the technical field of signal processing, and discloses a frequency spectrum sensing method and system based on Rayleigh fading channel signal envelope so as to further improve the detection performance. The method comprises the following steps: intercepting the signal sampling value into an array with equal length according to integral multiple of carrier period, calculating correlation characteristics in adjacent periods, and constructing an approximate correlation matrix, wherein matrix elements are signal autocorrelation quantity of adjacent spaced sampling periods; then, a statistic is constructed according to the property of the sub-diagonal element of the approximate correlation matrix, and the spectrum of the authorized user is judged to be in a silent state or a working state according to the statistic result. In the invention, the statistic increases the center distance between the detection probability distribution function and the false alarm probability distribution function, improves the convergence rate of the detection probability distribution function, greatly optimizes the detection performance, and has the advantages of no relation with noise and less dependence on signal correlation.

Description

Frequency spectrum sensing method and system based on Rayleigh fading channel signal envelope
Technical Field
The invention relates to the technical field of signal processing, in particular to a frequency spectrum sensing method and system based on Rayleigh fading channel signal envelope.
Background
With the development of wireless communication technology, the access amount of wireless devices is increasing, and the available spectrum resources are extremely scarce. However, the usage rate of some licensed bands (tv bands) is low, which results in a great waste of spectrum, and meanwhile, a large amount of newly developed communication devices can only be crowded in an unlicensed band (ISM) due to the availability of unlicensed bands, which seriously hinders the development of wireless communication technology. The cognitive radio technology realizes flexible management of frequency spectrum resources by opportunistic access of idle frequency spectrum, and has great significance for development of future radio communication technology.
Spectrum sensing is one of the key technologies of cognitive radio, and whether available wireless spectrum exists can be judged only through the sensing technology. The traditional three sensing technologies: matched filter detection, energy detection and cyclostationary detection are first proposed. Through years of research, the method plays an important role in promoting the development of cognitive radio technologies, but the technologies are limited in specific use, so that the detection performance is poor. The matched filtering detection has higher tolerance to prior information of an authorized user, and the actual meaning of the detection technology is not great if no authorized user is matched; energy detection is particularly suitable for sensing a user to perform spectrum sensing as a blind sensing algorithm, but the use of the detection technology firstly estimates the power of superimposed noise, and the energy detection cannot be realized due to a noise wall generated by the instability of the noise power, and the detection performance of a signal with low signal-to-noise ratio is sharply reduced. To overcome these deficiencies, some improved algorithms based on energy detection are also continuously proposed; the cyclostationary detection is provided based on the periodic characteristic of the authorized user signal, the receiving end signal must satisfy the cyclostationary in the broad sense, and the signal and the noise are required to be strictly uncorrelated, and the defects of large data computation amount, long perception time and the like are caused by the need of calculating the cyclostationary spectral density of the receiving signal. In order to overcome the defects of the traditional detection technology, signal period map related detection, eigenvalue detection, covariance matrix detection and the like are successively provided, however, new problems occur, the signal period map related detection solves the problems occurring when the signal-to-noise ratio is low, but partial prior information of signals is needed, and the covariance matrix detection needs stronger correlation of sampled signals.
Disclosure of Invention
The invention aims to disclose a frequency spectrum sensing method and a frequency spectrum sensing system based on Rayleigh fading channel signal envelope so as to further improve the detection performance.
In order to achieve the above object, the present invention discloses a spectrum sensing method based on rayleigh fading channel signal envelope, comprising:
step S1, obtaining the transmitting-end modulation signal propagated through the rayleigh fading channel, to obtain:
Figure BDA0001335504990000021
wherein, L is the number of propagation paths; cnThe nth propagation path amplitude;
Figure BDA0001335504990000022
for receiving signals at tInstantaneous phase of the moment; tau isnDelay time for the nth propagation path; w (t) is additive noise at the receiving end,
Figure BDA0001335504990000023
complex envelope for the transmit baseband signal; f. ofcModulating a carrier frequency; re [. C]Representing a real part;
step S2, based on y (t), a time-varying nonlinear signal with Rayleigh complex envelope is obtained, the envelope waveform is a (t), comprising
Figure RE-GDA0001444122020000024
Let the sampling period be Ts＝1/(Nfc) That is, if the number of samples collected in one carrier period is N, then t is nTsThe sampling signal at the moment is:
Figure BDA0001335504990000025
ignore TsAnd constructing a vector:
Figure BDA0001335504990000026
intercepting the signal sampling value into an array with equal length according to integral multiple of carrier period, calculating the correlation characteristic in adjacent periods, and constructing an approximate correlation matrix as follows:
Figure BDA0001335504990000027
wherein K is an odd number of 3 or more, i is 0 or more and K is j or less,
Figure BDA0001335504990000028
and step S3, constructing statistic according to the sub-diagonal element property of the approximate correlation matrix, and judging whether the frequency spectrum of the authorized user is in a silent state or a working state according to the statistic result.
In order to achieve the above object, the present invention also discloses a spectrum sensing system based on rayleigh fading channel signal envelope, comprising:
the first processing module is used for acquiring the transmitting end modulation signal after being propagated through the rayleigh fading channel, and obtaining:
Figure BDA0001335504990000031
wherein, L is the number of propagation paths; cnThe nth propagation path amplitude;
Figure BDA0001335504990000032
is the instantaneous phase of the received signal at time t; tau isnDelay time for the nth propagation path; w (t) is additive noise at the receiving end,
Figure BDA0001335504990000033
complex envelope for the transmit baseband signal; f. ofcModulating a carrier frequency; re [. C]Representing a real part;
a second processing module for making the envelope waveform a (t) based on y (t) being a time-varying nonlinear signal with Rayleigh complex envelope, having
Figure RE-GDA0001444122020000035
Let the sampling period be Ts＝1/(Nfc) That is, if the number of samples collected in one carrier period is N, then t is nTsThe sampling signal at the moment is:
Figure BDA0001335504990000035
ignore TsAnd constructing a vector:
Figure BDA0001335504990000036
intercepting the signal sampling value into an array with equal length according to integral multiple of carrier period, calculating the correlation characteristic in adjacent periods, and constructing an approximate correlation matrix as follows:
Figure BDA0001335504990000037
wherein K is an odd number of 3 or more, i is 0 or more and K is j or less,
Figure BDA0001335504990000038
and the third processing module is used for constructing statistic according to the property of the sub-diagonal elements of the approximate correlation matrix and judging that the frequency spectrum of the authorized user is in a silent state or a working state according to the statistic result.
Based on the method and system of the present invention, optionally, the constructing statistics according to the secondary diagonal element properties of the approximate correlation matrix, and determining that the spectrum of the authorized user is in the silent state or the working state according to the statistics result specifically includes:
step S31, the spectrum sensing can be equivalent to the following binary assumption problem, including:
Figure BDA0001335504990000041
wherein H0 denotes the silence of the authorized user; h1 denotes authorized user work;
when the authorized user is silent,
Figure BDA0001335504990000042
obtaining: the matrix when H0 is assumed to be true is:
Figure BDA0001335504990000043
when the user is authorized to work with the device,
Figure BDA0001335504990000044
wherein rho is not less than 0ij1 is less than or equal to 1 in the ith 1/fcTime period and jth 1/fcCorrelation coefficient of envelope magnitude in time period, and pij＝ρji(ii) a Obtaining: the matrix when H1 is assumed to be true is:
Figure BDA0001335504990000045
step S32, the frequency change based on the envelope is very weak relative to the carrier frequency, the envelopes of the sending end signal after channel attenuation in the adjacent carrier period have the same correlation coefficient, and the rho is led to beijρ, where | i-j | ═ 1;
step S33, transforming the above-mentioned silence and true approximate correlation matrix in working state to obtain matrix M respectively:
Figure BDA0001335504990000046
and
Figure BDA0001335504990000051
wherein the content of the first and second substances,
Figure BDA0001335504990000052
step S34, taking the sub diagonal element M of the matrix MijAnalysis was performed to construct a statistic T:
Figure BDA0001335504990000053
obtaining: if T>1, authorizing the user to be in a working state; if T is 1, the authorized user is in a silent state.
Optionally, the method and system further include: and setting the false alarm probability of the statistic, and calculating a detection threshold value and a detection probability according to the false alarm probability.
By adopting the technical scheme of the invention, the correlation requirement on the sampling signal is changed to the requirement on the correlation of the signal envelope, and the signal envelope has lower frequency spectrum and stronger correlation on the same sampling signal. In order to improve the detection performance, carrier information of a signal is utilized, a signal sampling value is intercepted into an array with equal length according to integral multiple of a carrier (central frequency spectrum) period, and an approximate correlation matrix based on signal envelope is constructed by only calculating correlation characteristics in adjacent periods. Compared with the traditional correlation matrix, the approximate correlation matrix detection increases the center distance (the expected distance is increased) of the detection probability distribution function and the false alarm probability distribution function and improves the convergence speed (the variance is reduced) of the detection probability distribution function and the false alarm probability distribution function, so that the detection performance of the approximate correlation matrix detection is better for the same false alarm probability, and the detection threshold is only related to the intercepted array quantity and is not related to the system noise. Compared with energy detection, the method has no relation with noise power, so that the problem of incapability of detection due to uncertainty of noise does not occur. Compared with the traditional correlation detection, the method has the advantages that the requirement of signal correlation is lowered, the same false alarm probability constraint is realized, the calculation of the detection threshold is simplified, and the detection performance is greatly improved.
Detailed Description
The present invention will be described in further detail below in order to enable those skilled in the art to better understand the technical solution of the present invention.
Example 1
The embodiment discloses a spectrum sensing method based on Rayleigh fading channel signal envelope.
The method is provided with a transmitting end modulation signal:
Figure BDA0001335504990000061
wherein the content of the first and second substances,
Figure BDA0001335504990000062
complex envelope for the transmit baseband signal; f. ofcModulating a carrier frequency; re [. C]The representation takes the real part.
After propagation through the rayleigh fading channel, at the receiving end:
Figure BDA0001335504990000063
wherein, L is the number of propagation paths; cnThe nth propagation path amplitude;
Figure BDA0001335504990000064
is the instantaneous phase of the received signal at time t; tau isnDelay time for the nth propagation path; w (t) is the additive noise at the receiving end.
It is easy to know that y (t) is a time-varying nonlinear signal with complex envelope being rayleigh distribution, and let the envelope waveform be a (t) as follows:
Figure BDA0001335504990000065
wherein a (t) obeys Rayleigh distribution, and the envelope average power is 2 deltaa 2The corresponding probability density function is:
Figure BDA0001335504990000066
Figure BDA0001335504990000067
the uniform distribution is satisfied, and the corresponding probability density function is:
Figure BDA0001335504990000068
and a (t) and
Figure BDA0001335504990000069
are independent of each other.
Thus, spectrum sensing can be equivalent to the following binary assumption problem:
Figure BDA00013355049900000610
h0 denotes the silence of the authorized user; h1 denotes an authorized user working.
Let the sampling period be Ts＝1/(Nfc) I.e. the number of samples collected in a carrier period isN, then at t ═ nTsThe sampling signal at the moment is:
Figure BDA00013355049900000611
ignore TsLet us order
Figure BDA0001335504990000071
Defining K as an odd number greater than or equal to 3, and constructing an approximate correlation matrix as:
Figure BDA0001335504990000072
Figure BDA0001335504990000073
where 0 ≦ i, j ≦ K, E is the expectation in statistics. In the matrix shown in formula (9), the distribution characteristics are: the diagonal line is the autocorrelation quantity of the sampling signal; the elements in the same row are consistent from the diagonal line to the left and are all related quantity of the sampling period corresponding to the elements in the diagonal line and the previous period; and taking the diagonal line to the right and the elements in the same row are not consistent, starting with the sampling period corresponding to the elements in the diagonal line, solving the signal correlation quantity of two adjacent sampling periods one by one according to the sampling sequence, and sequentially arranging the obtained results on the right side of the diagonal line elements corresponding to the row in the approximate correlation matrix.
1. When the authorized user is silent:
Figure BDA0001335504990000074
Figure BDA0001335504990000075
for noise power, there is a matrix when H0 is assumed to be true:
Figure BDA0001335504990000076
2. when the authorized user is working:
Figure BDA0001335504990000077
wherein rho is not less than 0ij1 is less than or equal to 1 in the ith 1/fcTime period and jth 1/fcNumber of correlations of the envelope amplitudes within the time period, and pij＝ρji. The matrix with the assumption that H1 is true is:
Figure BDA0001335504990000081
further observation shows that both matrices are symmetric matrices, and the main diagonal elements of the matrices satisfy formula (15):
Figure BDA0001335504990000082
then one can define M (M) of K if H0 is trueij) The matrix is:
Figure BDA0001335504990000083
for the case that H1 is true, further analysis shows that the frequency variation of the envelope varies very weakly with respect to the carrier frequency, so that the envelopes of the transmitting-end signal after channel attenuation in adjacent carrier periods can be considered to have the same correlation coefficient, and ρ can be made to beijρ (where | i-j | ═ 1). Obtaining:
Figure BDA0001335504990000084
wherein the content of the first and second substances,
Figure BDA0001335504990000085
and (3) taking the sub diagonal elements of the matrix M for analysis, and constructing a statistic T:
Figure BDA0001335504990000086
since K is an odd number, ideally: if T is greater than 1, the authorized user is in a working state; if T is 1, the authorized user is in a silent state.
As is apparent from the theorem of majorities, the statistic T follows a normal distribution. The performance analysis for statistic T is as follows:
1. when the authorized user is in the silent state, there are:
a1, mean value:
Figure BDA0001335504990000091
b1, variance:
Figure BDA0001335504990000092
2. when the authorized user is in the working state, the statistic T is as follows:
a2, mean value:
Figure BDA0001335504990000093
b2, variance:
Figure BDA0001335504990000094
then under two assumptions, the probability density function for the statistic T is:
Figure BDA0001335504990000095
Figure BDA0001335504990000096
in practical situations, the noise signal is not completely white noise because the number of sampling points is not infinite. Setting the detection threshold value as eta, then there is a detection probability P of statistic T according to Bayesian ruleD|TAnd false alarm probability PFA|TComprises the following steps:
Figure BDA0001335504990000097
Figure BDA0001335504990000098
wherein:
Figure BDA0001335504990000099
in spectrum sensing, a false alarm probability P needs to be assumedFA|TMaking the detection probability P under the constraint of alphaD|TAnd max. According to the Neyman-Pearson criterion, the detection threshold values can be obtained as follows:
η＝2ε0 2Q-1(α)+μ0 (25)
there is therefore a probability of detection:
Figure BDA0001335504990000101
in summary, the spectrum sensing method based on the rayleigh fading channel signal envelope in the embodiment of the present invention can be further summarized as the following steps:
(1) determining N, K and false alarm probability alpha;
(2) constructing a vector Y (i) from the sampled values y (n);
(3) calculating r from equation (10)ijTo construct a matrix
Figure BDA0001335504990000103
(4) To matrix
Figure BDA0001335504990000102
All elements are divided by the value of the main diagonal element to construct the matrix M (M)ij)；
(5) And a structural statistic T, and calculating μ from equations (19) to (20)0,ε0 2,μ1,ε1 2Obtaining a probability density function (21) of the statistic T1;
(6) calculating a detection threshold value eta by the formula (25);
(7) calculating a detection probability P from the formula (26)D|T。
In this embodiment, further, to verify the performance of the statistics, the spectrum sensing algorithm of the envelope matrix is simulated under different parameter conditions.
Simulating one, setting correlation coefficient rho of received signal enveloped in adjacent carrier wave period as 0.9, false alarm probability PFA|TThe detection probability obtained under different limiting conditions is known from simulation results, the influence of the envelope noise power on the detection probability is larger, and the signal-to-noise ratio is improved, so that the detection performance can be greatly improved. If the false alarm probability is limited to PFA|T0.1, when γ is 0.01(-40dB), PD|TWhen the value is 0.3, the detection performance is obviously extremely low; when γ is 0.2(-14dB), PD|TAnd (0.96) to completely meet the requirement of detection performance. If the algorithm only analyzes the envelope power of the sampling signal theoretically, the envelope noise power ratio is likely to be further improved and the performance is also greatly improved due to the fact that the sampling signal contains the carrier power in actual use.
And simulating two, and assuming that gamma is 0.1(-20dB), wherein the influence of the correlation coefficient of the sampling signal on the detection performance is influenced. According to the simulation result, the following results are obtained: the stronger signal correlation performance greatly improves the detection performance, and therefore, the signal correlation can be improved by increasing the sampling frequency, but the requirement of sampling equipment is increased and the calculation amount is increased.
Simulation three, limit PFA|TAnd when the envelope noise power ratio is 0.1, the envelope noise power ratio corresponds to the detection probability. According to the simulation result, the following results are obtained: when the signal envelope noise power is lower, the influence of the correlation coefficient on the detection performance is limited, and with the increase of the signal envelope noise power ratio, the signal with the larger correlation coefficient (more dense sampling) can quickly improve the detection performance, but when rho is lower>At 0.9, the improvement of the detection performance is not remarkable, and therefore it is not preferable to improve the detection performance by increasing the sampling rate without limitation.
It should be noted that, in this embodiment, the process of proving the formula (13) is as follows:
Figure BDA0001335504990000111
because a (t) and
Figure BDA0001335504990000112
are independent of each other, and
Figure BDA0001335504990000117
satisfy [ -pi, pi [ -pi [ ]]Evenly distributed, having:
Figure BDA0001335504990000113
then there are:
Figure BDA0001335504990000114
when i is not equal to j, the envelope spectrum of the received signal is lower, and the correlation is larger (rho is more than or equal to 0)ij1) and additive white noise is uncorrelated, thus:
Figure BDA0001335504990000115
when i ═ j, the received signal envelope follows the following exponential distribution with a probability density of:
Figure BDA0001335504990000116
then there are:
Figure BDA0001335504990000121
and the following steps:
Figure BDA0001335504990000122
namely, the method comprises the following steps:
Figure BDA0001335504990000123
in summary, the spectrum sensing method based on rayleigh fading channel signal envelope disclosed in this embodiment switches the correlation requirement for the sampled signal to the requirement for the signal envelope correlation, and because the signal envelope has a lower spectrum, there is a stronger correlation for the same sampled signal. In order to improve the detection performance, carrier information of a signal is utilized, a signal sampling value is intercepted into an array with equal length according to integral multiple of a carrier (central frequency spectrum) period, and an approximate correlation matrix based on signal envelope is constructed by only calculating correlation characteristics in adjacent periods. Compared with the traditional correlation matrix, the approximate correlation matrix detection increases the center distance (expected distance is increased) between the detection probability distribution function and the false alarm probability distribution function and improves the convergence speed (variance is reduced) of the detection probability distribution function and the false alarm probability distribution function, so that the detection performance of the approximate correlation matrix detection is better for the same false alarm probability, and the detection threshold is only related to the intercepted array quantity and is not related to the system noise. Compared with energy detection, the method has no relation with noise power, so that the problem that the detection cannot be carried out due to uncertainty of noise does not occur. Compared with the traditional correlation detection, the method has the advantages that the requirement of signal correlation is lowered, the same false alarm probability constraint is realized, the calculation of the detection threshold is simplified, and the detection performance is greatly improved.
Example 2
Corresponding to the above method embodiments, this embodiment discloses a spectrum sensing system based on rayleigh fading channel signal envelope, including:
the first processing module is used for acquiring the transmitting end modulation signal after being propagated through the rayleigh fading channel, and obtaining:
Figure BDA0001335504990000124
wherein, L is the number of propagation paths; cnThe nth propagation path amplitude;
Figure BDA0001335504990000125
is the instantaneous phase of the received signal at time t; tau isnDelay time for the nth propagation path; w (t) is additive noise at the receiving end,
Figure BDA0001335504990000126
complex envelope for the transmit baseband signal; f. ofcModulating a carrier frequency; re [. C]Representing a real part;
a second processing module for making the envelope waveform a (t) based on y (t) being a time-varying nonlinear signal with Rayleigh complex envelope, having
Figure RE-GDA0001444122020000134
Let the sampling period be Ts＝1/(Nfc) That is, if the number of samples collected in one carrier period is N, then t is nTsThe sampling signal at the moment is:
Figure BDA0001335504990000132
ignore TsAnd constructing a vector:
Figure BDA0001335504990000133
intercepting the signal sampling value into an array with equal length according to integral multiple of carrier period, calculating the correlation characteristic in adjacent periods, and constructing an approximate correlation matrix as follows:
Figure BDA0001335504990000134
wherein K is an odd number of 3 or more, i is 0 or more and K is j or less,
Figure BDA0001335504990000135
and the third processing module is used for constructing statistic according to the property of the sub-diagonal elements of the approximate correlation matrix and judging that the frequency spectrum of the authorized user is in a silent state or a working state according to the statistic result.
Optionally, the third processing module further includes:
the first submodule is used for equating the spectrum sensing as a binary hypothesis problem which comprises the following steps:
Figure BDA0001335504990000136
wherein H0 denotes the silence of the authorized user; h1 denotes authorized user work;
when the authorized user is silent,
Figure BDA0001335504990000137
obtaining: the matrix when H0 is assumed to be true is:
Figure BDA0001335504990000138
when the user is authorized to work with the device,
Figure BDA0001335504990000139
wherein rho is not less than 0ij1 is less than or equal to 1 in the ith 1/fcTime period and jth 1/fcCorrelation coefficient of envelope magnitude in time period, and pij＝ρji(ii) a Obtaining: the matrix when H1 is assumed to be true is:
Figure BDA0001335504990000141
and the second submodule is used for enabling the envelope of the signal at the transmitting end after channel attenuation in adjacent carrier periods to have the same correlation coefficient based on the extremely weak change of the frequency change of the envelope relative to the carrier frequency to enable rhoijρ, where | i-j | ═ 1;
and a third submodule for transforming the said silence and true approximate correlation matrix under working state to obtain matrix M:
Figure BDA0001335504990000142
and
Figure BDA0001335504990000143
wherein the content of the first and second substances,
Figure BDA0001335504990000144
submodule four for taking sub diagonal element M of matrix MijAnalysis was performed to construct a statistic T:
Figure BDA0001335504990000145
obtaining: if T>1, authorizing the user to be in a working state; if T is 1, the authorized user is in a silent state.
Optionally, the system of this embodiment further includes:
and the fourth processing module is used for setting the false alarm probability of the statistic and calculating a detection threshold value and a detection probability according to the false alarm probability.
Similarly, the spectrum sensing system based on the rayleigh fading channel signal envelope disclosed in this embodiment switches the correlation requirement on the sampled signal to the requirement on the signal envelope correlation, and has stronger correlation on the same sampled signal because the signal envelope has a lower spectrum. In order to improve the detection performance, carrier information of a signal is utilized, a signal sampling value is intercepted into an array with equal length according to integral multiple of a carrier (central frequency spectrum) period, and an approximate correlation matrix based on signal envelope is constructed by only calculating correlation characteristics in adjacent periods. Compared with the traditional correlation matrix, the approximate correlation matrix detection increases the center distance (expected distance is increased) between the detection probability distribution function and the false alarm probability distribution function and improves the convergence speed (variance is reduced) of the detection probability distribution function and the false alarm probability distribution function, so that the detection performance of the approximate correlation matrix detection is better for the same false alarm probability, and the detection threshold is only related to the intercepted array quantity and is not related to the system noise. Compared with energy detection, the method has no relation with noise power, so that the problem that the detection cannot be carried out due to uncertainty of noise does not occur. Compared with the traditional correlation detection, the method has the advantages that the requirement of signal correlation is lowered, the same false alarm probability constraint is realized, the calculation of the detection threshold is simplified, and the detection performance is greatly improved.
While certain exemplary embodiments of the present invention have been described above by way of illustration only, it will be apparent to those of ordinary skill in the art that the described embodiments may be modified in various different ways without departing from the spirit and scope of the invention. Accordingly, the foregoing description is illustrative in nature and is not to be construed as limiting the scope of the invention as claimed.

Claims (6)

1. A method for spectrum sensing based on a rayleigh attenuated channel signal envelope, comprising:
step S1, obtaining the transmitting-end modulation signal propagated through the rayleigh fading channel, to obtain:
Figure FDA0003037213870000011
wherein, L is the number of propagation paths; cnThe nth propagation path amplitude;
Figure FDA0003037213870000012
is the instantaneous phase of the received signal at time t; tau isnFor the nth passA propagation path delay time; w (t) is additive noise of a receiving end, and s (t) is complex envelope of a transmitting baseband signal; f. ofcModulating a carrier frequency; re [. C]The representation is taken in the real part,
Figure FDA0003037213870000013
representing the phase at time t;
step S2, based on y (t), a time-varying nonlinear signal with Rayleigh complex envelope is obtained, the envelope waveform is a (t), comprising
Figure FDA0003037213870000014
Wherein
Figure FDA0003037213870000015
Let the sampling period be Ts＝1/(Nfc) That is, if the number of samples collected in one carrier period is N, then t is nTsThe sampling signal at the moment is:
Figure FDA0003037213870000016
ignore TsAnd constructing a vector:
Figure FDA0003037213870000017
wherein Y (i) is at t ═ nTsIn the sampling signals starting from the moment, a vector is formed by N sampling values in the ith carrier period;
a (i) is at t ═ nTsIn the sampling signals starting at the moment, vectors are formed by the amplitudes of the trigonometric functions corresponding to N sampling values in the ith carrier wave period;
w (i) is at t ═ nTsIn the sampling signal starting from the moment, a vector is formed by white noise values superposed in N sampling values in the ith carrier period;
intercepting the signal sampling value into an array with equal length according to integral multiple of carrier period, calculating the correlation characteristic in adjacent periods, and constructing an approximate correlation matrix as follows:
Figure FDA0003037213870000021
wherein K is an odd number of 3 or more, i is 0 or more and K is j or less,
Figure FDA0003037213870000022
wherein, k takes the value of 0 to (N-1) and is the serial number of the sampling signal in the ith or jth carrier cycle;
and step S3, constructing statistic according to the sub-diagonal element property of the approximate correlation matrix, and judging whether the frequency spectrum of the authorized user is in a silent state or a working state according to the statistic result.
2. The method for sensing frequency spectrum based on rayleigh attenuated channel signal envelope according to claim 1, wherein the step S3 includes:
step S31, the spectrum sensing can be equivalent to the following binary assumption problem, including:
Figure FDA0003037213870000023
wherein H0 denotes the silence of the authorized user; h1 denotes authorized user work;
when the authorized user is silent,
Figure FDA0003037213870000024
obtaining: the matrix when H0 is assumed to be true is:
Figure FDA0003037213870000025
when the user is authorized to work with the device,
Figure FDA0003037213870000026
wherein rho is not less than 0ij1 is less than or equal to 1 in the ith 1/fcTime period and jth 1/fcCorrelation coefficient of envelope magnitude in time period, and pij＝ρji，
Figure FDA0003037213870000027
Represents the phase at time t;
obtaining: the matrix when H1 is assumed to be true is:
Figure FDA0003037213870000031
Figure FDA0003037213870000037
when the authorized user works, the transmitting power of the authorized user contained in the acquisition signal at the receiving end;
Figure FDA0003037213870000032
the noise power of additive white noise contained in the collected signal at the receiving end;
step S32, the frequency change based on the envelope is very weak relative to the carrier frequency, the envelopes of the sending end signal after channel attenuation in the adjacent carrier period have the same correlation coefficient, and the rho is enabled to beijρ, where | i-j | ═ 1;
step S33, transforming the above-mentioned silence and true approximate correlation matrix in working state to obtain matrix M respectively:
Figure FDA0003037213870000033
and
Figure FDA0003037213870000034
wherein the content of the first and second substances,
Figure FDA0003037213870000035
step S34, taking the sub diagonal element M of the matrix MijAnalysis was performed to construct a statistic T:
Figure FDA0003037213870000036
obtaining: if T>1, authorizing the user to be in a working state; if T is 1, the authorized user is in a silent state.
3. The method for sensing spectrum based on rayleigh attenuated channel signal envelope according to claim 1 or 2, further comprising:
and setting the false alarm probability of the statistic, and calculating a detection threshold value and a detection probability according to the false alarm probability.
4. A system for spectrum sensing based on a rayleigh attenuated channel signal envelope, comprising:
the first processing module is used for acquiring the transmitting end modulation signal after being propagated through the rayleigh fading channel, and obtaining:
Figure FDA0003037213870000041
wherein, L is the number of propagation paths; cnThe nth propagation path amplitude;
Figure FDA0003037213870000042
is the instantaneous phase of the received signal at time t; tau isnDelay time for the nth propagation path; w (t) is additive noise of a receiving end, and s (t) is complex envelope of a transmitting baseband signal; f. ofcModulating a carrier frequency; re [. C]The representation is taken in the real part,
Figure FDA0003037213870000043
representing the phase at time t;
a second processing module for making the envelope waveform a (t) based on y (t) being a time-varying nonlinear signal with Rayleigh complex envelope, having
Figure FDA0003037213870000044
Wherein
Figure FDA0003037213870000045
Let the sampling period be Ts＝1/(Nfc) That is, if the number of samples collected in one carrier period is N, then t is nTsThe sampling signal at the moment is:
Figure FDA0003037213870000046
ignore TsAnd constructing a vector:
Figure FDA0003037213870000047
wherein Y (i) is at t ═ nTsIn the sampling signals starting from the moment, a vector is formed by N sampling values in the ith carrier period;
a (i) is at t ═ nTsIn the sampling signals starting at the moment, vectors are formed by the amplitudes of the trigonometric functions corresponding to N sampling values in the ith carrier wave period;
w (i) is at t ═ nTsIn the sampling signal starting from the moment, a vector is formed by white noise values superposed in N sampling values in the ith carrier period;
intercepting the signal sampling value into an array with equal length according to integral multiple of carrier period, calculating the correlation characteristic in adjacent periods, and constructing an approximate correlation matrix as follows:
Figure FDA0003037213870000051
wherein K is an odd number of 3 or more, i is 0 or more and K is j or less,
Figure FDA0003037213870000052
and the third processing module is used for constructing statistic according to the property of the sub-diagonal elements of the approximate correlation matrix and judging that the frequency spectrum of the authorized user is in a silent state or a working state according to the statistic result.
5. The system according to claim 4, wherein the third processing module comprises:
the first submodule is used for equating the spectrum sensing as a binary hypothesis problem which comprises the following steps:
Figure FDA0003037213870000053
wherein H0 denotes the silence of the authorized user; h1 denotes authorized user work;
when the authorized user is silent,
Figure FDA0003037213870000054
obtaining: the matrix when H0 is assumed to be true is:
Figure FDA0003037213870000055
when the user is authorized to work with the device,
Figure FDA0003037213870000056
wherein rho is not less than 0ij1 is less than or equal to 1 in the ith 1/fcTime period and jth 1/fcCorrelation coefficient of envelope magnitude in time period, and pij＝ρji(ii) a Obtaining: the matrix when H1 is assumed to be true is:
Figure FDA0003037213870000057
Figure FDA0003037213870000058
when the authorized user works, the transmitting power of the authorized user contained in the acquisition signal at the receiving end;
Figure FDA0003037213870000059
the noise power of additive white noise contained in the collected signal at the receiving end;
and the second submodule is used for enabling the envelope of the signal at the transmitting end after channel attenuation in the adjacent carrier period to have the same correlation coefficient based on the extremely weak change of the frequency change of the envelope relative to the carrier frequency to enable rhoijρ, where | i-j | ═ 1,
Figure FDA0003037213870000061
representing the phase at time t;
and a third submodule for transforming the said silence and true approximate correlation matrix under working state to obtain matrix M:
Figure FDA0003037213870000062
and
Figure FDA0003037213870000063
wherein the content of the first and second substances,
Figure FDA0003037213870000064
submodule four for taking sub diagonal element M of matrix MijAnalysis was performed to construct a statistic T:
Figure FDA0003037213870000065
obtaining: if T>1, authorizing the user to be in a working state; if T is 1, the authorized user is in a silent state.
6. The system for spectrum sensing based on rayleigh attenuated channel signal envelopes of claim 4 or 5, further comprising:
and the fourth processing module is used for setting the false alarm probability of the statistic and calculating a detection threshold value and a detection probability according to the false alarm probability.
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