DyMo: Dynamic Monitoring of Large Scale LTE-Multicast Systems

1.6 MB·

by  Yigal Bejerano

DyMo: Dynamic Monitoring
of Large Scale LTE-Multicast Systems
Yigal Bejerano∗, Chandru Raman†, Chun-Nam Yu∗, Varun Gupta‡, Craig Gutterman‡,
Tomas Young†, Hugo Infante†, Yousef Abdelmalek@ and Gil Zussman‡
∗ Bell Labs, Nokia, Murray Hill, NJ, USA.
† Mobile Networks, Nokia, Murray Hill, NJ, USA.
‡ Electrical Engineering, Columbia University, New York, NY, USA.
@ Verizon Wireless, Basking Ridge, NJ, USA.
7
1
0 Abstract—LTEevolved Multimedia Broadcast/MulticastService
2 (eMBMS)isanattractivesolutionforvideodeliverytoverylarge
groups in crowded venues. However, deployment and manage-
n
ment of eMBMS systems is challenging, due to the lack of real-
a
J time feedback from the User Equipment (UEs). Therefore, we
presenttheDynamicMonitoring(DyMo)systemforlow-overhead
0
feedback collection. DyMo leverages eMBMS for broadcasting
1
Stochastic Group Instructions to all UEs. These instructions

indicatethereportingratesasafunctionoftheobservedQuality Fig. 1. The DyMo system architecture: It exchanges control information
I] of Service (QoS). This simple feedback mechanism collects very withtheMulticastCoordinationEntity(MCE)ofBSswhichusesoftsignal
N limited QoS reports from the UEs. The reports are used for combining for eMBMS. The Instruction Control module uses broadcast to
dynamically partition the UEs into groups, each sending QoS reports at a
. network optimization, thereby ensuring high QoS to the UEs. different rate. The reports are sent to the Feedback Collection module and
s We present the design aspects of DyMo and evaluate its per-
c allow the QoS Evaluation module to identify an SNR Threshold. It is used
[ formance analytically and via extensive simulations. Specifically, bytheMCSControlmoduletospecifytheoptimalMCStotheMCEs.
we show that DyMo infers the optimal eMBMS settings with
1 extremely low overhead, while meeting strict QoS requirements Unfortunately, the eMBMS standard [4] only provides a
v under different UE mobility patterns and presence of network mechanism for UE QoS reporting once the communication
9 component failures. For instance, DyMo can detect the eMBMS terminates, thereby making it unsuitable for real-time traffic.
0 Signal-to-Noise Ratio (SNR) experienced by the 0.1% percentile Recently,theMinimizationofDriveTests(MDT)protocol[6]
8 oftheUEswithRootMeanSquareError(RMSE)of0.05%with
was extended to provide eMBMS QoS reports periodically
2 only5to10reportspersecondregardlessofthenumberofUEs.
from all the UEs or when a UE joins/leaves a BS. However,
0
. in crowded venues with tens of thousands of UEs (e.g., [1]),
1
0 I. INTRODUCTION even infrequent QoS reports by each UE may result in high
7 signalingoverheadandblockingofunicasttraffic.2 Duetothe
1 Wireless video delivery is an important service. However, limitedabilitytocollectfeedback,adeploymentofaneMBMS
: unicast video streaming over LTE to a large user population system is very challenging. In particular, it is hindered by the
v
i in crowded venues requires a dense deployment of Base following limitations:
X Stations (BSs) [1]–[3]. Such deployments require high capital
(i) Extensive and time consuming radio frequency surveys:
r and operational expenditure and may suffer from extensive
Such surveys are conducted before each new eMBMS
a
interference between adjacent BSs.
deployment. Yet, they provide only limited information
LTE-eMBMS (evolved Multimedia Broadcast/Multicast
from a few monitoring nodes.
Service) [4], [5] provides an alternative method for content
(ii) Conservativeresourceallocation:TheeMBMSMCSand
delivery in crowded venues which is based on broadcasting to
Forward Error Correction (FEC) codes are set conserva-
a large population of User Equipment (UEs) (a.k.a. eMBMS
tively to increase the decoding probability.
receivers). As illustrated in Fig. 1, in order to improve the
(iii) Oblivious to environmental changes: It is impossible to
Signal-to-Noise Ratio (SNR) at the receivers, eMBMS uti-
infer QoS degradation due to environmental changes,
lizes soft signal combining techniques.1 Thus, a large scale
such as new obstacles or component failures.
Modulation and Coding Scheme (MCS) adaptation should be
Clearly, there is a need to dynamically tune the eMBMS
conductedsimultaneouslyforalltheBSsbasedontheQuality
parameters according to the feedback from UEs. However, a
of Service (QoS) at the UEs.
key challenge for eMBMS parameter tuning for large scale
1AlltheBSsinaparticularvenuetransmitidenticalmulticastsignalsina 2ABScanonlysupportalimitednumberofconnectionswhiletheminimal
timesynchronizedmanner. durationforanLTEconnectionisintheorderofhundredsofmilliseconds.
1
groups is obtaining accurate QoS reports with low overhead.
Schemesforefficientfeedbackcollectioninwirelessmulticast
networkshaverecentlyreceivedconsiderableattention,partic-
ulalty in the context of WiFi networks (e.g., [7]–[10]). Yet,
WiFi feedback schemes cannot be easily adapted to eMBMS
since unlike WiFi, where a single Access Point transmits to
a node, transmissions from multiple BSs are combined in
Fig. 2. Operation of DyMo for a sample UE QoS distribution: UEs are
eMBMS. Efforts for optimizing eMBMS performance focus
partitionedintotwogroupsbasedontheirSNRandeachgroupisinstructed
onperiodicallycollectingQoSreportsfromallUEs(e.g.,[11]) tosendQoSreportsatadifferentrate.Thepartitioningisdynamicallyadjusted
but such approaches rely on extensive knowledge of the user based on the reports to yield more reports from UEs whose SNR is around
theestimatedSNRThreshold.
population (for more details, see Section II-B).
In this paper, we present the Dynamic Monitoring (DyMo) SNR below the threshold, termed as outliers, may suffer from
system designed to support efficient LTE-eMBMS deploy- poor service. The MCS Control module utilizes the SNR
ments in crowded and dynamic environments by providing Threshold to configure the eMBMS parameters (e.g., MCS)
accurate QoS reports with low overhead. DyMo identifies the accordingly. Finally, the QoS Evaluation module continually
maximaleMBMSSNRThreshold suchthatonlyasmallnum- refines group partitions based on the reports.
ber of UEs with SNR below the SNR Threshold may suffer We focus on the QoS Evaluation module and develop a
frompoorservice3.ToidentifytheSNRThresholdaccurately, Two-step estimation algorithm which can efficiently identify
DyMo leverages the broadcast capabilities of eMBMS for fast the SNR Threshold as a one time estimation. We also de-
dissemination of instructions to a large UE population. velop an Iterative estimation algorithm for estimating the
Each instruction is targeted at a sub-group of UEs that SNR Threshold iteratively, when the distribution changes due
satisfies a given condition. It instructs the UEs in the group to UE mobility or environmental changes, such as network
tosendaQoSreportwithsomeprobabilityduringareporting component failures. Our analysis shows that the Two-step
interval.4 We refer to these instructions as Stochastic Group estimation and Iterative estimation algorithms can infer the
Instructions. For instance, as shown in Fig. 2, DyMo divides SNR Threshold with a small error and limited number of
UEs into two groups. UEs with poor or moderate eMBMS QoS reports. It is also shown that they outperform the Order-
SNR are requested to send a report with a higher rate during Statistics estimation method, a well-known statistical method,
the next reporting interval. In order to improve the accuracy which relies on sampling UEs with a fixed probability. For
of the SNR Threshold, the QoS reports are analyzed and the instance, the Two-step estimation requires only 400 reports
grouppartitionsandinstructionsaredynamicallyadaptedsuch when estimating the 1% percentile to limit the error to 0.3%
that the UEs whose SNR is around the SNR Threshold report for each re-estimation. The Iterative estimation algorithm
more frequently. The SNR Threshold is then used for setting performs even better than the Two-step estimation and the
the eMBMS parameters, such as the MCS and FEC codes. maximum estimation error can be bounded according to the
From a statistics perspective, DyMo can be viewed as a maximum change of SNR Threshold.
practical method for realizing importance sampling [12] in We conduct extensive at-scale simulations, based on real
wireless networks. Importance sampling improves the expec- eMBMS radio survey measurements from a stadium and an
tation approximation of a rare event by sampling from a urban area. It is shown that DyMo accurately infers the SNR
distributionthatoverweighstheimportantregion.Withlimited Threshold and optimizes the eMBMS parameters with low
knowledgeoftheSNRdistribution,DyMoleveragesStochastic overhead under different mobility patterns and even in the
Group Instructions to narrow down the SNR sampling to event of component failures. DyMo significantly outperforms
UEs that suffer from poor service and consequently obtains alternative schemes based on the Order-Statistics estimation
accurate estimation of the SNR Threshold. To the best of method which rely on random or periodic sampling.
our knowledge, this is the first realization of using broadcast Our simulations show that both in a stadium-like and
instructions for importance sampling in wireless networks. urban area, DyMo detects the eMBMS SNR value of the
The DyMo system architecture is illustrated in Fig. 1. It 0.1% percentile with Root Mean Square Error (RMSE) of
operatesonanindependentserverandexchangescontrolinfor- 0.05% with only 5 messages per second in total across the
mation with several BSs supporting eMBMS. The Instruction whole network. This is at least 8 times better than Order-
Controlmoduleinstructsthedifferentgroupstosendreportsat Statistics estimation based methods. DyMo also infers the
differentrates.ThereportsaresentviaunicasttotheFeedback optimal SNR Threshold with RMSE of 0.3 dB regardless of
Collection module and allow the QoS Evaluation module to the UE population size, while the error of the best Order-
identify an accurate SNR Threshold. The SNR Threshold is Statisticsestimationmethodisabove1dB.DyMoviolatesthe
determined such that only a predefined number of UEs with outlier bound (of 0.1%) with RMSE of at most 0.35 while
the best Order-Statistics estimation method incurs RMSE of
3While various metrics can be used for QoS evaluation, we consider the over 4 times. The simulations also show that after a failure,
commonlyusedeMBMSSNR,referredtoasSNR,asaprimarymetric.
DyMo converges instantly (i.e., in a single reporting interval)
4Ahigherprobabilityresultsinahigherreportingrate,andtherefore,we
willuserateandprobabilityinterchangeably. to the optimal SNR Threshold. Thus, DyMo is able to infer
2
the maximum MCS while preserving QoS constraints. TABLEI
To summarize, the main contributions of this paper are three- NOTATION.
Symbol Semantics
fold:
m ThenumberofUEsinthevenue,alsothe
(i) We present the concept of Stochastic Group Instructions
numberofactiveeMBMSreceiverinstaticsettings.
for efficient realization of importance sampling in wireless m(t) ThenumberofactiveeMBMSreceiversattimet.
networks. hv(t) TheindividualSNRvalueofUEv
attimeintervalt.
(ii) We present the system architecture of DyMo and efficient
s(t) TheSNRThresholdattimet.
algorithms for SNR Threshold estimation. p QoSThreshold-ThemaximalportionofUEs
(iii) We show via extensive simulations that DyMo performs withindividualSNRvaluehv(t)<s(t).
r OverheadThreshold-Anupperboundonthe
well in diverse scenarios.
averagenumberofreportsinareportinginterval.
The principal benefit of DyMo is its ability to infer the
system performance based on a low number of QoS reports. Yet, extensive QoS reports impose significant overhead on
It converges very fast to the optimal eMBMS configuration LTEnetworks,whicharealreadyhighlycongestedincrowded
and it reacts very fast to changes in the environment. Hence, venues[1].Anefficientfeedbackschemewasproposedin[11]
it eliminates the need for service planning and extensive field but it relies on knowledge of path loss (or block error) of the
trials.Further,DyMoiscompatiblewithexistingLTE-eMBMS entire UE population to form the set of feedback nodes.
deployments and does not need any knowledge of the UE Recently,[18]proposedamulticast-basedanonymousquery
population. scheme for inferring the maximum MCS that satisfies all
The rest of the paper is organized as follows. We provide UEs without sendingindividual queries.However, the scheme
background information about eMBMS and a brief review cannot be implemented in current LTE networks, since it
of related work in Section II. We introduce the model and will require UEs to transmit simultaneous beacon messages
objective in Section III. We present the DyMo system in in response to broadcast queries.
SectionIV.ThealgorithmsforSNRthresholdestimationwith WiFi Multicast: Most of the wireless multicast schemes
theiranalysisaregiveninSectionV.Thenumericalevaluation are designed for WiFi networks. Some rely on individual
resultsappearinSectionVIbeforeconcludinginSectionVII. feedback from all nodes for each packet [9], [10]. Leader-
Some details of our analysis are given in the Appendix. Based Schemes [19]–[21] collect feedback from a few se-
lected nodes with the weakest channel quality. Cluster-Based
II. BACKGROUNDINFORMATION FeedbackSchemesin[8],[22]balanceaccuratereportingwith
A. eMBMS Background minimization of control overhead by selecting nodes with the
LTE-Advanced networks provide broadcast services by weakest channel condition in each cluster as feedback nodes.
using evolved Multimedia Broadcast/Multicast Service (eM- However, WiFi multicast solutions cannot easily be applied
BMS) [13]. eMBMS is best suited to simultaneously deliver to LTE-eMBMS systems. First, in WiFi, each node is associ-
common content like video distribution to a large number ated with an Access Point, and therefore, the Access Point is
of users within a contiguous region of cells. eMBMS video aware of every node and can specify the feedback nodes. In
distribution is offered as an unidirectional service without LTE, eMBMS UEs could be in the idle state and the network
feedbackfromtheUEnorretransmissionsoflostpackets.This may not be aware of the number of active UEs. Second,
isenabledbyallcellsactinginacoordinatedSingleFrequency eMBMS is based on simultaneous transmission from various
Network(SFN)arrangement,i.e.,transmittingidenticalsignals BSs. Thus, unlike in WiFi where MCS adaptation is done at
in a time synchronized manner, called Multicast Broadcast each Access Point independently, a common MCS adaptation
Single Frequency Network (MBSFN). The identical signals should be done at all BSs.
combine over the air in a non-coherent manner at each of the
III. MODELANDOBJECTIVE
user locations, resulting in an improved Signal-Noise Ratio
(SINR). Thus, what is normally out-of-cell interference in A. Network Model
unicastbecomesusefulsignalineMBMS.Foravoidingfurther We consider an LTE-Advanced network with multiple base
interference from cells not transmitting the same MBSFN stations (BSs) providing eMBMS service to a very large
signal, the BSs near the boundary of the MBSFN area are group of m UEs in a given large venue (e.g., sports arena,
used as a protection tier and they should not include eMBMS transportation hub).5 Such venues can accommodate tens of
receivers in their coverage areas. thousands of users. The eMBMS service is managed by a
singleDyMoserverasshowninFig.1andalltheBSstransmit
B. Related Work
identical multicast signals in a time synchronized manner.
Wireless multicast control schemes received considerable The multicast flows contain FEC code that allows the UEs to
attention in recent years (see survey in [7] and references tolerate some level of losses (cid:96) (e.g., up to 5% packet losses).
therein). Below we briefly review the most relevant papers.
All UEs can detect and report the eMBMS QoS they expe-
LTE-eMBMS: Most previous work on eMBMS (e.g., [14]– rience. More specifically, time is divided into short reporting
[17]) assumes individual feedback from all the UEs and pro-
posesvariousMCSselectionorresourceallocationtechniques. 5Inthispaper,weconsideronlytheUEssubscribingtoeMBMSservices.
3
intervals, a few seconds each. We assume that the eMBMS TABLEII
SNR distribution of the UEs does not change during each EXAMPLEOFTHEDyMoFEEDBACKREPORTOVERHEAD.
reporting interval.6 We define the individual SNR value h (t), No. Report Avg.reports Avg. Rate
v Group ofUEs Prob. perinterval persec permin
such that at least a given percentage 1 − (cid:96) (e.g., 95%) of H 250 20% 50 5 ≈100%
the eMBMS packets received by an UE v during a reporting L 2250 2% 45 ≈5 ≈12%
interval t have an SNR above h (t). For a given SNR value,
v functionoftheobservedQoS(i.e.,eMBMSSNR).Inresponse,
h (t), there is a one-to-one mapping to an eMBMS MCS such
v each UE independently determines whether it should send a
that a UE can decode all the packets whose SNR is above
QoS report at the current reporting interval.
h (t) [16], [17]. The remaining packets (cid:96) can be recovered
v
QoS Evaluation: The UE feedback is used to estimate the
by appropriate level of FEC assuming (cid:96) is not too large. A
eMBMS SNR distribution, as shown in Fig. 2. Since the
summary of the main notations used throughout the paper are
system needs to determine the SNR Threshold, s(t), the
given in Table I.
estimation of the low SNR range of the distribution has to
B. Objective be more accurate. To achieve this goal, the QoS Evaluation
We aim to design a scalable efficient eMBMS monitoring modulepartitionstheUEsintotwoormoregroups,according
and control system for which the objective is outlined below to their QoS values. This allows DyMo to accurately infer
and that satisfies the following constraints: the optimal value of s(t), by obtaining more reports from
UEs with low SNR. We elaborate on the algorithms for s(t)
(i) QoSConstraint–GivenaQoSThresholdp(cid:28)1,atmost
estimation in Section V.
a fraction p of the UEs may suffer from packet loss of
morethan(cid:96).Thisimpliesthat,withFEC,afraction1−p MCS Control: Since the eMBMS signal is a combination
of the UEs shouldreceive all of the transmitteddata. We of synchronized multicast transmissions from several BSs,
refertothesetUEsthatsufferfrompacketlossafterFEC the unicast SNR can be used as a lower bound on the
as outliers and the rest are termed normal UEs. eMBMS SNR. Therefore, the initial eMBMS MCS and FEC
(ii) OverheadConstraint–TheaveragenumberofUEreports are determined from unicast SNR values reported by the UEs
during a reporting interval should be below a given duringunicastconnections.Then,aftereachreportinginterval,
Overhead Threshold r. the QoS Evaluation module infers the SNR Threshold, s(t),
and the MCS Control module determines the desired eMBMS
Objective: Accurately identify at any given time t the maxi-
settings, mainly the eMBMS MCS and FEC, according to
mumSNRThreshold,s(t)thatsatisfiestheQoSandOverhead
commonly used one-to-one mappings [16], [17].
Constraints.
Namely, the calculated s(t) needs to ensure that a fraction
1−p of the UEs have individual SNR values h (t)≥s(t).
v B. Illustrative Example
The network performance can be maximized by using s(t)
to calculate the maximum eMBMS MCS that meets the QoS
DyMo operations and the Stochastic Group Instructions
constraint[16],[17].Thisallowsreducingtheresourceblocks
concept are demonstrated in the following example. Consider
allocatedtoeMBMS.Alternativelyforaservicesuchasvideo,
an eMBMS system that serves 2,500 UEs with the QoS
the video quality can be enhanced without increasing the
Constraint that at most p = 1% = 25 UEs may suffer from
bandwidth allocated to the video flow.
poor service. Assume a reporting interval of 10 seconds. To
IV. THEDyMoSYSTEM infertheSNRThreshold,s(t),thatsatisfiestheconstraint,the
UEs are divided into two groups:
This section introduces the DyMo system. It first presents
• High-Reporting-Rate (H): 10% (250) of UEs that experi-
theDyMosystemarchitecture,whichisbasedontheStochas-
ence poor or moderate service quality report with probability
tic Group Instructions concept. Then, it provides an illustra-
of 20%, i.e., an expected number of 50 reports per interval.
tive example of DyMo operations along with some technical
aspects of eMBMS parameter tuning. • Low-Reporting-Rate(L):90%(2250)oftheUEsthatexpe-
riencegoodorexcellentservicequalityreportwithprobability
A. System Overview
of 2%, implying about 45 reports per interval.
We now present the DyMo system architecture, shown in Table II presents the reporting probability of each UE and the
Fig. 1. number of QoS reports per reporting interval by each group.
Feedback Collection: This module operates in the DyMo It also shows the number of QoS reports per second and the
server and in a DyMo Mobile-Application on each UE. At the reporting rate per minute (i.e., the expected fraction of UEs
beginning of each reporting interval, the Feedback Collection that send QoS reports in a minute). Since the QoS Constraint
module broadcasts Stochastic Group Instructions to all the implies that only 25 UEs may suffer from poor service, these
UEs.TheseinstructionsspecifytheQoSreportprobabilityasa UEs must belong to group H. Although only 10 QoS reports
are received at each second, all the UEs in group H send QoS
6TheSNRofeachindividualeMBMSpacketisarandomvariableselected
reports at least once a minute. Thus, the SNR Threshold can
from the UE SNR distribution. We assume that this distribution does not
changesignificantlyduringthereportinginterval. be accurately detected within one minute.
4
C. Dynamic eMBMS Parameter Tuning quantile estimate F−1(p) is asymptotically normal [24] with
r
mean p and variance
BesidestheMCS,DyMocanleveragetheUEfeedbackand
the calculated SNR Threshold, s(t), for optimizing other eM- p(1−p)
Var[pˆ]= (1)
BMS parameters including FEC, video coding and protection r
tier.Whilethisaspectisnotthefocusofthisstudy,webriefly
discussthechallengesandthesolutionsfordynamictuningof
For SNR Threshold estimation, F is the SNR distribution
the eMBMS parameters.
of all UEs. A direct way to estimate the SNR Threshold s(t)
Once the SNR Threshold s(t) is selected, DyMo tunes the
is to collect QoS reports from r randomly selected UEs, and
eMBMS parameters accordingly. Every time DyMo changes
calculate the empirical quantile F−1(p) as an estimate.7
theeMBMSparameters,theconsumptionofwirelessresources r
for the service is affected as well. For instance, when the eM-
B. The Two-Step Estimation Algorithm
BMS MCS index is increased, some of the wireless resources
allocated for eMBMS are not needed and can be released. WenowpresenttheTwo-stepestimationalgorithmthatuses
Alternatively, the service provider may prefer to improve the twogroupsforestimatingtheSNRThreshold,s(t),inastatic
video quality by instructing the content server to increase the setting. We assume a fixed number of UEs, m, and a bound r
video resolution. Similarly, before the eMBMS MCS index on the number of expected reports. By leveraging Stochastic
is lowered, the wireless resources should be increased or GroupInstructions,DyMoisnotrestrictedtocollectingreports
the video resolution should be reduced to match the content uniformly from all UEs and can use these instructions to
bandwidth requirements to the available wireless resources. improve the accuracy of s(t). One way to realize this idea is
Since the eMBMS signal is a soft combination of the to perform a two-step estimation that approximates the shape
signals from all BSs in the venue, any change of eMBMS of the SNR distribution before focusing on the low quantile
parameters must be synchronized at all the BSs to avoid tail. The Two-step estimation algorithm works as follows:
interruption of service. The fact that all the clocks of the BSs
Algorithm 1: Two-Step Estimation for the Static Case
are synchronized can be used and a scheme similar to the two
phasecommitprotocol(whichiscommonlyusedindistributed 1) Select p and p such that p p = p. Use p as the
1 2 1 2 1
databases [23]) can be used. percentile boundary for defining the two groups.
2) Select number of reports r and r for each step such
1 2
that r +r =r.
V. ALGORITHMSFORSNRTHRESHOLDESTIMATION 1 2
3) Instruct all UEs to send QoS reports with probability
This section describes the algorithms utilized by DyMo r1/m and use these reports to estimate the p1 quantile
for estimating the SNR Threshold, s(t), for a given QoS xˆ1 =Fr−11(p1).
Constraint, p and Overhead Constraint r. In particular, it 4) Instruct UEs with SNR value below xˆ1 to send reports
addresses the challenges of partitioning the UEs into groups withprobabilityr2/(p1·m)andcalculatethep2 quantile
according to their SNR distribution as well as determining xˆ2=G−r21(p2) as an estimation for s(t) (G is the CDF
the group boundaries and the reporting rate from the UEs in of the subpopulation with SNR below xˆ1). (Gr2 is the
each group, such that the overall estimation error of s(t) is empirical CDF of the subpopulation with SNR below
minimized.Wefirstconsiderastaticsettingwithfixednumber xˆ1).
of eMBMS receivers, m, where the SNR values of UEs are
fixed. Then, we extend our solution to the case of dynamic Upper Bound Analysis of the Two-Step Algorithm: To
environments and UE mobility. simplifythenotation,weuser1 andr2 todenotetheexpected
number of reports at each step. From (1) we know that
A. Order Statistics
pˆ =F(xˆ ) and pˆ =G(xˆ )
1 1 2 2
We first briefly review a known statistical method in quan-
are unbiased estimators of p and p with variance
tile estimation, referred to as Order-Statistics estimation. It 1 2
provides a baseline for estimating s(t) and is also used by p (1−p ) p (1−p )
Var[pˆ ]= 1 1 and Var[pˆ ]= 2 2 (2)
DyMo for determining the initial SNR distribution in its first 1 r 2 r
1 2
iteration assuming a single group. Let F(x) be a Cumulative
Distribution Function (CDF) for a random variable X, the Our estimate xˆ2 has true quantile pˆ1pˆ2. Assume pˆ1 is less
quantile function F−1(p) is given by, inf{x|F(x)≥p}. than p1+(cid:15)1 and pˆ2 is less than p2+(cid:15)2 with high probability
Let X ,X ,...,X be a sample from the distribution F, (forexample,wecantake(cid:15)1 and(cid:15)2 tobe3timesthestandard
1 2 r
and F its empirical distribution function. It is well known
r
thattheempiricalquantileF−1(p)convergestothepopulation 7Note that F can have at most m points of discontinuity. Therefore, we
quantileF−1(p)atallpointsrpwhereF−1 iscontinuous[24]. assumepisapointofcontinuityforF−1 toenablenormalapproximation.
Iftheassumptiondoesnothold,wecanalwaysperturbpbyaninfinitesimal
Moreover, the true quantile, pˆ=F(F−1(p)), of the empirical amounttomakeitapointofcontinuityforF−1.
r
5
deviation for >99.8% probability). Then, the over-estimation 1 Step 2 Step 1 Step 2 Step
error is bounded by 150 150 150 150
(cid:15)= (p1+(cid:15)1)(p2+(cid:15)2) − p Frequency15000 Frequency15000 Frequency15000 Frequency15000
= p p +(cid:15) p +(cid:15) p +(cid:15) (cid:15) −p (3)
1 2 1 2 2 1 1 2
0 0 0 0
≈ (cid:15) p +(cid:15) p 0 0.01 0.02 0 0.01 0.02 0 0.01 0.02 0 0.01 0.02
1 2 2 1 Estimate of quantile 1%Estimate of quantile 1% Estimate of quantile .1%Estimate of quantile .1%
(a) (b)
after ignoring the small higher order term (cid:15)1(cid:15)2. The case for Fig.3. Estimatesof(a)p=1%and(b)p=0.1%quantilesfor500runsfor
under-estimation is similar. As shown in the Appendix, the the Order-Statistics estimation (1-step) method and the Two-step estimation
algorithm.
error is minimized by taking,
√ where L is a Lipschitz constant for SNR changes. For
p =p = p and r =r =r/2
1 2 1 2 example,wecanassumethattheUEs’SNRcannotchangeby
so that more than 5dB during a reporting interval. 8 This implies that
(cid:113)√ √
(cid:15) =(cid:15) =3 p(1− p)/(r/2) within the interval, only UEs with SNR below xˆ+5dB affect
1 2
the estimation of the p quantile (subject to small estimation
error in xˆ).
This leads to proposition 1.
DyMo only needs to monitor UEs with SNR below x =
L
Proposition 1. The distance between p and the quantile of xˆ+L. Denote the true quantile of xL, defined by F−1(xL),
the Two-Step estimator xˆ2, pˆ=F−1(x2), is bounded by as pL. To apply a process similar to the second step of the
(cid:114) √ √ Two-step estimation algorithm by focusing on UEs with SNR
√ p p(1− p)
6 2 below xL, first an estimate of pL is required. DyMo uses the
r previous SNR distribution to estimate p and instructs the
L
with probability at least 1−2(1−Φ(3)) > 99.6%, where Φ UEs to send reports at a rate q = r/(p ·m). Let Y be the
L
is the normal CDF. number of reports received during the last reporting interval,
then Y/m·q can be used as an updated estimator, pˆ, for p .
Wenowcomparethisresultagainsttheboundof3standard L L
(cid:112) This estimator is unbiased and has variance
deviationsintheOrderStatisticscase,whichis3 p(1−p)/r.
With some simple calculations, it can be easily shown that Var[pˆ]=Var[ Y ]= pL1−q (4)
if p ≤ 1/49 ≈ 2%, the Two-step estimation has smaller L m·q m q
error than the Order-Statistics estimation method. Essentially
t√he O√rder-Statistics estimation method has an error of order As a result, the Iterative Estimation algorithm works as fol-
p/ √r, while the Two-step estimation has an error of order lows:
p3/4/ r. Since p(cid:28)1, the difference can be significant.
Example: We validated the error estimation of the Two- Algorithm 2: Iterative Estimation for the Dynamic Case
step estimation algorithm and the Order-Statistics estimation 1) InstructUEswithSNRbelowxˆ+Ltosendreportsata
method by numerical analysis. We considered the cases of rateq.Constructanestimatorpˆ ofp fromthenumber
L L
p=1% and p=0.1% of uniform distribution on [0,1] using of received reports Y.
r=400 samples over population size of 106. The Two-step 2) Set p(cid:48) = p/pˆ . Find the p(cid:48) quantile x(cid:48) = G−1(p(cid:48)) and
L Y
estimation algorithm has smaller standard error compared to report it as the p quantile of the whole population (G is
theOrder-Statisticsestimation,asshowninFig.3.Itsaccuracy the CDF of the subpopulation with SNR below xˆ+L).
is significantly better for very small p.
The Two-step estimation algorithm can be generalized to 3 UpperBoundAnalysisoftheIterativeAlgorithm:Suppose
or more telescoping group sizes, but p will need to be much theestimationerrorofp isboundedby(cid:15) ,andtheestimation
L 1
smaller for these sampling schemes in order to reduce the error of p(cid:48) = p/pˆ is bounded by (cid:15) with high probability.
L 2
number of samples. Then, the estimation error is
C. The Iterative Estimation Algorithm p p
(cid:15)=( ±(cid:15) )p −p=( ±(cid:15) )p −p.
We now turn to the dynamic case in which DyMo uses the pˆL 2 L pL±(cid:15)1 2 L
SNRThresholdestimations(t−1)fromthepreviousreporting
The over-estimation error is bounded by
interval to estimate s(t) at the end of reporting interval t.
p
AssumethatthetotalnumberofeMBMSreceivers,m,isfixed (cid:15) +p (cid:15) . (5)
p −(cid:15) 1 L 2
and it is known initially. L 1
Suppose that DyMo has a current estimate xˆ of the SNR If we assume p −(cid:15) ≥p (we know p ≥p by the Lipschitz
L 1 L
threshold, s(t), and s(t) changes over time. We assume that assumption), then the bound can be simplified to (cid:15) +p (cid:15) .
1 L 2
thechangeinSNRofeachUEisboundedoveratimeperiod. The same bound also works for the under-estimation error.
Formally,
|hv(t1)−hv(t2)|≤L|t1−t2| 8Inoursimulations,eachreportingintervalhasadurationof12s.
6
If r denotes also the expected number of samples collected, 22 30000
r =IfpwLe·mass(cid:114)·uqm.pmTeLh(cid:15)1e−qs=taqn3d=par(cid:115)/d√dprer2L,vt(iha1tei−oenrprooLrfrmpˆoL)f≤pcˆan√piLsbrel.ewssritthteanna(cid:15)s: 135700000000 8111112024680 Num. of Active eMBMS Rec.1122 50505000000000000000 DAyctMivoe UEs
1 L L 1 900 6 0
with probability at least Φ(3). Since we assume p −(cid:15) ≥p 4 0 5 10 15 20 25 30
√ L 1 100 300 500 700 900 Time (minutes)
above,thisimplies(1−3/ r)pL≥p.Ifr≥100,thenp<0.7pL (a) (b)
will satisfy our requirement. Fig.4. (a)TheheatmapofSNRdistributionofUEs(b)theevolutionofthe
Thestandarddeviationofestimatingthep(cid:48) =p/pˆ quantile numberofactiveUEsovertimecomparedtothenumberestimatedbyDyMo
L forahomogeneousenvironment.
is
(cid:114)
1 p p 1
(1− )≤ √ , (6) 22 30000
Y pˆL pˆL 2 Y 20 Rec.25000 DAyctMivoe UEs
200 18 MS
by using the fact that x(1−x) ≤ 1/4 for x ∈ [0,1] and Y 16 MB20000
ietshxeptnheecYtenducmannubmebreboewrfeorleflpraoepprptosrrotrxseicrmeiiasvteerddea(bsaoynraaabnnldoyorlmmaragvleaar(ni≥adbl1Ye0)0.≥,Ifs0a.ty7h)re, 468000000 8111024 Num. of Active e11 505000000000
with high probability Φ(3) = 99.8%. Then, (6) is bounded 6 0
√ √ 1000 4 0 5 10 15 20 25 30
by 2/(3 r) ≥ 1/(2 0.7r) with high probability (Φ(3) = 200 400 600 800 1000 Time (minutes)
√
99.8%), and we can set (cid:15) = 2/ r. Substituting these back (a) (b)
2 Fig. 5. (a) The heatmap of UE SNR distribution in a stadium area of
into (5), gives us the following proposition. 1000×1000m2 and (b) the evolution of the number of active UEs over
timecomparedtothenumberestimatedbyDyMoforastadiumenvironment.
Proposition 2. The distance between p and the quantile of
the estimator x, pˆ=F−1(x), is approximately bounded by Similar to the Two-step estimation algorithm, DyMo allocates
r =r =r/2 reports to each group. The errors in estimating
p 1 2
5√L the total number of UEs m(t) will contribute to the error (cid:15)
r 1
in the estimation of p in (5). The error analysis in this case
L
with probability at least 1 − 2(1 − Φ(3)) > 99.6%, if the is largely similar.
expected sample size r ≥100 and p≤0.7p .
L
√ VI. PERFORMANCEEVALUATION
This shows that the error is of order p / r. We can see
L A. Methodology
that the estimation error can be smaller compared to the error
√ We perform extensive simulations to evaluate the perfor-
of order p3/4/ r in the static Two-step estimation if p is
L
mance of DyMo with various values of QoS Constraint, p,
small(i.e.,theSNRofindividualusersdoesnotchangemuch
OverheadConstraint,r,andnumberofUEs,m.Ourevaluation
during a reporting interval).
considers dynamic environments with UE mobility and a
Exponential Smoothing: DyMo applies exponential smooth- changingnumberofactiveeMBMSreceiversdenotedbym(t),
ing by weighing past and current reports to smooth the dynamically selected from the given set of m UEs in the
estimates of the SNR Threshold, s(t), and take older reports considered venue. In this paper, we present a few sets of
into account. It estimates the SNR Threshold as simulation results, which capture various levels of variability
of the SNR threshold, s(t), over time.
s(t)=αxˆ(t)+(1−α)s(t−1)
We consider a variant of DyMo where the number of active
wherexˆ(t)isthenewrawSNRThresholdestimateusingthe UEs is unknown and is estimated from its measurements. We
Iterative estimation above and s(t−1) is the SNR Threshold compare the performance of DyMo to four other schemes.
from the previous reporting interval. We set α=0.5 to allow To demonstrate the advantages of DyMo, we augment each
some re-use of past reports without letting them have too scheme with additional information, which is hard to obtain
strong an effect on the estimates (e.g., samples older than in practice. The evaluated benchmarks are the following:
7 reporting intervals have less than 1% weight). DyMo also • Optimal – Full knowledge of SNR values of the UEs at
any time and consequently accurate information of the SNR
uses the exponential smoothing method for estimating the
distribution. This is the best possible benchmark although
SNR distribution while taking into account QoS reports from
impractical, due to its high overhead.
previous reporting intervals.
• Uniform – Full knowledge of the SNR characteristics
Dynamic and Unknown Number of eMBMS Receivers: at any location while assuming uniform UE distribution and
If the total number of UEs, m(t), is unknown or changes static eMBMS settings. In practice, this knowledge cannot be
dynamically,DyMocanestimatem(t)byrequiringUEsabove obtained even with rigorous field trial measurements.
thethresholdxˆ+Ltosendreports.TheseUEscansendreports • Order-Statistics – It is based estimation of the SNR
at a lower rate, since m(t) is not expected to change rapidly. Threshold using random sampling. The active UEs send
7
0 22 0 22 its located. The rectangles have different mean SNR, but
20 20 the same standard deviation of roughly 5dB (as observed in
200 18200 18
16 16 real measurements). Thus, the SNR characteristics of each
400 14400 14 environment are determined by the mean SNR values of
600 12600 12 the rectangles at any reporting interval. To demonstrate the
10 10
800 8 800 8 performance of the different schemes, we discuss three types
6 6 of environments.
1000 41000 4
0 200 400 600 800 1000 0 200 400 600 800 1000 •Homogeneous:Inthehomogeneous9 settingthemeanSNR
(a) (b)
value of each rectangle is fixed and it is uniformly selected
Fig.6. TheheatmapoftheSNRdistributionofUEs(a)beforeafailureand
(b)afterafailure. in the range of 5−25dB. Fig. 4(a) provides an example of
the mean SNR values of such a venue as well as typical UE
reports with a fixed probability of r/E[m(t)] per second,
location distribution. In such instances, we assume random
assuming that the expected number of active UEs, E[m(t)],
mobility pattern, in which each UE moves back and forth
is known. We assume that the UEs are configured with this
betweentwouniformlyselectedpoints.Duringthesimulation,
reporting rate during initialization. In practice, E[m(t)] is not
50% of the UEs are always active, while the other 50% join
available. We also ignore initial configuration overhead in
and leave at some random time,as illustrated by Fig. 4(b). As
our evaluation. Order-Statistics is the best possible approach
we show later in such setting s(t) barely change over time.
when not using broadcast messages for UE configuration. We
• Stadiums: In a stadium, the eMBMS service quality is
consider two variants of Order-Statistics. The first is Order-
typically significantly better inside the stadium than in the
Statisticsw.o.History whichignoresSNRmeasurementsfrom
surrounding vicinity (e.g., the parking lots). To capture this,
earlierreportingintervals.ThesecondvariantOrder-Statistics
we simulate several stadium-like environments, in which the
w. History considers the history of reports.
stadium, in the center of the venue, has high eMBMS SNR
Both DyMo and Order-Statistics w. History perform the
withmeanvaluesintherangeof15−25dB.Ontheotherhand,
same exponential smoothing process for assigning weights
the vicinity has significantly lower SNR with means values of
to the measurements from previous reporting intervals with
5−10dB. An example of a stadium is shown in Fig. 5(a).
a smoothing factor of α=0.5. We use the following metrics
Weassumeamobilitypatterninwhich,theUEsmovefrom
to evaluate the performance of the schemes:
theedgestotheinsideofthestadiumin12mins,staytherefor
(i) Accuracy – The accuracy of the SNR Threshold esti- 3mins,andthengobacktotheedges.10 AsshowninFig.5(b),
mation, s(t). After calculating s(t) at each reporting
as the UEs move toward the center, the number of active UEs
interval,wechecktheactualSNRThresholdPercentilein
gradually increases from 10% of the UEs to 100%, and then
the accurate SNR distribution of the considered scheme.
declines again as they move away.
This metric provides the percentile of active UEs with
• Failures: Such an environment is similar to the homo-
individual SNR values below s(t).
geneous setting with a sudden event of a component failure.
(ii) QoSConstraintviolation–Thenumberofoutliersabove
In the case of a malfunctioning component, the QoS in some
theQoSConstraintp.Thenumberofoutliersofascheme
partsofavenuecandegradesignificantly.Tosimulatefailures,
inagivenreportingintervaltisdefinedastheactualSNR
we consider cases in which the eMBMS SNR is high with
Threshold Percentile of the scheme times the number of
a mean between 15−25dB. During the simulation, (around
active eMBMS receivers, m(t), at time t. the 10th minute), we mimic a failure by reducing the mean
(iii) Overhead Constraint violation – The number of reports
SNR values of some of the rectangles by over 10dB to the
above the Overhead Threshold, r, at each reporting
rangeof5−10dB.ThemeanSNRvaluesarerestoredtotheir
interval.
originalvaluesafterafewminutes.Figs.6(a)and6(b)provide
The total simulation time for each instance is 30mins with an example of the mean SNR values of such a venue before
5 reporting intervals per minute (each is 12s). During each and after a failure, respectively. We assume the same mobility
reporting interval, an active UE may send its SNR value at pattern like the homogeneous setting, as shown by Fig. 4(b).
most once. The accuracy of each SNR report is 0.1dB.
C. Performance over time
B. Simulated Environments
We first illustrate the performance of the different schemes
We simulated a variety of environments with different overtimeforthreegiveninstances,ahomogeneous,astadium
SNR distributions and UE mobility patterns. Although the andafailurescenarios,withm=20,000UEs,QoSConstraint
simulated environments are artificial, their SNR distributions p = 0.1%, and Overhead constraint r = 5 reports/sec, i.e.,
mimic those of real eMBMS networks obtained through field 60 messages per reporting interval. The number of permitted
trial measurements. To capture the SNR characteristics of an
environment, we divide its geographical area into rectangles 9Weusethetermhomogeneoussincethetermuniformisalreadyusedto
of 10m×10m. For each reporting interval, each UE draws denotetheUniformscheme.
10While significant effort has been dedicated to modeling mobility (e.g.,
its individual SNR value, h (t), from a Gaussian-like dis-
v [25], [26] and references therein), we use a simplistic mobility model since
tribution which is a characteristic of the rectangle in which ourfocusisonthemulticastaspectsratherthanthespecificmobilitypatterns.
8
NR Threshold Percentile00000.....12345 ODpytMimoal NR Threshold Percentile124680 UOOOnprrdditfieemorr raSSmlttaatt ww..o H Hisitst SNR Threshold345678 UODOOnpyrrdditMfieemorro raSSmlttaatt ww..o H Hisitst Num. of Outliers 1234500000 ODpytMimoal
S S
0 0 2 0
0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30
Time (minutes) Time (minutes) Time (minutes) Time (minutes)
(a) (b) (c) (d)
15
Num. of Outliers1246800000000000 UOOOnprrdditfieemorr raSSmlttaatt ww..o H Hisitst Spectral Effic. (Bits/Hz)0.003..354 ODpytMimoal Spectral Effic. (Bits/Hz)0000.0.0.345...354555 UOOOnprrdditfieemorr raSSmlttaatt ww..o H Hisitst Num. of Reports/Sec150 DOyrdMero Stat w.o Hist
0 0.25 0.25 0
0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30
Time (minutes) Time (minutes) Time (minutes) Time (minutes)
(e) (f) (g) (h)
Fig.7. Simulationresultsfromasinglesimulationinstancelastingfor30minsinacomponenthomogeneousenvironmentwith20,000UEsmovingsideto
sidebetweentworandompoints,withp=0.1andr=5messages/sec.(a)TheactualpercentileoftheSNRThresholdestimatedbyDyMo,(b)theactual
percentileoftheSNRThresholdestimatedbyOrder-Statistics,(c)theSNRThresholdestimation,(d)spectralEfficiencyofOptimalvs.DyMo,(e)spectral
EfficiencyofOptimalvs.Order-Statistics,(f)thenumberofOutliersbyusingDyMo,(g)thenumberofoutliersbyusingUniformandOrder-Statistics,and
(h)theQoSreportoverhead.
outliers depends on the number of active UEs at the current HistorygraduallyincreasetheirSNRThresholdestimates,due
reportinginterval.Inthethreeconsideredscenarios,itcanbe to the exponential smoothing process.
at most 20 at any given time. The key difference between The SNR Threshold estimation gap directly impacts the
the different instances is the rate at which the SNR Threshold number of outliers as well as the network utilization, i.e.,
changes.InthehomogeneousenvironmenttheSNRThreshold the spectral efficiency. Figs. 7(d) and 7(e) show the number
is almost fixed with very limited variability. In the case of of outliers of DyMo and Order-Statistics variants for the
the stadium, the SNR Threshold gradually changes as the homogeneous environment, respectively12, while Figs. 7(f)
UEs change their locations. In the failure scenario, the SNR and7(g)showthespectralefficiencyoftheschemes.Figs.7(d)
Threshold is roughly fixed but it drops instantly by 10dBs for and 7(f) reveal that after a short adaptation phase DyMo
the duration of the failure. converges to the optimal performance, i.e., spectral efficiency,
The results of the homogeneous, stadium and failure cases while preserving the QoS constraint. Fig. 7(f) show that both
are shown in Figs. 7, 8 and 9, respectively. Figs. 7(a), 7(b), Optimal and DyMo fluctuate between two spectral efficiency
8(a), 8(b), 9(a), and 9(b) show the actual SNR Threshold levels, 0.29 and 0.36 bit/sec/Hz, which results from oscillata-
percentileovertime.FromFigs.7(a),8(a)and9(a),weobserve tion between two MCS levels 3 and 4. Such oscillations can
that DyMo can accurately infer the SNR Threshold with an be easily suppressed by enforcing some delay between MCS
estimation error of at most 0.1%. Fig. 9(a) shows slightly increaseoperations.TheOrder-Statisticsvariantsoverestimate
higher error of 0.25% at the time of the failure (at the 7th the SNR threshold and suffer from higher number of outliers,
minute).TheOrder-Statisticsvariantssufferfrommuchhigher as shown by Fig. 7(e). The homogeneous setting represents
estimation error to the order of a few percentage points, as quasi-static environments with minor variation of the SNR
shown by Figs. 8(b), 8(b) and 8(b)11. This performance gap threshold,s(t).Insuchsettings,theUniformschemeprovides
results in different estimation accuracy of the SNR Thresh- a good estimation13 of s(t) and its number of outliers as well
old for DyMo and Order-Statistics schemes as illustrated in as the obtained spectral efficiency are comparable to DyMo.
Figs. 7(c), 8(c) and 9(c), respectively. These figures show that However, this is not the situation when s(t) is time varying.
the performance of DyMo and Optimal is almost identical. The number of outliers of DyMo and Order-Statistics vari-
Even in the event of a failure, DyMo reacts immediately and ants for the stadium environment is shown in Figs. 8(d)
detects the SNR Threshold accurately. The Order-Statistics and 8(e), respectively, while Figs. 9(d) and 9(e) illustrate the
variants react quickly to a failure but not as accurately as number of outliers of DyMo and Order-Statistics variants for
DyMo. After the recovery, both DyMo and Order-Statistics w.
12Noticethatthefigurepairs,(i)Figs.7(d)and7(e),(ii)Figs.8(d)and8(e)
11Notice that the pairs (i) Figs. 7(a) and 7(b), (ii) Figs. 8(a) and 8(b) as aswellas(iii)Figs.9(d)and9(e),usedifferentscalesfortheYaxes.
wellas(iii)Figs.9(a)and9(b)usedifferentscalesfortheYaxes. 13Assumingrigorousfieldtrialmeasurements.
9
10 12 35
SNR Threshold Percentile000.0.0.012..51525 O DpytMimoal SNR Threshold Percentile 2468 UOOOnprrdditfieemorr raSSmlttaatt ww..o H Hisitst SNR Threshold14680 UODOnpyrditMfiemoro raS-mEltastt iwm.aot eHist Num. of Outliers11223505050 ODpytMimoal
Order Stat w. Hist
0 0 2 0
0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30
Time (minutes) Time (minutes) Time (minutes) Time (minutes)
(a) (b) (c) (d)
Num. of Outliers123456000000000000 UOOOnprrdditfieemorr raSSmlttaatt ww..o H Hisitst Spectral Effic. (Bits/S/Hz)0001....46821 ODpytMimoal Spectral Effic. (Bits/S/Hz)0001....46821 UOOOnprrdditfieemorr raSSmlttaatt ww..o H Hisitst Num. of Reports/Sec1125050 DOyrdMero Stat
0 0.2 0.2 0
0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30
Time (minutes) Time (minutes) Time (minutes) Time (minutes)
(e) (f) (g) (h)
Fig. 8. Simulation results from a single simulation instance lasting for 30mins in a stadium environment with 20,000 UEs moving from the edges to the
center and back, with p = 0.1 and r = 5 messages/sec. (a) The actual percentile of the SNR Threshold estimated by DyMo, (b) the actual percentile of
the SNR Threshold estimated by Order-Statistics, (c) the SNR Threshold estimation, (d) spectral efficiency of Optimal vs. DyMo, (e) spectral efficiency of
Optimalvs.Order-Statistics,(f)thenumberofOutliersbyusingDyMo,(g)thenumberofOutliersbyusingUniformandOrder-Statistics,and(h)theQoS
reportoverhead.
the failure scenario, in this order. These figures show that the s(t) for the homogeneous environment, we observe that it
numberofoutliersthatresultsfromtheOrder-Statisticsw.His- yieldsaveryconservativeeMBMSMCSsettinginthestadium
toryandOrder-Statisticsw.o.Historyvariantsareoccasionally example, which causes low network utilization. In the failure
over 200 and 800, respectively. Whereas, DyMo ensures that scenario, the conservative eMBMS MCS of Uniform is not
the number of outliers at any time is comparable to Optimal sufficient to cope with the low SNR Threshold and it leads to
and in the worst case it exceeds the permitted number by less excessive number of outliers.
than a factor of 2.
Figs. 8(f) and 8(g) show the spectral efficiency for the
D. Impact of Various Parameters
stadium environment, whereas Figs. 9(f) and 9(g) show the
spectralefficiencyforthecomponentfailurecase.Thespectral We now turn to evaluate the quality of the SNR Threshold
efficiency for each case is correlated to the SNR Threshold. estimation and the schemes ability to preserve the QoS and
For the stadium environment, DyMo has spectral efficiency OverheadConstraintsundervarioussettings.Weusethesame
close to Optimal while Uniform has the lowest spectral ef- configuration of m = 20,000 UEs, p = 0.1% and r = 5
ficiency. In the event of a failure, the spectral efficiency of reports/sec and we evaluate the impact of changing the values
DyMofollowstheOptimalasexpectedfromtheSNRThresh- of one of the parameters. The results for the homogeneous,
old estimations. Since Order-Statistics variants typically over stadiumandfailurescenariosareshowninFigs.10,11and12,
estimate the SNR Threshold, they frequently determine MCS respectively. Each point in the figures is the average of 5
and consequently spectral efficiency that exceed the optimal different simulation instances of 30mins each with different
settings. Such inaccuracy leads to a high number of outliers. SNR characteristics and UE mobility patterns. The error bars
Figs.7(h),8(h) and9(h)indicateonlymildviolationofthe are small and not shown. In these examples, we compare
Overhead Constraint by both the DyMo and Order-Statistics DyMo only with Optimal and Order-Statistics w. History
variants. We observe that accurate SNR Threshold estimation whichisthebestperformingalternative.WeomittheUniform
allows DyMo to achieve near optimal spectral efficiency with scheme since it does not adapt to variation of s(t).
negligibleviolation ofthe QoSConstraint.The otherschemes First, we consider the impact of changing these param-
suffer from sub-optimal spectral efficiency, excessive number eters on the accuracy of the SNR Threshold estimation.
ofoutliers,orboth.Giventhatthepermittednumberofoutliers Figs.10(a),11(a),and12(a)showtheRootMeanSquareError
is at most 20, the Order-Statistics w. History and Order- (RMSE) in SNR Threshold percentile estimation vs. m, for
Statistics w.o. History schemes exceed this value sometimes homogeneous,stadiumandfailurescenarios,respectively.The
by a factor of 10 and 40, respectively. Among these two non-zero values of RMSE in Optimal are due to quantization
alternatives,Order-Statisticsw.Historyleadstolowernumber of SNR reports. The RMSE in the SNR Threshold estimation
of outliers. While Uniform provides accurate estimation of of DyMo is close to that of Optimal regardless of the number
10