Sensing for Spectrum Sharing in Cognitive LTE-A Cellular Networks

0.35 MB·

by  Prasanth Karunakaran

Sensing for Spectrum Sharing in Cognitive LTE-A
Cellular Networks
Prasanth Karunakaran∗, Thomas Wagner†, Ansgar Scherb† and Wolfgang Gerstacker∗
∗Institute for Digital Communications
Friedrich-Alexander-University Erlangen-Nu¨rnberg (FAU), Germany
Email: {karunakaran,gersta}@lnt.de
†Ericsson, Nu¨rnberg, Germany
Email: {thomas.wagner,ansgar.scherb}@stericsson.com
Abstract—In this work we present a case for dynamic spec- hypothesis testing problems where the competing hypotheses
trumsharingbetweendifferentoperatorsinsystemswithcarrier are the ”noise” hypothesis (H ) and the ”signal + noise”
0
aggregation (CA) which is an important feature in 3GPP LTE-A hypothesis (H ) [4][5]. In such a case, the secondary device
4 1
systems. Cross-carrier scheduling and sensing are identified as perform sensing at the beginning of a slot and starts trans-
1
key enablers for such spectrum sharing in LTE-A. Sensing is
mitting if the spectrum is sensed to be vacant. The main
0
classified as Type 1 sensing and Type 2 sensing and the role of
2 problem with such protocols is that it cannot react quickly
each in the system operation is discussed. The more challenging
if the primary transmission starts after the sensing interval
n Type2sensingwhichinvolvessensingtheinterferingsignalinthe
causing interference till the end of the slot. Recently, this
a presence of a desired signal is studied for a single-input single-
J output system. Energy detection and the most powerful test are problemhasbeenaddressedin[6][7]whereschemeshavebeen
formulated. The probability of false alarm and of detection are developed that allow sensing during the transmission phase of
0
analyzedforenergydetectors.Performanceevaluationsshowthat the secondary transmitter. The competing hypotheses for this
3
reasonable sensing performance can be achieved with the use of case are the ”serving cell signal + noise” (H1(cid:48)) hypothesis and
] channelstateinformation,makingsuchsensingpracticallyviable. the”servingcellsignal+interferingsignal+noise”hypothesis
I (H ). In [6] the authors propose zero-forcing beamforming by
N 2
I. INTRODUCTION
the secondary base station towards idle secondary users who
s. Dynamic spectrum access (DSA) based on cognitive radio can then sense as if there is no secondary signal. In [7] a
c technology is considered to be vital to achieve efficient spec- multiple-input multiple-output (MIMO) system is considered
[
trumutilization[1].Insuchsystems,usersareclassifiedasei- with pre-processing and post-processing based on singular

1 therprimaryusersorsecondaryusers,wheretheprimaryusers value decomposition (SVD) of channel matrix to decompose
v are the licensed users with highest priority. The secondary the system into parallel channels and the transmit power of
6 users sense the spectrum for primary user’s presence and use eachsubchannel,sensingtimeineachsubchannelandsensing
2 thespectrumfortransmissionwhenitisfreeortransmitjointly threshold are optimized to maximize the CR throughput while
2 with primary users without seriously affecting their communi- constraining the probability of false alarm and of detection.
8 cation. Mechanism designs for spectrum sharing in such cases These two approaches are not directly applicable to LTE-
.
1 are being developed [2]. Such DSA can be considered for A systems, because the transmission modes and precoding
0 future cellular networks, especially in the context of spectrum are standardized and sensing must be evaluated with these
4 sharing between different operators. Spectrum sharing allows restrictions. Therefore, in this work, we study the problem
1 a lightly loaded operator to dynamically share their spectrum of sensing in presence of a signal for a single-input single-
: toanotheroperatortherebyimprovingthespectrumutilization output configuration. MIMO configurations will be addressed
v
i andtheprofitability.Thisideabecomesparticularlyrelevantin in future works.
X thecontextofthe4Gcellularstandard3GPPLTE-Aduetothe
Energy detection (ED) is one of the most important and
r recently introduced carrier aggregation (CA) feature [3]. CA
a allows an operator to aggregate up to five LTE-A carriers of well studied methods for testing between H0 and H1 [4][5].
Even though ED is prone to noise variance uncertainties, it
20 MHz bandwidth each. When a single operator exclusively
still remain the favored method for practical implementations
owns a large bandwidth, the chance that the actual load from
due to its low computational complexity and ability to work
thecoverageareabeinglessthanthecapacityishigher.Hence
with unknown signals. In this work, we adapt the energy
a large spectrum deployment using CA is a suitable candidate
detectorof[5]fordistinguishingbetweenH(cid:48) andH .Thenwe
for spectrum sharing. 1 2
extend the energy detector to incorporate channel knowledge,
In traditional cognitive radio (CR) primary users are un- and the false alarm and detection probabilities are analyzed.
aware of the secondary users and it is the responsibility Performance results show that meaningful detection and false
of the secondary user to ensure that it does not interfere alarm probabilities can be achieved if channel knowledge can
with the primary user. Secondary users perform sensing to beexploited.Wealsoformulatethemostpowerfultestforthis
meet this requirement. Majority of the sensing studied in the scenario.
CR literature determine whether the spectrum is vacant (i.e.,
The paper is organized as follows. Section II describes the
usable) or not [4]. This task belongs to the class of binary
spectrum sharing possibilities in 3GPP LTE/LTE-A networks,
importance of cross-carrier scheduling, the role of sensing in
This work has been performed in the framework of Cognitive Mobile
spectrum sharing and the system model. In Section III the
Radio (CoMoRa) project, which is partly funded by the Federal Ministry of
EducationandResearch(BMBF)ofGermany. energy detector of [5] is formulated for our context and its
extension to the case of availability of channel knowledge
is provided. In Section IV we state the most powerful test,
and simulation results are presented in Section V. Section VI
provides the conclusion.
A Spectrum
BS1
II. SPECTRUMSHARINGMODELSANDSENSING Operator A
Consider a spectrum sharing system composed of two Shared Spectrum
3GPP LTE base stations, BS1 and BS2, belonging to two
different network operators as in Figure 1. The operators
are expected to have made certain agreements on spectrum
sharing related to spectrum pricing, time scale of sharing, B Spectrum
amount of tolerable interference caused to each other etc.
BS2
Due to OFDMA transmission, LTE base stations can consider
Operator B
sharing with varying degrees of time-frequency granularity.
The choices for spectrum sharing granularity in LTE can be Fig.1. Spectrumsharingbetweentwobasestations
understoodfromtheframestructureofLTE[3].Aradioframe
in LTE occupies the full system bandwidth and spans 10 ms.
Each radio frame is composed of 10 subframes, where each performsthetraditionalcognitiveradiohypothesistestbetween
subframe is further divided in the frequency domain in units H and H . For the following discussions, it is assumed that
0 1
of physical resource blocks (PRBs). A PRB, which is also BS1 has a higher priority than BS2. Based on the spectrum
the smallest time-frequency scheduling granularity available sharing granularity, we distinguish between two schemes.
in LTE systems, consists of 12 contiguous subcarriers and 14
A. Long-Term Spectrum Sharing
OFDM symbols and occupies a 180 kHz × 1 ms slice in the
time-frequencyplane.Thusthegranularityofspectrumsharing Inlong-termsharing,thespectrumsharinggranularityisof
canbeconsideredfromthesmallestunitofaPRBtotheorder theorderofseveralhundredsofradioframes.Twopossibilities
of several radio frames. can be considered for long-term sharing. In the first type, the
spectrum sharing is controlled using licenses obtained via the
Another restricting feature for spectrum sharing is the
backhaul. When BS1 does not require the spectrum, it turns
control channel structure. In LTE-A (Release 10) the Physical
off the transmission. BS2 can start using the spectrum when it
Downlink Control Channel (PDCCH) must be transmitted in
is granted a license. Though sensing can aid BS2 in detecting
the first three OFDM symbols of a subframe and are mapped
the availability of spectrum, it is not essential for this type of
across several subcarriers. If there is only one LTE-A carrier,
operation.Inthesecondtype,sharingiscontrolledviasensing
then the control channels of both operators will collide and
alone and does not involve license acquisition. This is more
could adversely affect control channel coverage. In CA with
suitable for a relatively smaller granularity, say tens of radio
multiple carriers, LTE-A supports scheduling transmissions
frames.Aperformancecriterionforsharingcouldbeanupper
over a carrier via control channels sent over another carrier.
limitonthedegradationcausedtothehigherpriorityuser.The
This feature, known as cross-carrier scheduling, allows to cir-
lower priority operator could be charged a higher price if it
cumventthecontrolchannelcollisionsifbothoperatorshaveat
violates the upper limit. As mentioned earlier, two types of
leastoneexclusivecarrierforthemselves.Thecontrolchannels
sensing can be considered in this context. In Type 1 sensing,
canbesentovertheexclusivecarrierswithoutcollisionswhile
the goal is to distinguish between signal and noise. Type 1
spectrum sharing can happen in another aggregated carrier.
sensing is mainly performed by the users of BS2 to detect
AnotherpossibilityistheEnhanced-PDCCH(E-PDCCH)[13]
the end of transmission by BS1. BS2 can then start to occupy
in the recently standardized version LTE-A Release 11. E-
the spectrum. The hypotheses for a single-input single-output
PDCCHsarenotrestrictedtothefirstthreeOFDMsymbolsbut
system, involved in Type 1 sensing are given as
transmitted in certain resources of the data channels and thus
have the potential to be used in a spectrum shared operation. H :y(kT )=n(kT ); k =1,2,...,N
0 s s t
(1)
We consider the downlink scenario and sensing is per- H1 :y(kTs)=g(kTs)+n(kTs); k =1,2,...,Nt.
formed by user equipment (UE) (or dedicated sensing equip-
where y(t) is the received signal, g(t) is the received signal
ments installed by the operators). This is a reasonable as-
from BS1 (or BS2 when sensing is performed by users of
sumption because it is the UE which is affected by downlink
BS1), n(t) is the additive white Gaussian noise (AWGN),
interference and the base station is usually not equipped with
T is the receiver sampling interval and N is the number
adownlinkreceiver.Thesensingresultcouldbereportedback s t
of samples in a unit of spectrum sharing granularity. Energy
to the serving base station via uplink messaging. The sensing
detection, cyclostationarity based detection and other methods
and reporting, in our view, is controlled by the base station.
of detection of traditional cognitive radio systems can be used
For example, the base station might instruct certain UEs to do
in Type 1 sensing.
sensing on particular PRBs or subframes. It is also assumed
that the base station informs the selected UEs about whether InType2sensing,thesensingisperformedwhilereceiving
the PRBs or subframes to be sensed carry the base station’s theservingcellsignaltodetectthestartoftransmissionbythe
transmissions or not. This assists the UE to determine which other base station. Type 2 sensing is beneficial to both BS1
testtoperformwhenthePRBsarenotallocatedforUE’sown and BS2. For BS2, it allows to stop the transmission quickly
transmission. If the serving cell’s signal is not present, the UE when BS1 start its transmission again. Another advantage of
Type 2 sensing for BS2 is that it allows another opportunity to be exchanged over the X2 interface between coordinating
to rectify the miss-detection from Type 1 sensing. The use of base stations. It is not clear whether such an information
Type2sensingforBS1istoidentifytheinterferencefromBS2 exchangeispossiblebetweendifferentoperators.Eventhough
and the statistics of such events could be used to assess the it is possible, sensing would supplement in achieving a higher
impactofspectrumsharingwithBS2.Thehypothesesinvolved flexibility as information exchange over X2 can happen only
in Type 2 sensing are given by every20mswhichalonecontains2000PRBsineach20MHz
carrier [3].
(cid:48)
H :y(kT )=s(kT )+n(kT ); k =1,...,N (2)
1 s s s t
In the remainder of the paper, we describe Type 1 and
H :y(kT )=s(kT )+g(kT )+n(kT ); k =1,...,N .
2 s s s s t
Type 2 sensing from the point of view of a BS1 user. The
where s(t) is the received signal from serving base station hypotheses for sensing by a BS2 user can be easily written in
and the other parameters are same as in (1). Energy detection asimilarfashion.InType1sensing,performedbyaBS1user,
is possible for Type 2 sensing. However, cyclostationarity the competing hypotheses after the FFT (subcarrier domain)
based detection is difficult as both s(t)and g(t) have similar are given by
cyclostationary features. H :y =n ; i=1,2,...,N
0 i i
(3)
B. Short-Term Spectrum Sharing H :y =h x +n ; i=1,2,...,N,
1 i 2 2i i
In short-term spectrum sharing, sharing can be performed where yi is the received symbol in the ith resource element,
within a subframe with the smallest granularity of a physical h2 ∼ CN(0,σ22) is the complex Gaussian channel coefficient
resourceblock(PRB).BS1andBS2cannotbeturnedoffcom- fromBS2(interferingcell)withvarianceσ22,ni ∼CN(0,σn2)
pletely during a short interval because LTE base stations must is the AWGN at the receiver, x2i is the transmit symbol from
transmit signals such as common reference signals (CRS), BS2 in the ith resource element of the PRB with symbol
synchronization signals, control channels etc. Synchronization energyEx =E[|x2i|2],andN representsthenumberofusable
of the base stations and certain scheduling restrictions might resource elements in a PRB. This model assumes Rayleigh
benecessarytosupportshort-termspectrumsharing.Thebasic fadingandisaccurateunderlowfrequencyandtimeselectivity
operation is as follows. When BS2 wants to transmit in a conditions.
particular PRB, it performs Type 1 sensing in that PRB in
As in long-term sharing, Type 2 sensing could be per-
the current subframe to decide whether it can transmit data on
formedbyBS2userstocheckifBS1istransmittingonaPRB
that PRB in the next subframe. If the PRB is not occupied
where BS2 is already active. This can help BS2 to control
in the current subframe, BS2 assumes that it is free and
the interference generated due to either a miss-detection in
starts to transmit in the next subframe. There is always the
Type1sensingoraschedulingchangeatBS1.Type2sensing
possibility that in the next subframe that PRB is occupied due
also allows BS1 to identify interfering events caused by BS2.
to new scheduling at BS1, making the sensing result from the
Cyclostationarity based detection is not possible for Type 2,
previoussubframeinvalid.However,underlowloadconditions
but energy detection and other methods could be considered.
such collisions may not be frequent. Also, due to the random
For a BS1 user, the hypotheses of Type 2 sensing after the
geometry of users, not all the collisions will result in data
FFT are given by
decoding failure. In any case, such causality problems could
(cid:48)
becircumventedbysacrificingsomeschedulingflexibility,for H1 :yi =h1x1i+ni; i=1,2,...,N (4)
example, a scheduling bias may be introduced to favour time H :y =h x +h x +n ; i=1,2,...,N,
2 i 1 1i 2 2i i
continuity of occupied PRBs. Type 1 sensing can also be
where h ∼ CN(0,σ2) is the complex Gaussian channel
performed by BS1 to reduce collisions with BS2 whenever 1 1
coefficient from BS1 (serving cell) with variance σ2, x is
possible. For example, if sensing reveals that there is a suffi- 1 1i
the transmit symbol from BS1 in the ith resource element of
cientnumberofPRBsunusedbyBS2,BS1canmeetitsusers’
the PRB with symbol energy E = E[|x |2] and the other
demand with those. The hypotheses involved are the same as x 1i
parameters same as in (3).
in (1). However, here the signals used must be filtered to pass
only the frequency contents of the PRB of interest. Similar to Algorithms for Type 2 sensing are developed in the
testingforhypothesesin(1)energydetection,cyclostationarity following sections and the sensing/detection performance is
based detection etc. could be employed for this. Some of characterized in terms of the probability of false alarm (P )
f
these sensing methods could also be performed after the fast and the probability of detection (P ) [10] defined as
d
Fourier transform (FFT) of an OFDM receiver. It is easy to (cid:48)
P =P(Decide H |H True) (5)
see that energy detection is possible after the FFT whereas f 2 1
cyclostationarity based methods are not (because the cyclic Pd =P(Decide H2|H2 True). (6)
prefix is removed prior to the FFT). Note that for long-term
spectrum sharing, time domain sensing should be preferred as III. ENERGYDETECTION
the granularity in frequency is the whole bandwidth, and also A. Energy detector without channel knowledge (ED1)
the energy of the cyclic prefix can be utilized. Theenergydetectorwithoutchannelknowledgeisthesame
as that of [5], but applied for differentiating between H(cid:48) and
The inter-cell interference coordination (ICIC) and the 1
H , and is given by
enhanced ICIC (eICIC) features of LTE-A could be made 2
useful for spectrum sharing. However, these techniques were N
2 (cid:88)
developed for handling the marco interference and the marco- e = |y |2
1 σ2 i (7)
pico interference suffered by the users belonging to a single n i=1
operator.Theseschemesrequirepartialschedulinginformation Decide H if e >t .
2 1 1
Givenh ,h ,x andx ,thePDFsofy underH(cid:48) andH B. Energy detector with channel knowledge (ED2)
1 2 1i 2i i 1 2
are CN(h x ,σ2) and CN(h x +h x ,σ2) respectively.
1 1i n 1 1i 2 2i n Detectorsareusuallybuilttomaintainafixedaveragefalse
Hence the PDF of e under both hypotheses is a non-central
1 alarm probability of δ . δ is usually set to be small, for
chi-squarePDFwith2N degreesoffreedombutwithdifferent Pf Pf
example5%.Thentheobjectiveistomaximizetheprobability
non-centrality parameters λ and λ [[8], Eq. (2.1.117-124)].
1 2 of detection for the fixed false alarm probability (Neyman-
H(cid:48) :e ∼ χ2 (λ ) Pearson criterion [10][11]). For an energy detector under time
1 1 2N 1
varying channel conditions, keeping a fixed threshold is not
N
where λ = 2 |h |2(cid:88)|x |2 optimum. The performance can be improved by adjusting the
1 σ2 1 1i threshold such that at each channel realization the threshold
n i=1
exactly meets the target false alarm probability. For a given
2N
≈ |h |2E channel realization h , the threshold corresponding to δ is
σ2 1 x 1 Pf
n (8) computed using the inverse of (9) as
H :e ∼ χ2 (λ )
2 1 2N 2
N
where λ = 2 (cid:88)|h x +h x |2 (cid:16)(cid:112) √ (cid:17)
2 σn2 i=1 1 1i 2 2i {t(λ1,δPf)=u|QN λ1, u =δPf}. (13)
2N
≈ (|h |2+|h |2)E .
σ2 1 2 x The corresponding detector is given by
n
For a given channel state h , a false alarm occurs when N
1 2 (cid:88)
tphreobeanbeilrigtyy iesxgcieveednsbtyh1e threshold t1 and the corresponding e2 = σn2 i=1|yi|2 (14)
Decide H if e >t(λ ,δ ).
Pf(t1|h1)=P(e1√>t1|√h1) (9) 2 2 1 Pf
=Q ( λ , t )
N 1 1
However, in order to realize the detector of (14), the non
(cid:32)(cid:115) (cid:33)
2N √ centrality parameter λ = 2N|h |2E should be computed
=Q |h |2E , t , 1 σ2 1 x
N σ2 1 x 1 whichinturnisafunctionofcnhannelpower|h |2.Fortunately,
n 1
this is possible in 3GPP LTE where the base station transmits
the pilot signals known as common reference signals (CRS)
where Q (a,b) is the generalized Marcum Q-function always.Thesesignalsarewidebandandareavailableinevery
N
[5][8][9] and the probability of false alarm in Rayleigh fading PRB even if data transmission does not occur in that PRB.
is computed by averaging over the channel power γ =|h |2 This means that estimation of serving cell channel h can
1 1 1
Pf(t1)=(cid:90) ∞QN(cid:32)(cid:115)2σN2 γ1Ex,√t1(cid:33)σ12e(cid:18)−σγ112(cid:19)dγ1. atfhalwlesaedyeastleabcremtopreprirfsoobδramPbfeildbi.teyTchaouefsaδevethraefogtreheprversoehrbyoalbcdihlitat(nyλno1ef,lδfsPatlfast)eeaahclahr.imeTvhoeesf
0 n 1 Pf 1
(10) probabilityofdetectionisobtainedbyreplacingt1 in(12)with
As in [5] we use [[9], Eq. (30)] with p2 = NEσxn2σ12 and obtain t(λ1,δPf).
the closed-form expression for Pf(t1) For a non-central chi square PDF, the tail probability at
a particular value monotonically increases with non-centrality
Pf(t1)=e−t21(cid:26)N(cid:88)−2n1!(cid:18)t21(cid:19)n+ (11) paagraivmeentetra.ilHpernocbeabthileitythorefsδholdatls(oλ1m,δoPnfo)tocnoicrraelslypoinndcirnegasetos
n=0 Pf
(p2+1)N−1(cid:34)e2(pt21+1) −N(cid:88)−2 1 (cid:18) t1 (cid:19)n(cid:35)(cid:27). wbeicthaunsoen-tcheenttrharlietsyhopladramsheotuerldλ1b.eInhtuigithiverelywthheins mthaekesdesseinresde
n! 2(p2+1) signal power is higher and vice versa. This motivates an
n=0
approximation to the detector of (14) by varying the threshold
linearly with desired signal power. Specifically we choose the
Similarly, the probability of detection in Rayleigh fading
threshold as
is obtained by averaging over both channel powers γ =|h |2
1 1
and γ =|h |2
2 2
(cid:90) ∞(cid:90) ∞ (cid:32)(cid:115)2N √ (cid:33) t(|h |2)=t +E[e |H(cid:48)]=t + 2N(|h |2E +σ2). (15)
Pd(t1)= QN σ2 (γ1+γ2)Ex, t1 × (12) 1 2 2 1 2 σn2 1 x n
0 0 n
(cid:18) (cid:19) (cid:18) (cid:19)
1 −γ1 1 −γ2 Here t is a control parameter to achieve the desired
σ2e σ12 σ2e σ22 dγ1dγ2. probability2of false alarm. The advantage of such an approx-
1 2
imation is that it does not involve frequent computations of
We were not able to obtain a closed-form solution for the
the inverse of the generalized Marcum Q-function and hence
above integral. If needed, lookup tables could be constructed
is computationally simpler. The probability of false alarm and
from offline numerical integrations.
detectionwithlinearthresholdisobtainedbyreplacingt with
1
1For large N, the data randomness gets averaged out in (8) and the non- t(|h1|2) in (10) and (12) respectively, making them functions
centralityparametersonlydependontheaveragesymbolenergyEx. of t2 alone.
IV. MOSTPOWERFULTEST in a PRB is 168 (12 × 14). However, not all of them can
be used for sensing. This is because the common reference
The most powerful test (MPT) maximizes the probability
signals of the interfering base station are always on and
of detection for a fixed probability of false alarm [10][11].
The test is based on the ratio of joint PDFs of samples y = do not indicate whether the resource block is used for data
(y ,...,y )T under H(cid:48) and H and is given by transmission.WithoutgoingintotheprecisedetailsoftheLTE
1 N 1 2 standard,weassumeareferencesignaloverheadof15%which
L= p(y|H2) (16) gives a value of N = 142. Simulations are performed under
p(y|H1(cid:48)) SINR conditions of (σσ122 = 0 dB,σσ212 = 6 dB) and (σσ122 = 6
Decide H2 if L>t. dB,σ12 = 12 dB). Sim2ilar SINR connditions are expec2ted in
σ2
UnderH(cid:48) andagivenmodulationsignalsetX ,thereceived cellulnar deployments.
1 1k
samples y have a Gaussian mixture PDF,
i The performance of detectors is captured by the receiver
p(y |h ,X ,H(cid:48))= (cid:88) P(x )f (y −h x ) (17) operation characteristics (ROC) curve which is the probability
i 1 1k 1 1i n i 1 1i
of detection depicted versus probability of false alarm [10].
x1i∈X1k
Figure2providestheROCforthedifferentdetectorsdiscussed
1 (cid:88)
= |X | fn(yi−h1x1i), earlier under ideal channel estimation. As expected the MPT
1k x1i∈X1k performsbestachievinggreaterthan90%detectionprobability
at a false alarm probability of 5%. Even though such a
where f (u) is the PDF of n ∼ CN(0,σ2) and |X |
n n 1k detector is of prohibitive complexity, it serves as a perfor-
represents the cardinality of X . Using the fact that in LTE
1k mance benchmark [10][11] for comparisons. The detection
the transmission format does not change within a PRB and
probabilities achieved by the energy detector without channel
assuming independent symbols, the joint probability density
knowledge are quite low to have any real use. Reasonable
can be written as
detectionprobabilitiesareachieved,around87%at σ12 =0dB,
(cid:48) (cid:89)N (cid:48) by the energy detector with channel knowledge. Peσr22formance
p(y|h ,X ,H )= p(y |h ,X ,H ). (18)
1 1k 1 i 1 1k 1 degradesastheinterfererbecomesweaker.Theenergydetector
i=1
with linear threshold performs very close to the one with
Typically UEs are only aware of modulation formats for its inversegeneralizedMarcum-Qthresholdandindicatesthatthe
own data. Hence, when UEs are sensing PRBs which are not linear threshold is a suitable choice.
carrying its data, the modulation format is unknown. Thus the
modulation format is unknown in general and the final joint Figures 3 and 4 compare the analytical and simulation
PDF is obtained by averaging over all M possible modulation results for the detector without channel knowledge and the
formats detector with linear threshold, respectively. All analytical ex-
pressionsexcept(11)wereevaluatedvianumericalintegration.
M N
(cid:48) 1 (cid:88)(cid:89) (cid:48) The results shows a very close match between simulation and
p(y|H )= p(y |h ,X ,H ). (19)
1 M i 1 1k 1 analytical results. Hence, analytical results can be used to set
k=1i=1
the operating threshold for the target false alarm probability.
Similarly, under H we obtain
2
In order to study the impact of channel estimation errors
1
p(y |h ,h ,X ,X ,H )= × (20) and the effect of N, we adopt an AWGN estimation error
i 1 2 1k 2l 2 |X ||X |
1k 2l model. The error is introduced by injecting AWGN with
(cid:88)
f (y −h x −h x ). variance equal to the mean square error of the estimator.
n i 1 1i 2 2i
The normalized mean square error is computed based on the
x1i∈X1k,x2i∈X2l
CRS-LS curves of [12] for ITU PedB and 0 km/h. Specifi-
and cally, the normalized mean square error follows log(σ2 )=
nmse
1 (cid:88)M (cid:88)M (cid:89)N −SIN1R0(dB) −0.26, for an SINR range of around 0 dB to 30
p(y|H2)= M2 p(yi|h1,h2,X1k,X2l,H2). (21) dB. The results are provided in Figure 5. A lower value of
k=1l=1i=1 N =100isalsosimulated.Thiscorrespondstoanoverheadof
40%. Simulations show a decrease in detection probability of
For LTE systems, M = 3 with Xr1 = 4QAM, Xr2 = nearly 0.1 (at Pf = 0.05) due to estimation errors. Reducing
16QAM and Xr3 = 64QAM and r ∈ {1,2} for the system the number of samples to 100 results in an additional drop
under investigation. of around 0.05 in detection probability. The results show
that reasonable detection probabilities can be obtained with
V. PERFORMANCERESULTS the use of channel knowledge. Finally, we note that with
Simulations have been carried out to evaluate the per- the use of multiple antennas performance could be improved
formance. All results are averaged over 10000 channel real- significantly.
izations. In the figures, σ12 and σ12 identifies the signal-to-
interference ratio and signσa22l-to-noiσsn2e ratio, respectively. ’ED2 VI. CONCLUSION
(Exact)’identifiestheenergydetectorwithchannelknowledge We have introduced the problem of sensing in presence of
using the exact threshold (inverse of the generalized Marcum- a desired signal which is relevant in the context of spectrum
Q function) and ’ED2 (Linear)’ identifies the energy detector sharing between cellular operators. Detectors are developed
with linear threshold. The total number of resource elements and analyzed in the context of an LTE-A based system. It is
1 1 P: Simulation, 2/2=0dB, 2/2=6dB
f 1 2 1 n
0.9 Pf: Analytical, 12/22=0dB, 12/n2=6dB
0.9 P: Simulation, 2/2=0dB, 2/2=6dB
d 1 2 1 n
0.8 0.8 Pd: Analytical, 12/22=0dB, 12/n2=6dB
0.7
0.7
0.6
Pd00..56 MPT 2/2=0dB, 2/2=6dB Probability0.5
1 2 1 n
ED2 (Exact) 2/2=0dB, 2/2=6dB 0.4
0.4 1 2 1 n
ED2 (Linear) 12/22=0dB, 12/n2=6dB 0.3
0.3 ED1 2/2=0dB, 2/2=6dB
1 2 1 n
MPT 2/2=6dB, 2/2=12dB 0.2
1 2 1 n
0.2 ED2 (Exact) 2/2=6dB, 2/2=12dB
1 2 1 n 0.1
0.1 ED2 (Linear) 12/22=6dB, 12/n2=12dB
ED1 2/2=6dB, 2/2=12dB 0
1 2 1 n -0.5 0 0.5 1 1.5
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t2n2/2N
Pf Fig. 4. Comparison of analytical results and simulation results for ED2
(Linear)withN =142.
Fig.2. ReceiverOperatingCharacteristicsforidealchannelestimation.
1
1
0.9
P: Simulation, 2/2=0dB, 2/2=6dB
f 1 2 1 n
0.9 P: Analytical, 2/2=0dB, 2/2=6dB 0.8
f 1 2 1 n
0.8 Pd: Simulation, 12/22=0dB, 12/n2=6dB 0.7
P: Analytical, 2/2=0dB, 2/2=6dB
d 1 2 1 n
0.7 0.6
2/2=0dB, 2/2=6dB, Ideal Ch., N = 142
Probability00..56 Pd00..45 1121212///2222222===066dddBBB,,, 1121212///nn2n2n2===611d22BddBB, N,, IN d==e 11a44l 22Ch., N=142
0.4 0.3 2/2=0dB, 2/2=6dB, Ideal Ch., N=100
1 2 1 n
2/2=0dB, 2/2=6dB, N=100
0.3 0.2 12/22=6dB, 12/n2=12dB, Ideal Ch., N=100
1 2 1 n
0.2 0.1 12/22=6dB, 12/n2=12dB, N=100
0.1 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
P
f
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Fig.5. EffectofchannelestimationerrorforED2(Linear).
t2/2N
1n
Fig.3. ComparisonofanalyticalresultsandsimulationresultsforED1with
N =142.
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