A Kalman Filter Approach for DistinguishingChannel and Collision Errorsin IEEE 802.11 Networks
I. Tinnirello
∗
, A. Sgora
+
∗
Universit`a di Palermo, Dip. di Ing. Elettrica, Elettronica e delle Telecomunicazioni, Italy(ilenia.tinnirello@tti.unipa.it)
+
University of Aegean, Department of Information and Communication Systems Engineering, Greece(asgora@aegean.gr)
Abstract
—In the last years, several strategies for maximizingthe throughput performance of IEEE 802.11 networks have beenproposed in literature. Speciﬁcally, it has been shown that optimizations are possible both at the Medium Access Control (MAC)layer, and at the Physical (PHY) Layer. In fact, at the MAC layer,it is possible to minimize the channel waste due to collisionsand backoff expiration times, by tuning the minimum contentionwindow as a function of the network congestion level. At the PHYlayer, it is possible to improve the transmission robustness, byselecting a suitable modulation/coding scheme as a function of thechannel quality perceived by the stations. However, the feasibilityof these optimizations rely on the availability of MAC/PHYmeasurements, which are often impracticable or very rough.In this paper, we propose a joint MAC/PHY estimator basedon a bidimensonal extended kalman ﬁlter, devised to separatelytrack the collision probability and the channel error probabilitysuffered by each station. To this purpose, we derive a relationshipbetween the unobservable system state and measurements whichare perfomed in a distributed way by all the competing stations.
I. I
NTRODUCTION
One of the key factor for the wide success of IEEE 802.11Wireless Local Area Networks (WLANs) is the simplicity androbustness of the Medium Access Control (MAC) protocol employing the Distributed Coordination Function (DCF). Basedon the wellknown carrier sense paradigm, with an exponentialbackoff mechanisms devised to minimize the probability of simultaneous transmission attempts by multiple stations, DCFis able to work in presence of interference, which is verycritical for networks operating in unlicensed spectrum. Sourcesof interference affecting a given station may include not onlyother stations sharing the channel on the same network, butalso external noise, for example, from microwave ovens andoverlapping networks. The former endogenous interferenceaffects the MAC layer; the latter exogenous interference affectsthe physical (PHY) layer.In the last years, several strategies for maximizing thethroughput performance of DCF in presence of interferencehave been proposed in literature. Speciﬁcally, it has beenshown that optimizations are feasible both at the MAC layerand at the PHY layer. On one side, it is possible to minimizethe channel waste due to collisions and backoff expirationtimes, by tuning the minimum contention window as a functionof the number of interfering stations [2], [3], [4]. While, in thestandard IEEE 802.11 protocol [1], the backoff parameterswere hardwired in the PHY layer, the idea of adaptivelysetting the backoff window has been recently taken intoconsideration in the new 802.11e standard amendment [5].By exploiting this new possibility, adaptive tunings of thecontention have been proposed in [6], [7], [8]. On the otherside, it is possible to improve the transmission robustness, byselecting a suitable modulation/coding scheme as a functionof the channel quality perceived by the stations. Differentrate selection algoritms, known as link adaptation algorithms,may be implemented in commercial cards, according to thehardware latency for switching from a rate to another and tothe capability of buffering perpacket rate descriptors [9].However, the feasibility of these optimizations rely onthe availability of MAC/PHY measurements, which are oftenimpracticable or very inaccurate. Regarding the estimation of the MAC interference, we have to consider that the protocoloperations do not allow to directly retrieve the network congestion level. In fact, DCF does not rely on a privileged stationto control the access to the channel. Even considering theexistence of an Access Point (AP), as in infrastructure mode,the information available at the AP is limited to the numberof associated stations, a number which may be very differentfrom the number of stations actually in contention. Moreover,in presence of generic trafﬁc sources, the number of activestations is not directly related to the network congestion status.Regarding the estimation of the PHY interference, we have toconsider that the detection of frame errors due to poor Signalto Noise Ratio (SNR) is not immediate, since the collisiondetection is not available for wireless transmissions. Differentsolutions, based on special control frames, acknowledgementmonitoring or tracking of consecutive failures [10], [11],[12], have been designed for indirectly distinguishing betweencollisioninduced and channelinduced errors. Most of themhave some drawbacks in terms of overhead or accuracy of thechannel error rate estimator.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
9781424423248/08/$25.00 © 2008 IEEE.
In this paper, we propose an efﬁcient technique for distinguishing and quantifying the MAC and PHY interferencesuffered in errorprone 802.11 networks. The technique istotally distributed, thus enabling each station for individuallyevaluating the perceived interference conditions. Our solutionstarts from the approach introduced in [13], where an ExtendedKalman ﬁlter coupled with a change detection mechanism hasbeen deﬁned for tracking the number of competing terminals in802.11 errorfree networks. In constrast to [13], we introducean additional state dimension, devised to account for thechannel error rate, and we deﬁne a different state variable forrepresenting the network congestion level, i.e. the perceivedcollision probability.The rest of the paper is organized as follows. In Section II,we brieﬂy review the IEEE 802.11 Distributed CoordinationFunction. In Section III we derive our measurement modelwhich relates the network state to some observable parameters,available to all stations. In section IV, we introduce ourExtended Kalman Filter approach coupled to a change detection ﬁlter. In Section V we evaluate the performance of theproposed estimation technique. Finally, concluding remarksare given in Section VI.II. 802.11 D
ISTRIBUTED
C
OORDINATION
F
UNCTION
We assume that the reader is familiar with the IEEE 802.11Distributed Coordination Function (DCF) and its performanceevaluation. Thus, we brieﬂy summarize the protocol operationsand the modeling approaches used for our estimator derivation.The DCF is based on a Carrier Sense Multiple Accesswith Collision Avoidance protocol (CSMA/CA). A stationwith a new frame to transmit has to monitor the channelstate, until it is sensed idle for a period of time equal to aDistributed InterFrame Space (DIFS). If the channel is sensedbusy before the DIFS expiration, the station has to add afurther backoff delay before transmitting, in order to avoid asynchronization with other station transmissions. The backoff interval is slotted for efﬁciency reasons, and is uniformlychosen in the range
(0
,w
−
1)
, where
w
is the
ContentionWindow
. In DCF,
w
follows a truncated exponential incrementlaw (doubling from
CW
min
up to
CW
max
), according tothe number of consecutive failed transmissions. In fact, sincepacket failures are considered a consequence of simultaneousaccesses performed by two or more stations, the incrementof the backoff range reduces the probability of two furtheridentical backoff extractions.Frame transmissions have to be explicitely acknowledgedwith ACK frames, because the CSMA/CA does not rely onthe capability of the stations to detect a collision by hearingthe channel. The ACK frames are immediately transmitted atthe end of a frame reception, after a period of time calledShort InterFrame Space (SIFS) shorter than a DIFS. If thetransmitting station does not receive the ACK within a speciﬁed ACK Timeout, it reschedules the packet transmission,according to the given backoff rules. Stations which receivea corrupted frame have to wait for an Extended InterFrameSpace (EIFS) before resuming the backoff process. When a
Fig. 1. DCF channel operations and equivalent slotted model.
packet is retransmitted on the channel, a speﬁc retry bit in theMAC header is set to 1.DCF deﬁnes an additional fourway handshaking technique,according to which the transmission of a data frame occursafter a preliminar exchange of two short
Request to Send
(RTS)and
Clear to Send
(CTS) control frames. This mechanismsallows to combact the hidden terminals problem and to reducethe collision times. A detailed performance discussion aboutthe effectiveness of the fourway technique can be found in[3].III. M
EASUREMENT
M
ODEL
Our goal is the estimation of a bidimensional network state:the collision probability
p
c
and the channel error rate
p
e
.Both the parameters are not directly accessible to the stationsmonitoring the channel state. In fact, each station is able todetect its transmission failures by means of ACK timeouts,but it is not able to infer whether the failure is due to channelimpairment or to collisions with other stations. Thus, someindirect measurements of the network state need to be deﬁned,in order to proceed with our estimation.Because of the carrier sense feature of the access protocol,each contending station has to continuously monitor the channel state. We argue that such a monitoring can be enough forindirectly probing the
external
interference and the
internal
congestion level of the network. For performing our probes,we model the channel state in terms of slotted idle/busy slots,whose temporal size is not uniform [3]. An idle slot size isequal to a backoff slot during which the channel is sensedidle, while a busy slot size is equal to the time during whichthe channel is sensed busy plus the ﬁnal idle time required forbackoff resuming. In other words, frame transmission times,ACK times and DIFS or EIFS intervals are embedded into asingle channel busy slot.A ﬁrst measurement available from channel monitoringis obviously the probability to fail a transmission, i.e. toretransmit a frame. Each station can keep counting the numberof performed transmissions
T
and the number of experiencedACK timeouts
A
[12]. The retransmission probability
p
r
canbe measured as
p
r
=
A/T
, where the superscript indicatesa measurement sample. Whenever the channel error rate isuniform among the stations and the stations are permanently incontention (
saturated
stations), the overall failure rate is constant for all stations. This assumption can be realistic whether
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
9781424423248/08/$25.00 © 2008 IEEE.
all stations transmit to a common receiver, which locallyperceives constant channel error rate due to external interference. In this case, it is possible to increase the measurementsamples by looking at all the successful channel transmissions.Since each station has to decode the MAC header of all thereceived frames for ﬁltering its own frames, the retry bit inthe MAC header can be used for counting the total number of retransmissions
R
and the total number of successful frames
S
. In this case, the retransmission probability can be evaluatedas
p
r
=
R/S
.A second measurement available from channel observations,is the collision probability
p
c
, which represents a speciﬁccomponet on the overall failure rate. To perform such a measurement, each station cannot consider its own transmissionoutcomes, because it is not possible to classify the failureevents. However, it can monitor
all
the other channel slots, byconsidering idle slots as potential successes and busy slots aspotential collisions [13], [12]. In other words, the monitoringstation can infer that in each idle slots a frame could havebeen transmitted without colliding. Conversely, in each busyslot, it would have been resulted in a collision. Thus, thecollision probability can be obtained by counting the numberof observed busy slots,
C
busy
, and dividing this sum by thetotal number
B
of observation slots on which the measurementis taken, i.e.:
p
c
=
C
busy
/B
. Figure 1 shows an exampleof actual channel monitoring and equivalent model slots. Theﬁgure also indicates the classiﬁcation of channel slots intoobservation slots and successful slots, for a given stationwhose transmissions are indicated in red. Note that thesetransmissions are not included in the observation slots, becausethe tagged station cannot recognize the actual collisions.The channel error rate can be easily related to the
(
p
c
,p
r
)
measuremets, by considering tha a retransmission is srcinatedby either a collision or a channel error, as:
p
e
=
p
r
−
p
c
1
−
p
c
(1)
A. Measurement Noise
Being
p
c
and
p
r
the actual collision and retransmissionprobability, respectively, we can assume that each measurement sample is given by the sum of the actual parameter tobe measured and a measurement noise:
p
c
(
k
) =
p
c
(
k
) +
v
c
(
k
)
p
r
(
k
) =
p
c
(
k
) + [1
−
p
c
(
k
)]
·
p
e
(
k
) +
v
r
(
k
)
(2)Obviously, the measurement noise depends on the numberof observation slots and transmission slots on which themeasurement is performed. Speciﬁcally, a
p
c
measurementsample computed on
B
observation slots is a random variablewith binomial distribution:
Prob
p
c
=
bB
=
Bb
p
bc
(1
−
p
c
)
B
−
b
b
∈
(0
,B
)
(3)The mean value and variance of the measure
p
c
are obviously
p
c
and
p
c
(1
−
p
c
)
/B
. Analogously, a
p
r
measurement samplecomputed on
T
transmission slots is a random variable withbinomial distribution:
Prob
p
r
=
sT
=
T s
p
sr
(1
−
p
r
)
T
−
s
s
∈
(0
,T
)
(4)whose mean value is the actual
p
r
value and variance is
p
r
(1
−
p
r
)
/T
. If the
p
r
samples are computed on the totalnumber of successful frames
S
, the binomial distributionchanges accordingly, and the measurement variance is reducedto
p
r
(1
−
p
r
)
/S
.It follows that the noise components
v
c
and
v
r
are binomialrandom variables, whose mean value is zero, and whosevariance depends on the network state and on the measurementinterval.IV. R
UN

TIME
I
NTERFERENCE
E
STIMATION
We represent the bidimensional interference state in termsof collisioninduced and channelinduced error probability
(
p
c
,p
e
)
. During each interval
I
, each monitoring stationcounts the number of busy slots
C
busy
(
I
)
, observation slots
B
(
I
)
, ACK timeouts
A
(
I
)
and frame transmissions
T
(
I
)
(orretransmitted frames
R
(
I
)
and successful transmissions
S
(
I
)
).These parameters are then used to perform a bidimensionalmeasurement
(
p
c
,p
r
)
. Measurements can be smoothed at runtime by applying an autoregressive ﬁlter. They can then beprocessed to produce a timedependent estimation of network state:
p
c
(
k
) =
α
c
p
c
(
k
−
1) + (1
−
α
c
)
p
c
(
k
)
p
e
(
k
) =
α
r
[
p
c
(
k
−
1)+(1
−
p
c
(
k
−
1))
p
e
(
k
−
1)]+(1
−
α
r
)
p
r
(
k
)
−
p
c
(
k
)1
−
p
c
(
k
)
(5)where
k
is the discrete time instant corresponding to end of the
k
th interval
I
at which the new measurements
(
p
c
,p
r
)
areavailable, and the numerator of the
p
e
(
k
)
expression representsthe smoothed
p
r
measurement. The ﬁlter coefﬁciencies
α
c
and
α
r
, which represent the system memory, have to be chosen astradeoff between accuracy and tracking capability.Alternatively, we can deﬁne an Extended Kalman Filter,working on the same measurement samples
(
p
c
,p
r
)
, able toexploit several additional information, such as heterogeneoustimevarying variance of the measurements and knowledgeabout the updating laws for network interference. The deﬁnition of a Kalman Filter relies on the deﬁnition of a state model,in terms of state updating laws and relationship betweenmeasurements and state. The network interference state istrivially represented by the collision probability
p
c
(
k
)
andby the channel error probability
p
e
(
k
)
suffered by a givenestimating station at discrete time
k
. In absence of furtherinformation about trafﬁc and channel models, we assume thatthe network state evolves according to the law:
p
c
(
k
) =
p
c
(
k
−
1) +
w
c
(
k
)
p
e
(
k
) =
p
e
(
k
−
1) +
w
e
(
k
)
(6)where the random variable
w
c
(
k
)
indirectly accounts for stations that have become active or inactive, and
w
e
(
k
)
accountsfor changes in the PHY interference over the last time interval.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
9781424423248/08/$25.00 © 2008 IEEE.
The relationships between measurements and state variablesare given by equation 2. For this measurement model, the linearized sensitivity matrix
H
, which relates the state variationsto the measurement variations at time
k
, can be computed as:
1 01
−
p
e
1
−
p
c
(7)We propose a dynamic tuning of the measurement variances,on the basis of the state estimation and observation samples
B
(
k
)
and
T
(
k
)
revelead during the
k
th interval:
V ar
[
v
c
(
k
)] =
ˆ
p
c
(
k
)
·
(1
−
ˆ
p
c
(
k
))
B
(
k
)
V ar
[
v
r
(
k
)] =
ˆ
p
r
(
k
)
·
(1
−
ˆ
p
r
(
k
))
T
(
k
)
(8)where
ˆ
p
c
(
k
)
and
ˆ
p
r
(
k
)
are the expected measurements at time
k
. We veriﬁed that there is a negligible correlation betweenthe
p
c
and
p
r
measurements.In absence of state evolution models, the tuning of thestate noise is more complicated. In fact, the noise variances
V ar
[
w
c
(
k
)]
and
V ar
[
w
e
(
k
)]
should be set to 0, or at least to avery small value, when the number of competing stations andthe channel error rate appear to remain constant. Conversely,when it appears that the network state has changed, they shouldbe set to large values, for enabling prompt ﬁlter reactions.Since the state model does not require that
w
c
(
k
)
and
w
e
(
k
)
are stationary processes, we propose a dynamic tuning of thestate noise variance, according to the detection/undetection of state changes.Among the several available statistical tests for revealingstate changes, we have implemented two independent changedetection ﬁlters, based on the CUSUM (CUmulative SUMmary) test [14], for both the innovation components
z
c
=
p
c
−
ˆ
p
c
and
z
r
=
p
r
−
ˆ
p
r
. For convenience, we use two relatedprocess
s
c
and
s
r
, which represent the innovation processes
z
c
and
z
r
normalized to their standard deviation.Alarms coming from the CUSUM tests are used to adaptively set the variance
V ar
[
w
c
(
k
)]
and
V ar
[
w
e
(
k
)]
of boththe state noise
w
c
and
w
e
. When the change detection ﬁlterdoes not detect a state change (i.e. no alarm arrives at time
k
),
V ar
[
w
c
] = 0
and
V ar
[
w
e
] = 0
. Conversely, upon analarm generated at time
k
, the value
V ar
[
w
c
]
and
V ar
[
w
e
]
are set (for the instant of time
k
only) to sufﬁciently largevalues. This represents a noise impulse in the state updateequation, which allows the Kalman ﬁlter to ”move away” fromthe former estimate and therefore to rapidly converge to a newestimate.V. P
ERFORMANCE
E
VALUATION
We consider an infrastructure network scenario in which avarying number of contending stations transmit towards theAP. The hypothesis of a common receiver can justify the useof a channel model whose error rate is uniform for all thestations. However, working in infrastructure mode is not arequirement for the feasibility of our estimation technique. Infact, our estimator can still work in adhoc networks, becauseit is based on channel observations independently carried outby each station.
0 0.2 0.4 0.6 0.8 120010002001000
P r o b a b i l i t y
Time [seconds]Station AStation BpepcpepcActual peKalmanARMA1
Fig. 2. Interference estimation in terms of
(
p
c
, p
e
)
in case of heterogeneouschannel error rate.
0 0.2 0.4 0.6 0.8 101002000100200
P r o b a b i l i t y
Time [seconds]pr’=A/Tpr’=R/SpepcpepcActual peKalmanARMA1
Fig. 3. Interference estimation in terms of
(
p
c
, p
e
)
in case of uniform channelerror rate.
Figure 2 shows our bidimensional interference estimationfor two different stations. In this simulation experiment, weassume that each transmitter experiences a different channelerror rate. Speciﬁcally, we set for each station a random
p
e
value, uniformly chosen in the range
[0 : 1]
, and a total numberof contending stations equal to 10. In the ﬁgure, we plot theestimations carried out by station A experiencing an high errorrate (namely
p
e
(
A
) = 0
.
565
), and by station B experiencinga low error rate (namely
p
e
(
B
) = 0
.
057
). The measurementsamples are collected every 0.5s for both the stations. From theﬁgure, we see that the Kalman ﬁlter approach give good resultsdespite of the highvariance of the
p
r
samples. Conversely, theARMA ﬁlter with a smoothing factor
α
c
=
α
r
= 0
.
95
gives agood accuracy for the
p
c
estimation, but a very poor accuracyfor the
p
e
one. The error is very critical for station A, whose
p
e
estimation results biased to a value much higher than theactual one. Moreover, the ARMA ﬁlters result less promptthan the Kalman ones. Note also that the
p
c
estimation is notexaclty the same for the two contending stations. In fact, sinceeach station has a different channel access probability
τ
i
, as aresult of heterogeneous failure rates, the collision probabilityexperienced by a generic station results:
p
c
(
i
) = 1
−
nj
=1
(1
−
τ
j
)1
−
τ
i
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
9781424423248/08/$25.00 © 2008 IEEE.
0 0.2 0.4 0.6 0.8 160040020006004002000
P r o b a b i l i t y
Time [seconds]Station AStation BpepcpepcActual peKalmanARMA1ARMA2
Fig. 4. Interference estimation in terms of
(
p
c
, p
e
)
in case of dynamic loadconditions.
Given that this state model does not require any a priori hypothesis about the PHY interference suffered by eachtransmitter, it can obviously work in the case of uniformchannel conditions too. Figure 3 shows the
(
p
e
,p
c
)
estimationscarried out by a target station, in a network scenario with 10competing stations and a ﬁxed channel error rate
p
e
= 0
.
5
. Inthe ﬁgure, we compare the estimation results corresponding tothe measurement model proposed for the uniform interferencecase (leftmost plot) and for the general interference model(rightmost plot). From the ﬁgure, we see that the Kalman ﬁlterestimations show good responsiveness and accuracy with boththe measurement models. The only difference between the twocases is given by the decrement rate of the estimation variance,which is obviously slower when the
p
r
measurements are lessreliable. Conversely, the ARMA ﬁlter works well only for theuniform interference model. In case of general interferencemodel, longer
I
intervals or higher smoothing factors arenecessary for reducing the
p
r
variance, thus degrading thetracking capability of the estimator.Finally, ﬁgure 4 shows the interference estimations carriedout by two different stations, in case of dynamic load conditions. In this simulation experiment, we set again set for eachstation a random channel error rate, uniformly extracted in therange [0:1] and we use the general measurement model
p
r
=
A/T
. The number of contending stations change abruptlyat the time instants 70, 150, 250, 350 and 450. The alarmthreshold of the CUSUM ﬁlter has been set to 7, with anormalized drift parameter equal to 0.75. We experimentallychose these settings as a tradeoff between false alarm rateand responsiveness. From the ﬁgure, we conﬁrm the ARMAﬁlter inaccuracy in both the cases of
p
r
smoothing factor
α
r
(1) = 0
.
95
and
α
r
(2) = 0
.
995
. Indeed, the Kalman ﬁlteris able to track the network load changes, by maintaining analmost constant
p
e
estimation, whose variance suddenly growsupon each CUSUM ﬁlter alarm.VI. C
ONCLUSIONS
This paper has discussed the problem of estimating theinterference conditions suffered in IEEE 802.11 networks. Foreach station of the network, we considered two different interference components: interference due to simultaneous attemptsto access the channel by other stations (MAC interference),and interference generated by external noise and overlappingnetworks (PHY interference).We propose a measurement methodology able to evaluatenot only the overall packet retransmission rate, but alsothe collision rate only. Each station, is enabled to performsuch measurements, by independently monitoring the transmissions eventually occurring within each slottime. Thesemeasurements are then used by a bidimensional extendedKalman ﬁlter, coupled with a change detection ﬁlter, for a joint MAC/PHY network state estimation. Numerical resultsshow that our estimator is able to accurately track the contention level experienced in the network, by distinguishingthe failure rates due to simultaneous channel accesses fromthe channel error corruptions. Moreover, a comparison withdifferent ARMA ﬁlters, show that our approach is muchmore suitable for runtime estimations in dynamic interferenceconditions, since a simple measurement smoothing performedwith ARMA ﬁlters can lead to biased interference estimatesdue to the nonlinear relationships between system state andmeasurements.R
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
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