CN104980238B - A kind of cooperative frequency spectrum sensing method sparse based on group - Google Patents
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Abstract
The invention discloses a kind of cooperative frequency spectrum sensing method sparse based on group, comprise the following steps：First pass through basis expansion model and solve primary user m in position xmApproximate transmission power spectrum density ΦmF geographic area A is divided into discrete mesh point by ()The NgIndividual mesh point is respectively positioned onVirtual grid, then cognitive user t is in position xtReceiving power spectrum density Φt(f), ΦtF () is the approximation of cognitive user power spectral density, obtain N × 1 dimension receiving power spectrum density estimated vector, by estimate and approximation simultaneous, obtains system model：To NbNg× 1 n dimensional vector n η is grouped, further according to NbNgThe group result of × 1 n dimensional vector n η is using the sparse N of FOCUSS Algorithm for Solving groupbNg× 1 n dimensional vector n η, estimates η and just can obtain the frequency band of primary user's occupancy and the position of primary user.The present invention need not again make decisions to the frequency spectrum that has recovered and can just obtain the information of frequency spectrum.
Description
Technical field
The invention belongs to wireless communication technology field, it is related to a kind of cooperative frequency spectrum sensing method, and in particular to one kind is based on
The sparse cooperative frequency spectrum sensing method of group.
Background technology
Wireless frequency spectrum is the resource of wireless communication system and its preciousness, and current wireless frequency spectrum exist resource extremely it is dilute
Lack and utilize insufficient predicament, cognitive radio (CR) is the effective technology for solving the problem.Frequency spectrum perception is cognition wireless
The key technology of electricity, according to system bandwidth, frequency spectrum perception can be divided into narrow band spectrum and perceive and broader frequency spectrum perception.Broader frequency spectrum sense
The purpose known is：Spectrum interposition is found in broad frequency range.Broader frequency spectrum is perceived and can be roughly divided into two classes：Based on how Gui this
The broader frequency spectrum of special rate sampling is perceived and perceived with the broader frequency spectrum based on compressed sensing (CS).According to Shannon Sampling Theory, tradition
The sample frequency that perceives of broader frequency spectrum need more than or equal to how Gui this special rate, this results in high sampling rate and complexity.
Because there are a large amount of spectrum interpositions in broader frequency spectrum so that broader frequency spectrum has natural openness.CS is that solution is dilute
The effective ways of the problem of dredging.CS allow broadband signal with owe how Gui this special rate (less than how Gui this special rate) sampled, than tradition
Broader frequency spectrum perceive needed for sample number substantially reduce, this reduces broader frequency spectrum perceive cost.Solved using CS
The common method of broader frequency spectrum perception problems is：The first step, openness using frequency spectrum carries out broader frequency spectrum recovery；Second step,
Each sub-band to broader frequency spectrum carries out detection judgement, judges whether the sub-band is taken by primary user.But this method
Needs make decisions the geographical position of the frequency band and primary user that could obtain primary user's occupancy to the frequency spectrum for having recovered again.
The content of the invention
A kind of shortcoming it is an object of the invention to overcome above-mentioned prior art, there is provided collaboration frequency spectrum sparse based on group
Cognitive method, the method need not again make decisions the frequency band that just obtains primary user's occupancy and primary to the frequency spectrum that has recovered
The geographical position at family.
To reach above-mentioned purpose, the cooperative frequency spectrum sensing method sparse based on group of the present invention is comprised the following steps：
If the broad spectrum that primary user can take is B Hz, the broad spectrum is divided into ν=1,2 ...,
NbIndividual sub-band, in position xmPlace, NmIndividual primary user and NtIndividual cognitive user is distributed in the A of geographic area, according to base expanded mode
Type (basis expansion model, BEM), the approximate transmission power spectrum density Φ of primary usermF () is：
Wherein,It is one group of rectangular base of nonoverlapping unit height, ηmvIt is primary user m in the ν frequency band
Upper ΦmF expansion coefficient that () launches under unit height rectangular base；
Cognitive user t is in position xtReceiving power spectrum density ΦtF () is：
Wherein, γmtIt is the path loss between primary user m and cognitive user t positions, σt 2It is the noise variance of receiving terminal；
Geographic area A is divided into discrete mesh pointPrimary user is set to be distributed in NgIndividual mesh point
On, the NgIndividual mesh point is respectively positioned onVirtual grid, then cognitive user t is in position xtReceiving power
Spectrum density ΦtF () is：
Wherein, γgtIt is the path loss between mesh point g and cognitive user t positions, γgt=γ (| | xg-xt| |),It is 1 × NbNgN dimensional vector n,In each single item be γgt·bνF (), (5) formula is cognitive radio receiving power
The approximate expression of spectrum density.The estimate of cognitive radio receiving power spectrum density is drawn by cyclic graph method of estimation again, will be estimated
Value is obtained with (5) formula simultaneous：
Wherein,It is in frequency to estimate for receiving power spectrum density estimated vector is tieed up in N × 1
It is superimposed in column after doing N point sampling values, BtEach single item in vector is1NFor complete 1 vector, e are tieed up in N × 1tIt is error,
Using to the sparse N of groupbNg× 1 n dimensional vector n η is grouped, further according to NbNgThe group result of × 1 n dimensional vector n η is utilized
The sparse N of FOCUSS Algorithm for Solving groupbNg× 1 n dimensional vector n η, then by the sparse N of groupbNgThe solving result of × 1 n dimensional vector n η substitutes into formula
(9) and in (10), and collaborative spectrum sensing is completed according to formula (9) and formula (10).
If NmThe location sets of individual primary userIn broad frequency range BHz, if cognitive user is on ground
Manage the position x of region AtIt is known, the position of primary user's emitter is unknown, hmt(n；L) it is main customer location xmTo cognition
Customer location xtL footpaths channel impulse response, umN () is m-th transmission signal of primary user, um(n) and channel hmt(n；l)
It is independent, then the signal y that cognitive user t is receivedtN () is：
Wherein, v (n) is additive white Gaussian noise.
By in formula (2) substitution formula (3), then cognitive user t is in position xtReceiving power spectrum density ΦtF () is converted to：
Cognitive user t is obtained in position x according to formula (4)tReceiving power spectrum density ΦtF () is：
Using to the sparse N of groupbNgThe concrete operations that × 1 n dimensional vector n η is grouped are：
Will by the position candidate of primary userIt is divided into NgIndividual group of { ηg:G=1,2 ..., Ng, each candidate
The corresponding N in positionbIndividual sub-band, has N in every groupbElement { ηgν:ν=1,2 ..., Nb, work as NmIndividual primary user is not located at position candidate
xg, then the N to that should organizebIndividual element all 0；Work as NmIndividual primary user is located at position candidate xg, then the N to that should organizebIndividual element
In at least one for non-zero, the corresponding element of sub-band that primary user takes is non-zero, remaining all 0.
Introduce regular terms | | η | |m,p, wherein, m=1/2, p=1, sparse in internal layer m norm introducing groups, outer layer p norms are drawn
Enter sparse between group, then | | the η | | that has regular termsm,pOptimized model be：
Above-mentioned formula (11) is non-convex optimization problem, and FOCUSS algorithms contain L suitable for solution is this kind ofm(m<1) regularization
Problem；
By FOCUSS Algorithm for Solving formula (11), the sparse N of group is obtainedbNg× 1 n dimensional vector n η.
The invention has the advantages that：
The cooperative frequency spectrum sensing method sparse based on group of the present invention when in use, the width that primary user may be taken
Spectral range is divided into NbIndividual sub-band, and geographic area is divided into discrete mesh point, so as to by by frequency spectrum perception this
Individual binary hypothesis test problem is converted into sparse spike estimation problem, recycles the sparse group technology of group and FOCUSS algorithms to ask
Solution N × 1 dimension receiving power spectrum density estimated vector, collaboration frequency spectrum is carried out further according to N × 1 dimension receiving power spectrum density estimated vector
Perceive, therefore the frequency spectrum that has recovered need not again be made decisions and can just obtain the information of frequency spectrum, simplify perception,
The occupancy situation of broader frequency spectrum is more intuitively shown, while estimating the position of primary user.The present invention is according to sparse system in addition
Sparse sparse group's sparse characteristic and between group is carried out to the expansion coefficient of primary user's power spectral density in the group that number vector has
Recover, improve the efficiency and accuracy of recovery.
Brief description of the drawings
Fig. 1 is the geographical position figure that the inventive method estimates the primary user and cognitive user for obtaining；
Fig. 2 is the normalization MSE correlation curves of the present invention and contrast algorithm.
Specific embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings：
The cooperative frequency spectrum sensing method sparse based on group of the present invention is comprised the following steps：
If NmIndividual primary user is distributed in the A of geographic area, NmThe location sets of individual primary user areNt
Individual cognitive user is also distributed about in the A of geographic area, in monitoring broadband B, if cognitive user is in the position x of geographic area AtIt is
Know, the position of primary user's emitter is unknown, channel hmt(n；L) it is main customer location xmTo cognitive user position xtL
Footpath channel impulse response, umN () is m-th transmission signal of primary user, um(n) and channel hmt(n；L) it is independent, then cognitive user
The signal y that t is receivedtN () is：
Wherein, v (n) is additive white Gaussian noise, will receive sample ytN () is divided into multiple coherent blocks, every piece comprising N number of
Sample, n sample is divided into n=iN+q, q=0,1 ..., N-1, i coherent block.
Monitoring broadband B is divided into ν=1,2 ..., NbIndividual sub-band, according to basis expansion model, each primary user's
Approximate transmission power spectrum density ΦmF () is：
Wherein,It is one group of rectangular base of nonoverlapping unit height, ηmvIt is transmission power spectrum density in list
The expansion coefficient launched under the height rectangles substrate of position.
It is assumed that hmt(n；L) it is 0 average, frequency response is Hmt(n；F), path loss model is γmt=E | Hmt(n；f)|2=
γ(||xm-xt| |), wherein γmtIt is the path loss between primary user m and cognitive user t positions, is not having noisy situation
Under, in the presence of single primary user's emitter, the receiving power spectrum density of cognitive user t is Φt(f)=γmtΦm(f), in noise
In the presence of, cognitive user t is in position xtReceiving power spectrum density ΦtF () is：
Wherein,It is the noise variance of receiving terminal, (2) formula is updated in (3) formula, obtains：
If primary user's emitter is distributed in NgIn individual position candidate, this NgIndividual position candidate is located at's
Virtual grid, geographic area A is divided into discrete mesh point, and primary user's emitter is located at NgN in individual position candidatemIndividual position
Put, it is assumed that ηgνIt is relative to position xgSpreading coefficient, γgtIt is position candidate xgTo cognitive user position xtPath loss,
Relative to NgIndividual primary user's position candidate, cognitive user is in position xtReceiving power spectrum density：
Wherein,It is 1 × NbNgN dimensional vector n, 1 × NbNgEach single item in n dimensional vector n is γgt·bν(f), by ηgν
It is superimposed by row, forms NbNg× 1 n dimensional vector n η.
The position of available frequency band and primary user's emitter is just estimated that by estimated vector η, to estimate that η will lead to
Cross to ΦtF () carries out Power estimation, the reception signal y at cognitive user ttN the Fourier transformation of () isIt is relevant at each
Block i calculating cycle figuresIn order to reduce the influence of multipath fading, position xtCognitive user
The cyclic graph of each coherent block is carried out averagely as the following formula using exponentially weighted moving average (EWMA) (EWMA)：
Wherein, i is coherent block, and t is cognitive radio, and N is the sampling number of each coherent block, and τ is forgetting factor, here
τ=0.99 is taken,It is that, by the estimate of EWMA, EWMA is used for substituting cyclic graph averagely, it is cognitive user in position
xtReception PSD estimate, the approximation simultaneous that estimate and (5) formula are drawn is shown below：
Wherein etIt is error, based on (2) formula and (7) formula, can obtains：
Assuming thatRepresent N × 1 n dimensional vector nWhereinIt is sampling
Frequency, obtaining vector matrix model is：
Wherein, BtEach single item in vector is1NRepresent N × 1 and tie up complete 1 vector, without loss of generality, by noise side
Difference moves to equation left side, is included inIn, obtain：
Wherein,
Based on basis expansion model and virtual grid model, frequency spectrum perception problem is converted into the coefficient in system model (10)
The estimation problem of vector η, this is a sparse estimation problem, and the openness of vector η is present in spatial domain and two aspects of frequency domain.It is first
It is first openness, the number N of primary user's emitter in spatial domainmRelative to the number N of position candidategFor it is very small, if primary user
It is not located at mesh point xg, then corresponding model coefficientAll it is 0.Secondly frequency domain is openness, the frequency band that primary user takes
It is sub-fraction relative to whole broader frequency spectrum, when primary user's emitter is located at mesh point xg, primary user's the ν frequency band of occupancy
When, ηgνNon-zero, it can be seen that coefficient vector η be not only it is sparse, and with the sparse characteristic of group, such as Fig. 1 institutes
Show.
1st, it is sparse using group, η is grouped.
Will by the position candidate of primary userIt is divided into NgIndividual group of { ηg:G=1,2 ..., Ng, each candidate
The corresponding N in positionbIndividual sub-band, has N in every groupbElement { ηgν:ν=1,2 ..., Nb, work as NmIndividual primary user is not located at position candidate
xg, then the N to that should organizebIndividual element all 0；Work as NmIndividual primary user is located at position candidate xg, then the N to that should organizebIndividual element
In at least one for non-zero, the corresponding element of sub-band that primary user takes is non-zero, remaining all 0.
2nd, solved using FOCUSS algorithms
According to above group result, due to group's sparse characteristic sparse between group in this group, regular terms is introduced | | η |
|m,p, wherein, m=1/2, p=1 are sparse in internal layer m norm introducing groups, sparse between outer layer p norm introducing groups, then have regular terms | |
η||m,pOptimized model be：
Above-mentioned formula (11) is non-convex optimization problem, and FOCUSS algorithms contain L suitable for solution is this kind ofm(m<1) regularization
Problem；
By FOCUSS Algorithm for Solving formula (11), the sparse N of group is obtainedbNg× 1 n dimensional vector n η.
For the Optimized model of formula (11), the specific steps solved using FOCUSS algorithms are included：
A) maximum iteration of imputation method is T, and the outage threshold of algorithm is ξ, and parameter during emulation is set to T=100,
ξ=10-3；
B) Optimized model is written as the form of Lagrangian functions：Wherein, λ
For Lagrange multiplier, m=1/2, p=1 are tieed up in N × 1；
C) stationary point of above-mentioned Lagrangian is sought, even first-order partial derivative is 0, is shown below：
D) first-order partial derivativeIt is each in partial derivative
Item can be expressed asWherein α (η)=p,It is right
Angular moment battle array；
E) can be solved by step c) and d)：
f)WithSimultaneous is obtained：This isImplicit function form, therefore adopt
Optimal solution is calculated with alternative mannerIterative process is：If calculating
Method reaches iterations T, or ought | | η (k+1)-η (k) | | between iteration twice2<During ξ, algorithm stops, and η now is institute
The vector to be estimated asked.
Emulation experiment
Assuming that there is Nt=10 cognitive users cooperation monitoring frequency spectrums, it is assumed that only exist a primary user be distributed in 100m ×
In the region of 100m, cognitive user is evenly distributed on the region.The accurate location of primary user is unknown, it is assumed that primary user is located at
NgOn=100 mesh points, the broad frequency range of cognitive user monitoring is 21M to 30MHz, and BEM models include Nb=10 units
The frequency substrate of height, a width of W=1MHz of band of each substrate, if primary user takes 4 frequency bands, then coefficient vector η is NgNb=
1000 n dimensional vector ns, and only 4 nonzero values, path loss model are model only with distance dependent, can be expressed as：γgt=min
{1,(||xg-xt||2/d0)-η, wherein d0=50, η=3, using 6 footpath Rayleigh channels, uniform power delay distribution, algorithm repeatedly
Generation number T=100, outage threshold is that error twice between iteration is less than 10-3。
Fig. 1 is the position of cognitive user and primary user's emitter, and cognitive user is circle mark, primary user's emitter in Fig. 1
Position shown in blue asterisk in Fig. 1, it is assumed that the noise variance of each cognitive userAll identical, Fig. 2 is normalized
MSE with noise variance variation diagram, as seen from Figure 2：The method of the present invention is better than L1/2Regularization method and Sparse Group
Lasso algorithms, can obtain estimated accuracy higher, the occupancy situation of effective estimated spectral.
Claims (4)
1. a kind of cooperative frequency spectrum sensing method sparse based on group, it is characterised in that comprise the following steps：
If the broad spectrum that primary user can take is B Hz, the broad spectrum is divided into ν=1,2 ..., NbHeight
Frequency band, position existsNmIndividual primary user and position existNtIndividual cognitive user is distributed in geographic areaIt is interior,
Then there is primary user m in position xmTransmission power spectrum density ΦmF () is：
Wherein,It is one group of rectangular base of nonoverlapping unit height, ηmvFor primary user m on the ν frequency band Φm
F expansion coefficient that () launches under unit height rectangular base；
Cognitive user t is in position xtReceiving power spectrum density ΦtF () is：
Wherein, γmtIt is the path loss between primary user m and cognitive user t positions, σt 2It is the noise variance of receiving terminal；
By geographic areaIt is divided into discrete mesh pointIf primary user is distributed in NgThe N of individual mesh pointmIt is individual
On position, the NgIndividual mesh point is respectively positioned onVirtual grid, then cognitive user t is in position xtReception work(
Rate spectrum density ΦtF () is：
Wherein, γgtIt is the path loss between mesh point g and cognitive user t positions, γgt=γ (| | xg-xt| |),For
1×NbNgN dimensional vector n,In each single item be γgt·bνF (), obtains cognitive radio and connects according to cyclic graph method of estimation
The estimate of power spectral density is received, the estimate further according to (5) formula and cognitive radio receiving power spectrum density is obtained：
Wherein,For receiving power spectrum density estimated vector is tieed up in N × 1,By to estimate in frequency
It is superimposed what is obtained in column after doing N point sampling values, BtEach single item in vector is1NFor complete 1 vector, e are tieed up in N × 1tFor by mistake
Difference,
Using to the sparse N of groupbNg× 1 n dimensional vector n η is grouped, further according to NbNgThe group result of × 1 n dimensional vector n η utilizes FOCUSS
The sparse N of Algorithm for Solving groupbNg× 1 n dimensional vector n η, draws the frequency band of primary user's occupancy and the geographical position of primary user, completes cooperation
Frequency spectrum perception.
2. the cooperative frequency spectrum sensing method sparse based on group according to claim 1, it is characterised in that
If NmThe location sets of individual primary userIn broad frequency range B Hz, if cognitive user is in geographic region
DomainPosition xtIt is known, the position of primary user's emitter is unknown, hmt(n；L) it is main customer location xmTo cognitive user
Position xtL footpaths channel impulse response, umN () is m-th transmission signal of primary user, um(n) and channel hmt(n；It is l) independent,
The signal y that then cognitive user t is receivedtN () is：
Wherein, v (n) is additive white Gaussian noise.
3. the cooperative frequency spectrum sensing method sparse based on group according to claim 1, it is characterised in that
By in formula (2) substitution formula (3), then cognitive user t is in position xtReceiving power spectrum density ΦtF () is converted to：
Cognitive user t is obtained in position x according to formula (4)tReceiving power spectrum density ΦtF () is：
。
4. the cooperative frequency spectrum sensing method sparse based on group according to claim 1, it is characterised in that using sparse to group
NbNgThe concrete operations that × 1 n dimensional vector n η is grouped are：
Will by the position candidate of primary userIt is divided into NgIndividual group of { ηg:G=1,2 ..., Ng, each position candidate
Correspondence NbIndividual sub-band, has N in every groupbElement { ηgν:ν=1,2 ..., Nb, work as NmIndividual primary user is not located at position candidate xg,
The then N to that should organizebIndividual element all 0；Work as NmIndividual primary user is located at position candidate xg, then the N to that should organizebIn individual element
At least one is non-zero, and the corresponding element of sub-band that primary user takes is non-zero, and remaining all 0.
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