-
A Concept for Efficient System-Level Simulationsof OFDMA Systems
with Proportional Fair Fast
SchedulingJan Ellenbeck, Johannes Schmidt, Ulrike Korger, and
Christian Hartmann
Institute for Communication NetworksTechnische Universitat
Munchen
Email: [email protected]
AbstractSystem-level simulations of packet-based
orthogonalfrequency-division multiple access (OFDMA) cellular
networksrequire a proper consideration of the channel-dependent
fastfading/scheduling in order to produce meaningful results.
How-ever, generating the time and frequency selective fast
fadingchannels and performing detailed channel-adaptive
schedulingfor each user in a multi-cellular system is
computationally tooexpensive in most system-level simulations. To
this end, wepropose an efficient mapping technique that allows to
accuratelycharacterize the performance of the fast-scheduling
system usingtwo parameters: the average effective post-scheduling
SINR gainand the ratio of allocated resources, both conditioned on
the SINRand the velocity of a user in a scenario defined by the
numberof co-scheduled users. To derive these parameters for
differentnumbers of users at different velocities and SINR levels,
weperform detailed link level simulations including fast
schedulingfor the downlink of a Long Term Evolution (LTE)
system.
I. INTRODUCTION
Performance evaluation by means of computer simulationhas always
been an important technique during the develop-ment and
standardization of wireless systems. But as wirelesssystems have
become more and more complex from generationto generation, the
computational complexity of simulations hasincreased tremendously
as well. In order to limit the scope ofthe simulation and the
simulation time, typically only certainaspects of a system that are
in the focus of the investigation aremodeled in detail. Other
aspects are then either not modeledat all or only in a highly
abstracted way.
One aspect of wireless systems that demands high compu-tational
complexity is the modeling of the fast fading behaviorof the
wireless channel. While this computational effort ismandatory to
study the performance of, e.g., fast channel-aware scheduling
schemes, it becomes excessive1 for system-level simulations focused
on longer-term aspects such asthe system behavior under varying
traffic load or inter-cellinterference coordination. However, if
fast fading would not bemodeled in a simulation, the performance
gain from channel-aware scheduling would be neglected. This gain on
the onehand results from the transmitters knowledge of the
current(estimated) channel conditions which allows
link-adaptation.
1In a scenario consisting of 57 cells each serving 20 mobiles
and assumingan LTE system with 5 MHz and SISO links, 57 20 (5
MHz/15 kHz) 14, 000 symbols/s 5 109 channel samples/s would have to
be computed.
On the other hand, an additional multi-user scheduling gain
isachieved because different mobiles will have different
channelrealizations so that for each resource the base station can
selectthe user with the best conditions on that resource
(multi-userdiversity).
In this paper, we therefore propose an abstraction mecha-nism
that yields the average performance of fast schedulingwithout
incurring the computational overhead of generatingthe fast fading
channel in every single simulation run. Mostoften, system-level
simulations are not designed to capturethe individual performance
in one specific scenario but ratheraverage results from multiple
random scenario realizationsare derived. Thus, our approach is to
first characterize thesystems average fast scheduling performance
by means ofextensive off-line simulations that focus on the fast
schedulingbehavior in a single-cell. During these detailed
simulations,many random scenarios are generated and the channel
ismodeled using a standard channel model to obtain time-variantand
frequency-selective fading. Using these results we are thenable to
perform efficient system-level simulations that yieldvalid
performance results with low computational complexity.The vastly
reduced computational complexity of this abstractmodel allows the
user to extend the simulations scope to, e.g.,bigger multi-cell
scenarios or more complex protocol stacks.
As the paper does not specifically focus on the schedul-ing
algorithm itself (e.g., with respect to fairness), we haveselected
the popular proportional fair (PF) scheduling algo-rithm first
introduced in [1]. Its fast scheduling performanceis characterized
by the achieved effective per-user
signal-to-interference-and-noise-ratio (SINR) gain, compared to
thelong-time mean SINR, and by the ratio of the resourcesassigned
to a single user vs. the total resources. Using thesetwo key
parameters as inputs and a modified PF schedulingmetric, we perform
system-level simulations with an abstractmodel. We show that the
throughputs achieved using theabstract model with drastically
reduced computational com-plexity match the ones achieved in
detailed simulations withsmall residual error.
Despite the PF schedulers popularity, there is only a lim-ited
amount of analytical studies published in the literatureand in the
few existing papers like [2] and [3] simplifyingassumptions have to
be made. These simplifications usually
-
Abstract PF Scheduler
Detailed PF Scheduler Pathloss Shadowing
Fast Fading
Model Accuracy?
Per user TP
Per user TP
Interference
Pathloss
Shadowing
Interference
SINR
CQI
Ratio k,v,N (SINR)
Gaink,v,N (SINR)
argmaxuser k
MI(SINRk + k,v,N ) k,v,NpastTPk(t)
(SINRest)argmax
user k
MI(SINRest,k(t, r))pastTPk(t)
Fig. 1. Overview of the Fast Scheduling Abstraction Model
limit the study to single channel systems, do not consider
ameasurement feedback delay, or employ a PF metric based onthe SINR
rather than on the realizable data rate. In order toallow for a
detailed modeling of the system that yields thenecessary effective
SINR gains and ratios, we thus resort toextensive simulations.
There are a number of publications onsimulative performance
evaluations of fast scheduling and theachievable multi-user
diversity gains in OFDMA systems [4],showing that the achievable
gains tend to be higher for lowchannel quality and grow with the
number of users. However,none of them provides the effective gains
and ratios as neededfor our abstraction concept and we are not
aware of prior workintroducing an abstraction of the fast
scheduling performancefor efficient system-level simulations as
proposed in this paper.
The remainder of the paper is structured as follows. In Sec-tion
II we introduce the proposed abstraction for the system-level
simulation. In Section III we discuss our simulationmodel. In
Section IV the simulation results are presentedand in Section V the
accuracy of the model is shown. Theconclusions in Section VI end
the paper.
II. ABSTRACT SYSTEM LEVEL PROPORTIONAL FAIRSCHEDULING MODEL
A. Fast Scheduling PreliminariesTo perform channel-adaptive fast
scheduling in the down-
link, the base station (BS) needs timely information about
theinstantaneous channel conditions of all mobile stations
(MSs)across the whole system bandwidth. For this purpose, the
MSstransmit channel quality indicators (CQIs) to report the
highestbit rate modulation and coding scheme they could
successfullyreceive on a certain subband. The CQIs are based on the
SINRsand aggregate the signal attenuation by pathloss,
shadowing,and fast fading as well as noise and inter-cell
interference, cf.the upper part of Fig. 1.
There is always a delay between the CQI measurementand the time
instant the resource allocation based on theCQI report takes
effect. In the following, we will refer tothis as the scheduling
delay that is needed for the channelmeasurement and processing by
the MS and the transmissionto the BS where the scheduling takes
place. The accuracyof the channel estimation decreases with longer
scheduling
delays and shorter channel coherence times. The gain
fromscheduling with link adaptation is highest for slowly
varyingchannels and diminishes as MSs reach higher speeds.
Different users in a cell will have different channel
realiza-tions. Using CQI feedback from multiple users the
schedulercan allocate a physical resource block (PRB) to a MS
whichhas reported good channel conditions on that part of
thespectrum. The resulting multi-user diversity gain grows withthe
number of MSs to schedule. To summarize, we expectthe realizable
scheduling gain to grow with either shorterscheduling delays,
slower MS movement and thus lowerchannel variability, or higher
number of users.
B. Detailed Proportional Fair Scheduling ModelFor our
simulations we use the popular proportional fair
scheduler. It aims at exploiting the multi-user diversity
whileensuring a certain degree of fairness among the users.
Ac-cording to these goals, it selects for each PRB r the user k
toschedule by employing the following metric (1):
k = argmaxuser k
MI(SINRest,k(t, r))pastTPk(t)
(1)
pastTPk(t) =t1=1
Rr=1
MI(SINRk(, r)) xk(, r) (2)
In every transmission time interval (TTI) t and for eachPRB r,
the scheduler picks the user with the best ratio2 ofthe expected
data rate MI(SINRest,k(t, r)) over the amountof already transmitted
bits pastTPk(t) as defined by (2). Weuse a binary variable xk(, r)
= 1 to indicate that user kis scheduled on PRB r at t = . Here, we
derive the datarate as the average mutual information (MI)
transmitted withinone PRB during one TTI according to the channel
estimateSINRest,k(t, r) (provided by user k in the form of a CQI
report)or the actual received SINRk(t, r), respectively.
If the CQI reporting is fast enough for the time varyingchannel,
the effect of proportional fair scheduling is that fadingdips can
be avoided and users realize an effective SINR gaincompared to,
e.g., a round robin scheduler. Besides achievingan effective
post-scheduling SINR gain, PF scheduling alsogives more resources
to users who suffered low past through-puts so that a different
distribution of resource allocationratios results. These two
characteristics of proportional fairfast scheduling will be
evaluated in the following. In Fig. 3(b)we show that in our
simulations the generic implementationof the PF scheduler yields a
distribution of user throughputsthat fulfills the 10-50 metric
fairness criterion, cf. [5], [6].C. Abstract Proportional Fair
Scheduling Model
As motivated in the introduction, the fast fading behaviorof the
wireless channel is computationally expensive to modeldue to its
short timescale variations and complex modeling.Longer timescale
effects like signal attenuation due to pathloss
2Note that constant factors like the number of symbols per PRB
are omittedfrom the metric as they are identical for all users.
-
and shadowing, however, are easily covered by
system-levelsimulations. These two effects together with the
thermal andreceiver noise and the inter-cell interference
contribute to themean SINRk for a user k which can be seen as a
long-enoughaverage of the instantaneous SINRk(t, r).
The proposed efficient system-level proportional fairscheduling
model as depicted in the lower part of Fig. 1allows for an
efficient simulation based on long-term averagesSINRk while still
taking the benefits of channel-aware fastscheduling into account.
This is achieved by modifying thescheduling metric (1) of a user k
by two parameters thatare pre-computed off-line for different
combinations of thenumber of co-scheduled users N , the velocity v
of the userk and its perceived long-term SINRk. These parameters
arethe effective post-scheduling gain k,v,N (SINRk) and
thescheduling ratio k,v,N (SINRk), which captures the
slightdifferences in the share of resources that the PF
schedulerassigns to different mobiles:
k,v,N =N T=1Rr=1 xk(, r)
T R . (3)
The two parameters scheduling gain k,v,N (SINRk) andscheduling
ratio k,v,N (SINRk) are the key inputs for theproposed abstract
scheduling model. In Section III we discusshow we derive them by
means of extensive simulations. InSection IV the simulation results
are presented and we discussthe dependence of k,v,N (SINRk) and
k,v,N (SINRk) on thespeed of the user v and the total number of
users N in thecell.
For the abstract system-level scheduling algorithm we
againassume a proportional fair scheme. Instead of SINRest,k(t,
r)as in metric (1) we now use the long-term average SINRk andapply
the effective gain k,v,N (SINRk) to characterize thepost-scheduling
improvements. Now the numerator is constantover time for a user k
and the denominator (2) can be separatedinto
T=1
Rr=1 xk(, r) times the constant throughput per
allocated resource. Hence, the metric would always select
theuser with the least number of previously allocated
resourcesyielding a round robin behavior. In order to achieve the
correctscheduling ratios and thus the correct throughputs, we
modifythe metric (1) by multiplying with the user specific
schedulingratio k,v,N to obtain the following PF abstract
schedulingmetric:
k = argmaxuser k
MI(SINRk + k,v,N (SINRk)) k,v,NpastTPk(t)
. (4)
D. Applicability for system-level simulationsThe results
presented in this paper are applicable to system-
level simulations of the LTE downlink. The approach itselfis
also valid for arbitrary OFDMA systems with channeldependent
proportional fair scheduling.
Differentiating the scheduling gain with respect to the
post-scheduling effective SINReff = SINR +k,v,N (SINR) on theone
hand and the different scheduling ratios on the other hand,allows a
realistic system-level simulation with packet-basedscheduling. The
knowledge of the effective post-scheduling
15 10 5 0 5 10 15 20 25 300
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
SINR [dB]
Thr
ough
put [
bit/s
/Hz]
Shannon boundused mapping
MI
SINR effSINR
Gain k,v,N
Fig. 2. Link performance model mapping SINR to MI [8] and
illustrationhow the scheduling gain = SINReff SINR is computed.
10 0 10 20 300
0,2
0,4
0,6
0,8
1
SINR [dB]
P(S
INR
< a
bsci
ssa)
(a) User geometry resulting frommodel and calibration offset
0 1 2 30
0,2
0,4
0,6
0,8
1
MS throughput normalized to average
P(M
S th
roug
hput
< a
bsci
ssa)
(b) Scheduling fairness criterion (10-50 metric) [5], [6]
Fig. 3. Calibration of simulations to meet standard evaluation
references
SINReff allows using standard packet/block error
modelingtechniques as discussed, e.g., in [7]. The knowledge of
thescheduling ratios allows determining a realistic number
ofallocated resources for each user.
In order to obtain the appropriate gains and ratios,
thesystem-level simulation needs to employ the correct group sizeN
corresponding to the number of active MSs that currentlycompete for
the resources. With bursty traffic sources thegroup size N will
change over time.
III. SIMULATION SETUPTo evaluate the performance of proportional
fair scheduling
in fast fading environments we conduct simulations using
theSpatial Channel Model Extended (SCME). The SCME [9],[10] is a
geometry-based stochastic spatial channel model.We use the SCME to
generate time-varying channel impulseresponses with drifting delays
for each MS from which weobtain the channel transfer function H(f,
t) using the Fouriertransform. This gives us random realizations of
a time- andfrequency-selective fast fading channel including the
pathloss.We assume that the cyclic prefix length is sufficient to
elim-inate any intra-cell interference. In our simulation, only
thechannel-dependent fading, the pathloss of the link between
the
-
BS and the served MS, and the thermal noise is modeled
ex-plicitly. All other effects (e.g., antenna gains, penetration
loss,noise figures, and inter-cell interference levels)
contributing tothe received SINR are summarized in a fixed
calibration offset, which we tune to achieve a typical SINR
distribution withinthe cell, cf. Fig 3(a):
SINR = PTx + 20 log10 (|H(f, t)|) Nthermal (5)From these SINR
values, which we compute for each
resource element (RE), we derive the mutual information thatcan
be transmitted per RE from the BS to the MS. Theemployed mapping
(6) is based on Shannons channel capacityand assumes an
implementation loss factor = 0.6. It takesinto account the
modulation and coding schemes as well asthe HARQ mechanisms
available in LTE [8]:
MI(SINR) =
0 : SINR < 10 dB log2
(1 + 10SINRdB/10
): else
4.4 : SINR > 22 dB(6)
As the motivation of our abstract scheduling model is
toaccurately represent the achievable throughputs, we computea
mutual information effective (post-scheduling) SINReff [11].To
derive SINReff we first compute the average amount of bitsper
resource element MI a user has obtained over the course ofthe
simulation. Using this average mutual information value,we perform
a reverse mapping as shown in Fig. 2 to obtainthe SINReff value.
Finally, we then compute the effectivescheduling gain k,v,N =
SINReffSINR as the difference ofeffective and mean SINR. The
inverse mapping function (7)is defined for minimum and maximum SINR
values between-10 dB and 22 dB, respectively:
SINReff(MI) = 10 log10(2MI/ 1
). (7)
TABLE IRADIO SIMULATION PARAMETERS
Parameter ValueTransmission direction DownlinkAntenna
configuration SISOSCME scenario Urban MacroCenter frequency 2
GHzCell radius 500 mPathloss model SCME standard (COST231
based)
L = 34.5 + 35 log10(d/[m]) [dB]Shadowing No shadowingSCME
options Drifting delays and angles enabledSystem bandwidth 5 MHz
with R = 25 PRBsBS Tx power PTx = 29 dBm per 180 kHz PRBSymbols per
slot 7 for normal CP lengthSub-carrier spacing 15 kHzNoise
assumption Nthermal = 121.4 dBm per 180 kHz PRBCalibration offset =
23.5 dBScheduling delay 4 ms from end of measurement to start of
TxMS velocity distribution Channel Mix (60% at 3 km/h, 30% at
30
km/h, and 10% at 120 km/h) [7]MS distribution Uniformly
distributed over cell areaNumber of drops 10,000 randomly generated
MS distributionsDuration per drop T = 50 TTIs with a duration of
1ms each
IV. SIMULATION RESULTS
In figures 4, 5, and 6 we present the scheduling gainsand
scheduling ratios that result for mobiles from the 3km/h, 30 km/h,
and 120 km/h velocity groups of the channelmix, respectively. To
evaluate the results, we aggregate theindividual effective SINR
gains and ratios of all MSs fromall 10,000 scenario drops into m =
1 . . .M discrete binsaccording to their mean SINR. For each bin we
compute andplot the average of all effective scheduling gains and
ratiosfalling into that bin. These averaged results serve as the
inputparameters for the abstract PF scheduling model introduced
inSec. II. The individual gains are distributed around the
plottedcurves with standard deviations of, e.g., up to 1 dB in Fig.
4(a).
At 3 km/h, the scheduling delay of 4 ms is much shorterthan the
channel coherence time so that the CQI feedback isstill accurate.
Hence, for users from the slow velocity groupa substantial
scheduling gain can be realized in most cases,as shown in Fig.
4(a). As expected [4], the achievable gainsincrease with the number
of active users due to the growingmulti-user diversity. The
marginal gains decrease until almostno further gain is realized at
about 20 MSs. At high meanSINRs the gains diminish and become
negative for meanSINRs > 22 dB. The reason is that the effective
SINR isupper-bounded by this value, cf. Fig. 2.
At 30 km/h, Fig. 5(a) shows that due to higher time-variability
of the fast fading, almost no scheduling gains canbe realized with
the assumed scheduling delay of 4 ms. At120 km/h, the situation is
even worse as depicted in Fig. 6(a).Note that with our assumed
mobility mix, only 40% (30%at 30 km/h and 10% at 120 km/h) of the
MSs will have therespective high velocities while the remaining 60%
of the MSswho are assumed to be at v = 3 km/h benefit from the
gainsshown in Fig. 4(a).
Fig. 5 and 6 show mostly negative scheduling gains. Theselosses
are not primarily caused by the attempt to perform fastscheduling
but rather are an effect of the employed MI-basedeffective SINR
mapping3.
In the figures 4(b), 5(b), and 6(b) the corresponding
schedul-ing ratios are shown. We need these ratios to reflect
theslight differences in the number of resources the PF
schedulerallocates to a certain class of MSs. For the vast majority
ofMSs the scheduling ratios are close to 1 meaning that the
MSsreceive about the same number of resources. The higher
ratiosshown for MSs with very low mean SINR in the left parts
ofFig. 5(b) and 6(b) represent very rare cases as the velocitiesare
underrepresented in the assumed mix in addition to thelow
probability of the considered SINR levels, cf. Fig. 3(a).
3To see this, consider the case of 1 MS. No fast scheduling is
performedin this case as the single MS gets all the resources.
Still, for all velocitiesFig. 4 6 show a significant loss in terms
of effective SINR as compared to themean SINR. The reason for this
effect is that the instantaneous SINR levelsfluctuate around the
mean SINR due to the fast fading. Low instantaneousSINRs then lead
to zero throughputs while the benefit of high instantaneousSINRs is
limited by the link performance model, cf. Fig. 2.
-
5 0 5 10 15 20 253
2
1
0
1
2
3
4
mean SINR [dB]
effe
ctiv
e S
INR
gai
n [d
B]
40 MSs20 MSs10 MSs5 MSs2 MSs1 MS
(a) Effective SINR gains k,v,N (SINR)
5 0 5 10 15 20 250.5
1
1.5
2
mean SINR [dB]
sche
dulin
g ra
tio
40 MSs20 MSs10 MSs5 MSs2 MSs
(b) Scheduling ratios k,v,N (SINR)
Fig. 4. Gains and scheduling ratios experienced by a mobile k
with v = 3 km/h for different numbers of total users N
5 0 5 10 15 20 253
2
1
0
1
2
3
4
mean SINR [dB]
effe
ctiv
e S
INR
gai
n [d
B]
40 MSs20 MSs10 MSs5 MSs2 MSs1 MS
(a) Effective SINR gains k,v,N (SINR)
5 0 5 10 15 20 250.5
1
1.5
2
mean SINR [dB]
sche
dulin
g ra
tio
40 MSs20 MSs10 MSs5 MSs2 MSs
(b) Scheduling ratios k,v,N (SINR)
Fig. 5. Gains and scheduling ratios experienced by a mobile k
with v = 30 km/h for different numbers of total users N
V. EVALUATION OF SYSTEM-LEVEL SCHEDULING MODEL
In the previous section we have presented the results forour
detailed simulation. Using the resulting average schedulinggains
and ratios, we have conducted simulations using ourabstract PF
scheduling model as introduced in Section II-C. Inthe abstract
simulations we use the mean SINR computed fromthe pathloss and
offset values as in the detailed simulationsthus yielding the same
SINR CDF as in Fig. 3(a). The PFscheduling is performed according
to metric (4).
As we are not interested in the performance of a particularMS,
we evaluate the average system performance of a typicalMS which is
characterized by its mean SINR, velocity v, andby the number N of
co-scheduled MSs. Thus, we only rely onthe average effective gain
and scheduling ratios even thoughthe gains of individual MSs vary
in the detailed simulations.
For each combination of v and N we compute the meanthroughputs
TPdet(m) and TPabs(m) in the detailed and ab-stract simulation,
respectively. To compare the throughputs andderive the modeling
error, we again assign each MS to oneof m = 1 . . .M discrete SINR
bins. In Table II we show theweighted root mean square error
(wRMSE) which we computeusing (8) with a SINR bin resolution of 1
dB. The weightingfactor P (m) represents the probability of the
respective SINRbin according to Fig. 3(a):
wRMSE =
Mm=1
(TPdet(m) TPabs(m)
TPdet(m)
)2 P (m). (8)
We observe that the wRMSE is in general small whichunderlines
the applicability and accuracy of our proposedabstract proportional
fair scheduling model. Possible error
-
5 0 5 10 15 20 253
2
1
0
1
2
3
4
mean SINR [dB]
effe
ctiv
e S
INR
gai
n [d
B]
40 MSs20 MSs10 MSs5 MSs2 MSs1 MS
(a) Effective SINR gains k,v,N (SINR)
5 0 5 10 15 20 250.5
1
1.5
2
mean SINR [dB]
sche
dulin
g ra
tio
40 MSs20 MSs10 MSs5 MSs2 MSs
(b) Scheduling ratios k,v,N (SINR)
Fig. 6. Gains and scheduling ratios experienced by a mobile k
with v = 120 km/h for different numbers of total users N
TABLE IIWEIGHTED RMSE OF MS THROUGHPUTS
Number v = 3 km/h v = 30 km/h v = 120 km/hof MSs N1 0.05% 0.06%
0.03%2 2.37% 1.96% 2.42%5 2.30% 1.54% 3.30%10 1.69% 0.23% 2.48%20
1.11% 1.24% 1.43%40 0.93% 2.07% 0.55%
sources include the bin size of 1 dB and the imperfectemulation
of scheduling ratios due to finite simulation times.The small wRMSE
values for the 1 MS case underline theaccuracy of the employed
mutual information-based SINReffmapping. The close match between
the values obtained fromthe proposed abstract model and the
detailed simulations isespecially remarkable as the abstract
simulation only needsa fraction of the simulation time. The CPU
time in oursimulations was reduced from about 2 weeks to about 2
hoursbecause the time-consuming generation of the fast
fadingchannel using the SCME model accounts for about 99% ofthe
time in the detailed simulation.
VI. CONCLUSIONWe have proposed an efficient method to very
accurately
include the effects of fast scheduling into system-level
simu-lations of multicellular OFDMA networks without adding
sig-nificant computational complexity. This is achieved by
detailedoff-line single cell fast scheduling simulations from
whichtwo parameters are derived that are sufficient to representthe
fast scheduling effects in system-level simulations. Wehave
provided and discussed an array of numerical results,demonstrating
the feasibility and the benefit of this approach.Our simulations
and results assume LTE system parametersbut the approach is
applicable to any OFDMA system with
fast channel-dependent scheduling based on MS feedback.
Webelieve that our concept can be useful for many researchersfacing
similar challenges when evaluating OFDMA-based net-works on a
system level.
ACKNOWLEDGMENTThe authors would like to thank the German
Research
Foundation DFG for funding part of this work.
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vol. 4, Sept. 1114, 2005,pp. 23062311.
/ColorImageDict > /JPEG2000ColorACSImageDict >
/JPEG2000ColorImageDict > /AntiAliasGrayImages false
/CropGrayImages true /GrayImageMinResolution 200
/GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true
/GrayImageDownsampleType /Bicubic /GrayImageResolution 300
/GrayImageDepth -1 /GrayImageMinDownsampleDepth 2
/GrayImageDownsampleThreshold 2.00333 /EncodeGrayImages true
/GrayImageFilter /DCTEncode /AutoFilterGrayImages true
/GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict >
/GrayImageDict > /JPEG2000GrayACSImageDict >
/JPEG2000GrayImageDict > /AntiAliasMonoImages false
/CropMonoImages true /MonoImageMinResolution 400
/MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true
/MonoImageDownsampleType /Bicubic /MonoImageResolution 600
/MonoImageDepth -1 /MonoImageDownsampleThreshold 1.00167
/EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode
/MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None
] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false
/PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000
0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true
/PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ]
/PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier ()
/PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped
/False
/CreateJDFFile false /Description > /Namespace [ (Adobe)
(Common) (1.0) ] /OtherNamespaces [ > /FormElements false
/GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks
false /IncludeInteractive false /IncludeLayers false
/IncludeProfiles true /MultimediaHandling /UseObjectSettings
/Namespace [ (Adobe) (CreativeSuite) (2.0) ]
/PDFXOutputIntentProfileSelector /NA /PreserveEditing false
/UntaggedCMYKHandling /UseDocumentProfile /UntaggedRGBHandling
/UseDocumentProfile /UseDocumentBleed false >> ]>>
setdistillerparams> setpagedevice
