On the Effect of I/Q Imbalance on Energy Detection and a Novel Four-Level Hypothesis Spectrum Sensing

0.29 MB·English

by  Omid Semiari

On the Effect of I/Q Imbalance on Energy
Detection and a Novel Four-Level Hypothesis
Spectrum Sensing
Omid Semiari, Student Member, IEEE, Behrouz Maham, Member, IEEE, and Chau Yuen, Senior Member, IEEE
5
1
0
algorithms cannot be applied to cognitive radio systems. For
2 Abstract—Direct-conversion transceivers are in demand, due
to low implementation cost of analog front-ends.However, these instance, a compensation method for I/Q distortions based on
n
transmittersorreceiversintroduceimperfectionssuchasin-phase a novel pilot pattern is proposed in [14]. Since there is no
a
J and quadrature-phase (I/Q) imbalances. In this paper, we first cooperationbetweentheprimarytransmitterandthesecondary
3 investigate the effect of I/Q imbalance on the performance of receiver in a cognitive radio network, this method and other
primary system, and show that these impairments can severely
2 algorithms evolved out of channel estimation techniques are
degradetheperformanceofcognitiveradiosystemthatarebased
not applicable in a cognitive radio system. Although the
on orthogonal frequencydivisionmultiplexing(OFDM)multiple
]
T accessscheme. Next,wedesignanewfour-level hypothesisblind negative effects of I/Q imbalance can be severe, there has
detector for spectrum sensing in such cognitive radio system, not been sufficient studies on the impact of I/Q imbalance in
I
. and show that the proposed detector is less vulnerable to I/Q cognitiveradiosystem,andthewaytomitigateit.In[15],[16],
s
imbalance than conventional two-level detectors.
c Neyman-Pearsondetector[17]havebeenexploitedtoperform
Index Terms— Cognitive radio, I/Q imbalance, blind detection,
[
spectrumsensinginthepresenceoftransceiverI/Qimbalance.
fading channels, OFDMA

1 Our work differs as we propose a multi-level detector and
v I. INTRODUCTION study the problem through minimum average cost detection
0 [18] criterion.
8 Cognitive radio is a promising approach to alleviate the
Inthispaper,weconsidertheeffectofinterferenceimposed
9 spectrum scarcity faced by today wireless communication
by I/Q imbalance on the performance of the primary system
5 systems. The spectrum utilization has been noticed to be less
0 with blind spectrum sensing at the secondary user. By blind
than10%in practice[1],and thusleadsto the idea of reusing
. spectrum sensing, we mean that the secondary user does not
1 spectrum by a secondary network [2]. In a cognitive radio
0 network,secondaryor unlicensedusersbenefitbyopportunis- have access to the instantaneous channel state information
5 of the primary link, which is the same assumption as in
ticallyaccessingthespectrum,whileprimaryorlicensedusers
1 [19]. In order to tackle the effects of I/Q imbalance, we
are protected from the interference.
:
v propose a four-level hypothesis blind detector for the first
Therecentdevelopmentinintegratedcircuit(IC)technology
i time, and compare the performance of the proposed detector
X and incorporation of complete phase-locked loop devices in
to the conventional two-level detector under the scenario of
r low-costICpackageshavemadedirect-conversiontransceivers
a widely accepted. Nevertheless, in contrary to their desir- I/Q imbalance impaired transceivers.
The subsequent sections of this paper are organized as
able characteristics, the implementation of direct-conversion
follows. Section II describes the system model under the
transceivers causes various impairments associated with the
effect of I/Q imbalance and explains the idea of utilizing
analog components. The in-phase and quadrature-phase (I/Q)
periodogram detector. In Section III, we analyze the effects
imbalance has been known as a major source of analog
of secondary transmitter I/Q imbalance on outage probability
impairments in high-speed wireless communication systems
of the primary system. In Section IV, we explain how I/Q
[3].
imbalance can affect the spectrum sensing by the secondary
The effect of I/Q imbalance on traditional communication
user. A four-level hypothesis blind detector is proposed to
systems have been comprehensively investigated in previous
address the problems of I/Q imbalance, and the detection
works [4]–[10], and various compensation algorithms have
problem is formulated. Section V compares the performance
been proposed [11]–[14]. However, many of the proposed
of the new detector with conventional two-level detectors.
Conclusion is given in Section VI.
Copyright (c) 2013 IEEE. Personal use of this material is per-
mitted. However, permission to use this material for any other pur-
poses must be obtained from the IEEE by sending a request to II. SYSTEMMODEL
[email protected]. Omid Semiari and Behrouz Maham are with
We consider a cognitive radio network where the primary
Electrical and Computer Engineering department, University of Tehran,
Iran, e-mails: {omid.semiari,bmaham}@ut.ac.ir. Chau Yuen is systemutilizesOFDMAtechniqueforitsuplinktransmission.
with Singapore University of Technology and Design, Singapore, e-mail: We assume an overlay cognitive radio system in which the
[email protected]
secondaryusershouldnotinterferewithprimaryuserchannels
poreUniversityTechnologyandDesign(grantno.SUTD-ZJU/RES/02/2011),
andinpartbytheIranTelecommunications ResearchCenter (ITRC). and access only vacant channel. The primary system consists
of U primary users and dedicates total number of K subcar-
riers to them. Each primary user transmits a set of designated
data symbols s for k K/2, K/2+1,...,K/2 and
u,k
∈ {− − }
u 1,2,...,U ,wheres istakenfromanM-PSK symbol
u,k Fig.1. BlockdiagramofapriodogramdetectorforOFDM-basedspectrum
∈{ }
constellation and only one user transmit on a single subcar- sensing.
rier, i.e., orthogonal multiuser transmission. Without loss of
generality, we discard the user index u, since we assume the receiver can be written as
same modulation scheme for all primary users, i.e., M-PSK
symbol constellation. The average power of each subcarrier yk =αT,phk Pksk+βT,phk P−ks†−k+ωk, (3)
is assumed to be Pk, k K/2, K/2 + 1,...,K/2 . where ωk is the noipse with independpent and identically dis-
∈ {− − }
We assume that no data is transmitted on the direct current tributed (i.i.d.) Gaussian distribution with zero mean and
(DC) subcarrierandK is an evennumber.The cyclicprefixis variance σn2, i.e., ωk ∼N(0,σn2).
assumedtobelongerthantheimpulseresponseofthechannel A typical energy detector consists of a low pass filter to
and hence, there is no inter-carrier interference. In addition, remove the out-of-band noise and adjacent interference, an
weassumethatthesecondaryuserknowsaprioriinformation analog to digital converter, as well as a square law device to
about potential primary systems including frame structure, compute the energy. However, this implementation computes
subcarrierstructureliketheDiscreteFourierTransform(DFT) theenergyofsignalwithintheentirefrequencybandthatisnot
size, the transmission parameters (fundamental symbol rate, a preferable approach to perform the spectrum sensing [27].
cyclic prefix length), and the level of interference tolerance Hence, a periodogram solution is proposed in [27], which is
of primarysystems [20].After removingthe cyclic prefixand depicted in Fig.1. In this figure, indices i and k represent the
DFT operation, the channel in the subcarrier k can be repre- time domain and frequency domain, respectively. From (3),
sentedasacomplexchannelh ,whichismodeledasRayleigh the output of periodogram detector is given by
k
fadingwith independentGaussiandistributedrandomvariable 1 N 1 N 1 N
oOfFDvaMria-bnacseedσsh2yks.teImt sharessubletesninsahomwuntuathlaintteI/rQferiemncbealbaentcweeeinn Zk = N Xi=1|yk,i|2 = N Xi=1Xk,i = N Xi=1(yR2,i+yI2,i)
(4)
subcarriers that are located symmetrically to the DC carrier
where y and y denote real and imaginary parts of y ,
R I k
[21], [22]. In this paper, we focus on transmitter’s I/Q im-
respectively. In addition, variables N and X represent
k,i
balance, since the direct-conversionarchitecture is commonly
the number of time-domain data packets and the square-law
employed in transmitters [23]. We assume that both primary
detector’s output for the i-th data packet of k-th subcarrier,
and secondarydirect-conversiontransmittersare wideband,in
respectively.
whichthe inter user interferenceimposedby I/Q imbalanceis
probable. III. I/Q IMBALANCE EFFECTON PRIMARY SYSTEM
In practice, there is neither ideal amplitude matching nor PERFORMANCE METRIC
exact π/2 phase difference among I and Q signals. Thus, the Inthissection,weanalyzetheeffectofinterferenceimposed
actual transmitted signal xk, which is differentfrom the ideal by secondary user on the performance of primary system.
transmitted signal, can be modeled as [24]: This interference occurs due to the I/Q imbalance of the
secondary user transmitter. Fig.2 demonstrates a cognitive
xk =αT Pksk+βT P−ks†−k, (1) radionetworkwithanOFDMAuplinktransmissionofprimary
where (.)† denotes thpe complex cponjugate. Moreover, the users. Meanwhile, the secondary user senses subcarrier k in
ordertodecideifitisvacant.Inthisexample,neitherprimary
signals sent by primary users are assumed to be normalized,
user1norprimaryuser2transmitsdataonsubcarrierk,while
i.e., E s = E s = 1. From (1), at the primary
k k
{| |} {| − |} the primary user 2 transmits over subcarrier -k. The two-level
transmitter,thereis aninterferenceinducedbyI/Q imbalance,
which can be a significant performance limiting factor, espe- energydetector’sdecisionforsubcarrierkisbasedonlyonthe
cially in the mobileuplinks. The degreeof I/Q imbalancecan signal’saveragedpowerink-thsubcarrier.Infact,althoughthe
secondaryusermaybeawareofthetransmitI/Qimbalance,it
beevaluatedintermsofanimagerejectionratio(IRR),which
risecdeeifivenre,drebsypeAcTtiv=ely||αβ[TT2||522].anPdarAamRe=ter||sαβRRα||22 faonrdtrβansminit(te1r)aanrde ojufstthinecoFrFpTorabtleosctkhefoinrfodremciadtiinogndoenrivseudbcfarorrmierthke,kr-ethgaorudtlpeusst
T T of the state of subcarrier k. Hence, if the secondary user
two complex scalars given by −
usestwo-leveldetectorforspectrumsensing,itwouldtransmit
α =cos(θ )+jǫ sin(θ ), β =ǫ cos(θ ) jsin(θ ),
T T T T T T T T over subcarrier k, then as a result, primary user 2 would be
−
(2)
impairedbytheI/Qimbalancefromsecondaryuser.Asshown
and ǫ and θ represent the amplitude and phase mismatch
T T inFig.2,thesecondarytransmissiononanidlesubcarrier,e.g.
of transmitter I/Q signals, respectively [26]. In addition, α
R subcarrierk, introducesaninterferenceonsubcarrier k.The
and β are defined based on (2), but with respect to the −
R primary receiver treats the secondary interference as noise.
receiver mismatch parameters. From now, we use subscripts
Hence, the received signal at the primary receiver is
T,p and T,s to differentiate between the transmit I/Q imbal-
anceparametersofthe primaryuser andthatof the secondary yp,−k = P−ks−kg−k+βT,s P0s†s,kh−k+wp (5)
user, respectively. From (1), the received signal at secondary p p
thresholds more intelligently and detect vacant subcarriers
more precisely. We model the four possible cases that could
happen at a secondary receiver as follows:
H :Only Noise
0
H :I/Q Imbalance+Noise
 1
HH2::PPrriimmaarryy uusseerr ssiiggnnaall++NI/QoisIembalance+Noise.
3
The first state occurs when the secondary user receives only
noise and there is no data transmission by any of the primary
users in both k-th and -k-th subcarriers. The second state
happens when there is transmission in subcarrier -k by one
Fig.2. Anexample ofasecondaryuser,interfering withOFDMAprimary of the primary users, while subcarrier k is left vacant. Hence,
users uplink transmission due to I/Q imbalance caused by cognitive radio the secondary user senses the interference plus noise, where
systemtransceivers.
the interference is due to the I/Q imbalance of secondary
where g k denotesthe channelcoefficientof the primarylink receiver or primary transmitter or both of them. If primary
onsubca−rrier k,P0 isthetransmittedpowerofthesecondary usertransmitsinsubcarrierk,thensecondaryusersensesonly
−
user, and ss,k is secondary signal on subcarrier k. Moreover, primary signal plus noise as stated by the third hypothesis.
wp istheadditiveGaussiannoise oftheprimaryreceiverwith The forth state stands for the transmission of data over both
zero mean and variance of Np, i.e., wp N(0,Np) and k-th and -k-th subcarriers by primary users. Therefore, at this
∼
is independent of channel coefficients. Assuming a primary state the secondary user receives a signal associated with the
uplink transmission with a fixed transmission rate of Rp, the k-th subcarrier and also an interference plus noise.
outage probability is defined as ρ0 , rp < Rp [28]. From The proposed detector is able to differentiate the interfer-
{ }
(5), and by considering the normalized bandwidth, the data enceimposedbymirroredsubcarrierfromthemainsignal,i.e.,
rate rp is given by bydetectingH1.Thisisimportant,becausesecondaryusercan
P k g k 2 usethisgroupofsubcarriersincasethatsecondarytransmitter
rp =log2(1+γ)=log2 1+ N + β− | 2−P| h 2 , doesnotsufferfromconsiderableI/Q imbalance.Evenforthe
(cid:18) p | T,s| 0| −k| (cid:19) (6) secondaryuserwithhightransmitI/Qimbalance,thisdetector
where γ denotes the signal to interference plus noise ratio helpsuser to be aware of the primarytransmission on subcar-
(SINR). The outage probability can then be expressed as rier k andavoid interferingwith primarysystem.According
ρ0 = Pr γ <γth , where γth =2Rp 1. Hence, to th−e four-level hypothesis model and the expression for the
{ } −
ρ =Pr X1 <γ received signal from (3) and (4), the hypothesis test can be
0 th
1+X formulated as
(cid:26) 2 (cid:27)
mwThheeaernreefσo=XX2re11Z,−=at∞nh∞dePNP−Xoprku{2σtXag2ag−1reek<ptawrnγoodtbhaσe(bxX21ipl2+oit=nyXean|2tβt)iT|atNXh,lsep|r22aP}pn0frdiσXmoh22ma−(rxkyv2,a)rrrdeeiscaxpeb2eilv,ecestirvwec(ila7tyhn). HHHH2130 ::::ZZZZkkkk ==== NNNN1111 PPPNiNiNiNi====1111||||ω(((βααkTTT,i,,,|ppp2hhhkkk,,,iii)))ppPPPkk−,,iikss,ikks,,ii†−+k,iω+k,iω|2k,i|2 (9)
be calρcu0l=ateZd0a∞s 1−e−γthσ(X21+1x2)!(cid:18)σX122e−σxX222(cid:19)dx2 comFrpolmex(r3a)n,diot+mi(sPβvaTorb,ipavhbiokle,ui.s)pHthePan−tcekt,,hipesy†−rke=,cie+iyvωedk,i+s|i2g.jnyal ykwhiserae
=1− σ2 σ+X21σ2 e−σNX2p1γth . (8) k R,k I,k
IV. FOUR-LEIVM(cid:18)EPLAXHIR1YEPDOTSXHP2EE(cid:19)CSITSRTUEMSTSEFNOSRINI/GQ IMBALANCE yR,k−=IRme{{ααTT,,pppPPkksskk++ββTT,,pppPP−−kkss†−†−kk}}hhRI,,kk+ωR,k,
Inthissection,weintroduceafour-levelhypothesistest,and yI,k =Re{αT,ppPksk+βT,ppP−ks†−k}hI,k
a[1p8p]l.yTBoauynesdiearnstmanidnitmheummoavtievraatgioencoofstthceritperroiopnosteodthfoisurm-loedveell +Im{αT,ppPksk+βT,ppP−ks†−k}hR,k+ωI,k(,10)
p p
hypothesistest, again considerthe scenariodepicted in Fig.2. and ω and ω represent real and imaginary parts of
R,k I,k
Inadditiontotheproblemdiscussedinprevioussection,I/Q ω , respectively. It can be checked from (10) that real and
k
imbalances imposed by primary users can make a secondary imaginarypartsofy areGaussianrandomvariableswithzero
k
user assume a vacant subcarrier busy. This would rise the mean and identical variances. In addition, y and y are
R,k I,k
probability of false alarm and degrades the system perfor- uncorrelated[29].Hence, they are independentand y can be
k
mance. Therefore, we use this notion to propose a four-level representedasacomplexGaussianrandomvariable.Thus,the
hypothesis test, where the detector can adjust the decision probability density function of their square is given by [30]
f (x)=f (x)= √2π1xσ2e−2σx2 if x≥0, (11) In Appendix A, it is shown that S01 < S02 < S03, S02 <
yR2 yI2 (0 if x<0, S12 < S13, and S03 < S13 < S23. Thus, the expressions in
wheref (.)andσ2 denotetheprobabilitydensityfunctionof (17) can be simplified as:
X
variable X and the variance of either real or imaginary part Λ0 : 0<z <S01 , Λ1 : S01 <z <S12 ,
{ } { }
of yk, respectively. In addition, considering the fact that yR2 Λ2 :{S12 <z <S23}, Λ3 :{0<S23 <z}. (19)
andy2 areindependent,andfrom(11),theprobabilitydensity
I In order to analyze the effect of I/Q imbalance, we calculate
function of X is
k
the probability of false alarm, i.e., when there is no signal
f (x)= ∞f (x s)f (s)ds= x 1 e−2σx2 ds transmission in subcarrierk , but secondaryuser assumes that
Xk Z−∞yR2 − yI2 Z0 2πσ2 s(x−s) the channel is busy. Equivalently,
= 1 e−2σx2 1 2 du= 1pe−2σx2. (12) Pfa =P(H2|H1)+P(H2|H0)+P(H3|H1)+P(H3|H0)
2πσ2 √1 u2 2σ2
Z0 − = [P(z H1)+P(z H0)]dz+ [P(z H1)+P(z H0)]dz.
From (12), the conditionalprobability density function of X | | | |
k ZΛ2 ZΛ3
can be represented as exponential distribution as follows: (20)
From (15), the integralscan be evaluatedusing the following:
x
fX(x|Hi)=(02σ1i2e−2σi2 iiff xx≥<00,, (13) P(H3|Hi)= P(z|Hi)= ∞ Γ(1N)(N1σ2)Nz(N−1)e−Nzσi2dz
ZΛ3 ZS23 i
where i=0,1,2,3 and = σ2Γ(N1 +1) ∞(Nzσ2)N−1e−(Nzσi2)dz
σ2 = 1σ2 i ZS23 i
σσσ0312222 === 1222211(((|||nβααTTT,,,ppp|||222PPP−kk||kss|kks||−22k)σ|2h2σkh2+k)σ+02σ02 (14) wfohree,refrΓom(.,=(.2)0Γi)s(a1Ntnhde)Z(i2nNS1c∞2σ)o3i2mthtpeNle−ptr1eoebg−aatbmditlmi=tayfoΓuf(nΓfNcat(l,isNoeNSn)2σa3[i2l3a)1r,m]. cTahn(e2rb1ee)-
The period+g2rRame(αdeTt,epcβtoTr,p,√inPtrkopduPce−dksinksS†−ekc)t)ioσnh2kII+, cσo12m.putes ePxpr=esΓse(dNa,sNS1σ212)−Γ(N,NS2σ312) + Γ(N,NS1σ202)−Γ(N,NS2σ302)
the average of FFT output for N time domain windowed fa
Γ(N) Γ(N)
data packets for each frequency slot. The overall output of
Γ(N, S23 ) Γ(N, S23 ) Γ(N, S12 ) Γ(N, S12 )
the detector for each frequency slot is a Gamma distributed Nσ2 Nσ2 Nσ2 Nσ2
+ 1 + 0 = 1 + 0 .
random variable, since it is a sum of N exponential random Γ(N) Γ(N) Γ(N) Γ(N)
variables with identical means, i.e., Z = 1 N y 2. (22)
k N i=1| i,k| Similarly, the probability of detection is given by
Therefore, we have
fZk(z|Hi)=(0Γ(1N)(N1σi2)Nz(N−1)e−Nzσi2 Piiff zz ≥<00,, PD ==PΓ((HN2,|HNS21σ2)22)+P(ΓH(3N|H,3NS)2σ322) + Γ(N,NS2σ332) . (23)
Γ(N) − Γ(N) Γ(N)
(15)
It must be noted that different side information is needed
where Γ(.) is the gamma function [31, Sec. (8.31)].
in order to calculate the detection thresholds. For instance,
Now, we apply the minimum average cost criterion to this
the statistics of the interference link between primary users
model.Withoutlosinganygenerality,a uniformcosttest with
and secondary users, i.e. σ2 , could be inferred by listening
equal prior probabilities is assumed for all hypotheses. Thus, hk
to the downlink transmission of the primary system [28]. In
H is selected if [18]
i addition, the determination of primary transmitter IRR values
f (z H ) or transmit power requires either explicit signaling from the
Zk | i >1 for i,j =0,1,2,3 and i=j. (16)
f (z H ) 6 primarysystemtothesecondaryusers,ortheprimarytransmit
Zk | j
power could be estimated if secondary user roughly knows
It can be shown that by applying the conditions in (16), four
about its distance from the nearby primary user. This work
decision regions are obtained as follows:
couldalsobeextendedtoMIMOsystemsinwhichlocalization
and other array-antenna techniques are incorporated.
Λ : 0<z <S ,0<z <S ,0<z <S
0 { 01 02 03} V. SIMULATIONRESULTS
Λ : S <z <S ,S <z <S
 1 { 01 12 01 13} (17) In this section, we provide simulations to evaluate the
Λ2 :{S12 <z <S23,S02 <z <S23} analytical results provided in previous sections. We assume
Λ3 : S03 <z,S13 <z,S23 <z , a cognitive radio network with an OFDMA primary system
{ }
where Λi is the corresponding region of each hypothesis and with four users, i.e., U = 4. Moreover, the total number of
subcarriers is K = 512, i.e., 128 subcarrier per user with
N2lnσi2 16-PSK constellation. We also assume a secondary user that
σ2
S =S = j for i,j =0,1,2,3 and i=j. (18) uses blind detection for spectrum sensing, based on the four-
ij ji σ1j2 − σ1i2 6 level hypothesis test proposed in Section IV. The magnitude
its detection procedure. This helps the detector to sense the
0.7
SSiimmuullaattiioonn,, PBrinoaproys deedt edcettoerc, tAorT,= A−T3=5−d3B5dB spectrumbased onthevarianceofbothnoiseand interference
0.6 SSiimmuullaattiioonn,, PBrinoaproys deedt edcettoerc, tAorT,= A−T2=5−d2B5dB which leads to lower probability of false alarm.
Simulation, Proposed detector, AT=−15dB
0.5 SAAinnmaaullyylattiicctiaaolln,, ,PB Brinoinaparoyrsy de dedet edtececttoteorc,r t,Ao ArT,T= A=−T−3=15−5d3dB5BdB Fig.4 demonstrates both analytical and simulation results
Analytical, Proposed detector, AT=−25dB of I/Q imbalance effect on probability of false alarm for
Analytical, Binary detector, AT=−25dB
0.4 AAnnaallyyttiiccaall,, PBrinoaproys deedt edcettoerc, tAorT,= A−T1=5−d1B5dB the proposed detector by considering various ∆SNR =
Pfa 10logSNR1, which denotesthe signalto noise ratio difference
0.3 SNR2
between the subcarriers k and k. Fig.4 shows that even for
−
0.2 ∆SNR= 10dB,theprobabilityoffalsealarmissignificantly
−
increased.
0.1
The comparison of joint transmitter-receiver I/Q imbalance
00 5 10 15 20 25 30 35 40 effect on the probability of detection with the case when
SNR[dB]
1 I/Q imbalance exists only in transmitters is shown in Fig.
5. The joint transmitter-receiver I/Q imbalance effect can
Fig.3. Thecomparisonbetweentheprobabilityoffalsealarmoftheproposed
four-leveldetectorandtheconventionaltwo-leveldetectorfordifferentvalues be investigated based on the procedure introduced in this
ofIRRs.Thedashedandsolidcurvesrepresenttheprobabilityoffalsealarm paper. Indeed, it can be proven that the variance of received
forconventional detectorandproposeddetector, respectively. Theresultsare
signal may differ from that of presented in Section IV,
obtained fordifferent values ofIRRsandfortheconstant transmitted power
ofsubcarrier−k,i.e.,SNR2=−10dB. nevertheless the detector output distributions are identical in
both scenarios. Hence, the probability of false alarm and
the probability of detection could be found accordingly. As
Analytical, ∆SNR=−10 dB
Analytical, ∆SNR=0 dB expected from analytical results, effect of I/Q imbalance on
0.5 Analytical, ∆SNR=10 dB
Simulation, ∆SNR=−10 dB the receiver’s probability of detection is serious when direct-
Simulation, ∆SNR=0 dB conversion transceivers are used. However, direct-conversion
0.4 Simulation, ∆SNR=10 dB
receivers offer significant power saving, hence they might be
Pfa0.3 aspreferableasdirect-conversiontransmitterstobeutilizedin
wireless communication devices [23].
0.2 Eventually, Fig. 6 depicts the impact of I/Q imbalance of
thesecondarytransmitterontheoutageprobabilityofprimary
0.1
receiver. It clearly demonstrates that the I/Q imbalance in
secondarytransmitter can dramatically affectthe performance
0
0 5 10 15 20 25 30 35 40 of the primary system.
SNR[dB]
1
Fig. 4. The probability of false alarm for different ∆SNR values, when VI. CONCLUSION
IRR=-15dB.Thedashedandsolidcurvesrepresenttheanalyticalresultsand
In this paper, the effects of I/Q imbalance on both pri-
thesimulations, respectively.
mary and secondary systems have been investigated. It was
of the frequencydomain channel coefficients h and h are explained how I/Q imbalance can make the secondary user
k k
assumed independent Rayleigh distributed random va−riables interfere to an OFDMA primary system if the secondary
with variance σ2 = σ2 = 1. In order to examine the user employs binary detector. Therefore, we design a new
hk h−k
statistical aspects of energy detector, simulations are done detector based on four-level hypothesis for blind spectrum
over 20 million samples and for one sample package, i.e., sensing in an overlay cognitive radio system. The detection
N = 1. Here, we define the transmitted signal to noise algorithm jointly considers the information of DFT blocks
rSaNtiRo2fo=r suPb−ckaσ|sr2−rike|r2,kreasnpdect−ivkelya.sWSeNRco1ns=iderPokσ|rsnt2kh|o2goannadl obthuyetpiptusrtospfyoomrsemadesdtpreeitcceaicfiltoccrosduuenbctceraerrparsaieertsr.taShniedmputrhloaebtiaionbntielirrtfeyesruoelfntsfcaeslshieomwaploatrshmeadt,
signaling,henceninterferenceisonlyduetotheI/Qimbalance.
while avoids interfering to primary system.
SecondaryreceivertreatsprimaryinterferenceastheGaussian
noise, since it is not completely aware of the primarysignal’s APPENDIX A
modulation parameters. The SNR at each subcarrier can be From (14) and assuming λ = 1 as well as σ2 >σ2, it is
i σ2 2 1
determined by priodogram detector described in Section II. obvious that 0 < λ < λ < λ <iλ . Moreover, from (18),
3 2 1 0
The comparison between the proposed four-level detector we have
and the conventional two-level detector is shown in Fig.3. ln(λ ) ln(λ )
S =S =N2 i − j
Basedontheresults,theproposeddetectorislessvulnerability ij ji λ λ
i j
to the I/Q imbalance effect than the two-level detector. Since −
∆F(x)
the two-level detector sets its detection threshold based only ,N2 for i,j =0,1,2,3 and i=j, (24)
on the estimated noise variance, the interference imposed by ∆x (cid:12)λi,λj 6
other subcarriers can fool the detector. On the other hand, where F(x) = ln(x(cid:12)(cid:12)). Therefore, (24) suggests that Sij is of
theformofF(x)differentiation,i.e., 1,whichisadecreasing
the proposed detector uses the joint information of both x
function of x. Hence, S < S < S , S < S < S ,
subcarriers k and k, by adding hypotheses H and H into 01 02 03 02 12 13
− 1 2 and S <S <S .
03 13 23
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