CN110830130A - Statistical frequency spectrum detection method in cognitive radio - Google Patents

Statistical frequency spectrum detection method in cognitive radio Download PDF

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CN110830130A
CN110830130A CN201911108502.5A CN201911108502A CN110830130A CN 110830130 A CN110830130 A CN 110830130A CN 201911108502 A CN201911108502 A CN 201911108502A CN 110830130 A CN110830130 A CN 110830130A
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李怡
李立
杨渭清
高寅生
张岩
马原原
徐阳扬
陈明
杨科锋
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Xian University
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Abstract

The invention discloses a statistical frequency spectrum detection method in cognitive radio, which comprises the following steps: setting an integral operation model; cumulative distribution function z from known experience of elements of received signal YiIn ascending order to obtain
Figure RE-DDA0002349729550000012
By passing
Figure RE-DDA0002349729550000011
Calculating a function ρ of a known empirical cumulative distribution function CDF(i)Then calculating to obtain vector rho, and arranging the elements of the vector rho in ascending order to obtain vector
Figure RE-DDA0002349729550000013
Calculating test statistic Ts(ii) a Given false alarm rate PfaCalculating a corresponding check threshold lambdasJudging the test statistic TsAnd λsTo determine whether a primary user is present. The statistical spectrum detection method in cognitive radio realizes spectrum sensing by utilizing the sequential quantile of the received signal samples, can robustly sense the occupation condition of a channel in real time, and verifies the performance of the channel through Monte Carlo simulation.

Description

Statistical frequency spectrum detection method in cognitive radio
Technical Field
The invention belongs to the technical field of frequency spectrum detection methods, and particularly relates to a statistical frequency spectrum detection method in cognitive radio.
Background
In a cognitive radio system, an important function of a secondary user is to detect whether a primary user occupies a channel, so that the secondary user accesses the channel without causing interference. Therefore, designing fast and accurate spectrum detection algorithms at low signal-to-noise ratios (SNRs) is a challenging task.
There have been many documents that propose many spectrum detection algorithms, and the main methods for performing spectrum detection using the prior knowledge of the primary user include: cyclostationary spectrum detection, matched filter detection and eigenvalue based spectrum detection. However, this method requires some parameters of the primary user transmission signal to be estimated, and if the required parameters are not accurately estimated, the detection performance is degraded. Such as: the cyclostationary frequency spectrum detection method requires a known modulation mode of a signal transmitted by a master user, and has long required sample time and high calculation complexity; a matched filter detection method which can maximize a signal-to-noise ratio (SNR) requires phase synchronization and information such as a modulation mode and a waveform of a known signal, and a matched filter is specially designed for each special signal, so that the method is difficult to realize in practice; the spectrum detection method based on the characteristic value needs a larger number of signal samples to achieve better detection performance, which results in longer detection time and cannot ensure real-time spectrum detection.
In practice, the signal structure and information of the master user cannot be known by the receiving end of the cognitive radio, so that an Energy (ED) detection method which does not need any prior information of the master user is widely applied. The ED detection method performs spectrum detection based on the difference between the energy of the transmitted signal and the interference noise, however, when the signal-to-noise ratio (SNR) is low, the difference between the signal energy and the noise is too small to distinguish the signal or the noise, which causes the detection performance of the ED detection method to be drastically degraded under the low signal-to-noise ratio (SNR).
Disclosure of Invention
The invention aims to provide a statistical frequency spectrum detection method in cognitive radio, which solves the problem that the detection result is inaccurate under the conditions of low signal-to-noise ratio and small samples in the existing detection method.
The technical scheme adopted by the invention is that a statistical frequency spectrum detection method in cognitive radio comprises the following steps:
step 1, establishing a model:
assuming that only one primary user and one secondary user use an AWGN channel, and no interference exists around the primary user and the secondary user; the baseband signal sampling point sequence collected by the secondary user from the cognitive channel is a complex sequence, but the real part and the imaginary part can be respectively detected, and the real part or the imaginary part in the complex sequence of the secondary user can be expressed as formula (1):
in the formula (1), the parameter yiRepresents the ith sample point in the complex sequence, the parameter h represents the receiving signal-to-noise ratio SNR, and the parameter m represents the main useSignals transmitted by the user, parameter wiThe ith sample of the real part Gaussian white noise of the zero mean and the unit variance is represented, and the parameter N represents the total number of sampling points obtained by sampling;
then the spectrum detection in the cognitive radio system under AWGN channel is represented as the following binary hypothesis testing model, as formula (2):
Figure BDA0002272029510000022
in the formula (2), the parameter H0Indicating that a primary user signal is absent; parameter H1Indicating the existence of a primary user signal; at H0In the case, the received signal is only white gaussian noise; at H1Under the condition, the received signal is a mixture of Gaussian white noise and a main user signal;
let Fn(Y) represents the empirical cumulative distribution function CDF of the received signal Y, as given by equation (3):
in formula (3), when the primary user does not transmit a signal, the received signal is gaussian white noise, and its sample Y0Cumulative distribution function F0(y) is the formula (4),
Figure BDA0002272029510000032
when a main user transmits signals, the sample Y is different due to different modulation modes and channel characteristics1,Y2,...Yi,YnNot likely to be from the same cumulative distribution function F0(y), the binary hypothesis test model in equation (2) can be expressed as:
Figure BDA0002272029510000033
step 2, accumulating the distribution function CDF according to the known experience of the elements of the received signal Y in step 1, namely ziIn ascending orderTo obtain
Figure BDA0002272029510000034
By the result of
Figure BDA0002272029510000035
Calculating a function ρ of a known empirical cumulative distribution function CDF(i)；
Step 3, obtaining a function rho according to the step 2(i)Calculating to obtain a vector rho, and arranging the elements of the vector rho in an ascending order to obtain a vector
Figure BDA0002272029510000036
Calculating a test statistic T according to equation (13)s；
Step 4, giving false alarm rate PfaCalculating a corresponding check threshold lambdas；
Step 5, judging the test statistic TsAnd a check threshold lambdasTo determine the presence of a primary user, when checking for a statistic TsIs greater than the check threshold lambdasAnd if not, the channel is considered to be idle.
The present invention is also characterized in that,
the specific steps of the step 2 are as follows:
step 2.1, calculate the known empirical cumulative distribution function CDF, function z, corresponding to the elements of the received signal Yi，
zi＝F0(yi),i∈S (6)
The parameter S in the formula (6) is a sample space;
step 2.2, function z in step 2.1iIn ascending order of magnitude, the function will be defined as z:
z＝[z1,z2,...,zN]T(7)
the elements of z are sorted in ascending order of magnitude and are recorded as:
Figure BDA0002272029510000041
wherein
Figure BDA0002272029510000042
Is a vector obtained by arranging z in ascending order;
step 2.3, the product obtained in step 2.2
Figure BDA0002272029510000043
Is passed through a beta function ziThe transformation yields equation (10):
ρi＝β(z(i)；i,N-i+1),i∈S (10)
β (z) in equation (10)(i)α, γ) represents beta CDF, where α, γ is the shape parameter of the distribution, and, at the same time, defines:
ρ＝[ρ1,ρ2,...,ρN]T(11)
when α is equal to i and γ is equal to N-i +1, ρ is partially integratediCan be simplified as follows:
Figure BDA0002272029510000044
in the formula (12), the parameter j represents a subscript, and j ═ i, i + 1.
Checking statistic T in step 3sThe expression of (a) is:
in formula (13), the parameter n represents the sample size.
False alarm rate P in step 3faAnd a check threshold λsSatisfies formula (14):
Pfa＝P{Ts＞λs|H0} (14)
wherein the check threshold lambdasCan be represented by P { Ts＞λs|H0α ', found α' as a level of significance, where the detection probability can be expressed as:
Pd＝P{Ts＞λs|H1}＝1-P{Ts≤λs|H1} (15)。
check threshold lambdasThe value range of (A): lambda is more than or equal to 9.1s≤195.4。
The invention has the beneficial effects that: the statistical spectrum detection method in cognitive radio realizes spectrum sensing by utilizing the sequential quantile of the received signal samples, can robustly sense the occupation condition of a channel in real time, and verifies the performance of the channel through Monte Carlo simulation.
Drawings
Fig. 1 is a graph of the detection probability under AWGN channel under different false alarm rates of N-30 in the embodiment of the statistical spectrum detection method of the present invention;
fig. 2 is a graph of detection probability under different signal-to-noise ratios for AWGN channel, where N is 30, false alarm rate is 0.1, in an embodiment of the statistical spectrum detection method of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a statistical spectrum detection method in cognitive radio, which realizes blind detection of a spectrum by utilizing sequential quantiles of received signal samples collected in a cognitive channel. The detection method is based on goodness of fit inspection, and the detection principle is as follows: if the channel is not occupied by the primary user, the sample sequence obtained by the secondary user through sampling in the cognitive radio channel is considered to be a Gaussian white noise sequence; if the master user occupies the channel, the obtained sample sequence is a result of superposition of the master user signal and Gaussian white noise, and the distribution of the sample point values does not conform to Gaussian distribution; therefore, whether the channel is occupied or not can be judged by checking whether the samples of the received signals obey Gaussian distribution or not, any prior knowledge of a master user is not needed, only a small segment of samples of the noise sequence is needed, and the influence of inaccurate parameter estimation on the detection performance is overcome.
The invention discloses a statistical frequency spectrum detection method in cognitive radio, which comprises the following steps:
step 1, model building
It is assumed that there is only one primary user and one secondary user, an AWGN channel (additive white gaussian noise channel) is used, and there is no interference around the primary user and the secondary user;
the baseband signal sampling point sequence collected by the secondary user from the cognitive channel is a complex sequence, but the real part and the imaginary part can be respectively detected, and the real part or the imaginary part in the complex sequence of the secondary user can be expressed as formula (1):
Figure BDA0002272029510000061
in the formula (1), the parameter yiRepresenting the ith sample point in the complex sequence, a parameter h representing the received signal-to-noise ratio (SNR), a parameter m representing the transmitted signal of a master user, and a parameter wiThe ith sample of the real part Gaussian white noise of the zero mean and the unit variance is represented, and the parameter N represents the total number of sampling points obtained by sampling;
then the spectrum detection in the cognitive radio system under AWGN channel is represented as the following binary hypothesis testing model, as formula (2):
Figure BDA0002272029510000062
in the formula (2), the parameter H0Indicating that a primary user signal is absent; parameter H1Indicating the existence of a primary user signal; at H0In the case, the received signal is only white gaussian noise; at H1Under the condition, the received signal is a mixture of Gaussian white noise and a main user signal;
let Fn(Y) represents the empirical Cumulative Distribution Function (CDF) of the received signal Y, as given by equation (3):
in formula (3), when the primary userThe received signal is white Gaussian noise when no signal is transmitted, and its sample Y0Cumulative distribution function F0(y) is the formula (4),
Figure BDA0002272029510000071
when a main user transmits signals, the sample Y is different due to different modulation modes and channel characteristics1,Y2,…Yi,YnNot likely to be from the same cumulative distribution function F0(y), the binary hypothesis test model in equation (2) can be expressed as:
assuming that the primary user signal is zero-mean cyclostationary, i.e., the received signal may be assumed to be ergodic, the statistics of the probability space may be replaced by the statistics of the time series. Based on goodness-of-fit inspection, the invention utilizes the high sensitivity of the sequential quantiles of the signal sampling points under low SNR and adopts the sequential quantiles of the signal sampling points to realize hypothesis inspection; any prior information of a master user is not needed, the defect that the detection performance of the ED detection method is not ideal under low SNR is overcome, and compared with the characteristic value detection method, the number of samples required by detection is small, and the rapid detection can be realized.
Step 2, calculating the function rho of the known empirical Cumulative Distribution Function (CDF) in the step 1(i)The method specifically comprises the following steps:
step 2.1, calculating the CDF of the known empirical cumulative distribution function corresponding to the elements of the received signal Y, i.e. the function zi，
zi＝F0(yi),i∈S (6)
The parameter S in the formula (6) is a sample space;
step 2.2, function z in step 2.1iIn ascending order of magnitude, the function will be defined as z:
z＝[z1,z2,…,zN]T(7)
arranging the elements of z in ascending order of magnitude:
z(1)≤z(2)≤…≤z(N)(8)
is recorded as:
Figure BDA0002272029510000081
wherein
Figure BDA0002272029510000082
Is a vector obtained by arranging z in ascending order;
step 2.3, the product obtained in step 2.2
Figure BDA0002272029510000083
Is passed through a beta function ziThe transformation yields equation (10):
ρi＝β(z(i)；i,N-i+1),i∈S (10)
β (z) in equation (10)(i)α, γ) represents beta CDF, where α, γ is the shape parameter of the distribution, and, at the same time, defines:
ρ＝[ρ1,ρ2,…,ρN]T(11)
when α is equal to i and γ is equal to N-i +1, ρ is partially integratediCan be simplified as follows:
Figure BDA0002272029510000084
in the formula (12), the parameter j represents a subscript, and j is equal to i, i +1, …, N;
step 3, obtaining a function rho according to the step 2(i)Calculating to obtain a vector rho, and arranging the elements of the vector rho in an ascending order to obtain a vector
Figure BDA0002272029510000085
Calculating a test statistic T according to equation (13)s；
Figure BDA0002272029510000086
In the formula (13), the parameter n represents the sample capacity,
test statistic TsSmaller values of (d) mean closer to the known noise profile;
step 4, giving false alarm rate PfaCalculating a corresponding check threshold lambdasWherein the false alarm rate PfaAnd a check threshold λsSatisfies formula (14):
Pfa＝P{Ts＞λs|H0} (14)
wherein the check threshold lambdasCan be represented by P { Ts＞λs|H0α ', found α' as a level of significance, where the detection probability can be expressed as:
Pd＝P{Ts＞λs|H1}＝1-P{Ts≤λs|H1} (15)
although the received signal samples are independently co-distributed, the elements of the vector p are correlated and therefore it is mathematically difficult to derive a closed expression for the threshold.
The application adopts a large number of emulations (N is more than or equal to 15 and less than or equal to 50, and P is more than or equal to 0.01 and less than or equal tofa≦ 1.0) to approximately obtain test statistic TsIs checked for a threshold lambdasAs shown in table 1.
TABLE 1 test statistic T for different sample numbers and significance levelssCorresponding threshold
As shown in table 1: check threshold lambda obtained by Monte Carlo simulationsThe effective value is 4 digits after the decimal point, and for convenience of representation, the two digits after the decimal point are approximately taken in the application.
Step 5, judging the test statistic TsAnd a check threshold lambdasTo determine the presence of a primary user, when checking for a statistic TsIs greater than the check threshold lambdasAnd then the master user is considered to transmit the signal,otherwise the channel is considered idle.
In order to verify the result of theoretical analysis, Matlab simulation and analysis are given for comparing the performance of the statistical spectrum detection algorithm and the performance of the ED detection method under the AWGN channel:
as shown in fig. 1, when the number N of samples is 30 and the SNR is-10 dB and-5 dB, respectively, the Receiver Operating Characteristic (ROC) curve of the statistical spectrum detection algorithm and the ED detection method is compared, and the simulation result is obtained by performing 10000 monte carlo simulations, it is obvious that the detection probability of the proposed algorithm approaches 1 faster than that of the ED detection method.
In order to further verify the influence of the signal-to-noise ratio on the detection performance, as shown in fig. 2, the performance comparison curve of the spectrum detection algorithm and the ED detection method is calculated when the false alarm rate of the significance level is 0.1, the number N of samples is 30, and the SNR of the signal-to-noise ratio varies from-20 dB to 0 dB. When N is 30 and SNR is-5 dB, the detection probability of the invention is 0.89, and the detection probability of ED is only 0.42, the detection probability of the invention is 0.47 higher than that of ED method, obviously, the calculation obviously improves the disadvantage that the performance of ED detection method is not ideal under low signal-to-noise ratio.
In summary, the following steps: the invention carries out spectrum detection by using the sequential quantile of the signal sample collected in the cognitive non-channel, can realize spectrum detection under the condition of no prior information of any main user, and overcomes the defect of non-ideal detection performance of an ED method under the condition of low signal-to-noise ratio (SNR). Compared with the ED detection method, the method is less influenced by noise uncertainty, and compared with the characteristic value detection method, the number of the required samples is less, so that the rapid detection can be realized.

Claims (5)

1. A statistical spectrum detection method in cognitive radio is characterized by comprising the following steps:
step 1, establishing a model:
assuming that only one primary user and one secondary user use an AWGN channel, and no interference exists around the primary user and the secondary user; the baseband signal sampling point sequence collected by the secondary user from the cognitive channel is a complex sequence, but the real part and the imaginary part can be respectively detected, and the real part or the imaginary part in the complex sequence of the secondary user can be expressed as formula (1):
Figure FDA0002272029500000011
in the formula (1), the parameter yiRepresenting the ith sample point in the complex sequence, a parameter h representing the received signal-to-noise ratio SNR, a parameter m representing the transmitted signal of a master user, and a parameter wiThe ith sample of the real part Gaussian white noise of the zero mean and the unit variance is represented, and the parameter N represents the total number of sampling points obtained by sampling;
then the spectrum detection in the cognitive radio system under AWGN channel is represented as the following binary hypothesis testing model, as formula (2):
Figure FDA0002272029500000012
in the formula (2), the parameter H0Indicating that a primary user signal is absent; parameter H1Indicating the existence of a primary user signal; at H0In the case, the received signal is only white gaussian noise; at H1Under the condition, the received signal is a mixture of Gaussian white noise and a main user signal;
let Fn(Y) represents the empirical cumulative distribution function CDF of the received signal Y, as given by equation (3):
in formula (3), when the primary user does not transmit a signal, the received signal is gaussian white noise, and its sample Y0Cumulative distribution function F0(y) is the formula (4),
Figure FDA0002272029500000021
when a main user transmits signals, the sample Y is different due to different modulation modes and channel characteristics1,Y2,…Yi,YnNot likely to be from the same cumulative distribution function F0(y), the binary hypothesis test model in equation (2) can be expressed as:
Figure FDA0002272029500000022
step 2, accumulating the distribution function CDF according to the known experience of the elements of the received signal Y in step 1, namely ziIn ascending order to obtain
Figure FDA0002272029500000023
By the result of
Figure FDA0002272029500000024
Calculating a function ρ of a known empirical cumulative distribution function CDF(i)；
Step 3, obtaining a function rho according to the step 2(i)Calculating to obtain a vector rho, and arranging the elements of the vector rho in an ascending order to obtain a vector
Figure FDA0002272029500000025
Calculating a test statistic T according to equation (13)s；
Step 4, giving false alarm rate PfaCalculating a corresponding check threshold lambdas；
Step 5, judging the test statistic TsAnd a check threshold lambdasTo determine the presence of a primary user, when checking for a statistic TsIs greater than the check threshold lambdasAnd if not, the channel is considered to be idle.
2. The method for detecting statistical frequency spectrum in cognitive radio according to claim 1, wherein the specific steps in the step 2 are as follows:
step 2.1, calculate the known empirical cumulative distribution function CDF, function z, corresponding to the elements of the received signal Yi，
zi＝F0(yi),i∈S (6)
The parameter S in the formula (6) is a sample space;
step 2.2, function z in step 2.1iIn ascending order of magnitude, the function will be defined as z:
z＝[z1,z2,...,zN]T(7)
the elements of z are sorted in ascending order of magnitude and are recorded as:
Figure FDA0002272029500000033
wherein
Figure FDA0002272029500000034
Is a vector obtained by arranging z in ascending order;
step 2.3, the product obtained in step 2.2
Figure FDA0002272029500000035
Is passed through a beta function ziThe transformation yields equation (10):
ρi＝β(z(i)；i,N-i+1),i∈S (10)
β (z) in equation (10)(i)α, γ) represents beta CDF, where α, γ is the shape parameter of the distribution, and, at the same time, defines:
ρ＝[ρ1,ρ2,...,ρN]T(11)
when α is equal to i and γ is equal to N-i +1, ρ is partially integratediCan be simplified as follows:
Figure FDA0002272029500000031
in the formula (12), the parameter j represents a subscript, and j ═ i, i + 1.
3. The method as claimed in claim 2, wherein the statistical T statistic is checked in step 3sThe expression of (a) is:
Figure FDA0002272029500000032
in formula (13), the parameter n represents the sample size.
4. The method as claimed in claim 3, wherein the false alarm rate P in step 3 isfaAnd a check threshold λsSatisfies formula (14):
Pfa＝P{Ts＞λs|H0} (14)
wherein the check threshold lambdasCan be represented by P { Ts＞λs|H0α ', found α' as a level of significance, where the detection probability can be expressed as:
Pd＝P{Ts＞λs|H1}＝1-P{Ts≤λs|H1} (15)。
5. the method as claimed in claim 4, wherein the detection threshold λ issThe value range of (A): lambda is more than or equal to 9.1s≤195.4。
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