CN105025583A - Stepped frequency spectrum sensing method based on energy and covariance detection - Google Patents

Abstract

The invention discloses a stepped frequency spectrum sensing method based on energy and covariance detection, relates to the frequency spectrum sensing field of cognitive radio, and aims at solving the problem that a present energy detection method is low in the detection accuracy. Energy detection is carried out at a user end; if it is detected that a main user uses an authorized frequency spectrum, a cognitive user keeps silent; if a result of energy detection is a frequency spectrum cavity, secondary detection, namely covariance detection, is needed; and a result of the covariance detection is still that the authorized frequency spectrum is not used, the cognitive user can occupy the authorized frequency spectrum for communication. Thus, advantages of energy detection and covariance detection are effectively integrated; when the channel state is sound, energy detection which is easy to implement is carried out to sense the frequency spectrum; and when the signal to noise ratio is low, secondary detection is carried out by utilizing the high statistic characteristics of covariance detection, and thus, the detection accuracy is improved.

Description

Based on the substep frequency spectrum sensing method that energy and covariance detect

Technical field

The present invention relates to the frequency spectrum perception field of cognitive radio.

Background technology

Along with the develop rapidly of wireless communication technology, people are to the demand of band resource also sharp increase thereupon.But the utilization of frequency spectrum resource is still in a lower level in a lot: existing wireless communication technology occupies a large amount of frequency spectrum resources, it is fewer and feweri that new business develops the frequency spectrum that can utilize, and authorized the spectrum utilization of frequency range to there is a large amount of idle phenomenon simultaneously.The monitoring of current spectral resource service condition and result of study are shown, authorized the idle ratio of frequency spectrum along with time and region difference from 15% to 85% not etc.

For solving the rare of frequency spectrum resource and its distribution contradiction, propose cognitive radio technology (Cognitive Radio, CR), this technology is regarded as the technology of the most application prospect solving current frequency spectrum resource anxiety, is also the preferred plan of generally acknowledged this problem of solution.

Frequency spectrum perception technology is the important component part of cognitive radio networks, it make unauthorized user can under certain condition intelligence acquisition and use unappropriated frequency range, thus improve the availability of frequency spectrum.In research in recent years, frequency spectrum perception technology defines comparatively ripe theoretical foundation, but in order to realize protection authorized user while the unauthorized system of permission uses better, requires more and more higher to the algorithm of frequency spectrum perception technology.

Under complex electromagnetic environment or weak state of signal-to-noise, energy detection algorithm has the shortcoming that detectability sharply reduces, and it has lower detecting reliability to path transmission problems such as incorrect noise.

Summary of the invention

The present invention is the problem that the detection accuracy in order to solve existing energy detection method is low, thus provides a kind of substep frequency spectrum sensing method detected based on energy and covariance.

Based on the substep frequency spectrum sensing method that energy and covariance detect, at cognitive radio system, it is realized by following steps:

Step one, the frequency spectrum perception of cognitive radio system is equivalent to dualism hypothesis model:

$\left.\begin{array}{c}{H}_0:r\left(n\right)=w\left(n\right)\\ H_1:r\left(n\right)=h\·x\left(n\right)+w\left(n\right)\end{array}\right\}$

In formula: n=1,2 ..., N; The hits of signal when N is detection; X (n) and w (n) is the sample value of signal and noise respectively, and independently of one another; H represents the channel gain between primary user and cognitive user; H ₀representing only has noise to exist, and there is not authorized user; H ₁represent that authorized user exists;

At actual signal r (n) that the n moment receives, energy measuring is carried out to cognitive user, obtains energy measuring statistic Y:

$Y=\frac{1}{N}\·\underset{n=1}{\overset{N}{\Σ}}{\left|r\left(n\right)\right|}^2$

Energy measuring statistic Y and the decision threshold λ preset are compared, if Y> is λ, then adjudicates primary user and exist, be i.e. H ₁state, then cognitive user is selected keep silent or separately seek other channels, and frequency spectrum perception terminates;

If Y≤λ, then adjudicate authorized user and do not exist, be i.e. H ₀state, then perform step 2;

If step 2 cognitive user termination receives l continuous print signal sample data, l is positive integer, then the vector representation of energy measuring statistic Y (k), transmit X (k) and noise N (k) is:

Y(k)＝[y(k),y(k-1),…,y(k-l+1)]

X(k)＝[x(k),x(k-1),…,x(k-l+1)]

N(k)＝[n(k),n(k-1),…,n(k-l+1)]

Then the statistics covariance matrix of energy measuring statistic Y (k), transmit X (k) and noise N (k) is respectively:

R _Y＝E[Y ^T(k)Y(k)]

R _X＝E[X ^T(k)X(k)]

R _N＝E[N ^T(k)N(k)]＝σ _w ²·I _l

In formula: I _lfor l rank unit matrix; σ _wfor the variance of noise;

And have:

R _Y＝R _X+R _N＝R _X+σ _w ²·I _l

That is:

The statistics covariance matrix R of receiving end signal is replaced with sample covariance matrix S _y, and add up auto-correlation function with sample autocorrelation function ξ (l) approximate substitution, its expression formula is:

$S=\left|\begin{array}{ccccc}\mathrm{\ξ}\left(0\right)& \mathrm{\ξ}\left(1\right)& \mathrm{\ξ}\left(2\right)& ...& \mathrm{\ξ}(l-1)\\ \mathrm{\ξ}\left(1\right)& \mathrm{\ξ}\left(0\right)& \mathrm{\ξ}\left(1\right)& ...& \mathrm{\ξ}(l-2)\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ \mathrm{\ξ}(l-1)& \mathrm{\ξ}(l-2)& \mathrm{\ξ}(l-3)& ...& \mathrm{\ξ}\left(0\right)\end{array}\right|$

$\mathrm{\ξ}\left(m\right)=\frac{1}{N}\·\underset{k=0}{\overset{N-1}{\Σ}}y\left(k\right)\·y(k-m),m=0,1,\mathrm{2...}l-1$

In formula: S is symmetrical matrix;

By all absolute value in auto-correlation function │ ξ (0) │ and S on comparative sample covariance matrix diagonal and mean value, primary user's signal can be adjudicated and whether exist;

Setting detection threshold is detection statistic be on sample covariance matrix diagonal in auto-correlation function │ ξ (0) │ and S all absolute value and the ratio of mean value, represent then have with Ф

In formula:

${\mathrm{\φ}}_1=\frac{1}{l}\·\underset{i=1}{\overset{l}{\Σ}}\underset{j=1}{\overset{l}{\Σ}}\left|S_{ij}\right|;$

${\mathrm{\φ}}_2=\frac{1}{l}.\underset{i=1}{\overset{l}{\Σ}}\left|S_{ii}\right|;$

Judge that when the detection statistic of cognitive user end is greater than thresholding primary user is just at busy channel, otherwise be judged to be spectrum interposition state, cognitive user can use; Complete the substep frequency spectrum perception detected based on energy and covariance.

Detection threshold establishing method be:

Be symmetrical matrix by sample covariance matrix S, have:

$\left\{\begin{array}{c}{\mathrm{\φ}}_1=\left|\mathrm{\ξ}\left(0\right)\right|+\frac{2}{l}\·\underset{i=1}{\overset{l-1}{\Σ}}(l-i)\left|\mathrm{\ξ}\left(i\right)\right|\\ {\mathrm{\φ}}_2=\left|\mathrm{\ξ}\left(0\right)\right|\end{array}\right.$

In the non-existent situation of primary user's signal, i.e. H ₀time, have:

$E\left({\mathrm{\φ}}_1\right)=(1+(l-1)\·\sqrt{\frac{2}{N\mathrm{\π}}})\·{{\mathrm{\σ}}_w}^2$

$\left\{\begin{array}{c}E\left({\mathrm{\φ}}_2\right)={{\mathrm{\σ}}_w}^2\\ var\left({\mathrm{\φ}}_2\right)=\frac{2}{N}\·{{\mathrm{\σ}}_w}^4\end{array}\right.$

Then the false alarm probability of covariance arithmetic is:

In formula: Q (x) is the complementary CDF function of standard gaussian;

Then detection threshold for:

The beneficial effect that the present invention obtains: because energy measuring detection perform under low signal-to-noise ratio environment sharply declines, and the fluctuation of background noise also certainly will cause the change of receiving terminal signal to noise ratio in actual conditions, therefore transmit according to primary user and feature relatively independent between noise, adopt covariance arithmetic to carry out performance balance to low signal-to-noise ratio.

The invention has the advantages that, first cognitive user end adopts the energy measuring based on time domain to enter judgement, when channel situation is better, the first step detects and can more adequately judge frequency spectrum service condition, if judgement is spectrum interposition, also has covariance to detect and carry out second judgement, thus reducing false drop rate, reduce cognitive user causes interference possibility to primary user simultaneously.If adopt adaptive threshold decision algorithm in first step energy measuring, then detection perform will have and improve greatly.

Accompanying drawing explanation

Fig. 1 is energy measuring principle schematic of the present invention;

Fig. 2 is energy of the present invention and covariance substep detection method schematic flow sheet;

Fig. 3 is the detection probability contrast simulation schematic diagram of three kinds of detection algorithms; Wherein curve 31 is detection probability curves of Cov method; Curve 32 is detection probability curves of Energy method; Curve 33 is detection probability curves of Energy-Cov method;

Fig. 4 is the probability of false detection contrast simulation schematic diagram of three kinds of detection algorithms; Wherein curve 41 is probability of false detection curves of Cov method; Curve 42 is probability of false detection curves of Energy method; Curve 43 is probability of false detection curves of Energy-Cov method;

Fig. 5 is that the multiplicative complexity of three kinds of detection modes compares emulation schematic diagram; Wherein curve 51 is multiplication computation amount curves of Energy-Cov method; Curve 52 is multiplication computation amount curves of Energy method; Curve 53 is multiplication computation amount curves of Cov method;

Fig. 6 is that the addition complexity of three kinds of detection modes compares emulation schematic diagram; Wherein curve 61 is additional calculation discharge curves of Energy-Cov method; Curve 62 is additional calculation discharge curves of Energy method; Curve 63 is additional calculation discharge curves of Cov method;

Fig. 7 is the emulation schematic diagram that method of the present invention needs the probability carrying out second step detection;

Fig. 8 is multiplication computation amount (secondary) the emulation schematic diagram of method of the present invention with smoothing factor l; Wherein curve 81 is multiplication computation amount curves of Energy-Cov method; Curve 82 is multiplication computation amount curves of Energy method; Curve 83 is multiplication computation amount curves of Cov method;

Fig. 9 is additional calculation amount (secondary) the emulation schematic diagram of method of the present invention with smoothing factor l; Wherein curve 91 is additional calculation discharge curves of Energy-Cov method; Curve 92 is additional calculation discharge curves of Energy method; Curve 93 is additional calculation discharge curves of Cov method;

Embodiment

Embodiment one, the substep frequency spectrum sensing method detected based on energy and covariance, it is realized by following steps:

Step one, first carry out energy measuring at cognition end, described detection method as shown in Figure 1:

In Fig. 1, the actual signal that r (n) receives in the n moment for cognitive user; The signal that x (n) launches for primary user; W (n) is Gaussian noise (awgn channel), and its average is 0, and variance is definite value.The frequency spectrum perception problem of cognitive radio system can be equivalent to a dualism hypothesis model:

$\left.\begin{array}{c}{H}_0:r\left(n\right)=w\left(n\right)\\ H_1:r\left(n\right)=h\·x\left(n\right)+w\left(n\right)\end{array}\right\}---\left(1\right)$

Wherein, n=1,2 ..., N.The hits (detection duration) of signal when N is detection; X (n) and w (n) is the sample value of signal and noise respectively, and they are separate each other; H represents the channel gain between primary user and cognitive user; H ₀representing only has noise to exist, and there is not authorized user; H ₁represent that authorized user exists.

The detection statistic Y of energy detection system is expressed as:

$Y=\frac{1}{N}\·\underset{n=1}{\overset{N}{\Σ}}{\left|r\left(n\right)\right|}^2---\left(2\right)$

Statistic Y and decision threshold λ is compared, if Y> is λ, then adjudicates primary user and exist, be i.e. H1 state; If Y≤λ, then adjudicate authorized user and do not exist (spectrum interposition), be i.e. H ₀state.

In signal sampling number N mono-timing, if the average power of noise keeps constant, according to central-limit theorem, statistic Y is approximate meets Gaussian Profile, that is:

$\left\{\begin{array}{c}{H}_0:Y~Normal({{\mathrm{\σ}}_w}^2,\frac{2}{N}{{\mathrm{\σ}}_w}^4)\\ H_1:Y~Normal({{\mathrm{\σ}}_x}^2+{{\mathrm{\σ}}_w}^2,\frac{2}{N}{\left({{\mathrm{\σ}}_x}^2+{{\mathrm{\σ}}_w}^2\right)}^2)\end{array}\right.---\left(3\right)$

σ in formula _x ²for the average power that primary user transmits, σ _w ²for the variance (average power) of noise.

The performance index weighing energy measuring are generally detection probability P _dwith false alarm probability P _f.Cognitive radio technology requires to protect primary user not to be interfered as much as possible, and the detection probability namely for primary user is the bigger the better.The design of detection system is also that false alarm probability is little as far as possible, i.e. systematic function optimization when ensureing that detection probability is high as far as possible usually.Adopt Neyman-Pearson (NP) to detect herein, make false alarm probability P _fthe a certain value α that can tolerate, and detection probability P _dp can be ensured when getting maximum _f≤ α.NP standard makes detection probability and false alarm probability to reach ideal values, but depends on false alarm probability P due to decision threshold λ _f, therefore P _fvalue limited.

According to central-limit theorem, the signal received in cognitive user termination can think zero-mean gaussian process, simultaneously receiving end signal disturb by the white Gaussian noise of zero-mean (desirable additive white Gaussian noise channel).Again according to the definition of signal detection and estimation, detection probability and the false alarm probability that can obtain energy measuring are:

$P_d=P\left(Y>\mathrm{\λ}\right|H_1)=Q\left(\frac{\mathrm{\λ}-({{\mathrm{\σ}}_x}^2+{{\mathrm{\σ}}_w}^2)}{\sqrt{2/N}\·({{\mathrm{\σ}}_x}^2+{{\mathrm{\σ}}_w}^2)}\right)---\left(4\right)$

$P_f=P\left(Y>\mathrm{\λ}\right|H_0)=Q\left(\frac{\mathrm{\λ}-{{\mathrm{\σ}}_w}^2}{\sqrt{2/N}\·{{\mathrm{\σ}}_w}^2}\right)---\left(5\right)$

Wherein: Q (x) is the complementary CDF function of standard gaussian, signal to noise ratio

Can obtain decision threshold λ according to formula (5) is:

$\mathrm{\λ}={{\mathrm{\σ}}_w}^2\·(1+\sqrt{2/N}\·Q^{-1}(P_f\left)\right)---\left(6\right)$

Can λ be offset by (4) and (5), thus obtain the relation of N and γ:

N＝2[Q ^-1(P _f)-Q ^-1(P _d)·(1+γ)] ²·γ ^-2(7)

Except the balance of detection probability and false alarm probability, according to IEEE 802.22 standard, the detection time for frequency spectrum perception must not more than 2sec.

Although energy measuring is a kind of traditional detection method, it is without the need to knowing the prior information of signal and realizing simple, and have certain superiority, energy measuring can only as rough detection method in advance.If want the performance making energy measuring to have further lifting, also need the impact considering that algorithm brings antimierophonic robust performance (energy measuring is responsive on noise average power fluctuation) and channel fading.

If the result of step 2 energy measuring be primary user just at busy channel, then cognitive user can be selected to keep silent or separately seek other channels.If the result of energy measuring is spectrum interposition, then carry out the detection of second step covariance.

The propagation in a communications system of primary user's signal is often through processes such as over-sampling, modulation, encryptions, also various decline and time delay can be subject in wireless channel, thus the statistics covariance matrix of primary user's signal and noise or auto-correlation function different often, utilize the covariance detection algorithm of this characteristic by the difference of the statistics covariance matrix of signal and noise, build new detection statistic, and compare with thresholding, judge whether primary user uses frequency spectrum resource.

If cognitive user termination receives l continuous print signal sample data, then the vector representation of statistic Y (k), transmit X (k) and noise N (k) is such as formula shown in (8).

Y(k)＝[y(k),y(k-1),…,y(k-l+1)]

X(k)＝[x(k),x(k-1),…,x(k-l+1)] (8)

N(k)＝[n(k),n(k-1),…,n(k-l+1)]

Then the statistics covariance matrix of Y (k), X (k) and N (k) is respectively:

R _Y＝E[Y ^T(k)Y(k)]

R _X＝E[X ^T(k)X(k)] (9)

R _N＝E[N ^T(k)N(k)]＝σ _w ²·I _l

I in formula (9) _lfor l rank unit matrix.Primary user's signal is uncorrelated with noise under normal circumstances, so have:

R _Y＝R _X+R _N＝R _X+σ _w ²·I _l(10)

Also namely:

The covariance matrix of obvious acquisition statistic Y is more difficult, therefore still utilizes the thought of sampling to carry out sample covariance calculating to statistic, replaces the statistics covariance matrix R of receiving end signal with sample covariance matrix S _y, and add up auto-correlation function with sample autocorrelation function ξ (l) approximate substitution, its expression formula is such as formula shown in (12), (13).

$S=\left|\begin{array}{ccccc}\mathrm{\ξ}\left(0\right)& \mathrm{\ξ}\left(1\right)& \mathrm{\ξ}\left(2\right)& ...& \mathrm{\ξ}(l-1)\\ \mathrm{\ξ}\left(1\right)& \mathrm{\ξ}\left(0\right)& \mathrm{\ξ}\left(1\right)& ...& \mathrm{\ξ}(l-2)\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ \mathrm{\ξ}(l-1)& \mathrm{\ξ}(l-2)& \mathrm{\ξ}(l-3)& ...& \mathrm{\ξ}\left(0\right)\end{array}\right|---\left(12\right)$

$\mathrm{\ξ}\left(m\right)=\frac{1}{N}\·\underset{k=0}{\overset{N-1}{\Σ}}y\left(k\right)\·y(k-m),m=0,1,\mathrm{2...}l-1---\left(13\right)$

Wherein: S is symmetrical matrix.By all absolute value in auto-correlation function │ ξ (0) │ and S on comparative sample covariance matrix diagonal and mean value, primary user's signal can be adjudicated and whether exist.Detection threshold is made to be detection statistic is the ratio of said two devices, represents with Ф, then have:

In formula:

${\mathrm{\φ}}_1=\frac{1}{l}\·\underset{i=1}{\overset{l}{\Σ}}\underset{j=1}{\overset{l}{\Σ}}\left|S_{ij}\right|$

${\mathrm{\φ}}_2=\frac{1}{l}.\underset{i=1}{\overset{l}{\Σ}}\left|S_{ii}\right|$

Judge that when the detection statistic of cognitive user end is greater than thresholding primary user is just at busy channel, otherwise be judged to be spectrum interposition state, cognitive user can use.

Analyze the detection threshold setting means based on covariance arithmetic below.

Be symmetrical matrix by sample covariance matrix S, have:

$\left\{\begin{array}{c}{\mathrm{\φ}}_1=\left|\mathrm{\ξ}\left(0\right)\right|+\frac{2}{l}\·\underset{i=1}{\overset{l-1}{\Σ}}(l-i)\left|\mathrm{\ξ}\left(i\right)\right|\\ {\mathrm{\φ}}_2=\left|\mathrm{\ξ}\left(0\right)\right|\end{array}\right.---\left(15\right)$

In the non-existent situation of primary user's signal, namely during H0, have:

$E\left({\mathrm{\φ}}_1\right)=(1+(l-1)\·\sqrt{\frac{2}{N\mathrm{\π}}})\·{{\mathrm{\σ}}_w}^2---\left(16\right)$

$\left\{\begin{array}{c}E\left({\mathrm{\φ}}_2\right)={{\mathrm{\σ}}_w}^2\\ var\left({\mathrm{\φ}}_2\right)=\frac{2}{N}\·{{\mathrm{\σ}}_w}^4\end{array}\right.---\left(17\right)$

In about the analysis of interchannel noise, pointed out that channel is additivity narrowband Gaussian white noise channel, have smooth performance, thus the false alarm probability of covariance arithmetic can be expressed as:

Can obtain detection threshold by formula (18) is:

In the thresholding expression formula of covariance arithmetic, the determination of thresholding is only determined by sample points l (also claiming smoothing factor), total sampling number N and false alarm probability, although be both fixed threshold to adjudicate, but the signal to noise ratio of the threshold value of covariance arithmetic and receiving terminal has nothing to do, therefore its detectability is not by the interference of noise fluctuations, and this compensate for the deficiency of classic algorithm by signal to noise ratio restriction.

When primary user's busy channel, i.e. H ₁parameter situation in situation is:

$\begin{array}{c}\mathrm{\φ}=\frac{{\mathrm{\φ}}_1}{{\mathrm{\φ}}_2}\≈E\left(\frac{{\mathrm{\φ}}_1}{{\mathrm{\φ}}_2}\right)=1+\frac{{{\mathrm{\σ}}_x}^2}{{{\mathrm{\σ}}_x}^2+{{\mathrm{\σ}}_w}^2}\·{\mathrm{\γ}}_{H1}\\ =1+\frac{\mathrm{\γ}}{\mathrm{\γ}+1}\·{\mathrm{\γ}}_{H1}\end{array}---\left(20\right)$

Wherein:

${\mathrm{\γ}}_{H1}\stackrel{\mathrm{\Δ}}{=}\frac{2}{l}\underset{i=1}{\overset{l-1}{\Σ}}(l-i)\·\left|{\mathrm{\α}}_i\right|;$

α _i＝E[s(k)s(k-i)]/σ _x ²；

γ is receiving terminal signal to noise ratio;

α _ifor the dependency expression formula between signal sampling point;

γ _h1for overall relevance expression formula;

When sampling number N is tending towards infinity, γ _h1to be greater than 1, correlated performance is at this moment better, and detection perform is more excellent, and γ _h1by correlation and the signal to noise ratio decision of sampled signal.

According to above H ₁the conclusion of situation, the detection probability of known system is:

The advantage of energy detection algorithm is not need prior information, and algorithm is comparatively simple, but the performance of energy measuring will decline to some extent in low signal-to-noise ratio situation.Although the threshold value of covariance arithmetic is also determined in CFAR situation, but pass through statistical calculation, this algorithm can utilize the dependency relation between signal to enter a judgement well, its threshold value and receiving terminal signal to noise ratio have nothing to do, thus avoid the impact of incorrect noise on detection perform comparatively feasiblely.

Energy and covariance detect the substep algorithm synthesis advantage of two kinds of algorithms, first by energy measuring, anticipation is carried out to frequency spectrum service condition at cognitive user end, in low signal-to-noise ratio situation, if judgement is for primary user is just at use authority frequency spectrum, then cognitive user enters silent status or separately seeks other frequency spectrums; If judgement is spectrum interposition, then proceeds covariance and detect, draw final judging result.

If use P _{d_en}represent the detection probability of energy measuring, P _{f_en}represent energy measuring false alarm probability, P _{d_cov}represent the detection probability that covariance detects, P _{f_cov}represent the false alarm probability that covariance detects, still use P ₀represent the probability of primary user's unoccupied channel, use P ₁represent the probability of primary user's busy channel, then the detection perform of substep algorithm is:

P _d＝P _{d_en}+(1-P _{d_en})·P _{d_cov}(22)

P _f＝P _{f_en}+(1-P _{f_en})·P _{f_cov}(23)

P _error＝P ₀·P _f+P ₁·(1-P _d) (24)

$\begin{array}{c}{P}_{stable}=1-P_{unstable}=1-P({\mathrm{\&gamma;}}_{\mathrm{\&beta;}}<{\mathrm{SNR}}_{wall})\\ =1-{\&Integral;}_{\frac{1}{\mathrm{\&beta;}}\mathrm{\&gamma;}}^{\frac{{\mathrm{\&beta;}}^2-1}{\mathrm{\&beta;}}}f\left({\mathrm{\&gamma;}}_{\mathrm{\&beta;}}\right){\mathrm{d\&gamma;}}_{\mathrm{\&beta;}}=1-{\&Integral;}_{\frac{1}{\mathrm{\&beta;}}\mathrm{\&gamma;}}^{\frac{{\mathrm{\&beta;}}^2-1}{\mathrm{\&beta;}}}\frac{\mathrm{\&beta;}}{{\mathrm{\&beta;}}^2-1}\&CenterDot;\frac{\mathrm{\&gamma;}}{{{\mathrm{\&gamma;}}_{\mathrm{\&beta;}}}^2}{\mathrm{d\&gamma;}}_{\mathrm{\&beta;}}\\ =\left\{\begin{array}{c}0,\mathrm{\&gamma;}<\frac{{\mathrm{\&beta;}}^2-1}{{\mathrm{\&beta;}}^2}\\ \frac{{\mathrm{\&beta;}}^2\mathrm{\&gamma;}-{\mathrm{\&beta;}}^2+1}{{({\mathrm{\&beta;}}^2-1)}^2},\frac{{\mathrm{\&beta;}}^2-1}{{\mathrm{\&beta;}}^2}<\mathrm{\&gamma;}<{\mathrm{\&beta;}}^2-1\\ 1,\mathrm{\&gamma;}\&GreaterEqual;{\mathrm{\&beta;}}^2-1\end{array}\right.\end{array}---\left(25\right)$

Detect in the various performance parameters of substep algorithm as can be seen from energy and covariance, the accuracy of detection system is determined jointly by two kinds of algorithms, owing to not carrying out the process of any signal domain in covariance detection algorithm to received signal, thus the stability of system is still determined by received signal to noise ratio and sampling number N.

In algorithm complex, if using the account form of detection statistic as the criterion of algorithm complex, then when total sampling number is N, energy detection algorithm is total N multiplying, the computing of (N-1) sub-addition in the computing of statistic Y; If sample points is l, then statistic Ф in covariance arithmetic ₁carry out Nl multiplication altogether, (Nl-1) sub-addition, statistic Ф ₂carried out (l-1) sub-addition altogether, detection statistic Ф has carried out Nl multiplication altogether, (Nl+l-2) sub-addition.

System needs the probability carrying out second step detection can be expressed as formula (3-5):

P ₂＝P ₀·(1-P _{f_en})+P ₁·(1-P _{d_en}) (26)

Detecting total amount of calculation so is step by step:

Sum_multi＝N+P ₂·Nl (27)

Sum_plus＝(N-1)+P ₂·(Nl+l-2) (28)

Obvious substep algorithm compares to the complexity that simple energy measuring adds systems axiol-ogy, the magnitude relationship of its operand and covariance arithmetic and P ₂relevant with the value of l.

Effect of the present invention is verified below with concrete l-G simulation test:

In MATLAB environment, above-mentioned algorithm is emulated, can very clearly see from Fig. 3, the received signal to noise ratio of cognitive end is lower, and the detection probability that the detection probability of covariance arithmetic detects compared to simple energy measuring and covariance is more much bigger, and is obviously better than the performance of energy measuring.Can also see in Fig. 3, Fig. 4 and substep algorithm and simple energy detection algorithm and covariance arithmetic being compared, the flase drop situation of substep algorithm is starkly lower than the simple situation using energy measuring and covariance to detect.Substep algorithm table reveals comparatively superior detection perform.The Detection Information detecting substep algorithm based on energy and covariance refers to table 1.

Table 1

Due to sampling number selected in simulation process and sample points all less, thus very low lower than detection probability during-10dB in signal to noise ratio, probability of false detection is very high, thus in simulation result, the variation tendency of detection perform remains directive significance.The detectability of substep algorithm is better than the detectability of simple a certain algorithm.Can also see from Fig. 4, when sampling number less (N=32), sample points less (l=4), substep algorithm is when signal to noise ratio is higher than-5dB, its probability of false detection presents the trend being greater than covariance and detecting, proposition due to substep algorithm be based under low signal-to-noise ratio environment to the raising of energy measuring performance, thus such variation tendency is acceptable.

Can find from the statistics of table 1 and Fig. 5,6, although the detection perform of substep algorithm is better, but substep algorithm in complexity far above time domain energy detection algorithm, especially, in low signal-to-noise ratio situation, its amount of calculation, particularly multiplication computation amount are apparently higher than single algorithm, this will make its detection speed decline to some extent, when sampling number N is larger, smoothing factor l improves, the difference in this speed also can be more obvious, as shown in Figure 8.On the other hand, Fig. 7 shows the probability needing to carry out covariance arithmetic detection in substep algorithm, and along with the increase of signal to noise ratio, first step energy measuring can carry out frequency spectrum perception under required detection perform, the design original intention of this and this algorithm matches, and confirms the reasonability of algorithm.

Substep detection algorithm all can face noise wall problem in each step detects, in detecting in the first step, over-sampling and preliminary treatment are carried out to signal, thus once enter second step detection, its signal will have certain distortion, cause the raising of noise wall, thus limit simplifying of sampling point value, also namely from stability, substep detection algorithm also exists the possibility improving minimum sampling point value.

To analyze the performance that energy and covariance detect substep detection algorithm as can be seen from above, must compromise between detection accuracy and algorithm complex in the application of low signal-to-noise ratio.

Advantage of the present invention:

Because energy measuring detection perform under low signal-to-noise ratio environment sharply declines, and the fluctuation of background noise also certainly will cause the change of receiving terminal signal to noise ratio in actual conditions, therefore transmit according to primary user and feature relatively independent between noise, adopt covariance arithmetic to carry out performance balance to low signal-to-noise ratio.The advantage of substep algorithm is, first cognitive user end adopts the energy measuring based on time domain to enter judgement, when channel situation is better, the first step detects and can more adequately judge frequency spectrum service condition, if judgement is spectrum interposition, also has covariance to detect and carry out second judgement, thus reduce false drop rate to a certain extent, reduce cognitive user causes interference possibility to primary user simultaneously.If adopt adaptive threshold decision algorithm in first step energy measuring, then detection perform will have and improve greatly.

Although substep detection algorithm has comparatively good detection perform, because needs calculate correlation function in the process of algorithm realization, therefore used more multiplying, this can cause more hardware spending.Therefore should estimate to some extent the applied environment of algorithm in actual applications, thus the algorithm selecting cost performance to be relatively suitable for carries out frequency spectrum perception.

Claims (2)

1., based on the substep frequency spectrum sensing method that energy and covariance detect, it is characterized in that: at cognitive radio system, it is realized by following steps:

Step one, the frequency spectrum perception of cognitive radio system is equivalent to dualism hypothesis model:

$\left.\begin{array}{c}{H}_0:r\left(n\right)=w\left(n\right)\\ H_1:r\left(n\right)=h\&CenterDot;x\left(n\right)+w\left(n\right)\end{array}\right\}$

In formula: n=1,2 ..., N; The hits of signal when N is detection; X (n) and w (n) is the sample value of signal and noise respectively, and independently of one another; H represents the channel gain between primary user and cognitive user; H ₀representing only has noise to exist, and there is not authorized user; H ₁represent that authorized user exists;

At actual signal r (n) that the n moment receives, energy measuring is carried out to cognitive user, obtains energy measuring statistic Y:

$Y=\frac{1}{N}\&CenterDot;\underset{n=1}{\overset{N}{\&Sigma;}}{\left|r\left(n\right)\right|}^2$

Energy measuring statistic Y and the decision threshold λ preset are compared, if Y> is λ, then adjudicates primary user and exist, be i.e. H ₁state, then cognitive user is selected keep silent or separately seek other channels, and frequency spectrum perception terminates;

If Y≤λ, then adjudicate authorized user and do not exist, be i.e. H ₀state, then perform step 2;

If step 2 cognitive user termination receives l continuous print signal sample data, l is positive integer, then the vector representation of energy measuring statistic Y (k), transmit X (k) and noise N (k) is:

Y(k)＝[y(k),y(k-1),…,y(k-l+1)]

X(k)＝[x(k),x(k-1),…,x(k-l+1)]

N(k)＝[n(k),n(k-1),…,n(k-l+1)]

Then the statistics covariance matrix of energy measuring statistic Y (k), transmit X (k) and noise N (k) is respectively:

R _Y＝E[Y ^T(k)Y(k)]

R _X＝E[X ^T(k)X(k)]

R _N＝E[N ^T(k)N(k)]＝σ _w ²·I _l

In formula: I _lfor l rank unit matrix; σ _wfor the variance of noise;

And have:

R _Y＝R _X+R _N＝R _X+σ _w ²·I _l

That is:

The statistics covariance matrix R of receiving end signal is replaced with sample covariance matrix S _y, and add up auto-correlation function with sample autocorrelation function ξ (l) approximate substitution, its expression formula is:

$S=\left|\begin{array}{ccccc}\mathrm{\&xi;}\left(0\right)& \mathrm{\&xi;}\left(1\right)& \mathrm{\&xi;}\left(2\right)& ...& \mathrm{\&xi;}(l-1)\\ \mathrm{\&xi;}\left(1\right)& \mathrm{\&xi;}\left(0\right)& \mathrm{\&xi;}\left(1\right)& ...& \mathrm{\&xi;}(l-2)\\ .& .& .& .& .\\ .& .& .& .& .\\ .& .& .& .& .\\ \mathrm{\&xi;}(l-1)& \mathrm{\&xi;}(l-2)& \mathrm{\&xi;}(l-3)& ...& \mathrm{\&xi;}\left(0\right)\end{array}\right|$

$\mathrm{\&xi;}\left(m\right)=\frac{1}{N}\&CenterDot;\underset{k=0}{\overset{N-1}{\&Sigma;}}y\left(k\right)\&CenterDot;y(k-m),m=0,1,2...l-1$

In formula: S is symmetrical matrix;

By all absolute value in auto-correlation function │ ξ (0) │ and S on comparative sample covariance matrix diagonal and mean value, primary user's signal can be adjudicated and whether exist;

Setting detection threshold is detection statistic be on sample covariance matrix diagonal in auto-correlation function │ ξ (0) │ and S all absolute value and the ratio of mean value, represent then have with Ф

In formula:

${\mathrm{\&phi;}}_1=\frac{1}{l}\&CenterDot;\underset{i=1}{\overset{l}{\&Sigma;}}\underset{j=1}{\overset{l}{\&Sigma;}}\left|S_{ij}\right|;$

${\mathrm{\&phi;}}_2=\frac{1}{l}\&CenterDot;\underset{i=1}{\overset{l}{\&Sigma;}}\left|S_{ii}\right|;$

When the detection statistic Ф of cognitive user end is greater than detection threshold time judge that primary user is just at busy channel, otherwise be judged to be spectrum interposition state, cognitive user can use; Complete the substep frequency spectrum perception detected based on energy and covariance.

2. the substep frequency spectrum sensing method detected based on energy and covariance according to claim 1, is characterized in that detection threshold establishing method be:

Be symmetrical matrix by sample covariance matrix S, have:

$\left\{\begin{array}{c}{\mathrm{\&phi;}}_1=\left|\mathrm{\&xi;}\left(0\right)\right|+\frac{2}{l}\&CenterDot;\underset{i=1}{\overset{l-1}{\&Sigma;}}(l-i)\left|\mathrm{\&xi;}\left(i\right)\right|\\ {\mathrm{\&phi;}}_2=\left|\mathrm{\&xi;}\left(0\right)\right|\end{array}\right.$

In the non-existent situation of primary user's signal, i.e. H ₀time, have:

$E\left({\mathrm{\&phi;}}_1\right)=(1+(l-1)\&CenterDot;\sqrt{\frac{2}{N\mathrm{\&pi;}}})\&CenterDot;{{\mathrm{\&sigma;}}_w}^2$

$\left\{\begin{array}{c}E\left({\mathrm{\&phi;}}_2\right)={{\mathrm{\&sigma;}}_w}^2\\ \mathrm{var}\left({\mathrm{\&phi;}}_2\right)=\frac{2}{N}\&CenterDot;{{\mathrm{\&sigma;}}_w}^4\end{array}\right.$

Then the false alarm probability of covariance arithmetic is:

In formula: Q (x) is the complementary CDF function of standard gaussian;

Then detection threshold for: