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A Kalman Filter Approach for Distinguishing Channel and Collision Errors in IEEE 802.11 Networks

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A Kalman Filter Approach for Distinguishing Channel and Collision Errors in IEEE 802.11 Networks
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  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 opti-mizations 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 bi-dimensonal 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 em-ploying the Distributed Coordination Function (DCF). Basedon the well-known 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 hard-wired 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 per-packet 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 con-gestion 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 betweencollision-induced and channel-induced 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. 978-1-4244-2324-8/08/$25.00 © 2008 IEEE.  In this paper, we propose an efficient technique for dis-tinguishing and quantifying the MAC and PHY interferencesuffered in error-prone 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 error-free 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 de-tection 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 spec-ified 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 four-way 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 four-way technique can be found in[3].III. M EASUREMENT  M ODEL Our goal is the estimation of a bi-dimensional 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 chan-nel 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 con-stant 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. 978-1-4244-2324-8/08/$25.00 © 2008 IEEE.  all stations transmit to a common receiver, which locallyperceives constant channel error rate due to external interfer-ence. 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 mea-surement, 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 measure-ment 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 collision-induced and channel-induced 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 bi-dimensionalmeasurement  (  p  c ,p  r ) . Measurements can be smoothed at run-time by applying an auto-regressive filter. They can then beprocessed to produce a time-dependent 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 heterogeneoustime-varying variance of the measurements and knowledgeabout the updating laws for network interference. The defini-tion 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 sta-tions 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. 978-1-4244-2324-8/08/$25.00 © 2008 IEEE.  The relationships between measurements and state variablesare given by equation 2. For this measurement model, the lin-earized 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 SUM-mary) 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 adap-tively 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 ad-hoc 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 high-variance 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. 978-1-4244-2324-8/08/$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 pri-ori 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 condi-tions. 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 inter-ference 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 trans-missions eventually occurring within each slot-time. Thesemeasurements are then used by a bi-dimensional 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 con-tention 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 run-time estimations in dynamic interferenceconditions, since a simple measurement smoothing performedwith ARMA filters can lead to biased interference estimatesdue to the non-linear relationships between system state andmeasurements.R EFERENCES[1] IEEE Standard 802.11 - 1999; Wireless LAN Medium Access Control(MAC) and Physical Layer (PHY) Specifications; November 1999.[2] B. P. Crow, I. Widjaja, J. G. Kim, P. T. Sakai, “IEEE 802.11 WirelessLocal Area Networks”, IEEE Commun. magazine, September 1997, pp.116-126.[3] G. Bianchi, “Performance Analysis of the IEEE 802.11 DistributedCoordination Function”, IEEE Journal of Selected Areas in Commu-nication, March 2000.[4] Y.C. Tay, K.C. Chua, “A capacity analysis for the IEEE 802.11 MACprotocol”, ACM/Baltzer Wireless Networks Vol. 7, No. 2, March 2001,pp. 159-171.[5] IEEE 802.11e Supplement to Part 11: Wireless Medium Access Control(MAC) and Physical Layer Specification: Medium Access Control(MAC) Enhancements for Quality of Service (QoS)”, October 2005.[6] L. Gannoune, S. Robert, “Dynamic Tuning of the Contention WindowMinimum (CWmin) for Enhanced Service Differentiation in IEEE802.11 Wireless Ad-Hoc Networks ”, Proc. of IEEE PIMRC 2004,September 2004, Vol. 1, pp. 311-317.[7] C. Wang, Bo Li, Lemin Li, “A new collision resolution mechanismto enhance the performance of IEEE 802.11 DCF”, IEEE Trans.onVehicular Technology, July 2004, Vol. 53, n. 4, pp. 1235-1246.[8] L. Zhao, J. Zhang, K. Yang, H. Zhang, “Using Incompletely CooperativeGame Theory in Mobile Ad Hoc Networks”, Proc. of IEEE ICC 2007,June 2007, pp. 3401-3406.[9] M. Lacage, M. Hossein, T. Turletti, “IEEE 802.11 rate adaptation: apractical approach”, ACM MSWiM 2004, October 2004, pp. 126-134.[10] H. Kim, et al. “A simple congestion-resilient link adaptation algoritmfor IEEE 802.11 WLANs”, IEEE GLOBECOM 2006, November 2006,pp. 1-6.[11] J. Kim, et al, “CARA: Collision-Aware Rate Adaptation for IEEE 802.11WLANs”, IEEE INFOCOM 2006, April 2006, pp. 1 -11.[12] D. Malone, P. Clifford, D.J. Leith, “MAC Layer Channel QualityMeasurement in 802.11”, IEEE Communication Letters, February 2007,Vol.11, n.2, pp. 143-145.[13] G. Bianchi, I. Tinnirello, “Kalman filter estimation of the number of competing terminals in an IEEE 802.11 network”, IEEE INFOCOM2003, March-April 2003, Vol. 2, pp. 844-652.[14] F. Gustafsson, “Adaptive filtering and change detection”, John Wiley &Sons, Ltd, 2000. 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. 978-1-4244-2324-8/08/$25.00 © 2008 IEEE.
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