CN105471528B - A kind of cooperation spectrum sensing method adaptively adjusted - Google Patents

A kind of cooperation spectrum sensing method adaptively adjusted Download PDF

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CN105471528B
CN105471528B CN201510833459.4A CN201510833459A CN105471528B CN 105471528 B CN105471528 B CN 105471528B CN 201510833459 A CN201510833459 A CN 201510833459A CN 105471528 B CN105471528 B CN 105471528B
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CN105471528A (en
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郑紫微
秦闯
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Beijing Xuhui Xinrui Technology Co ltd
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Ningbo University
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Abstract

The present invention relates to the cooperation spectrum sensing method adaptively adjusted, after the optimal threshold value for getting energy measuring judgement including cognitive user successively, energy detection results and itself signal to noise ratio are sent to frequency spectrum perception fusion center respectively；Frequency spectrum perception fusion center counts respectively perceives authorized user's frequency spectrum as seizure condition, the cognitive user number of idle condition, calculate the sensing results of cognitive user and sincere coefficient, average detected probability, global detection probability, the global false dismissal probability that authorized user's frequency spectrum is seizure condition are calculated, and average detected probability, global detection probability, global false dismissal probability and the global false-alarm probability that authorized user's frequency spectrum is idle condition；After establishing the frequency spectrum perception error function based on cognitive user number, optimum synergistic cognitive user number is used as using numerical value corresponding to frequency spectrum perception error function minimum value, frequency spectrum perception fusion center fusion calculation amount is reduced, and completes cooperation spectrum after optimum synergistic cognitive user is got and perceives.

Description

A kind of cooperation spectrum sensing method adaptively adjusted
Technical field
The present invention relates to wireless communication field, more particularly to a kind of cooperation spectrum sensing method adaptively adjusted.
Background technology
As the key technology for solving communication spectrum resource scarcity, cognitive radio (Cognitive Radio, CR) can " waiting for an opportunity " is utilized and shared to idle frequency spectrum, and then solves frequency spectrum resource problem in short supply.
The Basic Ways of cognitive radio are：Cognitive user uses frequency spectrum perception to the frequency of mandate in surrounding environment first Spectrum resource is continued to monitor, and then under conditions of ensureing that authorized user can preferentially take this section of frequency spectrum, cognitive user is certainly Adaptively adjust and communicated on transceiver to idle frequency spectrum, idle frequency spectrum resource is utilized with effective, sufficient.Work as cognitive user Perceive (or detection) to authorization user signal occur when, cognitive user then will quickly vacate the channel of its " waiting for an opportunity " occupancy, with Authorized user's use is given, and then avoids disturbing the proper communication of authorized user.It can be seen that frequency spectrum perception used by cognitive user Situation be present for authorization user signal to detection performance of authorized user's detection with height, frequency spectrum perception technology in method requirement Clinical significance of detecting it is great.
In actual environment, in order to reduce the factors such as multipath fading, shadow effect and incorrect noise to detection The adverse effect of performance, the cooperation spectrum sensing method based on multiple cognitive users are suggested in succession.In existing cooperation spectrum In cognitive method, most cooperation spectrum sensing methods assume that each cognitive user uses energy detection method, pass through default fixation Judging threshold detects to the signal energy of reception, and then each cognitive user sends testing result and melted to frequency spectrum perception Conjunction center carries out fusion treatment, to reach the purpose accurately perceived to frequency spectrum.
However, existing cooperation spectrum sensing method still has some shortcomings part：On the one hand, in the collaboration frequency of reality During spectrum perceives, cognitive user received signal energy changes, but existing cooperation spectrum sensing method does not account for When cognitive user received signal energy changes, default fixed sentence threshold value is unfavorable for cognitive user and makes accurate energy The problem of amount detection, this will cause each cognitive user to have relatively low detection performance in actual energy detection, is unfavorable for improving The whole detection performance of collaborative perception；On the other hand, existing cooperation spectrum sensing method does not account for frequency spectrum perception fusion The huge fusion calculation amount problem at center, reduced so as to cause frequency spectrum perception fusion center to make the efficiency of fusion detection, delay Each cognitive user in time takes or exited the detecting period of idle frequency spectrum.
The content of the invention
The technical problems to be solved by the invention are to provide a kind of acquisition that can either be adaptive for above-mentioned prior art Each cognitive user carries out the optimal threshold value of energy measuring judgement, can determine optimum synergistic cognitive user again, reduces frequency spectrum sense Know the cooperation spectrum sensing method of the adaptive adjustment of fusion center fusion calculation amount.
Technical scheme is used by the present invention solves above-mentioned technical problem：A kind of cooperation spectrum adaptively adjusted perceives Method, for authorized user, frequency spectrum perception fusion center and N number of cognitive user composition cognition wireless network in, its feature It is, in turn includes the following steps：
(1) N number of cognitive user carries out local energy detection to the spectrum occupancy of authorized user, and by frequency spectrum perception knot Fruit and cognitive user itself signal to noise ratio are sent respectively to frequency spectrum perception fusion center；Wherein, cognitive user is labeled as CRi(i= 1,2 ..., N), cognitive user CRiItself signal to noise ratio is snri, authorized user is labeled as PU, and frequency spectrum perception fusion center is labeled as FC；
(2) the frequency spectrum perception result that frequency spectrum perception fusion center FC is sent according to N number of cognitive user, count N number of cognition and use The cognitive user number that authorized user's PU frequency spectrums are seizure condition is perceived in family to be m (1≤m≤N), perceive authorized user PU Frequency spectrum is that the cognitive user number of idle condition is N-m；Wherein, authorized user PU frequency spectrums are that seizure condition is designated as H1, authorize and use Family PU frequency spectrums are that idle condition is designated as H0；
(3) signal to noise ratio that frequency spectrum perception fusion center FC is sent according to N number of cognitive user, m is calculated and perceives mandate use Family PU frequency spectrums are seizure condition H1Cognitive user sincerity coefficient κ1,jAnd it is the free time that N-m, which perceive authorized user PU frequency spectrums, State H0Cognitive user sincerity coefficient κ2,t；Wherein, sincere coefficient κ1,jAnd κ2,tCalculation formula it is as follows：
(4) respective sensing results and sincere coefficient κ of the frequency spectrum perception fusion center FC according to m cognitive user1,j, point Not Ji Suan authorized user PU frequency spectrums be seizure condition H1Average detected probabilityGlobal detection probabilityWith this occupancy State H1Corresponding global false dismissal probabilityAnd authorized user PU frequency spectrum is idle condition H0Average detected probabilityGlobal detection probabilityThis idle condition H0Corresponding global false dismissal probabilityWith global false-alarm probabilityWherein, the process comprises the following steps (4-1) to step (4-3)：
(4-1) establishes the global error detection probability P of m cognitive user collaborative perceptione, obtain the energy on decision-making thresholding Measure inspection optimization function gamma*And the optimal threshold value γ of energy measuringopt, and it is seizure condition H to calculate authorized user PU frequency spectrums1 Average detected probabilityWherein,
The global error detection probability P of m cognitive user collaborative perceptioneCalculation formula is as follows：
Wherein,Idle condition H is in for authorized user PU frequency spectrums0Probability,It is in and accounts for for authorized user PU frequency spectrums With state H1Probability；PfFor global false-alarm probability, PdFor global detection probability, PmFor global false dismissal probability；For corresponding position Seizure condition H is in authorized user PU frequency spectrums1M cognitive user average signal-to-noise ratio, Q (z) represents that normal Gaussian is complementary Integral function；γ is the threshold value of energy measuring,For the variance of white Gaussian noise；Wherein,snriTo recognize Know user CRiThe signal to noise ratio of itself；
Energy measuring majorized function γ on decision-making thresholding*It is defined as：
The optimal threshold value γ of energy measuringoptFor：
Authorized user PU frequency spectrums are seizure condition H1Average detected probabilityCalculation formula is as follows：
It is seizure condition H that (4-2) weighs user PU frequency spectrums according to gained1Average detected probabilityAnd m cognition is used The sincere coefficient κ at family1,j, it is seizure condition H to calculate authorized user PU frequency spectrums1Global detection probabilityWith this seizure condition H1Corresponding global false dismissal probabilityWherein, global detection probabilityWith global false dismissal probabilityCalculation formula It is as follows：
(4-3) is idle condition H according to gained authorized user PU frequency spectrums0Average detected probabilityAnd N-m recognizes Know the sincere coefficient κ of user2,t, it is idle condition H to calculate authorized user PU frequency spectrums0Global detection probabilityIt is idle with this State H0Corresponding global false dismissal probabilityGlobal false-alarm probabilityWherein, average detected probabilityIt is global Detection probabilityGlobal false dismissal probabilityWith global false-alarm probabilityCalculation formula difference it is as follows：
(5) frequency spectrum perception fusion center FC is seizure condition H according to authorized user PU frequency spectrums1Corresponding global false dismissal probabilityAnd authorized user PU frequency spectrums are idle condition H0Corresponding global false-alarm probabilityFoundation is based on cognitive user The frequency spectrum perception error function Fun (m) of number；Wherein, frequency spectrum perception error function Fun (m) calculation formula are as follows：
Wherein, PpuRepresent the probability that authorized user PU signals authorize frequency spectrum to occur at it；
(6) frequency spectrum perception error function Fun (m) frequency spectrum perception error minimum value Fun (m are calculated0), and with the frequency spectrum sense Know error function minimum value Fun (m0) corresponding to numerical value m0(m0≤ m) as the optimum synergistic cognitive user number for participating in collaborative perception Mesh, and to m cognitive user according to its corresponding snr value snriDescending arrangement is carried out, obtains the descending of m cognitive user Arrangement group；
(7) the preceding m in cognitive user descending arrangement group is chosen0Individual cognitive user is as the optimum synergistic for participating in collaborative perception Cognitive user；Wherein, the optimum synergistic cognitive user for marking selection respectively is CR'r, wherein, r=1,2 ..., m0；
(8) according to m in step (7)0Individual optimum synergistic cognitive user CR'rDetection probability, frequency spectrum perception fusion center FC The final detection result of N number of cognitive user collaborative perception is used as using the global detection probability after the OR criterions collaboration of weighting；Wherein, The OR criterions of weighting are as follows：
Wherein, Pd,rFor optimum synergistic cognitive user CR'rDetection probability, Pfa,rFor optimum synergistic cognitive user CR'r's False-alarm probability；QdFor the global detection probability after collaborative perception, QfaFor the global false-alarm probability after collaborative perception；m0For optimal association With the number of cognitive user；ωrFor optimum synergistic cognitive user CR'rWeight coefficient.
Compared with prior art, the advantage of the invention is that：By the sincere coefficient and the foundation that obtain each cognitive user After the global error detection probability of cognitive user collaborative perception, energy measuring majorized function and energy on decision-making thresholding are obtained The optimal threshold value that amount detection judges, to adapt to the change of each cognitive user received signal energy, and with the optimal threshold value Obtain the detection probability of each cognitive user；Then the frequency spectrum perception error function based on cognitive user number is established, and with frequency spectrum Cognitive user number corresponding to perceptual error function minimum acquires optimal association as optimum synergistic cognitive user number Same cognitive user, so as to while collaborative perception performance is ensured, reduce the fusion calculation amount of frequency spectrum perception fusion center, finally Complete collaborative perception.The cooperation spectrum sensing method can either be adaptive adjustment, obtain the judgement of cognitive user energy measuring Optimal threshold value, and can is enough under the premise of collaborative perception performance is ensured, it is determined that collaboration number is less than cognitive user total number most Good coordinating cognition user, reduce frequency spectrum perception fusion center fusion calculation amount.
Brief description of the drawings
Fig. 1 is the schematic flow sheet of the cooperation spectrum sensing method adaptively adjusted in the present embodiment.
Embodiment
The present invention is described in further detail below in conjunction with accompanying drawing embodiment.
As shown in figure 1, the cooperation spectrum sensing method adaptively adjusted in the present embodiment, for authorized user, frequency spectrum sense In the cognition wireless network for knowing fusion center and N number of cognitive user composition, in turn include the following steps：
(1) N number of cognitive user carries out local energy detection to the spectrum occupancy of authorized user, and by frequency spectrum perception knot Fruit and cognitive user itself signal to noise ratio are sent respectively to frequency spectrum perception fusion center；Wherein, cognitive user is labeled as CRi(i= 1,2 ..., N), cognitive user CRiItself signal to noise ratio is snri, authorized user is labeled as PU, and frequency spectrum perception fusion center is labeled as FC；N number of cognitive user is respectively CR1、CR2、CR3、…、CRN-1、CRN；N number of cognitive user CR1To CRNItself corresponding noise Than to be respectively snr1、snr2、snr3、…、snrN-1、snrN；
(2) the frequency spectrum perception result that frequency spectrum perception fusion center FC is sent according to N number of cognitive user, count N number of cognition and use The cognitive user number that authorized user's PU frequency spectrums are seizure condition is perceived in family to be m (1≤m≤N), perceive authorized user PU Frequency spectrum is that the cognitive user number of idle condition is N-m；Wherein, authorized user PU frequency spectrums are that seizure condition is designated as H1, authorize and use Family PU frequency spectrums are that idle condition is designated as H0；
(3) signal to noise ratio that frequency spectrum perception fusion center FC is sent according to N number of cognitive user, m is calculated and perceives mandate use Family PU frequency spectrums are seizure condition H1Cognitive user sincerity coefficient κ1,jAnd it is the free time that N-m, which perceive authorized user PU frequency spectrums, State H0Cognitive user sincerity coefficient κ2,t；Wherein, the credible journey of the made detection of cognitive user corresponding to sincere coefficient expression Degree, also characterize the detectability of cognitive user；Sincere coefficient is higher, shows that the detection probability of corresponding cognitive user is higher； Sincere coefficient κ1,jAnd κ2,tCalculation formula it is as follows：
(4) respective sensing results and sincere coefficient κ of the frequency spectrum perception fusion center FC according to m cognitive user1,j, point Not Ji Suan authorized user PU frequency spectrums be seizure condition H1Average detected probabilityGlobal detection probabilityWith this occupancy State H1Corresponding global false dismissal probabilityAnd authorized user PU frequency spectrum is idle condition H0Average detected probabilityGlobal detection probabilityThis idle condition H0Corresponding global false dismissal probabilityWith global false-alarm probabilityWherein, the process comprises the following steps (4-1) to step (4-3)：
(4-1) establishes the global error detection probability P of m cognitive user collaborative perceptione, obtain the energy on decision-making thresholding Measure inspection optimization function gamma*And the optimal threshold value γ of energy measuringopt, and it is seizure condition H to calculate authorized user PU frequency spectrums1 Average detected probabilityThe thresholding of energy measuring is the decision threshold in energy measuring；Wherein,
The global error detection probability P of m cognitive user collaborative perceptioneCalculation formula is as follows：
Wherein,Idle condition H is in for authorized user PU frequency spectrums0Probability,It is in and accounts for for authorized user PU frequency spectrums With state H1Probability；PfFor global false-alarm probability, PdFor global detection probability, PmFor global false dismissal probability；For corresponding position Seizure condition H is in authorized user PU frequency spectrums1M cognitive user average signal-to-noise ratio, γ be energy measuring threshold value,For the variance of white Gaussian noise；Wherein,snriFor cognitive user CRiThe signal to noise ratio of itself；
Energy measuring majorized function γ on decision-making thresholding*It is defined as：
By to the energy measuring majorized function γ on decision-making thresholding*Extreme value is sought, to obtain energy measuring judgement most Excellent threshold value γoptFor：
I.e. during each cognitive user utilizes energy measuring, when the judging threshold for received signal energy takes most Excellent threshold value γoptWhen, cognitive user can accurately detect the presence of received signal, meet, adapted to received signal The situation of energy dynamics change, so as to obtain more accurate energy measuring judging threshold, improves follow-up cognitive user The individually accuracy of detection and cooperation detection；
Authorized user PU frequency spectrums are seizure condition H1Average detected probabilityCalculation formula is as follows：
It is seizure condition H that (4-2) weighs user PU frequency spectrums according to gained1Average detected probabilityAnd m cognition is used The sincere coefficient κ at family1,j, it is seizure condition H to calculate authorized user PU frequency spectrums1Global detection probabilityWith this seizure condition H1Corresponding global false dismissal probabilityWherein, global detection probabilityWith global false dismissal probabilityCalculation formula It is as follows：
(4-3) is idle condition H according to gained authorized user PU frequency spectrums0Average detected probabilityAnd N-m recognizes Know the sincere coefficient κ of user2,t, it is idle condition H to calculate authorized user PU frequency spectrums0Global detection probabilityIt is idle with this State H0Corresponding global false dismissal probabilityGlobal false-alarm probabilityWherein, average detected probabilityIt is global Detection probabilityGlobal false dismissal probabilityWith global false-alarm probabilityCalculation formula difference it is as follows：
(5) frequency spectrum perception fusion center FC is seizure condition H according to authorized user PU frequency spectrums1Corresponding global false dismissal probabilityAnd authorized user PU frequency spectrums are idle condition H0Corresponding global false-alarm probabilityFoundation is based on cognitive user The frequency spectrum perception error function Fun (m) of number；The frequency spectrum perception error function Fun (m) characterizes cognitive user number as m When the error condition that perceives of corresponding cooperation spectrum；The frequency spectrum perception error amount is smaller, shows the detection that cooperation spectrum perceives Performance is better；Wherein, frequency spectrum perception error function Fun (m) calculation formula are as follows：
Wherein, PpuRepresent the probability that authorized user PU signals authorize frequency spectrum to occur at it；
(6) frequency spectrum perception error function Fun (m) frequency spectrum perception error minimum value Fun (m are calculated0), and with the frequency spectrum sense Know error function minimum value Fun (m0) corresponding to numerical value m0(m0≤ m) as the optimum synergistic cognitive user number for participating in collaborative perception Mesh, and to m cognitive user according to its corresponding snr value snriDescending arrangement is carried out, obtains the descending of m cognitive user Arrangement group；
Wherein, when the cognitive user number for participating in collaborative perception is m0When, the collaborative perception between cognitive user has most Small frequency spectrum perception error, now correspond to cooperation spectrum perception has stronger detection performance, and now m0Individual cognition is used Amount mesh can reduce calculating when succeeding spectral perceives fusion center FC fusions under the premise of smaller frequency spectrum perception error is ensured Amount, improve cooperation detection efficiency；
Because the signal to noise ratio of each cognitive user is still the key of its frequency spectrum detection performance of influence, therefore, according to noise Ratio size order makees descending arrangement, can facilitate using signal to noise ratio as the mark for distinguishing detection performance, have height to select The cognitive user of detection performance；
(7) the preceding m in cognitive user descending arrangement group is chosen0Individual cognitive user is as the optimum synergistic for participating in collaborative perception Cognitive user；Wherein, the optimum synergistic cognitive user for marking selection respectively is CR'r, wherein, r=1,2 ..., m0；
For example, the cognitive user descending arrangement group obtained after being arranged according to signal to noise ratio descending is { CR1, CR2、…、CRm0、 CRm0+1..., CRmWhen, then m before selecting0Individual cognitive user, i.e. { CR1, CR2、…、CRm0As the optimal of participation collaborative perception Coordinating cognition user, and correspondence markings CR respectively1To CRm0For optimum synergistic cognitive user CR'1To CR'm0；
(8) according to m in step (7)0Individual optimum synergistic cognitive user CR'rDetection probability, frequency spectrum perception fusion center FC The final detection result of N number of cognitive user collaborative perception is used as using the global detection probability after the OR criterions collaboration of weighting；Wherein, The OR criterions of weighting are as follows：
Wherein, Pd,rFor optimum synergistic cognitive user CR'rDetection probability, Pfa,rFor optimum synergistic cognitive user CR'r's False-alarm probability；QdFor the global detection probability after collaborative perception, QfaFor the global false-alarm probability after collaborative perception；m0For optimal association With the number of cognitive user；ωrFor optimum synergistic cognitive user CR'rWeight coefficient.Wherein, ωrIt is bigger, represent the weight system The detection performance of optimum synergistic cognitive user is stronger corresponding to number.

Claims (1)

1. a kind of cooperation spectrum sensing method adaptively adjusted, for authorized user, frequency spectrum perception fusion center and N number of recognize In the cognition wireless network for knowing user's composition, it is characterised in that in turn include the following steps：
(1) N number of cognitive user carries out local energy detection to the spectrum occupancy of authorized user, and by frequency spectrum perception result with And cognitive user itself signal to noise ratio is sent respectively to frequency spectrum perception fusion center；Wherein, cognitive user is labeled as CRi(i=1, 2 ..., N), cognitive user CRiItself signal to noise ratio is snri, authorized user is labeled as PU, and frequency spectrum perception fusion center is labeled as FC；
(2) the frequency spectrum perception result that frequency spectrum perception fusion center FC is sent according to N number of cognitive user, is counted in N number of cognitive user The cognitive user number that authorized user's PU frequency spectrums are seizure condition is perceived to be m (1≤m≤N), perceive authorized user's PU frequency spectrums It is N-m for the cognitive user number of idle condition；Wherein, authorized user PU frequency spectrums are that seizure condition is designated as H1, authorized user PU Frequency spectrum is that idle condition is designated as H0；
(3) signal to noise ratio that frequency spectrum perception fusion center FC is sent according to N number of cognitive user, m is calculated and perceives authorized user PU Frequency spectrum is seizure condition H1Cognitive user sincerity coefficient κ1,jAnd it is idle condition H that N-m, which perceive authorized user PU frequency spectrums,0 Cognitive user sincerity coefficient κ2,t；Wherein, sincere coefficient κ1,jAnd κ2,tCalculation formula it is as follows：
<mrow> <msub> <mi>&amp;kappa;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>snr</mi> <mi>j</mi> <mn>2</mn> </msubsup> </mrow> <mrow> <mfrac> <mn>1</mn> <mi>m</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msubsup> <mi>snr</mi> <mi>j</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> <msub> <mi>&amp;kappa;</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>snr</mi> <mi>t</mi> <mn>2</mn> </msubsup> </mrow> <mrow> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mi>m</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mi>m</mi> </mrow> </munderover> <msubsup> <mi>snr</mi> <mi>t</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>;</mo> </mrow>
(4) respective sensing results and sincere coefficient κ of the frequency spectrum perception fusion center FC according to m cognitive user1,j, count respectively It is seizure condition H to calculate authorized user PU frequency spectrums1Average detected probabilityGlobal detection probabilityWith this seizure condition H1Corresponding global false dismissal probabilityAnd authorized user PU frequency spectrum is idle condition H0Average detected probabilityGlobal detection probabilityThis idle condition H0Corresponding global false dismissal probabilityWith global false-alarm probabilityWherein, the process comprises the following steps (4-1) to step (4-3)：
(4-1) establishes the global error detection probability P of m cognitive user collaborative perceptione, obtain the energy inspection on decision-making thresholding Survey majorized function γ*And the optimal threshold value γ of energy measuringopt, and it is seizure condition H to calculate authorized user PU frequency spectrums1It is flat Equal detection probabilityWherein,
The global error detection probability P of m cognitive user collaborative perceptioneCalculation formula is as follows：
<mrow> <msub> <mi>P</mi> <mi>e</mi> </msub> <mo>=</mo> <msub> <mi>P</mi> <msub> <mi>H</mi> <mn>0</mn> </msub> </msub> <msub> <mi>P</mi> <mi>f</mi> </msub> <mo>+</mo> <msub> <mi>P</mi> <msub> <mi>H</mi> <mn>1</mn> </msub> </msub> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <msub> <mi>H</mi> <mn>1</mn> </msub> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <msub> <mi>H</mi> <mn>0</mn> </msub> </msub> <mo>;</mo> </mrow>
<mrow> <msub> <mi>P</mi> <mi>f</mi> </msub> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;gamma;</mi> <mo>-</mo> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> <mrow> <mfrac> <mn>2</mn> <mi>m</mi> </mfrac> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>4</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>d</mi> </msub> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;gamma;</mi> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mover> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> <mrow> <mfrac> <mn>2</mn> <mi>m</mi> </mfrac> <mrow> <mo>(</mo> <mn>2</mn> <mover> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>4</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mi>d</mi> </msub> <mo>;</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mi>z</mi> <mi>&amp;infin;</mi> </msubsup> <mfrac> <mn>1</mn> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </msup> <mi>d</mi> <mi>x</mi> <mo>;</mo> </mrow>
Wherein,Idle condition H is in for authorized user PU frequency spectrums0Probability,It is in for authorized user PU frequency spectrums and takes shape State H1Probability；PfFor global false-alarm probability, PdFor global detection probability, PmFor global false dismissal probability；Awarded for corresponding be in Power user PU frequency spectrums are in seizure condition H1M cognitive user average signal-to-noise ratio, Q (z) represents the complementary integration of normal Gaussian Function；γ is the threshold value of energy measuring,For the variance of white Gaussian noise；Wherein,snriUsed for cognition Family CRiThe signal to noise ratio of itself；
Energy measuring majorized function γ on decision-making thresholding*It is defined as：
<mrow> <msup> <mi>&amp;gamma;</mi> <mo>*</mo> </msup> <mo>=</mo> <munder> <mrow> <msub> <mi>argminP</mi> <mi>e</mi> </msub> </mrow> <mi>&amp;gamma;</mi> </munder> <mo>=</mo> <msub> <mi>P</mi> <msub> <mi>H</mi> <mn>0</mn> </msub> </msub> <mo>&amp;CenterDot;</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;gamma;</mi> <mo>-</mo> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> <mrow> <mfrac> <mn>2</mn> <mi>m</mi> </mfrac> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>4</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>P</mi> <msub> <mi>H</mi> <mn>1</mn> </msub> </msub> <mo>&amp;CenterDot;</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;gamma;</mi> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mover> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> <mrow> <mfrac> <mn>2</mn> <mi>m</mi> </mfrac> <mrow> <mo>(</mo> <mn>2</mn> <mover> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>4</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
The optimal threshold value γ of energy measuringoptFor：
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>&amp;gamma;</mi> <msub> <mo>|</mo> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>P</mi> <mi>e</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>&amp;gamma;</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mn>2</mn> </mfrac> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mn>2</mn> </msubsup> <msqrt> <mrow> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mo>+</mo> <mover> <mfrac> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mn>2</mn> </mfrac> <mo>&amp;OverBar;</mo> </mover> <mo>+</mo> <mfrac> <mrow> <mn>4</mn> <mover> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>+</mo> <mn>2</mn> </mrow> <mrow> <mi>m</mi> <mo>&amp;CenterDot;</mo> <mover> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> </mrow> </mfrac> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mfrac> <msub> <mi>P</mi> <msub> <mi>H</mi> <mn>0</mn> </msub> </msub> <msub> <mi>P</mi> <msub> <mi>H</mi> <mn>1</mn> </msub> </msub> </mfrac> <msqrt> <mrow> <mn>2</mn> <mover> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>+</mo> <mn>1</mn> </mrow> </msqrt> </mrow> </msqrt> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
Authorized user PU frequency spectrums are seizure condition H1Average detected probabilityCalculation formula is as follows：
<mrow> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mover> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <mo>(</mo> <mn>2</mn> <mo>/</mo> <mi>N</mi> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mover> <mrow> <mi>s</mi> <mi>n</mi> <mi>r</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
It is seizure condition H that (4-2) weighs user PU frequency spectrums according to gained1Average detected probabilityAnd m cognitive user Sincere coefficient κ1,j, it is seizure condition H to calculate authorized user PU frequency spectrums1Global detection probabilityWith this seizure condition H1It is right The global false dismissal probability answeredWherein, global detection probabilityWith global false dismissal probabilityCalculation formula is such as Under：
<mrow> <msub> <mi>D</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>=</mo> <mroot> <mrow> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>&amp;kappa;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> <mi>m</mi> </mroot> <mo>&amp;CenterDot;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mi>m</mi> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <mi>H</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>l</mi> </msup> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>;</mo> <msub> <mi>D</mi> <mrow> <mi>u</mi> <mi>n</mi> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>D</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>;</mo> </mrow>
(4-3) is idle condition H according to gained authorized user PU frequency spectrums0Average detected probabilityAnd N-m cognition is used The sincere coefficient κ at family2,t, it is idle condition H to calculate authorized user PU frequency spectrums0Global detection probabilityWith this idle condition H0Corresponding global false dismissal probabilityGlobal false-alarm probabilityWherein, average detected probabilityGlobal detection ProbabilityGlobal false dismissal probabilityWith global false-alarm probabilityCalculation formula difference it is as follows：
<mrow> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> <msqrt> <mrow> <mo>(</mo> <mn>2</mn> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
<mrow> <msub> <mi>D</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>=</mo> <mroot> <mrow> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mi>m</mi> </mrow> </munderover> <msub> <mi>&amp;kappa;</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>t</mi> </mrow> </msub> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mi>m</mi> </mrow> </mroot> <mo>&amp;CenterDot;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mi>N</mi> <mo>-</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mi>l</mi> </msup> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mi>l</mi> </mrow> </msup> <mo>;</mo> </mrow>
<mrow> <msub> <mi>D</mi> <mrow> <mi>F</mi> <mi>a</mi> <mi>i</mi> <mi>l</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>D</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>;</mo> </mrow>
(5) frequency spectrum perception fusion center FC is seizure condition H according to authorized user PU frequency spectrums1Corresponding global false dismissal probabilityAnd authorized user PU frequency spectrums are idle condition H0Corresponding global false-alarm probabilityFoundation is based on cognitive user The frequency spectrum perception error function Fun (m) of number；Wherein, frequency spectrum perception error function Fun (m) calculation formula are as follows：
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>F</mi> <mi>u</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>D</mi> <mrow> <mi>u</mi> <mi>n</mi> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>D</mi> <mrow> <mi>F</mi> <mi>a</mi> <mi>i</mi> <mi>l</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>D</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>D</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mroot> <mrow> <munderover> <mi>&amp;Pi;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>&amp;kappa;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> <mi>m</mi> </mroot> <mo>&amp;CenterDot;</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mi>m</mi> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mi>l</mi> </msup> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mi>l</mi> </mrow> </msup> <mo>)</mo> </mrow> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mroot> <mrow> <munderover> <mi>&amp;Pi;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mi>m</mi> </mrow> </munderover> <msub> <mi>&amp;kappa;</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>t</mi> </mrow> </msub> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mi>m</mi> </mrow> </mroot> <mo>&amp;CenterDot;</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mi>N</mi> <mo>-</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mi>l</mi> </msup> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>det</mi> <mo>,</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mi>l</mi> </mrow> </msup> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
Wherein, PpuRepresent the probability that authorized user PU signals authorize frequency spectrum to occur at it；
(6) frequency spectrum perception error function Fun (m) frequency spectrum perception error minimum value Fun (m are calculated0), and missed with the frequency spectrum perception Difference function minimum value Fun (m0) corresponding to numerical value m0(m0≤ m) as participate in collaborative perception optimum synergistic cognitive user number, And to m cognitive user according to its corresponding snr value snriDescending arrangement is carried out, obtains the descending arrangement of m cognitive user Group；
(7) the preceding m in cognitive user descending arrangement group is chosen0Individual cognitive user is as the optimum synergistic cognition for participating in collaborative perception User；Wherein, the optimum synergistic cognitive user for marking selection respectively is CR'r, wherein, r=1,2 ..., m0；
(8) according to m in step (7)0Individual optimum synergistic cognitive user CR'rDetection probability, frequency spectrum perception fusion center FC is to add Final detection result of the global detection probability as N number of cognitive user collaborative perception after the OR criterions collaboration of power；Wherein, weight OR criterions it is as follows：
<mrow> <msub> <mi>Q</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> </munderover> <msub> <mi>&amp;omega;</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>Q</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> </munderover> <msub> <mi>&amp;omega;</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>f</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>&amp;omega;</mi> <mi>r</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>P</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> </munderover> <msub> <mi>P</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> </mrow> </mfrac> <mo>,</mo> <mi>r</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>m</mi> <mn>0</mn> </msub> <mo>;</mo> </mrow>
Wherein, Pd,rFor optimum synergistic cognitive user CR'rDetection probability, Pfa,rFor optimum synergistic cognitive user CR'rFalse-alarm Probability；QdFor the global detection probability after collaborative perception, QfaFor the global false-alarm probability after collaborative perception；m0Recognize for optimum synergistic Know the number of user；ωrFor optimum synergistic cognitive user CR'rWeight coefficient.
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