Energy Detection Based Cooperative Spectrum Sensing in Cognitive Radio Networks
Saman Atapattu,Student Member,IEEE,Chintha Tellambura,Fellow,IEEE,and Hai Jiang,Member,IEEE
Abstract—Detection performance of an energy detector used for cooperative spectrum sensing in a cognitive radio network is investigated over channels with both multipath fading and shadowing.The analysis focuses on two fusion strategies:data fusion and decision fusion.Under data fusion,upper bounds for average detection probabilities are derived for four scenarios:1) single cognitive relay;2)multiple cognitive relays;3)multiple cognitive relays with direct link;and4)multi-hop cognitive relays.Under decision fusion,the exact detection and false alarm probabilities are derived under the generalized“k-out-of-n”fusion rule at the fusion center with consideration of errors in the reporting channel due to fading.The results are extended to a multi-hop network as well.Our analysis is validated by numerical and simulation results.Although this research focuses on Rayleigh multipath fading and lognormal shadowing, the analytical framework can be extended to channels with Nakagami-m multipath fading and lognormal shadowing as well.
Index Terms—Cognitive radio,cooperative spectrum sensing, data fusion,decision fusion,energy detection.
I.I NTRODUCTION
R ADIO spectrum,an expensive and limited resource,is surprisingly underutilized by licensed users(primary users).Such spectral under-utilization has motivated cognitive radio technology which has built-in radio environment aware-ness and spectrum intelligence[1].Cognitive radio enables opportunistic access to unused licensed bands.For instance, unlicensed users(secondary users or cognitive users)?rst sense the activities of primary users and access the spectrum holes(white spaces)if no primary activities are detected. While sensing accuracy is important for avoiding interference to the primary users,reliable spectrum sensing is not always guaranteed,due to the multipath fading,shadowing and hidden terminal problem.Cooperative spectrum sensing has thus been introduced for quick and reliable detection[2]–[5].
Among spectrum sensing techniques such as the matched ?lter detection(coherent detection through maximization of the signal-to-noise ratio(SNR))[6]and the cyclostationary feature detection(exploitation of the inherent periodicity of primary signals)[7],energy detection is the most popular method addressed in the literature[8].Measuring only the Manuscript received April15,2010;revised October11,2010;accepted December28,2010.The associate editor coordinating the review of this paper and approving it for publication was S.Affes.
This work was supported by the Natural Science and Engineering Research Council(NSERC)of Canada under a strategic grant,and the Alberta Innovates -Technology Futures,Alberta,Canada under a New Faculty Award.
The authors are with the Department of Electrical and Computer Engi-neering,University of Alberta,Edmonton,AB,Canada T6G2V4(e-mail: {atapattu,chintha,hai.jiang}@ece.ualberta.ca).
Digital Object Identi?er10.1109/TWC.2011.012411.100611received signal power,the energy detector is a non-coherent detection device with low implementation complexity.The performance of an energy detector has been studied in some research efforts[9]–[14].It performs poorly in low SNRs, and the estimation error due to noise may degrade detection performance signi?cantly[15].
When energy detection is utilized for cooperative spectrum sensing,secondary users report to a fusion center their sensing results,in either of the following methods.
Data fusion:Each cognitive user simply ampli?es the received signal from the primary user and forwards to the fusion center[2],[4],[16].Although secondary users do not need complex detection process,the reporting channel bandwidth should be at least the same as the bandwidth of the sensed channel.At the fusion center,different fusion techniques can be applied,such as maximal ratio combining (MRC)and square-law combining(SLC)[10].When MRC is used,channel state information(CSI)from the primary user to secondary users and from each secondary user to the fusion center is needed.When SLC is used with?xed ampli?cation factor at each secondary user,only CSI from secondary users to the fusion center is needed.However,if variable ampli?cation factor is applied,CSI from the primary user to secondary users and from secondary users to the fusion center is needed[17].The framework for two-user and multiple-user cooperative spectrum sensing with data fusion was introduced in[2],[3].However,an analytical study for the detection capability in the cooperative spectrum sensing has not been addressed.
Decision fusion:Each secondary user makes a decision (probably a binary decision)on the primary user activity,and the individual decisions are reported to the fusion center over a reporting channel(which can be with a narrow bandwidth). Capability of complex signal processing is needed at each secondary user.The fusion rule at the fusion center can be OR, AND,or Majority rule,which can be generalized as the“k-out-of-n rule”.Two main assumptions are made in the literature for simplicity:1)the reporting channel is error-free[18],[19]; and2)the SNR statistics of the received primary signals are known at secondary users[20].However,these assumptions are not practical in a real cognitive network.In[21],detection performance has been investigated by considering reporting errors with OR fusion rule under Rayleigh fading channels. To?ll the research gaps in cooperative spectrum sensing with data fusion and decision fusion,in this paper,we provide a rigorous analytical framework for cooperative spectrum sensing with data fusion,and investigate the detection per-formance with decision fusion in scenarios with reporting
1536-1276/11$25.00c?2011IEEE
errors and without SNR statistics of received primary signals.The rest of this paper is organized as follows.Section II brie ?y discusses preliminaries of energy detection and channel models.Sections III and IV are devoted to the analysis of cooperative spectrum sensing with data fusion and decision fusion,respectively.Section V presents our numerical and simulation results,followed by concluding remarks in Section VI.
II.P RELIMINARIES OF E NERGY D ETECTION AND
C HANNEL M ODELS
When a primary signal,x (t ),is transmitted through a wireless channel with channel gain ?,the received signal at the receiver,y (t ),which follows a binary hypothesis:?0(signal absent)and ?1(signal present),can be given as
y (t )={
w (t ):?0,
?x (t )+w (t ):?1,(1)
where w (t )is the additive white Gaussian noise (AWGN),which is assumed to be a circularly symmetric complex Gaus-sian random variable with mean zero and one-sided power spectral density N 0(i.e.,w (t )～CN (0,N 0)).A.Energy Detector over AWGN Channels
In energy detection,the received signal is ?rst pre-?ltered by an ideal bandpass ?lter which has bandwidth W ,and the output of this ?lter is then squared and integrated over a time interval T to produce the test statistic.The test statistic Λis compared with a prede ?ned threshold value λ[8].The probabilities of false alarm (P f )and detection (P d )can be evaluated as P r (Λ>λ∣?0)and P r (Λ>λ∣?1),respectively,to yield [9]
P f =Γ(u,λ2)Γ(u )
(2)P d =Q u (√
2γ,√λ),(3)where u =W T ,γis SNR given as γ=E s ∣?∣2/N 0,E s
is the power budget at the primary user,Q u (?,?)is the u th order generalized Marcum-Q function,Γ(?)is the gamma function,and Γ(?,?)is the upper incomplete gamma function.Probability of false alarm P f can easily be calculated using (2),because it does not depend on the statistics of the wireless channel.In the sequel,detection probability is focused.The generalized Marcum-Q function can be written as a circular contour integral within the contour radius r ∈[0,1).There-fore,expression (3)can be re-written as [22]
P d =
e ?λ2
j 2π∮Ωe (1z ?1)γ+λ
2z z u (1?z )dz,(4)where Ωis a circular contour of radius r ∈[0,1).The moment generating function (MGF)of received SNR γis ?γ(s )=E (e ?sγ),where E (?)means expectation.Thus,the average detection probability,P d ,is given by
P d =e ?λ2
j 2π∮Ωg (z )dz,(5)
where
g (z )=?γ(1?
1
z )e λ
2z z u (1?z )
.Since the Residue Theorem [23]in complex analysis is a powerful tool to evaluate line integrals and/or real integrals of functions over closed curves,it is applied for the integral in (5),with details given in Appendix A.
B.Average Detection Probability with Fading and Shadowing 1)With Small Scale Fading:The Rayleigh channel model is one of the common and simple models for multipath fading.For Rayleigh fading,the MGF is ?γ(s )=1/(1+γs ),where γis the average SNR.The average detection probability,P d ,under Rayleigh fading can be written in the form of expression (5)with
g (z )=
e λ
2z
(1+γ)z (u ?1)(1?z )(z ?
γ1+γ)
.
In radius r ∈[0,1),there are (u ?1)poles at the origin (z =0)and one pole at z =γ/(1+γ).Thus P d under Rayleigh fading can be derived as
P d ={
e ?λ2(Res (g ;0)+Res (g ;γ1+γ)):u >1
e ?λ
2(1+γ):u =1,
(6)where Res (g ;0)and Res (g ;γ/(1+γ))
denote the residues of the function g (z )at the origin and at z =γ/(1+γ),re-spectively,which are evaluated in Appendix A.An alternative expression for P d under Rayleigh fading has been obtained in [10],which is numerically equivalent with (6).
2)With Composite Multipath Fading and Shadowing:Shadowing effect can be modeled as a lognormal distribution (for signal amplitude).The SNR of the composite Rayleigh-lognormal or Nakagami-lognormal channel model follows a gamma-lognormal distribution,which does not have a closed-form expression [24].Therefore,we have accurately approxi-mated the composite Rayleigh-lognormal channel model by a mixture of gamma distributions as [25]
f γN (x )=
N ∑i =1
αi e ?ζi x ,
x ≥0,αi >0,ζi >0,
(7)
where αi =w i e ?(√
2σt i +μ)
√π∑N i =1w i
,ζi =e ?(
√
2σt i +μ)
ρ
,N is the number of terms in the mixture,t i and w i are abscissas and weight factors for the Gaussian-Laguerre integration,μand σare the mean and the standard deviation of the lognormal distribution,respectively,and ρis the unfaded SNR de ?ned as ρ?E s /N 0.The MGF of γN is ?γN (s )=∑N
i =1αi /(s +ζi ).Therefore,the average detection probability,P d ,under composite multi-path and shadowing can be evaluated in closed-form as
P d =? ? ?e ?λ2∑N i =1αi 1+ζi (Res (g i ;0)+Res (g i ;11+ζi )):u >1
∑N i =1αi ζi
e ?λ2ζi 1+ζi :u =1,
(8)
where
g i (z )=e λ
2z z (u ?1)(1?z )(z ?1
1+ζi
),and residues Res (g i ;0)and Res (g i ;1/(1+ζi ))
are given in Appendix A.Because of possibly severe multipath fading and
Fig.1.Illustration of a multiple-cognitive relay network. shadowing effects,the decision made by a single secondary user is not always reliable.In the following,cooperative spectrum sensing with data fusion and decision fusion is investigated,respectively.
III.C OOPERATIVE S PECTRUM S ENSING WITH D ATA
F USION
Without complex signal processing at secondary users,each secondary user acts as a relay node to the fusion center, referred to as a cognitive relay.This means a secondary user simply ampli?es the received signal and then,forwards the ampli?ed signal to the fusion center.
A.Cooperative Scheme
We consider a cognitive radio network(Fig.1),with a number n of cognitive relays(named r1,r2,...,r n).In the ?rst phase,all cognitive relays listen to the primary user signal.Instead of making individual hard decision about the presence or absence of the primary user,each cognitive relay ampli?es and forwards the noisy version of its received signal to the fusion center in the second phase.We assume that the communication channels between cognitive relays and fusion center are orthogonal to each other(e.g.,based on time division multiple access(TDMA)).In orthogonal channels, the fusion center receives independent signals from cognitive relays.The fusion center is equipped with an energy detector which compares the received signal energy with a pre-de?ned thresholdλ.
B.Single-Cognitive Relay Network
First we consider a single-cognitive relay network.In this case,we have three nodes,i.e.,the primary user,the cognitive relay,and the fusion center.The cognitive relay continuously monitors the signal received from the primary user.The received signal by the cognitive relay at time t,denoted y pr(t), is given by y pr(t)=θ?pr x(t)+w r(t)whereθdenotes the primary activity indicator,which is equal to1at the presence of primary activity,or equal to0otherwise,x(t) is the transmitted signal from the primary user with power E s,?pr is the?at fading channel gain between the primary user and relay,and w r(t)is the AWGN at the cognitive relay
with variance N0,r.Let G be the ampli?cation factor at the cognitive relay.Thus,the received signal at the decision maker (i.e.,the fusion center),denoted y rd(t),is given by
y rd(t)=G?rd y pr(t)+w d(t)
=θG?pr?rd x(t)+G?rd w r(t)+w d(t)
=θ?x(t)+w(t),
(9)
where?rd is the channel gain between the relay and the fusion center,and w d(t)is the AWGN at the fusion center. Further,?=G?pr?rd and w(t)=G?rd w r(t)+w d(t)can be interpreted as the equivalent channel gain between the primary user and the fusion center and the effective noise at the fusion center,respectively.
1)Ampli?cation Factor:In amplify-and-forward(AF)re-lay communications,it can be assumed that the relay node has its own power budget E r,and the ampli?cation factor is designed accordingly.First the received signal power is nor-malized,and then it is ampli?ed by E r.The CSI requirement depends on the AF relaying strategy,in which two types of relays have been introduced in the literature[17],[26]:
?Non-coherent power coef?cient:the relay has knowledge of the average fading power of the channel between the primary user and itself,i.e.,E[∣?pr∣2],and uses it to constrain its average transmit power.Therefore,G is given as
G=
√
E r
N0,r+E s E[∣?pr∣2]
.
?Coherent power coef?cient:the relay has knowledge of the instantaneous CSI of the channel between the primary user and itself,i.e.,?pr,and uses it to constrain its average transmit power.Therefore,G is given as
G=
√
E r
N0,r+E s∣?pr∣2
.
An advantage of the non-coherent power coef?cient over the coherent one is in its less overhead,because it does not need the instantaneous CSI,which requires training and channel estimation at the relay.In this research,we use the non-coherent power coef?cient which is also called as?xed-gain relay.The ampli?cation factor G can also be written as G2=E r/(CN0,r)where C=1+E s E[∣?pr∣2]/N0,r which is a constant.
2)Receiver Structure:The same receiver structure as in reference[9]is used.1The total effective noise in(9)can be modeled as w∣?
rd
～CN
(
0,(G2∣?rd∣2+1)N0
)
.The received signal is?rst?ltered by an ideal band-pass?lter.The?lter limits the average noise power and normalizes the noise variance.The output of the?lter is then squared and integrated over time T to form decision statisticΛ.Therefore,the false alarm probability and detection probability can be written as 1Note that cooperative spectrum sensing is not considered in reference[9].
(2)and (3),respectively,with γ=(γpr γrd )/(C +γrd )where γpr and γrd are SNRs of the links from the primary user to the cognitive relay and from the cognitive relay to the fusion center,respectively.
C.Multiple Cognitive Relays
A multiple-cognitive relay network is shown in Fig.1.We have n cognitive relays between the primary user and the fusion center,and ?pr i ,?pd and ?r i d denote the channel gains from the primary user to the i th cognitive relay r i ,from the primary user to the fusion center,and from the i th cognitive relay r i to the fusion center,respectively.All cognitive re-lays receive primary user’s signal through independent fading channels simultaneously.Each cognitive relay (say relay r i )ampli ?es the received primary signal by an ampli ?cation factor G r i given as G 2r i =E r i /(C i N 0,r i )(where E r i is the power budget at relay r i ,C i =1+E s E [∣?pr i ∣2]/N 0,r i ,and N 0,r i is the AWGN power at relay r i )and forwards to the fusion center over mutually orthogonal channels.
In [27],we consider MRC at the fusion center with known CSI.Therefore,the CSI of channels in the ?rst hop should be forwarded to the fusion center.On the other hand,CSI may not be available for energy detection (which is non-coherent).In contrast to MRC,receiver with SLC (which is a non-coherent combiner)does not need instantaneous CSI of the channels in the ?rst hop,and consequently results in a low complexity system.CSI of channels in the second hop is available at the ?lters for the noise normalization.The number n of outputs from all the branches in the SLC,
denoted {y i }n
i =1,are combined to form the decision statistic ΛSLC =∑n i =1y i .Under AWGN channels,ΛSLC follows a central chi-square distribution with nu degrees of freedom (DoF)and unit variance under ?0,and a non-central chi-square distribution with nu DoF under ?1.Further,effective
SNR after the combiner is γSLC =∑n
i =1γi where γi is the equivalent SNR of the i th relay path.The non-centrality parameter under ?1is 2γSLC .The false alarm and detection probabilities can be calculated using (2)and (3)by replacing u by nu and γby γSLC .
D.Detection Analysis for a Multiple-Cognitive Relay Network A closed-form solution for the exact average detection prob-ability P d in (5)seems analytically dif ?cult with the MGF of γwhich is given in [26,eq.(12)].However,ef ?cient numerical algorithms are available to evaluate a circular contour integral.We can use MATHEMATICA or MATLAB software packages that provide adaptive algorithms to recursively partition the integration region.With a high precision level,the numerical method can provide an ef ?cient and accurate solution for (5).In the following,we derive an upper bound of average detection probability.
1)Upper Bound of P d :The total SNR γof a multiple-cognitive relay network can be upper bounded by γup as γ≤γup =∑n i =1γmin i ,where γmin i =min (γpr i ,γr i d ),and γpr i and γr i d are the SNRs of the links from the primary user to cognitive relay r i and from cognitive relay r i to the fu-sion center,respectively.Therefore,for independent channels,
MGF of γup can be written as ?γup (s )=∏
n i =1?γmin i
(s )(note that ?γmin i
(s )is available in [27,eq.(20)]),to yield ?γup (s )=
n ∏i =1
γpr i +γr i d
γpr i γr i d 1
(s +γpr i +γr i d
γpr i γr i d
),(10)
where γpr i and γr i d are the average SNRs for links from the primary user to cognitive relay r i and from cognitive relay r i to the fusion center,respectively.Substituting (10)into (5),an
upper bound of P d ,denoted P up
d ,can b
e re-written as (5)with
g (z )=e λ2z z u ?n (1?z )n ∏i =11?Δi
z ?Δi
,
and
Δi =
γpr i γr i d
γpr i
+γr i d +γpr i γr i d
.
Two scenarios need to be considered:1)When u >n ,there are u ?n poles at the origin and n poles for Δi ’s (i =1,..,n )in radius r ∈[0,1),and 2)when u ≤n ,there are n poles at
Δi ’s (i =1,..,n )in radius r ∈[0,1).Therefore,P up
d can b
e derived as
P up d ={e ?λ2(Res (g ;0)+∑n
i =1Res (g ;Δi )):u >n e ?λ2∑n
i =1Res (g ;Δi ):u ≤n,
(11)where Res (g ;0)and Res (g ;Δi )
denote the residue of the function g (z )at the origin and Δi ,respectively.We refer readers to Appendix A for the details of the derivation of residue calculations Res (g ;?).E.Incorporation with the Direct Link
In preceding subsections,the fusion center receives only signals coming from cognitive relays.If the primary user is close to the fusion center,the fusion center can however have a strong direct link from the primary user.The direct signal can also be combined at the SLC together with the relayed signals.Then the total SNR at the fusion center can be written
as γ?=γd +∑n
i =1γi ,where γd is the SNR of the direct path.Assuming independent fading channels,the MGF of γ?can be written as
?γ?(s )=?γd (s )
n ∏i =1
?γi (s ),
where ?γd (s )is given by 1/(1+γd s )with γd =E (γd ),
and M γi (s )is given in [26,eq.(12)].As in preceding subsections,we can ?nd accurate average detection probability using numerical integration.An upper bound is derived in the following.In this case,g (z )in (5)can be written as
g (z )=(1?Δ)e λ2z
z u ?n ?1
(1?z )(z ?Δ)n ∏i =11?Δi z ?Δi
(12)
where Δ=γd /(1+γd ).When u >n +1,there are u ?n ?1
poles at the origin,one pole at Δand n poles for Δi ’s (i =1,..,n )in radius r ∈[0,1).When u ≤n +1,there are one pole at Δand n poles for Δi ’s (i =1,..,n )in radius r ∈[0,1).
Therefore,a tight upper bound of the detection probability, denoted P?,up
d
,can be derived in closed-form as
P?,up d =
?
?
?
e?λ2
(
Res(g;0)+Res(g;Δ)
+
∑n
i=1
Res
(
g;Δi
))
:u>n+1
e?λ2
(
Res(g;Δ)+
∑n
i=1
Res
(
g;Δi
))
:
u≤n+1.
(13)
All residues,Res(g;0),Res(g;Δ)and Res (
g;Δi
)
,are calcu-
lated in Appendix A.
F.Multi-hop Cognitive Relaying
Multi-hop communication is introduced as a smart way of providing a broader coverage in wireless networks.We exploit the same idea in a cognitive radio network because the coverage area can be broadened with less power consumption. Fixed-gain non-regenerative cognitive relays are considered in Rayleigh fading channels.Channels over different hops are non-identical.2
Consider a cognitive radio network with M hops between the primary user and the fusion center.There are M?1relays (r1,r2,...,r M?1)between the primary user and the fusion center.The end-to-end SNR can be expressed as
γ=?
?
M
∑
i=1
i∏
j=1
C j?1
γj
?
?
?1
whereγi is the instantaneous SNR of the i th hop and C j is the?xed-gain constant in relay r j and C0=1.Further,γcan be upper bounded as
γup=Z M
M
∏
i=1
γM+1?i
M
i
where Z M=(∏
M
i=1
C?(M?i)/M
i
)
/M[28].In[29],the
MGF ofγup is expressed using the Pad′e approximation method as
?γ
up (s)～=
Q
∑
i=1
μi s i
i!
+O(s Q+1)
where Q is a?nite number of terms of the truncated series,
μi=Z i M
M
∏
j=1
ˉγj i(M?j+1)
MΓ
(
i(M?j+1)
M
)
is the i th moment ofγup(hereˉγj is the average SNR over the j th hop),and O(s Q+1)is the remainder of the truncated series. After applying the Pad′e approximation,?γ
up
(s)is given as
?γ
up (s)～=
∑A
i=0
a i s i
1+
∑B
i=1
b i s i
=
B
∑
i=1
q i
s+p i(14)
where A and B are speci?ed orders of the numerator and the denominator of the Pad′e approximation,a i and b i are approximated coef?cients,and p i and q i can be obtained based 2Note that when we say two channels are identical,we mean they are identically distributed.on the second equality in(14),as detailed in[29,Sec.II-C], [30,Sec.IV].
Since?γ
up
(s)in(14)is a sum of rational functions, an upper bound of the average detection probability can be written using(5)to yield
P up d=
e?λ2
j2π
B
∑
i=1
q i
1+p i
∮
Ω
g i(z)dz,(15) where
g i(z)=
eλ2z
(
z?11+p
i
)
z u?1(1?z)
.
When u>1,there is a pole at z=1/(1+p i)and(u?1) poles at the origin,and when u=1,there is only a pole at z=1/(1+p i)of g i(z).Thus,P up d can be written as
P up d=
?
?
?
e?λ2
∑B
i=1
q i
1+p i
(
Res(g i;0)+Res
(
g i;11+p
i
))
:
u>1,
e?λ2
∑B
i=1
q i
1+p i
Res
(
g i;11+p
i
)
:u=1,
(16) where Res(g i;0)and Res(g i;1/(1+p i))are given in Ap-pendix A.We have also derived?γ
up
(s)in closed-form in Appendix B.To the best of the authors’knowledge,an exact closed-form expression for?γ
up
(s)is not available in the literature.The result will be helpful for exact numerical cal-culation of the upper bound for average detection probability, and other performance evaluation in multi-hop relaying. IV.C OOPERATIVE S PECTRUM S ENSING WITH D ECISION
F USION
Each cognitive relay makes its own one-bit hard decision:‘0’and‘1’mean the absence and presence of primary ac-tivities,respectively.The one-bit hard decision is forwarded independently to the fusion center,which makes the coopera-tive decision on the primary activity.
A.k-out-of-n Rule
We assume that the decision device of the fusion center is implemented with the k-out-of-n rule(i.e.,the fusion center decides the presence of primary activity if there are k or more cognitive relays that individually decide the presence of primary activity).When k=1,k=n and k=?n/2?,the k-out-of-n rule represents OR rule,AND rule and Majority rule, respectively.In the following,for simplicity of presentation, we use p f and p d to represent false alarm and detection probabilities,respectively,for a relay,and use P f and P d to represent false alarm and detection probabilities,respectively, in the fusion center.
1)Reporting Channels without Errors:If the sensing chan-nels(the channels between the primary user and cognitive relays)are identical and independent,then every cognitive re-lay achieves identical false alarm probability p f and detection probability p d.If there are error free reporting channels(the channels between the cognitive relays and the fusion center), P f and P d at the fusion center can be written as
Pχ=
n
∑
i=k
(
n
i
)
(pχ)i(1?pχ)n?i(17)
where the notation ‘χ’means ‘f ’or ‘d ’for false alarm or detection,respectively.
2)Reporting Channels with Errors:Because of the im-perfect reporting channels,errors occur on the decision bits which are transmitted by the cognitive relays.Assume bit-by-bit transmission from cognitive relays.Thus,each identical reporting channel can be modeled as a binary symmetric channel (BSC)with cross-over probability p e which is equal to the bit error rate (BER)of the channel.
Consider the i th cognitive relay.When the primary activity is present (i.e.,under ?1),the fusion center receives bit ‘1’from the i th cognitive relay when (1)the one-bit decision at the i th cognitive relay is ‘1’and the fusion center receives bit ‘1’from the reporting channel of the i th relay,with probability p d (1?p e );or (2)the one-bit decision at the i th cognitive relay is ‘0’and the fusion center receives bit ‘1’from the reporting channel of the i th relay,with probability (1?p d )p e .On the other hand,when the primary activity is absent (i.e.,under ?0),the fusion center receives bit ‘1’from the i th cognitive relay when (1)the one-bit decision at the i th cognitive relay is ‘1’and the fusion center receives bit ‘1’from the reporting channel of the i th relay,with probability p f (1?p e );or (2)the one-bit decision at the i th cognitive relay is ‘0’and the fusion center receives bit ‘1’from the reporting channel of the i th relay,with probability (1?p f )p e .Therefore,the overall false alarm and detection probabilities with the reporting error can be evaluated as
P χ=n ∑i =k
(n i
)(p χ,e )i (1?p χ,e )n ?i (18)
where p χ,e =p χ(1?p e )+(1?p χ)p e is the equivalent false alarm (‘χ’is ‘f ’)or detection (‘χ’is ‘d ’)probabilities of the i th relay.
Note that p e is the cross-over probability of BSC.It is typ-ically taken as a constant value (e.g.,p e =10?1,10?2,10?3)in a network with AWGN channels.In our system model,we can calculate p e analytically as BER calculation of different modulation schemes under multipath fading and shadowing effects.For binary phase shift keying (BPSK),BER can be calculated as p e =1
π∫π/20
?γ(1/sin 2θ)dθto yield p e =1
2(1?
√γ1+γ)
and
p e =
12N
∑i =1αi
ζi
(1?
√11+ζi
)
for Rayleigh fading and composite Rayleigh-lognormal fading,respectively.Here αi and ζi are de ?ned in (7).B.Multi-hop Cognitive Relaying
Consider a multi-hop wireless network for both identical and non-identical channels.Each cognitive relay makes a decision on the presence or absence of the primary activity and forwards the one-bit decision to the next hop.Each hop is modeled as BSC.We assume that there are M hops (i.e.,(M ?1)relays)between the primary user and the fusion center.A channel with (M ?1)non-identically cascaded BSCs,which
is equivalent to a single BSC with 1)effective cross-over probability P e given as (see Appendix C for the derivation)
P e =1
2(1?M ?1∏i =1(1?2p e,i ))where p e,i is the cross-over probability of the i th BSC and 2)
the approximately equivalent average SNR being the average SNR of the (M ?1)BSCs.A channel with (M ?1)identically cascaded BSCs,which is equivalent to a single BSC with
effective cross-over probability P e =12[1?(1?2p e )
M ?1
]and the average SNR being the average SNR of any BSC.Based on the channel gain of the equivalent single BSC,the detection and false alarm probabilities,p d and p f ,of the BSC can be derived,similar to the derivation in Section II.Then,the detection and false alarm probabilities under a multi-hop cognitive relay network can be given as P d =p d (1?P e )+(1?p d )P e and P f =p f (1?P e )+(1?p f )P e ,respectively.
V.N UMERICAL AND S IMULATION R ESULTS
This section provides analytical and simulation results to verify the analytical framework,and to compare the receiver operating characteristic (ROC)curves [8]of different scenarios that are presented in the previous sections.Note that each of the following ?gures contains both analytical result and simulation result,which are represented by lines and discrete marks,respectively.
We ?rst show the performance of the energy detector in non-cooperative cases (as discussed in Section II),which is an important starting point of the investigation in the cooperative cases.Fig.2thus illustrates ROC curves for small scale fading with Rayleigh channel and composite fading (multipath and shadowing)with Rayleigh-lognormal channel.We take N =10in (7),which makes the mean square error (MSE)between the exact gamma-lognormal channel model and the approximated mixture gamma channel model in (7)less than 10?4.The numerical results match well with their simulation counterparts,con ?rming the accuracy of the analysis.The energy detector capabilities degrade rapidly when the average SNR of the channel decreases from 10dB to -5dB.Further,there is a signi ?cant performance degradation of the energy detector due to the shadowing effect in higher average SNR (e.g.,γ=10dB and η=1).
Second,we focus on cooperative cases (discussed in Sec-tions III and IV).We are interested in the impact of the number of relays on detection capability.The upper bound of average detection probability,based on (11),and simulation results are shown in Fig.3.Note that the bound is tight for all the cases,and it is tighter when the number of relays increases.In-creasing the number of cognitive relays improves the detection capability dramatically.The presence of the direct path can signi ?cantly improve the detection performance.Thus,Fig.4shows the impact of the direct path on the detection capability.The direct path has an average SNR value as -5dB,-3dB,0dB,3dB or 5dB.We consider a network with n =1or n =3relays.The average SNR for other channels (from the primary user to each cognitive relay and from each cognitive relay to the fusion center)is 5dB.When the average SNR of the direct link is improved from -5dB to 5dB,ROC curves move
Fig.2.ROC curves of an energy detector over Rayleigh and Rayleigh-lognormal fading channels.
Fig.3.ROC curves for different number of cognitive relays over Rayleigh fading channels γ=5dB.
rapidly to the left-upper corner of the ROC plot,which means better detection capability.Therefore,it is better to utilize the direct link for spectrum identi ?cation in the mobile wireless communication networks with data fusion strategy,because there is a possibility for the fusion center and the primary user to be close to each other.The bound is much tighter when a stronger direct path exists.
Fig.5and Fig.6show the ROC curves for k -out-of-n rule in decision fusion strategy for error-free and erroneous reporting channels,respectively.Three fusion rules:OR,AND,and Majority rules,are considered.The average SNR in each link (from the primary user to each relay,and from each relay to
the fusion center)is 5dB.With error-free reporting channels,OR rule always outperforms AND and Majority rules,and Majority rule has better detection capability than AND rule.With erroneous reporting channels,the comparative performances of the three fusion rules are not as clearcut.However,OR rule outperforms AND and Majority rules in
Fig.4.ROC curves with the direct link over Rayleigh fading channels.
Fig.5.ROC curves for OR,AND and Majority fusion rules with error-free reporting channels.
lower detection threshold (λ)values (i.e.,higher P d and P f ).As shown in Fig.6,when n =5,OR rule has better performance than Majority rule and AND rule when λ<12.3dB and λ<14.3dB,respectively.With the erroneous reporting channels,we cannot expect (P f ,P d )=(1,1)at λ=0and (P f ,P d )→(0,0)when λ→∞on the ROC plot.When λ=0,P f =P d =∑n i =k (n i )(1?p e )i p n ?i
e ;and when λ→∞,P
f and P d approaches ∑n i =k (n i )p e i (1?p e )n ?i
.In both scenarios,the values of P d and P f depend only on the error probabilities of the reporting channels.We do not get reliable decision in these cases.
In Fig.7,we consider a multi-hop cognitive relay network and its detection capability over Rayleigh fading.The average SNR in each hop is 5dB.Note that for data fusion strategy,each ROC curve starts from (1,1)when λ=0to (0,0)when λgoes to in ?nity.On the other hand,for decision fusion strategy with erroneous reporting channels,when λ=0,we have P d =P f =1?P e ,and when λgoes to in ?nity,P d and P f approaches P e .Fig.7shows that the detection performances of
Fig.6.ROC curves for OR,AND and the Majority fusion rules with Rayleigh
Fig.7.ROC curves for a multi-hop cognitive relay network.
both data fusion strategy(represented by continuous lines)and decision fusion strategy(represented by dashed lines)degrade rapidly as the number of hops increases.
VI.C ONCLUSION
Detection performance of cooperative spectrum sensing is studied for data fusion and decision fusion strategies.A new set of results for the average detection probability is derived over Rayleigh and Raleigh-lognormal fading channels.For the data fusion strategy,the MGFs of received SNR of the primary user’s signal at the fusion center are utilized to derive tight bounds of the average detection probability.The results show that the detection capability increases with spatial diversity due to multiple cognitive relays.Further,the direct link has a major impact on the detection probability even for low average SNRs.For the decision fusion strategy in the cooperative spectrum sensing,the generalized k-out-of-n fusion rule is considered,with particular focus on the OR,AND,and Ma-jority rules.OR rule always outperforms AND and Majority rules,and Majority rule has better detection capability than AND rule with error-free reporting channels.However,given a probability of reporting error,the performance is limited by the reporting error.The detection performance of both strategies degrade rapidly when the number of hops increases.With reporting errors,the ROC curve of the decision fusion strategy cannot reach(1,1)at the right upper corner and cannot reach (0,0)at the left lower corner.Although the Rayleigh and Rayleigh-lognormal fading channels are considered here,the same analytical framework can be extended to Nakagami-m and Nakagami-lognormal fading channels with integer fading parameter m.
In this work,cognitive relays use orthogonal channels(e.g., based on TDMA)to forward received signal to the fusion center.The channel detection time may increase with the number of cognitive relays.Note that IEEE802.22standard allows for the maximum channel detection time as2seconds. Therefore,we recommend a moderate number of cooperative relays be utilized,based on the speci?c maximum channel detection time requirement.
A PPENDIX
A.Calculation of P d
If g(z)has the Laurent series representation,i.e.,g(z)=∑∞
i=?∞
a i(z?z0)i for all z,the coef?cient a?1of(z?z0)?1 is the residue of g(z)at z0[23].For g(z)given in(5),assume there are k different poles at z=ηi(i=1,2,...,k)and n i poles at z=ηi.With the Residue Theorem,P d can be calculated as P d=e?λ2
∑k
i=1
Res(g;ηi),where
Res(g;ηi)=
D n i?1(g(z)(z?ηi)n i)
z=ηi
(n i?1)!
,
and D n(f(z))denotes the n th derivative of f(z)with respect to z.
1)Residues of equation(6):
Res(g;0)=
D u?2
(
eλ2z
(1?z)(z?γ1+γ)
)
z=0
(1+γ)(u?2)!
,
Res
(
g;
γ
1+γ
)
=
(
1+γ
γ
)u?1
eλ2γ1+γ.
2)Residues of equation(8):
Res(g i;0)=
D u?2
(
eλ2z
(1?z)
(
z?1
1+ζi
)
)
z=0
(u?2)!
,
Res
(
g i;
1
1+ζi
)
=
(1+ζi)u eλ211+ζi
ζi
.
3)Residues of equation(11):
Res(g;0)=
D u?n?1
(
eλ2z
(1?z)
n∏
i=1
(
1?Δi
z?Δi
))
z=0
(u?n?1)!
,
Res(g;Δj)=
eλ2Δj
Δu?n
j
n∏
i=1,i=j
(
1?Δi
Δj?Δi
)
for j=1,....,n.
4)Residues of equation (13):
Res (g ;0)=
D u ?n ?2
((1?Δ)e λ2z (1?z )(z ?Δ)n
∏i =1
1?Δi
z ?Δi
)
z =0
(u ?n ?2)!
,
Res (g ;Δ)=e λ2ΔΔu ?n ?1n
∏i =1
1?Δi
Δ?Δi ,
Res (g ;Δj )=(1?Δ)e λ
2Δj
(Δj ?Δ)Δu ?n ?1
j
n ∏i =1,i =j
(1?Δi
Δj ?Δi
),
for j =1,....,n .
5)Residues of equation (16):
Res (g i ;0)=
1(u ?2)!D u ?2?
?e λ2z (1?z )(z ?
11+p i
)??
z =0
,
Res (g i ;
11+p i
)
=
e λ
21
1+p i
p i (1+p i )?u
.B.Exact Closed-form Expression for ?γup (s )in Section III-F With the aid of PDF of γup given in [28,eq.(20)]and the Laplace transform given in [31,eq.(07.34.22.0003.01)],?γup (s )can be evaluated in closed-form as
?γup (s )=√n P (2π)n ?12G υ,n n,υ[?n n s n 1n ,2n ,...n n Λ1,Λ2,...,Λn ](19)where
υ=n (n +1)
2,P =n ∏i =1
(2π)?n (n ?1)4(n +1?i )?1
2,
Λi
=
Δ(n +1?i,1),
?=n n
n ∏i =1
C n ?i i n ∏i =1
(γ(n +1?i ))?(n +1?i ),Δ(κ,?)?
(
?κ,?+1κ,...,?+κ?1
κ
),
G [?]is the Meijer’s G-function,and ?is real.
C.Cascaded BSC
The transition probability matrix T i of the i th hop can be written using the singular value decomposition as T i =P ?1Q i P ,where
P =(11
1?1),
Q i =(10
01?2p e,i ),
T i =
(1?p e,i p e,i
p e,i 1?p e,i ).Then,the equivalent transition probability matrix T for n -cascaded BSCs can be evaluated as T =∏n i =1T i to yield
T =12
(1+∏n
i =1(1?2p e,i )1?∏n i =1(1?2p e,i )1?∏n i =1(1?2p e,i )1+∏n
i =1(1?2p e,i )).Therefore,the effective cross-over probability P e is given as
P e =1
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Saman Atapattu (S’06)received the B.Sc.degree in electrical and electronics engineering from the University of Peradeniya,Sri Lanka in 2003and the M.Eng.degree in telecommunications from Asian Institute of Technology (AIT),Thailand in 2007.He is currently working towards the Ph.D.degree in electrical and computer engineering at the University of Alberta,Edmonton,AB,Canada.His research interests include cooperative communications,cog-nitive radio networks,and performance analysis of communication
systems.
Chintha Tellambura (F’11)received the B.Sc.de-gree (with ?rst-class honor)from the University of Moratuwa,Sri Lanka,in 1986,the M.Sc.degree in Electronics from the University of London,U.K.,in 1988,and the Ph.D.degree in Electrical Engineering from the University of Victoria,Canada,in 1993.He was a Postdoctoral Research Fellow with the University of Victoria (1993-1994)and the Univer-sity of Bradford (1995-1996).He was with Monash University,Australia,from 1997to 2002.Presently,he is a Professor with the Department of Electrical
and Computer Engineering,University of Alberta.His research interests focus on communication theory dealing with the wireless physical layer.
Prof.Tellambura is an Associate Editor for the IEEE T RANSACTIONS ON C OMMUNICATIONS and the Area Editor for Wireless Communications Systems and Theory in the IEEE T RANSACTIONS ON W IRELESS C OMMU -NICATIONS .He was Chair of the Communication Theory Symposium in Globecom’05held in St.Louis,
MO.
Hai Jiang (M’07)received the B.Sc.and M.Sc.degrees in electronics engineering from Peking Uni-versity,Beijing,China,in 1995and 1998,respec-tively,and the Ph.D.degree (with an Outstanding Achievement in Graduate Studies Award)in elec-trical engineering from the University of Waterloo,Waterloo,ON,Canada,in 2006.
Since July 2007,he has been an Assistant Profes-sor with the Department of Electrical and Computer Engineering,University of Alberta,Edmonton,AB,Canada.His research interests include radio resource
management,cognitive radio networking,and cross-layer design for wireless multimedia communications.
Dr.Jiang is an Associate Editor for the IEEE T RANSACTIONS ON V EHIC -ULAR T ECHNOLOGY .He served as a Co-Chair for the General Symposium at the International Wireless Communications and Mobile Computing Confer-ence (IWCMC)in 2007,the Communications and Networking Symposium at the Canadian Conference on Electrical and Computer Engineering (CCECE)in 2009,and the Wireless and Mobile Networking Symposium at the IEEE International Conference on Communications (ICC)in 2010.He received an Alberta Ingenuity New Faculty Award in 2008and a Best Paper Award from the IEEE Global Communications Conference (GLOBECOM)in 2008.
毕业设计（论文）题目：认知无线电中频谱感知技术研究专业： 学生姓名： 班级学号： 指导教师： 指导单位： 日期：年月日至年月日
摘要 无线业务的持续增长带来频谱需求的不断增加，无线通信的发展面临着前所未有的挑战。无线电频谱资源一般是由政府统一授权分配使用，这种固定分配频谱的管理方式常常会出现频谱资源分配不均，甚至浪费的情形，这与日益严重的频谱短缺问题相互矛盾。认知无线电技术作为一种智能频谱共享技术有效的缓解了这一矛盾。它通过感知时域、频域和空域等频谱环境，自动搜寻已授权频段的空闲频谱并合理利用，达到提高现有频谱利用率的目的。频谱感知技术是决定认知无线电能否实现的关键技术之一。 本文首先介绍了认知无线电的基本概念，对认知无线电在 WRAN 系统、UWB 系统及 WLAN 系统等领域的应用分别进行了讨论。在此基础上，针对实现认知无线电的关键技术从理论上进行了探索，分析了影响认知网络正常工作的相关因素及认知网络对授权用户正常工作所形成的干扰。从理论上推导了在实现认知无线电系统所必须面对的弱信号低噪声比恶劣环境下，信号检测的相关方法和技术，并进行了数字滤波器的算法分析，指出了窗函数的选择原则。接着详细讨论了频谱检测技术中基于发射机检测的三种方法：匹配滤波器检测法、能量检测法和循环平稳特性检测法。为了检验其正确性，借助 Matlab 工具，在Matlab 平台下对能量检测和循环特性检测法进行了建模仿真，比较分析了这两种方法的检测性能。研究结果表明：在低信噪比的情况下，能量检测法检测正确率较低，检测性能远不如循环特征检测。 其次还详细的分析认知无线电的国内外研究现状及关键技术。详细阐述了频谱感知技术的研究现状和概念，并指出了目前频谱感知研究工作中受到关注的一些主要问题，围绕这些问题进行了深入研究。 关键词：感知无线电；频谱感知；匹配滤波器感知；能量感知；合作式感知；
能量检测仿真实验代码： clear all;clc; n = 5; ps = 1; SNR1 = -5; SNR2 = -8; SNR3 = -10; % Sim_Times=10000; %Monter-Carlo times % m=5; T=0.001; % 信号带宽W W=5*10^4; % 采样频率 Fs = 2*W; m = T*W; n = 2*T*W; % F0=W; % Fs=2; % Sig=sqrt(2)*sin(2*pi*F0/Fs*t); %single tone samples, Fs=2F0 % 实际信噪比 snr1 = 10.^(SNR1/10); snr2 = 10.^(SNR2/10); snr3 = 10.^(SNR3/10); pn = (1/snr1)*ps; mu0 = n*pn; sigma0 = sqrt(2*n)*pn; mu = n*(pn+ps); sigma = sqrt(2*n*(pn^2+2*pn*ps)); % [noi,x0,mu0,sigma0,m0] = cnoi( n,pn ); % sig = randn(n,1); sig = 1; % 重复次数 count = 5000; % 能量检测判决门限 lambda = [200:20:600]; lambda1 = [500:20:900]; lambda2 = [700:30:1300]; % 置信度判决参数 % tt = [-5:0.4:3]; % cc = 10.^tt; % tt1 = [-1:0.1:1]; % cc1 = 10.^tt; % cc2 = [-0.01:0.001:0.01];
研究初期。大量文献。判断有无信号传输。识别信号类型。 1)匹配滤波器 主用户信号已知时最佳。感知速度快。但对信号已知信息的要求高，感知单元的实现复杂度极高（需要对大量类型信号的匹配滤波）。 2)基于波形的感知 已知主用户信号的patterns（用于同步等的前导序列等等），对观测数据做相关。在稳定性和收敛速度上比基于能量检测的感知要好。 判决门限的选取。信号功率因信道传输特性和收、发信机之间的距离的不确定性而难以估计。实际中，可由特定的虚警概率给出门限，此时只需知道噪声方差。 3)基于循环平稳性的感知 信号的平稳特征由信号或信号统计量（期望、自相关等）周期性引起。利用循环相关函数（而非功率谱密度）检测信号，可将噪声与信号分离。因为噪声广义平稳无相关量，而调制信号由于循环平稳而存在谱相关。循环谱密度（CSD）函数的计算是对循环自相关函数做傅里叶变换。循环频率与信号的基本频率一致时，CSD函数输出峰值。 4)基于能量检测的感知 低运算复杂度和低实现复杂度。缺点在于：判决门限的选择困难；无法区分能量来源是信号还是噪声； 低SNR条件下性能差。噪声水平的动态估计，降秩特征值分解法。GSM时隙能量检测，需与GSM系统同步，检测时间限制在时隙间隔内。FFT之后频域能量检测。检测概率在各种信道条件下的闭式解。 5)无线电识别 识别主用户采用的传输技术。获得更多的信息，更高的精度。比如蓝牙信号的主用户位置局限在10m 之内。特征提取和归类技术。各种盲无线电识别技术。 6)其它感知方法 多窗口谱估计。最大似然PSD估计的近似，对宽带信号接近最优。计算量大。 Hough变换。 基于小波变换的估计。检测宽带信道PSD的边界。 协同感知—— 协同（合作、协作）用来应对频谱感知中噪声不确定性、衰落和阴影等问题。解决隐终端问题，降低感知时间。提出有效的信息共享算法和处理增加的复杂度是协同感知要解决的难题。控制信道可利用：1）指配频带；2）非授权频带；3）衬于底层的UWB。 共享信息可以是软判决或硬判决结果。（基于能量检测的）感知合并方式：等增益合并、选择式合并、Switch & Stay（扫描式）合并。协同算法应：协议开支小；鲁棒性强；引入延迟小。 非协同感知，优点为计算和实现简单，缺点为存在隐终端问题、多径和阴影的影响。 协同感知，优点为更高的精度（接近最优）、可解决阴影效应和隐终端问题；缺点为复杂度高、额外通信流量开支和需要控制信道。 协同感知的两种实现形式： 1)中心式感知。中心单元广播可用频谱信息或直接控制CR通信。AP。硬信息合并、软信息合并。 2)分布式感知。彼此共享信息，自己对频谱做出判决。不需要配置基础结构网络。 外部感知—— 外部感知网络将频谱感知结果广播给CR。优点：可解决隐终端问题和衰落及阴影引起的不确定性；CR无需为感知分配时间，提高频谱效率；感知网络可以是固定的（避免电池供电）。外部感知可以是连续的或周期性的。感知数据传递给中心节点进一步处理，并将频谱占用信息共享。
对于频谱分析能量守恒的验证 A.环境：MA TLAB fftHvsL.m程序： %fftHvsL.m程序开始，MATLAB库函数fft()和手工函数对信号的频谱分析caiyangHZ=1000; dt=1/caiyangHZ; nfft=256; df=caiyangHZ/nfft; tfinal=dt*(nfft-1); t = 0:dt:tfinal; xinhaohz1=100*df; xinhaohz2=50*df; f1=3; f2=4; x=f1*sin(2*pi*xinhaohz1*t)+f2*sin(2*pi*xinhaohz2*t); m=8; N=256; nxd=bin2dec(fliplr(dec2bin([1:N]-1,m)))+1; y=x(nxd); for mm=1:m Nz=2^mm;u=1; WN=exp(-i*2*pi/Nz); for j=1:Nz/2 for k=j:Nz:N kp=k+Nz/2; t=y(kp)*u; y(kp)=y(k)-t; y(k)=y(k)+t; end u=u*WN; end end %自己编的FFT跟直接调用的函数运算以后的结果进行对比 y1=fft(x,256); Pyy=(abs(y)/nfft).^2; f = df*(0:127); figure(1); subplot(1,2,1);plot(f,Pyy(1:128)) axis([0,600,0,4.5]) title('.m by hand') xlabel('Frequency (Hz)') Pyy=(abs(y1)/nfft).^2;
Xilinx大学生竞赛项目申请报告提纲及说明 1． 项目背景 （1）项目名称：认知无线电的频谱检测 （2） 项目背景：随着无线通信需求的不断增长，可用的频谱资源越来越少，呈现日趋紧张的状况；另一方面，人们发现 全球授权频段尤其是信号传播特性较好的低频段的频谱利 用率极低。认知无线电技术为解决频谱利用率低的问题提 供了行之有效的方法。由于认知无线电在使用空闲频段进 行通信的同时不断地检测授权用户的出现，一旦检测到授 权用户要使用该频段，认知无线电用户便自动退出并转移 到其他空闲频段继续通信，确保在不干扰授权用户的情况 下，与他们进行频谱共享。这样一来，在没有增加新频段 的情况下提升了用户量，且保证授权用户和认知用户通信 的可靠性，大大提高了频谱的使用效率。 （3）项目内容：本次课题主要研究认知无线电频谱检测的FPGA 实现。目前最为常用的认知无线电频谱检测方法是能量检 测。我们将一路电视信号下变频至基带信号再进入电路调 理模块对信号进行50欧匹配，并对信号进行放大，然后用 宽带A/D对信号进行采样，将采样后的数字信号做8点FFT 运算，再通入能量和累加电路，最后通过能量阈值判决电 路，判断频带的利用情况，从而找到频谱空穴，为认知无 线电的功能实现打下基础。 （4）项目难点：（1）高效低成本的FFT模块的设计与实现。 （2）累加器和阈值判决电路模块的设计与实现。 （5）项目的开发意义：认知无线电的显著特征是具有认知能 力，认知功能包括频谱感知，频谱分析和频谱判决。频谱 感知用于频谱空穴检测，是认知无线电系统实现的前提之 一。 （6） 硬件开发平台：Spartan 3E Board 2． 频谱感知的背景知识 本次设计以四通道的电视信号为例进行实现，在我国一路电视信号的传输需要8M的带宽，那么传输四路电视信号需要32M的带宽才 能实现。 我们将该四路电视信号进行复信号处理和频谱搬移，使其生成I,Q 两路正交信号，其AD频率采样为32MHZ，为了检测各个通道的频谱
龙源期刊网 https://www.doczj.com/doc/e63218288.html, 无线电频谱检测技术研究 作者：侯晋军 来源：《科学与财富》2020年第02期 摘要：在我国不断繁荣昌盛的背景下，我国经济的不断发展，科技水平的不断提升，促进了我国的无线电技术的广泛应用，这不仅改善了我们日常生活，还使得我们的生活变得更加便利。在无线电技术应用范围变得愈加广泛的同时，对无线电网管理方面的问题也随之产生，这成为了阻碍无限电技术进一步发展的主要因素。 关键词：无线电;频谱检测;技术 引言 我们通常情况下所提及的无线电技术所指的就是通过运用无线电磁波搭载信息进行传输的一项通信技术，在通电的导线中改变电流的大小会在导线周围产生磁场，变化的磁场又会产生电场从而形成电磁波以无线电波的形式传播出去，利用这个原理可以将电信号进行调制搭载与无线电波上进行传输。 1无线电监测系统的基本原理 频谱监测系统的工作原理十分简单，利用频谱监测系统，能够有效的监测在无线电工作环境下所产生的数据，与此同时，运用频谱监测系统能够有效的检测出限制的频谱系统，并对其加以利用，从而实现对无线电资源的整合与合理地分配和利用，以解决频谱资源紧缺的问题，同时还能在一定程度上减少对无线电监测所产生的影响。运用无线电频谱监测技术的有利之处在于能够减少运用过程中对用户造成的影响，确保用户的正常使用，与此同时还能够对准确的检测出闲置的无线电频谱系统，并加以从分利用。无线电频谱监测技术时无线电监测技术中最有效的、应用范围最广的监测系统，在我们的日程生活中，无线电监测系统扮演者重要的角色，是我们不可或缺的一部分。 2无线电频谱监测关键技术的分类 2.1确定监测频段，合理设置扫描起止频率 设置无线电监测系统相关参数时，相关工作人员应尽可能地设置同种业务扫描频段，并合理设置扫描步进、滤波带宽及起止频率等，以提升无线电监测系统的运营效率。同时，工作人员可根据ITU频谱监测手册中关于频谱占用度测量技术指标的相关规定，科学合理地选择频段、扫描方式以及测量方法等，从而使无线电监测系统的回扫时间满足標准。此外，为进一步保证监测数据的准确性和合理性，工作人员设置连续监测时间时，应尽量合理地延长时间间
https://www.doczj.com/doc/e63218288.html,/article/11-09/422921315975560.html 频谱感知，是指认知用户通过各种信号检测和处理手段来获取无线网络中的频谱使用信息。从无线网络的功能分层角度看，频谱感知技术主要涉及物理层和链路层，其中物理层主要关注各种具体的本地检测算法，而链路层主要关注用户间的协作以及对本地感知、协作感知和感知机制优化3 个方面。因此，目前频谱感知技术的研究大多数集中在本地感知、协作感知和感知机制优化3个方面。文章正是从这3个方面对频谱感知技术的最新研究进展情况进行了总结归纳，分析了主要难点，并在此基础上讨论了下一步的研究方向。 1 本地感知技术 1.1 主要检测算法 本地频谱感知是指单个认知用户独立执行某种检测算法来感知频谱使用情况，其检测性能通常由虚警概率以及漏检概率进行衡量。比较典型的感知算法包括： 能量检测算法，其主要原理是在特定频段上，测量某段观测时间内接收信号的总能量，然后与某一设定门限比较来判决主信号是否存在。由于该算法复杂度较低，实施简单，同时不需要任何先验信息，因此被认为是CR系统中最通用的感知算法。 匹配滤波器检测算法，是在确知主用户信号先验信息(如调制类型，脉冲整形，帧格式)情况下的最佳检测算法。该算法的优势在于能使检测信噪比最大化，在相同性能限定下较能量检测所需的采样点个数少，因此处理时间更短。 循环平稳特征检测算法，其原理是通过分析循环自相关函数或者二维频谱相关函数的方法得到信号频谱相关统计特性，利用其呈现的周期性来区分主信号与噪声。该算法在很低的信噪比下仍具有很好的检测性能，而且针对各种信号类型独特的统计特征进行循环谱分析，可以克服恶意干扰信号，大大提高检测的性能和效率。 协方差矩阵检测算法，利用主信号的相关性建立信号样本协方差矩阵，并以计算矩阵最大、最小特征值比率的方法做出判决。文献[1]提出基于过采样接收信号或多路接收天线的盲感知算法。通过对接收信号矩阵的线性预测和奇异值分解(QR)得到信号统计值的比率来判定是否有主用户信号。 以上这些算法都是对主用户发射端信号的直接检测，基本都是从经典的信号检测理论中移植过来的。此外，近期一些文献从主用户接收端的角度提出了本振泄露功率检测和基于干扰温度的检测。有些文献对经典算法进行了改进，如文献[2]提出了一种基于能量检测-循环特征检测结合的两级感知算法。文献[3]研究了基于频偏补偿的匹配滤波器检测、联合前向和参数匹配的能量检测、多分辨率频谱检测和基于小波变换频谱检测等。表2归纳了文献中提及较多的一些感知算法，并对其优缺点进行了比较。
认知无线电的频谱感知技术研究 0 引言 随着无线通讯业务的增长，可利用的频带日趋紧张，频谱资源匾乏的题目日益严重。世界各国现行的频率使用政策除分配极少的ISM频段之外，大多采用许可证制度。而获得许可的用户，并非全部都是全天候占用许可频段，一些频带部分时间内并没有用户使用，另有一些偶然才被占用，即使系统频谱使用率低，仍无法将空间的频谱分配给其他系统使用，即无法实现频谱共享。怎样才能进步频谱利用率，在不同区域和不同时间段里有效地利用不同的空闲频道，成为人们非常关注的技术题目。为了解决该题目，Joseph Mito1a于1999年在软件无线电的基础上提出了认知无线电(Cognitive Radio，简称CR)的概念，要实现动态频谱接进，首先要解决的题目就是如何检测频谱空穴，避免对主用户的干扰，也就是频谱感知技术。CR用户通过频谱感知检测主用户是否存在，从而利用频谱空穴。 1 匹配滤波器检测(Matched Filtering) 匹配滤波器是一种最优的信号检测法，由于在输出端它能够使信号的信噪比达到最大。匹配滤波器最大的优点就是能够在短时间里获得高处理增益。但是使用匹配滤波器进行信号检测必须知道被检测的主用户信号的先验知识，比如调制方式、脉冲波形、数据包格式等，假如这些信息不正确就会严重影响其性能，同时匹配滤波器计算量也较大。因此它可以用来检测一些特定的信号，但是每类主用户认知无线电都要有一个专门的接收器，这就增加了系统的资源耗费量和复杂度。 2 能量检测(Energy Detector—Based Sensing) 能量检测是一种较简单的信号非相干检测方法。根据基本假设模型，在高斯加性白噪声(AWGN)信道情况下，采用能量检测法进行主用户信号检测的性能。在AWGN信道非衰落的环境中，可知信道增益h是确定的。在H1下，当接收到的信号超过判决门限进时，判定主用户信号存在。在H0下，当接收信号超过判决门限时，则会作出错误的判定。分别用Pd 和Pf，来表示检测到主用户的概率(检测概率)和错误判定警报的(虚警)概率，对H．Urkowitz 的研究结果进行简化，可以得到通过无衰落的AWGN信道检测的概率和虚警概率的近似表达式为 其中：γ是信噪；σ是一个正数；r0，r(，g)是方差；是完整和不完整Gamma函数；Qm是普遍马库姆(Marcum)函数，其定义为