CN106656376A - Cooperative spectrum sensing method based on feature value consistent estimation - Google Patents

Abstract

The invention discloses a cooperative spectrum sensing method based on feature value consistent estimation. The method comprises the specific realization steps that S1, a macro base station sends an authorized user signal; S2, a low-power small cellular base station receives the signal and carries out continuous sampling; S3, the low-power small cellular base station sends sensing data to a data fusion center and a receiving sample matrix is formed at the data fusion center; S4, the data fusion center obtains judgment statistic according to the receiving sample matrix; and S5, the data fusion center compares the judgment statistic with a judgment threshold, thereby judging whether an authorized user exist or not. According to the method, the spatial structure feature of the sending signal is taken into consideration and compared with a method of directly estimating a covariance matrix, the method has the advantage that the spectrum sensing performance is improved.

Description

A kind of cooperation frequency spectrum sensing method of feature based value consistent Estimation

Technical field

The invention belongs to wireless communication technology field, is related in the frequency spectrum perception and estimation theory in cognitive radio technology High dimensional feature value estimate, and in particular to a kind of cooperation frequency spectrum sensing method of feature based value consistent Estimation.

Background technology

With the fast development and the extensive application of Wireless Telecom Equipment of radio communication service, mobile data flow presents quick-fried The property sent out increases.In the case where frequency spectrum resource now is in short supply, the expansion of traditional macrocellular network to network capacity is limited, new The innovation of wireless network architecture becomes the inexorable trend of supporting network capacity.Intensive heterogeneous network is by macrocellular coverage Interior dense deployment low-power small cell base station, on the one hand can realize that multilayer strengthens and cover and marginal user performance improvement, be lifted Power system capacity, on the other hand, by reducing radius of society, increases cellulor quantity, improves the spatial multiplex ratio of frequency spectrum resource. Due to the dense deployment of cellulor, the channeling between cellulor and cellulor and between cellulor and macrocellular can bring Complicated interference problem.It is to solve complex jamming in intensive isomerous environment in combination with cellulor technology by cognitive radio technology The effective way of problem, concrete methods of realizing is, using macrocell user as authorized user, to strengthening what is covered outside macrocellular Small cell network adopts cognitive radio technology (abbreviation cognition network), before not interfering to the communication of macrocell user Put, intelligence reuses the mandate frequency spectrum resource of macro base station, the cross-layer interference problem in the intensive heterogeneous network of effectively solving is realized grand Coexisting between honeycomb and cognition network.

Cognitive radio technology is accessed to the opportunistic frequency spectrum for authorizing frequency spectrum and the recycling of idle frequency spectrum is by frequency Spectrum perceives what is realized.Traditional frequency spectrum sensing method include cyclostationary characteristic perceive, matched filter perceive, Energy-aware with And the perception based on covariance matrix characteristic value.These frequency spectrum perception algorithms are single user frequency spectrum perception, in actual communication Because the impact of shade and multipath fading can cause the decline of perceptual performance in environment, and cooperative spectrum sensing algorithm by using Multiple space diversitys for perceiving user's cooperation generation effectively alleviate these negative influences.Cooperative spectrum sensing is according to judgement machine The difference of system is divided into hard decision and soft-decision, and hard decision requires that each perceives user and makes local judgement and report court verdict To data fusion center, then final court verdict is obtained by data fusion center；Each perception user will in soft-decision mechanism Raw sensed sample data or local decision statistics are reported to fusion center so as to realize more accurately perceiving.Soft-decision In, when the sample data of all perception users is sent to fusion center, and the reception being made up of based on sample data fusion center The method that sample matrix makes decisions is based on the cooperation frequency spectrum sensing method of random matrix, wherein receiving the line number of sample matrix For the number of cooperative sensing user, referred to as data matrix dimension, columns is the sample number that each perceives user.

Traditional assumes sample number much larger than matrix dimension based on the cooperative spectrum sensing algorithm of random matrix, this Under the progressive hypothesis of tradition, sample covariance matrix is the optimal estimation for counting covariance matrix.But in intensive heterogeneous network, The dense deployment of cellulor causes data matrix dimension with sample number in the same order of magnitude, according to higher-dimension estimation theory, in data Matrix dimension and sample number tend to infinite and both ratio and tend under the progressive hypothesis of broad sense of constant simultaneously, sample covariance square Battle array can not provide the good estimation to counting covariance matrix, and the feature Distribution value of sample covariance matrix more disperses, maximum By too high estimation, by underestimation, sample characteristics is no longer the characteristic value for counting covariance matrix to minimal eigenvalue to characteristic value Consistent Estimation.The estimation of statistics covariance matrix is the critical process of frequency spectrum perception algorithmic derivation, estimates that the reduction of performance is straight Connect the performance that have impact on frequency spectrum perception.It is relatively fewer currently for the cognitive method of high dimensional data, it is existing based on covariance square Minimax characteristic value frequency spectrum perception algorithm (OAS-MME, the Estimated Covariance Matrix of battle array shrinkage estimation device Maximum–Minimum Eigenvalue Detection Based on Oracle Approximating Shrinkage Estimator) estimate that statistics covariance matrix improves the performance of frequency spectrum perception by using shrinkage estimation device, but it is directly right The estimation of higher-dimension covariance matrix fails to make full use of the space structure of sending signal, frequency spectrum perception performance to need further to be carried It is high.

The content of the invention

The estimation problem of higher-dimension statistics covariance matrix correlation unknown parameter, the present invention in order to solve frequency spectrum sensing method The higher-dimension of characteristic value is estimated in combination with frequency spectrum perception, to have obtained a kind of cooperative spectrum sensing of feature based value consistent Estimation (CEE-CSS, Consistent-Estimated Eigenvalues Based Cooperative Spectrum Sensing) Method.Method make use of sending signal space structure, and using the progressive consistent Estimation device for assuming lower eigenvalue of broad sense to feature Value is estimated, with good perceptual performance.Present invention can apply to cellulor is same with macrocellular frequently in intensive heterogeneous network During deployment, the authorized user in multiple cognitive cellulor cooperative sensing macrocellulars whether there is, so as to effectively avoid interlayer from doing Disturb, realize coexisting for macrocellular and cognition network.

In order to reach above-mentioned technique effect, a kind of cooperation frequency spectrum sensing method of feature based value consistent Estimation of the present invention The step that implements be：

Step 1：Macro base station sends authorization user signal.

Step 2：Low-power small cell base station receives signal and carries out continuous sampling.

Step 3：Perception data is sent to data fusion center by low-power small cell base station, in data fusion center composition Receive sample matrix.

Step 4：Data fusion center obtains decision statistics according to sample matrix is received.

Step 5：Decision statistics and decision threshold are compared and judge that authorized user whether there is by data fusion center.

It is an advantage of the current invention that：

(1) the space structure characteristic of sending signal is considered, is improve compared with directly estimation is carried out to covariance matrix The performance of frequency spectrum perception；

(2) using data higher-dimension (intensive cellulor deployment) in the case of the consistent Estimation device of characteristic value characteristic value is carried out Estimate, the good estimation of consistent Estimation device ensure that the performance of frequency spectrum perception；

(3) be not required to the prior informations such as the power and channel gain of known sending signal and noise, decision statistics only with The characteristic value of sample covariance matrix is relevant, it is adaptable to actual scene.

Description of the drawings

Fig. 1：The cognitive small cell network topological diagram of the embodiment of the present invention；

Fig. 2：The cooperation frequency spectrum sensing method flow chart of feature based value consistent Estimation provided in an embodiment of the present invention；

Fig. 3：In the present invention between algorithm perceptual performance and characteristic value separation condition the ROC curve figure of relation (slow fading is auspicious Sharp channel, signal to noise ratio snr=- 10dB, cooperation cellulor number M=16) (coordinate diagram)；

Fig. 4：In the present invention between algorithm perceptual performance and channel correlation coefficient relation P_d(rapid fading is auspicious for-SNR curve maps Sharp channel, false-alarm probability P_f=0.1, cooperation cellulor number M=16, sample N=50) (coordinate diagram)；

Fig. 5：Perceptual performance comparison diagram (slow fading Rayleigh channel, false-alarm probability P of the present invention and OAS-MME algorithms_f= 0.1, cooperation cellulor number M=16) (coordinate diagram).

Specific embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

The invention reside in providing a kind of cooperation frequency spectrum sensing method of feature based value consistent Estimation realizes intensive heterogeneous network Macrocellular and with coexisting between frequency cellulor in network.

The embodiment of the present invention cognitive small cell network topology as shown in figure 1, macrocellular network user be authorized user, make With allocated mandate frequency spectrum resource.The multiple intensive low-power cellulor nodes of deployment, little in macrocellular network coverage The signal of reception is sampled and is sent to data fusion center (FC, Fusion Center) by cellular basestation.In data fusion The heart obtains decision statistics based on sample matrix is received, by whether there is with threshold comparison decision authorized user.Perceiving Cellulor can utilize the frequency spectrum resource for having authorized when authorized user does not work, and at the same time, cognitive cellulor remains a need for carrying out Frequency spectrum perception, exits in time the use to frequency spectrum to avoid awarding macrocellular if the occurring again of authorized user is perceived Power user interferes.

Embodiment：

Referring to Fig. 2, a kind of cooperation frequency spectrum sensing method of feature based value consistent Estimation is embodiments provided, wrapped Include：Authorization user signal sends and receives 100：Macro base station sends authorization user signal, present invention assumes that authorization signal obeys zero Average power isGaussian Profile.

Signal receives and samples 200：Signal is received after steady fading channel by M small cell base station, it is assumed that Receiver end noise is additive white Gaussian noise, separate between noise and have an identical power σ², M small cell base station pair Reception signal carries out continuous sampling and respectively obtains N number of sample data.Use H₀And H₁Authorized user is represented respectively does not occur and occur two The situation of kind, the dualism hypothesis model of frequency spectrum perception is expressed as：

Wherein, x [n]=[x₁[n], x₂[n] ..., x_M[n]]^T(n=0,1 ..., N-1) is to be connect by M in sampling instant n The M dimension sample vectors that the sampling of receipts machine is obtained.W [n] represents average as zero, and covariance matrix is σ²I_MIndependent same distribution circulation it is right Claim multiple Gauss noise, be expressed asH is complex channel gain vector, assumes that channel increases in detecting period Benefit is constant.S [n] is n-th sample of authorization signal, it is assumed that it is zero to obey average, and variance isGaussian Profile.

Perceive sample data and be sent to data fusion center 300：Small cell base station is sent to data by sample data is perceived Fusion center, in data fusion center the reception sample matrix X=[x [0], x [1] ..., x [N-1]] of M × N-dimensional is constituted.

Obtain decision statistics 400：Data fusion center calculates decision statistics according to the expression formula of decision statistics, this The derivation of the decision statistics of invention is graceful Pearson criterion according to how, i.e., cause detection probability most when false-alarm probability is definite value Greatly.According to the sensor model set up, the difference for receiving the log-likelihood function of sample matrix is

L (X)=ln p (X | H₁)-ln p(X|H₀) (2)

H₀In the case of log-likelihood function contain unknown parameter σ², formula (3) is embodied as in the present embodiment

H₁In the case of log-likelihood function contain unknown parameterH and σ², formula is embodied as in the present embodiment (4)

Can be obtained using the computing formula and Woodbury matrix inversions equation of matrix determinant

Formula (5) and formula (6) are substituted into the expression formula (4) of log-likelihood function and abbreviation：

Because the power of the channel gain in actual scene and signal and noise is unknown, it is therefore desirable to these not Know that parameter is estimated, the expression formula of difference L (X) of the log-likelihood function after estimation is rewritten as

Wherein,For H₁In the case of estimation to channel gain,WithFor in the case of H1 to signal and noise power Estimate,For H₀In the case of estimation to noise power.

Known m-th real features value γ_mThe expression formula of consistent Estimation device be

Wherein K_mFor the tuple of m-th real features value, set For Sample covariance matrixK-th characteristic value.With regard toEquationM real solution in order For

In the signal model of the present invention, counting covariance matrix when authorized user is not present has M multiplex eigenvalue σ², because This unknown parameter σ²Consistent Estimation device be：

UtilizeReplace σ²H can be obtained₀In the case of log-likelihood function

In the presence of authorized user, statistics covariance matrix has M-1 weight minimal eigenvalue γ₁=σ²With 1 heavy eigenvalue of maximumUsing maximum sample characteristic valueCharacteristic vectorEstimate real eigenvalue of maximum γ₂Feature VectorCan obtainLog-likelihood function expression formula containing unknown parameter estimator Further abbreviation is：

Work as γ₁=σ²WithWhen two characteristic values meet characteristic value separation condition, characteristic value consistent Estimation Device can be more preferable to the estimation performance of characteristic value.Now require N/M ＞ ξ_MSet up, according to the sensor model set up, ξ_MIt is expressed as formula (13)

Wherein,For the solution of following formula

Formula (13) and formula (14) are substituted into N/M ＞ ξ_MIn obtain characteristic value separation condition establishment expression formula be：

Wherein,Represent signal to noise ratio.

By γ₁=σ²KindIn substitution formula (9), H can be obtained₁Unknown parameter in situation following formula (12) The expression formula (16) of estimator, and can provide when eigenvalue of maximum and minimal eigenvalue meet the separation condition in formula (15) Preferably estimate.

Formula (11) and formula (12) are substituted into formula (8) and are carried out the decision statistics that abbreviation obtains inventive algorithm：

Judgement authorized user whether there is 500：Data fusion center is by decision statistics T_CEE-CSSCompare with threshold value γ To judge whether authorized user occurs, as decision statistics T_CEE-CSSOccur more than authorized user is adjudicated during thresholding γ, otherwise award Power user does not occur, and perceives user using the mandate frequency spectrum resource, is expressed as

As a result represent：

In the perceptual performance that this part passes through simulating, verifying inventive algorithm, it is zero that sending signal obeys average in emulation Multiple Gauss is distributed and the power of signal is unknown；The transmission channel of authorization signal transmitting terminal and M small cell base station receiving terminal is flat Steady rayleigh fading channel, channel gain is unknown；The noise of small cell base station receiver is assumed to be identical and unknown.According to Strengthen cellulor the assessment models of technology in 3GPPRelease 12, set in emulation and cover in the range of a macrocellular 16 Small cell base station, and the value of sample number and cellulor quantity are in the identical order of magnitude.

Fig. 2 represents impact of the characteristic value separation condition to the perceptual performance of inventive algorithm.Consider that channel is that slow fading is auspicious Sharp channel, in detecting period channel gain be constant, signal to noise ratio snr=10log₁₀P values are -10dB.In this case, Understood according to formula (14), when N is more than 32 characteristic value separation condition is met.Different sample numbers shown in relatively Fig. 2 are corresponding to be connect Receipts machine operating characteristic curve (ROC, Receiver Operation Characteristic), as false-alarm probability (P_f, Probability of False Alarm) value be 0.1 when, the detection probability (P corresponding to N=35 and N=50_d, Probability of Detection) 0.9 is above, and as N=16, P_d=0.5, perceptual performance is worst.Therefore, spy is worked as When value indicative separation condition meets, estimator can be provided more accurately to be estimated, the perceptual performance of frequency spectrum perception algorithm is also more preferable.

Fig. 3 represents the impact of the correlation of channel to the perceptual performance of inventive algorithm.Consideration channel is rapid fading Rayleigh Channel, such as channel model when symbol period of signal is more than channel coherency time in narrow band communication, now channel gain It is random in detecting period, and because the C1osely Spaced Basing of small cell base station causes have correlation between channel.Pass through Spatial coherence between correlation matrix modeling channel, using correlation coefficient charts the size of inter-channel correlation is levied.It is solid in emulation Determine false-alarm probability P_f=0.1, cellulor number M=16, sample number N=50 represent the value of coefficient correlation with symbol c, when c difference For 0.5,0.75, and three P are obtained by 5000 Monte Carlo simulations when 0.95_d- SNR curve maps.Can from Fig. 3 Go out, the perceptual performance of inventive algorithm improves with the increase of signal to noise ratio, and channel coefficient correlation it is bigger when, perceive Performance is better.For example work as P_dWhen=0.9, relative to c=0.5, the perceptual performance of algorithm has the property higher than 3.5dB during c=0.75 Energy gain, and the performance gain of algorithm is higher than 7dB during c=0.95.Therefore, in intensive heterogeneous network, when perception of cooperating Small cell base station distance it is nearer when, the correlation between channel is bigger, the sample of different small cell base stations in the presence of authorization signal Correlation between this is also bigger, and the perceptual performance of inventive algorithm is better.

Fig. 4 compares the perceptual performance of inventive algorithm CEE-CSS and existing higher-dimension frequency spectrum perception algorithm OAS-MME. False-alarm probability P is fixed in emulation_f=0.1, cellulor number M=16, by 5000 Monte Carlo simulations two kinds of perception have been obtained The P of algorithm_d- SNR curve maps.From fig. 4, it can be seen that CEE-CSS can provide more preferable perceptual performance relative to OAS-MME. For example work as P_dWhen=0.9, relative to OAS-MME, CEE-CSS difference about 1dB and 0.5dB in N=50 and N=100 Performance gain.From comparing result, inventive algorithm is estimated by the space structure of consideration sending signal to characteristic value Meter, with more preferable perceptual performance compared with the OAS-MME algorithms estimated for statistics covariance matrix.

The present invention proposes a kind of cooperative spectrum sensing algorithm of feature based value consistent Estimation, and the method is applied to intensive Whether there is to realize macrocellular and cognition by multiple cognitive cellulor cooperative sensing macrocellular authorized users in heterogeneous network Coexisting between network.The consistent Estimation of characteristic value when the algorithm considers the space structure of sending signal and make use of higher-dimension Device, with good perceptual performance.

Claims (1)

1. a kind of cooperation frequency spectrum sensing method of feature based value consistent Estimation, including following step：

Step 1：Macro base station sends authorization user signal, and authorization signal is obeyed zero-mean power and isGaussian Profile；

Step 2：Small cell base station receives signal and carries out continuous sampling；

Signal is received after steady fading channel by M small cell base station, it is assumed that receiver end noise is additive Gaussian White noise, it is separate between noise and have an identical power σ², M small cell base station docks the collection of letters number carries out continuous sampling point N number of sample data is not obtained, if H₀And H₁Authorized user is represented respectively does not occur and occur two kinds of situations, the binary of frequency spectrum perception Hypothesized model is expressed as：

$\begin{array}{c}{H}_0:x\[n\]=w\[n\],n=0,1,\mathrm{...},N-1\\ H_1:x\[n\]=h\·s\[n\]+w\[n\],n=0,1,\mathrm{...},N-1\end{array}---\left(1\right)$

Wherein, x [n]=[x₁[n],x₂[n],…,x_M[n]]^T(n=0,1 ..., N-1) it is to be adopted by M receiver in sampling instant n M that sample is obtained dimension sample vector, w [n] represents average as zero, and covariance matrix is σ²I_MThe multiple height of independent same distribution Cyclic Symmetry This noise, is expressed asH is complex channel gain vector, assumes that channel gain is normal in detecting period Number, s [n] is n-th sample of authorization signal, it is assumed that it is zero to obey average, and variance isGaussian Profile；

Step 3：Small cell base station is sent to data fusion center by sample data is perceived, and in data fusion center M × N-dimensional is constituted Reception sample matrix X=[x [0], x [1] ..., x [N-1]]；

Step 4：Data fusion center obtains decision statistics according to sample matrix is received；

The difference of log-likelihood function for receiving sample matrix is

L (X)=lnp (X | H₁)-lnp(X|H₀) (2)

H₀In the case of log-likelihood function contain unknown parameter σ², it is expressed as：

$\ln p\left(X\right|H_0,{\mathrm{\σ}}^2)=-MNln\mathrm{\π}-MNln\left({\mathrm{\σ}}^2\right)-\frac{\underset{n=0}{\overset{N-1}{\Σ}}{x}^H\[n\]x\[n\]}{{\mathrm{\σ}}^2}---\left(3\right)$

H₁In the case of log-likelihood function contain unknown parameterH and σ², it is expressed as：

$\ln p\left(X\right|H_1,h,{\mathrm{\σ}}_s^2,{\mathrm{\σ}}^2)=-MNln\mathrm{\π}-N\ln |{\mathrm{\σ}}_s^2{\mathrm{hh}}^H+{\mathrm{\σ}}^{2}I|-\underset{n=0}{\overset{N-1}{\Σ}}{x}^H\[n\]{({\mathrm{\σ}}_s^2{\mathrm{hh}}^H+{\mathrm{\σ}}^{2}I)}^{-1}x\[n\]---\left(4\right)$

Can be obtained using the computing formula and Woodbury matrix inversions equation of matrix determinant

$|{\mathrm{\σ}}_s^2{\mathrm{hh}}^H+{\mathrm{\σ}}^{2}I|=\left({\mathrm{\σ}}_s^2\right|\left|h\right|{|}^2+{\mathrm{\σ}}^2){\left({\mathrm{\σ}}^2\right)}^{M-1}---\left(5\right)$

${({\mathrm{\σ}}_s^2{\mathrm{hh}}^H+{\mathrm{\σ}}^{2}I)}^{-1}=\frac{1}{{\mathrm{\σ}}^2}I-\frac{1}{{\mathrm{\σ}}^2}\frac{{\mathrm{\σ}}_s^2{\mathrm{hh}}^H}{{\mathrm{\σ}}^2+{\mathrm{\σ}}_s^2\left|\right|h|{|}^2}---\left(6\right)$

Formula (5) and formula (6) are substituted into the expression formula (4) of log-likelihood function and abbreviation：

$\begin{array}{c}\ln p\left(X\right|H_1,h,{\mathrm{\σ}}_s^2,{\mathrm{\σ}}^2)=-MNln\mathrm{\π}-N(M-1)ln\left({\mathrm{\σ}}^2\right)\\ -N\ln \left({\mathrm{\σ}}_s^2\left|\right|h|{|}^2+{\mathrm{\σ}}^2\right)-\frac{Ntr\left({\hat{R}}_x\right)}{{\mathrm{\σ}}^2}+\frac{{\mathrm{\σ}}_s^2\left|\right|h^{H}X|{|}^2}{\left({\mathrm{\σ}}_s^2\right|\left|h\right|{|}^2+{\mathrm{\σ}}^2){\mathrm{\σ}}^2}\end{array}---\left(7\right)$

Difference L (X) of the log-likelihood function after estimation is：

$L\left(X\right)=\ln p\left(X\right|H_1,\hat{h},{\widehat{\mathrm{\σ}}}_s^2,{\widehat{\mathrm{\σ}}}_{H_1}^2)-\ln p\left(X\right|H_0,{\widehat{\mathrm{\σ}}}_{H_0}^2)---\left(8\right)$

Wherein,For H₁In the case of estimation to channel gain,WithFor H₁In the case of estimation to signal and noise power,For H₀In the case of estimation to noise power；

Known m-th real features value γ_mThe expression formula of consistent Estimation device be：

${\widehat{\mathrm{\γ}}}_m=\frac{N}{K_m}\underset{k\∈{\mathrm{\κ}}_m}{\Σ}({\widehat{\mathrm{\λ}}}_k-{\widehat{\mathrm{\μ}}}_k)---\left(9\right)$

Wherein：K_mFor the tuple of m-th real features value, set For sample Covariance matrixK-th characteristic value；With regard toEquationM in order real solution is

Unknown parameter σ²Consistent Estimation device be：

${\widehat{\mathrm{\σ}}}_{H_0}^2=\frac{N}{M}\underset{k=1}{\overset{M}{\Σ}}({\widehat{\mathrm{\λ}}}_k-{\widehat{\mathrm{\μ}}}_k)---\left(10\right)$

UtilizeReplace σ², obtain H₀In the case of log-likelihood function

$\ln p\left(X\right|H_0,{\widehat{\mathrm{\σ}}}_{H_0}^2)=-MNln\mathrm{\π}-MNln\left({\widehat{\mathrm{\σ}}}_{H_0}^2\right)-\frac{Ntr\left({\hat{R}}_x\right)}{{\widehat{\mathrm{\σ}}}_{H_0}^2}---\left(11\right)$

In the presence of authorized user, statistics covariance matrix has M-1 weight minimal eigenvalue γ₁=σ²With 1 heavy eigenvalue of maximumUsing maximum sample characteristic valueCharacteristic vectorEstimate real eigenvalue of maximum γ₂Feature to AmountObtainLog-likelihood function expression formula containing unknown parameter estimator is further Abbreviation is：

$\begin{array}{c}\ln p\left(X\right)\left(X|H_1,\hat{h},{\widehat{\mathrm{\σ}}}_s^2,{\widehat{\mathrm{\σ}}}_{H_1}^2\right)=-MN\ln \mathrm{\π}-N\left(M-1\right)ln\left({\widehat{\mathrm{\σ}}}_{H_1}^2\right)\\ -N\ln \left({\widehat{\mathrm{\σ}}}_s^2\left|\right|\hat{h}|{|}^2+{\widehat{\mathrm{\σ}}}_{H_1}^2\right)-\frac{Ntr\left({\hat{R}}_x\right)}{{\widehat{\mathrm{\σ}}}_{H_1}^2}+\frac{N{\widehat{\mathrm{\λ}}}_M{\widehat{\mathrm{\σ}}}_s^2\left|\right|\hat{h}|{|}^2}{\left({\widehat{\mathrm{\σ}}}_s^2\right|\left|\hat{h}\right|{|}^2+{\widehat{\mathrm{\σ}}}_{H_1}^2)\·{\widehat{\mathrm{\σ}}}_{H_1}^2}\end{array}---\left(12\right)$

Work as γ₁=σ²WithWhen two characteristic values meet characteristic value separation condition, characteristic value consistent Estimation device pair The estimation performance of characteristic value can be more preferable；Now require N/M ＞ ξ_MSet up, according to the sensor model set up, ξ_MIt is expressed as formula (13)

$\begin{array}{c}{\mathrm{\ξ}}_M=\frac{1}{M}\underset{r=1}{\overset{2}{\Σ}}{K}_r{\left(\frac{{\mathrm{\γ}}_r}{{\mathrm{\γ}}_r-{\stackrel{\‾}{f}}_1}\right)}^2\\ =\frac{1}{M}\[\left(M-1\right){\left(\frac{{\mathrm{\γ}}_1}{{\mathrm{\γ}}_1-{\stackrel{\‾}{f}}_1}\right)}^2+{\left(\frac{{\mathrm{\γ}}_2}{{\mathrm{\γ}}_2-{\stackrel{\‾}{f}}_1}\right)}^2\]\end{array}---\left(13\right)$

Wherein,For the solution of following formula

$\frac{1}{M}\[\left(M-1\right)\frac{{\mathrm{\γ}}_1^2}{{({\mathrm{\γ}}_1-\stackrel{\‾}{f_1})}^3}+\frac{{\mathrm{\γ}}_2^2}{{({\mathrm{\γ}}_2-\stackrel{\‾}{f_1})}^3}\]=0---\left(14\right)$

Formula (13) and formula (14) are substituted into N/M ＞ ξ_MIn obtain characteristic value separation condition establishment expression formula be：

$N>{\left(1+\frac{1}{M\·\mathrm{\ρ}}\right)}^2{\[1+{\left(\frac{{(1+M\·\mathrm{\ρ})}^2}{M-1}\right)}^{-\frac{1}{3}}\]}^3---\left(15\right)$

Wherein,Represent signal to noise ratio；

By γ₁=σ²WithIn substitution formula (9), H is obtained₁The estimator of unknown parameter in situation following formula (12) Expression formula (16), and preferably estimated when eigenvalue of maximum and minimal eigenvalue meet the separation condition in formula (15)；

$\left\{\begin{array}{c}{\widehat{\mathrm{\γ}}}_2={\widehat{\mathrm{\σ}}}_s^2\left|\right|\hat{h}|{|}^2+{\widehat{\mathrm{\σ}}}_{H_1}^2=N({\widehat{\mathrm{\λ}}}_M-{\widehat{\mathrm{\μ}}}_M)\\ {\widehat{\mathrm{\γ}}}_1={\widehat{\mathrm{\σ}}}_{H_1}^2=\frac{N}{M-1}\underset{k=1}{\overset{M-1}{\Σ}}({\widehat{\mathrm{\λ}}}_k-{\widehat{\mathrm{\μ}}}_k)\\ {\widehat{\mathrm{\σ}}}_s^2\left|\right|\hat{h}|{|}^2={\widehat{\mathrm{\γ}}}_2-{\widehat{\mathrm{\γ}}}_1\end{array}\right.---\left(16\right)$

Formula (11) and formula (12) are substituted into formula (8) and carry out abbreviation, decision statistics are obtained：

$\begin{array}{c}{T}_{CEE-CSS}=\ln \frac{{\left(\underset{k=1}{\overset{M}{\Σ}}\left({\widehat{\mathrm{\λ}}}_k-{\widehat{\mathrm{\μ}}}_k\right)\right)}^M}{{\left(\underset{k=1}{\overset{M-1}{\Σ}}\left({\widehat{\mathrm{\λ}}}_k-{\widehat{\mathrm{\μ}}}_k\right)\right)}^{M-1}\left({\widehat{\mathrm{\λ}}}_M-{\widehat{\mathrm{\μ}}}_M\right)}-\frac{\underset{k=1}{\overset{M-1}{\Σ}}{\widehat{\mathrm{\λ}}}_k}{\frac{N}{M-1}\underset{k=1}{\overset{M-1}{\Σ}}\left({\widehat{\mathrm{\λ}}}_k-{\widehat{\mathrm{\μ}}}_k\right)}\\ +\frac{\underset{k=1}{\overset{M}{\Σ}}{\widehat{\mathrm{\λ}}}_k}{\frac{N}{M}\underset{k=1}{\overset{M}{\Σ}}\left({\widehat{\mathrm{\λ}}}_k-{\widehat{\mathrm{\μ}}}_k\right)}-\frac{{\widehat{\mathrm{\λ}}}_M}{N\left({\widehat{\mathrm{\λ}}}_M-{\widehat{\mathrm{\μ}}}_M\right)}\end{array}---\left(17\right)$

Step 5：Decision statistics and decision threshold are compared and judge that authorized user whether there is by data fusion center；

Data fusion center is by decision statistics T_CEE-CSSCompare to judge whether authorized user occurs with threshold value γ, work as judgement Statistic T_CEE-CSSOccur more than authorized user is adjudicated during thresholding γ, otherwise authorized user does not occur, this is awarded to perceive user's utilization Power frequency spectrum resource, is expressed as