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Modeling and optimizing IEEE 802.11 DCF forlong-distance links

Javier Simo-Reigadas, Andres Martınez-Fernandez, Javier Ramos-Lopez, and Joaquın Seoane-Pascual

Abstract—Most rural areas in developing countries are isolated due to the lack of appropriate low-cost communication technologies.Previous experiences have shown that IEEE 802.11 can be used for the deployment of large static mesh networks with only minorchanges to the MAC layer that enable WiFi transceivers to work properly even for very long distances (up to 100 Km in point to pointlinks, and almost 40 Km in point to multipoint setups). However, the impact of distance on performance of such long links has not beendeeply analysed. In addition, previous analytical models of IEEE 802.11 DCF can not be applied because they implicitly assume thatthe propagation time can be neglected. This paper formally studies the impact of the distance on the behaviour of IEEE 802.11 DCF,and presents an analytical model of IEEE 802.11 DCF that accounts for distances correctly. The model is validated with simulations andwithin a controlled experimental framework, based on wireless channel emulation. Finally, we propose adjustments for ACKTimeout,CTSTimeout, SlotT ime, and CWmin parameters that improve significantly the performance of DCF over long distances.

Index Terms—IEEE 802.11 DCF, wireless wide-area networks, developing countries.

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1 INTRODUCTION

THERE are extensive rural areas in the world wherepeople have no access at all to communication net-

works. This is especially true in rural areas of developingcountries, where the population is poor and dispersed,and telecom operators work with high costs of deploy-ment and low returns. Some analysts have underlinedthe strategical role that IEEE 802.11 [1], [2], [3], [4] andVoIP [5], [6] might play for setting up low-cost networksin such scenarios. The IEEE 802.11 standard and itsCSMA/CA MAC protocol were specifically conceivedfor wireless local area networks with maximum dis-tances of hundreds of meters among contiguous stations.Other TDMA-based standards, like IEEE 802.16-2004,are better options for metropolitan or rural broadbandwireless networks, at least from a technical point of view.However, 802.11 at present is the only affordable solutionin many rural scenarios within developing countries.Additionally experience has proved that long-distanceWiFi links are possible with some modification of theMAC layer [7], [8], [9], [10]. This experience suggeststhat a combination of long-distance point-to-point WiFilinks and medium-distance point-to-multipoint infras-tructures enables the deployment of low-cost broadbandwireless networks in rural areas. Now there is even agenerally accepted name for this kind of networks: WiLD(WiFi over Long Distances).

• Javier Simo-Reigadas, Andres Martınez-Fernandez, and Javier Ramos-Lopez are with the Department of Signal Theory and Communications,Universidad Rey Juan Carlos, Camino del Molino s/n, 28943 Fuenlabrada,Spain. E-mail: {javier.simo,andres.martinez,javier.ramos}@urjc.es.

• Joaquın Seoane-Pascual is with the Department of Telematics Engineering,Universidad Politecnica de Madrid, Ciudad Universitaria s/n, 28040Madrid, Spain. E-Mail: joaquin@dit.upm.es.

This work has been partially supported by Research Project TEC2007-68096-C02/TCM from Spanish Government.

In the last two years, several scientific publicationshave partially studied this problem, but only Leunget al. [11] tried to analyze the impact of distance onthe behavior of IEEE 802.11 DCF (Distributed Coordi-nation Function). However, their analysis is limited tothe feasibility of 802.11 as an alternative for cellularnetworks. Some authors have assumed implicitly thata CSMA/CA-based MAC is useless for long distances,and have proposed its replacement by a TDMA-basedMAC implemented on top of the IEEE 802.11 PHY [12],[13], though a previous try to analyze and optimize thestandard MAC has not been addressed. Our group hasalready demonstrated experimentally [14] that tuningcertain parameters of CSMA/CA may yield equivalentperformance to that of replacing the protocol. Thesemodifications are easier, cheaper, and compatible withlegacy systems. Additionally, many publications proposeanalytical models of IEEE 802.11 DCF ( [15], [16], [17],[18], [19] among others), but all of them implicitlyassume that stations are close to each other. Hence,these models can not be used when stations are severalkilometers apart from each other, as later demonstratedin this paper.

Firstly, we present a formal study of how distancebetween stations affects performance, exploring andidentifying causes. Then, a new analytical model ofIEEE 802.11 DCF is proposed which incorporates adistance dependency as a fundamental variable. Themodel has been solved numerically and the results havebeen compared with experimental long-distance point-to-point links, reproduced under controlled conditionsin our laboratory. Several tests have also been madeon a real rural WiFi network in Cuzco (Peru) [9] inorder to provide a qualitative validation under realisticconditions. The results show that the proposed modelcaptures correctly the behavior of long-distance links.

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Different network simulators have also been used inorder to perform a quantitative validation of the point-to-multipoint case, but we have found that none ofthem capture correctly the effect of the distance on theperformance of CSMA/CA, as explained later.

Secondly, the proposed model is used to explain indetail the problems found in real large WiFi networksand to propose the adjustments that optimize theirbehaviour. Beyond the very basic adjustment of theACKTimeout and CTSTimeout parameters, it is alsoknown that the slot time must be adapted to opti-mize the performance of DCF over long distances1. Wedemonstrate how the performance may be optimized byadjusting either the slot time or the CWmin parameter.With the proposed optimization, IEEE 802.11 DCF isshown to perform well in point to point links as longas 100 Km, or in point to multipoint links of almost 40Km with custom hardware.

The paper is organized as follows. Section II explainsthe main characteristics of WiLD networks, and SectionIII briefly introduces the operation of IEEE 802.11 DCF.Section IV examines the maximum allowed distancebetween stations as supported by the standards. Then,we consider the impact on performance as station sep-aration is extended beyond the maximum distance, andwe identify the cause of the performance degradation.Section V proposes an analytical model of DCF that cor-rectly accounts for the distance. Section VI explains whatmethods and materials have been used for validatingthe model, and Section VII analyses the results obtainedfrom the validation. Section VIII proposes several opti-mization rules for DCF, and finally, Section IX containsthe conclusions and future works.

2 RELEVANT CHARACTERISTICS OF WILDNETWORKS

There are quite a few well known examples of IEEE802.11-based networks in rural areas within developingcountries. Experience shows that this technology is oftenthe only one viable in poor remote areas. Some repre-sentative examples are [7], [8], [9], [10]. An impressivedeployment [20] is the linear network that connectsIquitos in the Peruvian Amazon with several rural healthcenters, covering a 500 km stretch along the Napo Riverup to the country’s northern border in 17 hops. Manyother examples are not mentioned in scientific papersyet, such as the recent linear network connecting ahospital to the capital city of Malawi along 162 km inthree hops [21].

These WiLD networks usually have a core network inwhich nodes are interconnected though long point-to-point (PtP) links, and access segments in which access

1. The MadWiFi driver for Linux allows the tuning of three pa-rameters: ACKTimeout, CTSTimeout, and the slot time. The athctrlcommand accepts a distance as input parameter and modifies themaccordingly. However, the values given to slot time are not necessarilyoptimal, as we will demonstrate in this paper. One can also assign avalue directly to any of those parameters within the proc filesystem.

points connected to the core network give access to endusers through mid-distance point-to-multipoint (PtMP)links. WiFi systems usually have two or more wire-less interfaces connected to different external antennas.Those systems replacing the standard MAC protocol[10] tend to avoid interferences among the connectedantennas by coordinating transmissions and receptionsvia different interfaces in the same router. Those usingthe standard CSMA/CA [20] have to exploit severaltechniques to avoid interferences, for example, the useof non-overlapping channels together with a sufficientvertical separation between antennas, and orthogonalpolarizations.

Regardless of the details of the approach, the finalresult is a static mesh IP network in which, from theMAC point of view, each PtP or PtMP link is a separateBSS (Basic Service Set) to be analyzed and optimized asan independent network.

3 A BRIEF INTRODUCTION TO IEEE 802.11DCFThe IEEE 802.11 MAC layer defines two coordinatingfunctions: DCF and PCF (Point Coordination Function),but only the first one has been widely implementedin real systems. DCF uses a Carrier Sense MultipleAccess protocol with Collision Avoidance (CSMA/CA)that considers all stations as peers (client stations oraccess points).

The following constant parameters form the basis ofDCF:

• Slot time (σ): quantum for defining the contentionwindow time unit and for defining other parame-ters.

• SIFS (Short Inter Frame Space): Time that separatesthe end of the reception of a frame and the start ofthe transmission of its ACK.

• DIFS (Distributed Inter Frame Space): A stationneeds to sense the channel idle during DIFS secondsbefore scheduling a new transmission or reactivat-ing the contention window countdown if it wasinterrupted due to another station’s transmission.Its duration depends on the slot time: DIFS =2σ + SIFS.

• EIFS (Extended Inter Frame Space): ReplacesDIFS when the last transmission that kept thechannel busy was corrupted.

A station intending to transmit has to first sensethe channel as idle during a DIFS time window. Then,it starts a contention period by calculating a randomnumber of time slots to wait and starts a countdown.The duration of each slot depends on the activity of thechannel, this is, idle slots have a fixed duration σ, butthe countdown freezes when the channel is sensed to bebusy. This produces a slot that contains a transmissionor a collision followed by DIFS or EIFS. When thecountdown finishes, the station transmits and starts atimer (ACKTimeout) to wait for an ACK that confirms

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the correct reception. If the ACK is received, the trans-mission is considered as successful, and the station isready to restart the whole process again with anotherframe. If ACKTimeout elapses and no ACK is received,a retransmission is started, following the same processuntil the maximum retransmission limit is reached. Thenumber of slots in the contention window is a uniformrandom variable obtained from the distribution [0, CWi].The range of the distribution, CWi + 1, grows exponen-tially each time the transmission is unsuccessful, startingat CWmin + 1 and ending at CWmax + 1.

The 802.11 MAC is strongly based in the carrier sense,but has a mechanism to deal with hidden nodes calledRTS/CTS (Request to Send / Clear to Send). Whenactivated, a station that is going to transmit a data framelonger than RTSThreshold sends firstly a very shortRTS frame (only 14 bytes). If the receiver gets the RTSframe correctly, it sends back a CTS frame, giving thefirst station the right to transmit the data frame. Boththe RTS and the CTS frames contain the informationconcerning the total foreseen duration of the transaction.This includes all the operations to the point where thechannel will again be definitely idle. Stations listeningto either the RTS or the CTS frame may initialize aninternal timer called NAV (Network Allocation Vector)that causes the same effect to the MAC as the physicalcarrier detection.

Other details of the MAC operation can be found inthe standards [1], [2], [3], and also [22], [23], [24] arerecommended for a better understanding.

4 DISTANCE IMPACTS ON IEEE 802.11 PER-FORMANCE

The IEEE 802.11 standard is designed to be used overshort distances. In this section, we briefly analyze theconstraints limiting the maximum distance at whichIEEE 802.11 may be used with good performance. Fora more extended version of the analysis made in thissection, see [25].

4.1 Limitations Imposed by the PHY

Any radio link is subject to a link budget: The signalreceived at one end is equal to the power transmittedat the other end plus the gain of the antennas at bothends minus the attenuation caused by the path loss andthe cables and connectors. The radio link is viable onlyif the received signal power level is greater than thereceiver’s sensitivity. In fact, a security margin is neededbecause of the channel variability caused by the weather,the presence of mobile objects, and other factors.

IEEE 802.11 works at ISM non-licensed bands thatrestrict the maximum transmitted power and the an-tenna gain. IEEE 802.11, 802.11b and 802.11g work inthe 2.4GHz band, while IEEE 802.11a works in 5GHzbands (the specific sub-band depends on the regulatorydomain). The regulations in the USA, Japan, and Europe

are very different, and countries in other regions may fol-low different rules, but many developing countries haveadopted the FCC (Federal Communications Commission)criteria. FCC permits up to 30dBm of transmitting powerwith omnidirectional antennas of gain up to 6dBi foromnidirectional communications. Directional links mayincrease the antenna gain with a penalty of 1dBm forevery 1dBi over 23dBi for the 5GHz band, or 1dBm forevery 3dBi over 6dBi for the 2.4GHz band.

The transmitting power restriction is a limiting factorin terms of distance. We have calculated approximatelythe distances that can be achieved with typical values oftransmitted power, sensitivity, antenna gain, and cableattenuation2. The propagation loss has to be estimatedfor each specific environment, as irregular terrains condi-tion has a considerable effect on the propagation. How-ever, a rough estimation of achievable distances obtainedby using the free space model is presented in Fig. 1.A stability margin of 20dB has been preserved overthe sensitivity for calculating the minimum acceptablereceived power level. We have calculated the maximumachievable distance for PtP links (both ends with direc-tional antennas), PtMP links (one end directional, theother end omnidirectional), and mesh networks withomnidirectional antennas in all nodes.

Fig. 1. Achievable distances for different bit rates underFCC 15.247 regulation for the 2.4 GHz band, dependingon the gain of antennas at both ends.

The coverage within the 5GHz band is similar becausethe propagation losses are higher at those frequencies,but better antenna gains compensate for this effect. Inreal networks, such as the one presented in [9], the linkbudgets correspond with these approximations. We cansee that very long links are feasible while still respectingthe power restrictions, specially with the most robust(slowest) modulations. Only concerning the PHY, PtPlinks as long as 140 Km are possible. In the case ofPtMP setups, a radius up to 35 Km is achievable. Mesh

2. Specifications taken from the datasheets of Ubiquity XR2 miniPCIcards, Hyperlink 12dBi dipole antennas and 24dBi grid antennas,normal u.FL-to-N pigtails and 3GHz outdoor coaxial cables

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networks in which nodes have omnidirectional antennaswould admit maximum distances between contiguousnodes of 9 Km or less. Beyond the power limitationsand the derived LOS (line of sight) requirement, the PHYdoes not contain any other restrictive aspects regardingthe distance.

4.2 MAC Layer Imposed BoundsThe description of DCF in the IEEE 802.11 standardfamily [1], [2], [3], [4] does not mention distances ordistance limits, but it accounts for the distance implicitlywherever the propagation time is considered. However,the standard assumes that the propagation time itself(defined by the AirPropagationTime variable) has a max-imum value of 1µs. Also the slot time, which is theonly MAC parameter that accounts for the propagationtime at a higher level, is also a PHY-dependent constant.Other parameters depend in turn on SlotTime (ACK-Timeout, DIFS). In other words, the standard expectsDCF to be used within a range of as much as somehundreds of meters. The original standards [1], [2] didnot define accurately the meaning of the AirPropaga-tionTime variable, but the last revision of the standard[4] states precisely that it is “twice the propagation time(in microseconds) for a signal to cross the maximumdistance between the most distant allowable STAs thatare slot synchronized”. It must be highlighted that thevirtual carrier mechanism neglects the propagation time,which causes the NAV to be inaccurate when distancesare longer than expected. Hence, the following elementsneed to be studied: (1) ACKtimeout & CTSTimeout, (2)the slot time, (3) the computation of the NAV for thevirtual carrier detection, (4) the Coverage Class, and (5)the DIFS. Each of these key elements are considered next.

4.2.1 ACKTimeout & CTSTimeoutIn basic mode, when ACKTimeout is too short for a givendistance, ACK frames arrive systematically too late atthe waiting station. If this happens, all ACK frames arediscarded and the standard indicates that every dataframe is retransmitted ShortRetryLimit times before beingdropped (default is 7 retransmissions). This behavior isillustrated in Fig. 2. If this happens, several copies ofeach packet arrive to destination correctly even if thetransmitter does not know it. The link works becausedata frames are in fact being received at the destination,but it exhibits a very poor performance.

In RTS/CTS mode, the sender node waits for a du-ration of the CTStimeout interval for the returned CTSframes, which does not arrive due to propagation delays.The cycle is repeated up to LongRetryLimit times (defaultvalue is 4 times). In this case the link does not workbecause data frames never pass through.

The value of the ACKTimeout parameter was notclearly established in the text of the original stan-dard. Some authors [2], [23]) have interpreted thatthe MAC formal description fixes the value of the

Fig. 2. Systematic loss of ACK frames due to a distanceexceeding the limit imposed by the ACKTimeout value.

ACKTimeout = SIFS + σSTD +ACK + PLCP , whereσSTD = Standard SlotT ime, PLCP is the total durationof the preamble plus the physical layer header, and ACKis the duration of the ACK MAC frame. Leung et al. [11]affirm that the value of ACKTimeout is not given in thestandard. However, the last revision of the standard [4]clearly states that

ACKTimeout = SIFS + σSTD + PLCP (1)

According to the standard, an aPHY-RXSTART-Indication has to be passed to the MAC layer beforethe ACKTimeout expires, or the ACK will be discarded.The SIFS time is consumed at the receiver side, andthe PLCP time is required for the transmitter’s PHY topass the aPHY-RX-START-Indication after the first bit ofthe ACK preamble is received. Hence, the slot time isin the sum because conceptually it contains the round-trip propagation time and enough time for the CCA(Clear Channel Assessment) mechanism. The round-trippropagation time is expected by the standard to last asmuch as 1µs (only enough for 150 m between stations),but the CCA leaves a minimum margin of 5µs in theslot time (enough for 750 m). For implementations of theMAC yielding a faster CCA, the time left for propagationhas to be longer.

For distances longer than 150m, we guarantee thatACKTimeout has a sufficient value by defining it as

ACKTimeout = SIFS + σSTD + 2δMAX + PLCP (2)

for long-distance 802.11 links, where δMAX is the maxi-mum propagation time in the BSS. As seen above, it hasbeen unclear for years what the value of ACKTimeoutshould be. We have checked real hardware in a con-trolled environment to determine how real cards imple-ment the ACKTimeout. A hardware channel emulatorElektrobit PropSim C8 was used for this purpose (Figure7). Two embedded computers running Voyage Linuxwith IEEE 802.11 cards were introduced in RF shieldedboxes and connected to each other through the emu-lator. We compared cards based on the two dominantchipsets for long range WiFi installations: Intersil Prism2.5 and Atheros AR5212. For cards based on the firstchipset, ACKTimeout is internally fixed and does notmatch the standard value, permitting links as long as

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23,5 Km for 2 Mbps bit rate. On the other hand, cardsbased on the Atheros chipset permit the adjustment ofthe ACKTimeout parameter. We were able to adjustACKTimeout to permit links as long as 105 Km. Highervalues of ACKTimeout were not possible due to hard-ware constraints 3.ACKTimeout tests were also run in two network

simulators: OPNET Modeler 11.5 and NS-2.30. Fig. 3represents an NS-2 simulation showing the throughputbetween two stations decreasing slowly as the distanceincreases, and that there is a sharp decrease when thedistance passes the ACKTimeout limit. The same behav-ior has been found in all hardware devices and softwaresimulators, but the sharp decrease occurs at differentdistances in all cases. At 2 Mbps of bitrate, the defaultmaximum distance was 5.8 Km for Atheros chipsets,23.5 Km for Prism 2.5 chipsets (fixed), 600m for NS-2(can be changed in the code), and 45 Km for OPNETsimulator (fixed). For further experiments, we developeda patch for NS-2.30 that makes it possible to set theDSSS MaxPropagationDelay value at simulation time(which in turn is used internally to set the ACKTimeout)[26].

Fig. 3. Rate versus distance for an FTP file transfer sim-ulated with NS-2.30 with DSSSMaxPropagationDelay =400µs.

For the rest of this paper, ACKTimeout is alwayssupposed to be modified as proposed in Equation 2.

4.2.2 The slot timeThe slot time is a PHY-dependent constant. For example,it is 20µs for 802.11b and 9µs for 802.11a and pure802.11g networks. These values have been estimated ac-counting for the time required for the CCA mechanism,the Rx/Tx turnaround time, the propagation time, and

3. MadWifi permits us to adjust ACKTimeout directly through theLinux proc-filesystem, or indirectly through the athctrl command.However, that number is stored in a hardware register that limits itsvalue to 744 µs for 802.11b, to 372 µs for 802.11g and to 409 µs for802.11a. Those values limit the range at the MAC level to 105, 49 and55 Km respectively.

the MAC processing delay. Some cards actually allow toadjust the slot time, but the basic standard [1] does notallow users to do so. In the following, we analyse theimpact of keeping the slot time at its standard value forany distance.

The principle underlying the slot time is that twostations intending to transmit will collide if, and onlyif, they start the transmission in the same time slot. Ifboth transmissions are scheduled for different slots, thesecond transmitting station will have the time to detectthe first transmission and will freeze and backoff, thusavoiding the collision. Obviously, this behaviour requiresthat the propagation time plus the CCA time is smallerthan σ.

Let us define the Vulnerability Interval (V I) betweentwo stations as the time interval during which the frametransmitted by one station could collide with the frametransmitted by another one at a given time. Let us definealso δQD = δDQ as the propagation delay between sta-tions EQ and ED. Note that a transmission is consideredsuccessful by the transmitter if it receives a correct ACKfrom the receiver. Let us define CCA as the time requiredby the receiver to perform the CCA function.

Consider the following scenario with three stationsEQ, ED and EX mutually visible. Station EQ transmitsa packet to ED, who answers with the correspondingACK. Station EX will try to transmit at the same time,possibly producing a collision. In general, if EQ trans-mits at time instant t, EX will only produce a collision ifit starts its transmission during the vulnerability intervalV IQ,X = (t− δQ,X −CCA, t+ δQ,X +CCA). Otherwise,either EQ does not transmit since it has detected atransmission from EX , or EX does not transmit sinceit has detected a transmission from EQ. However, theimpact on the performance will depend on the numberof slots starting in this V IQ,X interval. We define thenormalized vulnerability interval (NV I = V I

σ ), whosevalue depends on the distance. Let us consider thefollowing cases, represented in Fig. 4:

1) EX is very close to EQ so that δQ,X +CCA < σ2 . The

collision takes place only if EX starts the transmis-sion in the same slot as EQ, so NV IQ,X = 1. Casesa) and b) in Fig. 4 both match with this conditionand differ in the importance of the propagationtime compared to σ.

2) EX is far from EQ so that δQ,X +CCA > σ2 . Two or

more slots can start now during the V IQ,X . If EX

begins a transmission in any of them, a collisionwill take place. Note that the Bianchi model [23] orothers derived from it are no longer valid in thiscase, so we can establish a constraint of the form2δQ,X +2 ·CCA ≤ σ for these models. For 802.11b,where the slot time is 20µs, this constraint maybe approximately between 750 m and 2,5 Km, de-pending on the effective CCA time. For 802.11a/gthose values are 9µs and 750 m - 1.1 Km, respec-tively. The CCA time will be neglected in long-distance analysis because, as the distance grows,

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Fig. 4. Behaviour of the MAC in two contending stationsdepending on the distances between them.

δQX � CCA. Under these conditions, we can writeNV IQ,X =

2δQ,X

σ . The non-integer decimal part ofNV I corresponds to the probability that an extraslot beginning in the vulnerability interval, i.e.,the number of slots beginning in the vulnerabilityinterval is at least int

(2δQ,X

σ

)and the decimal part

of the fraction is the probability there is one moreslot or int

(2δQ,X

σ

)+ 1 slots beginning in V IQ,X .

If the slot time is not considered as constant, then theV IQ,X can always be minimized.

4.2.3 DIFSThe different inter-frame spaces are defined to assign dif-ferent priorities to ACK frames, PCF control frames andnormal DCF data frames. In a DCF network, the mainrole of DIFS is to prevent stations waiting for the channelfrom colliding with ACK frames. As DIFS = SIFS+2σ,Leung et al. [11] interpret that this marks a distancelimit corresponding to the round-trip propagation timeof approximately 2σ. In fact, the distance limit would belonger because the DurationID field in the data frameheader, which is used to set the NAV for the virtualcarrier sense mechanism, also accounts for the expected

ACK frame. However, the adaptation of the slot time,which is contained twice in the DIFS, would adapt thislimit to a longer distance if required.

4.2.4 NAV ComputationUntil now, it has been assumed that all the stations areable to listen to the others. However, this is unlikelyto happen where long distances and directive antennasare considered. When considering hidden nodes, thestandard offers the RTS/CTS mode, so that nodes thatcannot listen to any of the stations participating in a com-munication may know how long the channel is goingto be busy by using the virtual carrier detection, whichin turn is based on the information in the DurationIDfield contained either in the RTS or in the CTS packet.The standard accurately defines the way this time iscomputed, but it does not take the propagation time intoconsideration which produces an anomalous behaviourwhen long distance links are used. The magnitude ofthose inaccuracies depends greatly on the distances andvisibilities among the three stations involved [25].

If propagation times are long, stations receiving theRTS will receive the data frame much later than ex-pected, but they would not transmit during that timein a real case because the channel is still reserved for thetransmission of the data frame and the following ACK.The NAV is updated upon data frame reception, andthen the situation is the one presented in the previouspoint. On the other hand, stations receiving the CTS butnot the RTS could produce a collision until they receivethe CTS, but once they receive it, they will receive theACK correctly unless the round-trip propagation time islonger than ACK + DIFS, which is unlikely in a realsituation. If visibility between nodes is not symmetrical,other more complex situations could occur.

As a result, the probability of collision with hiddennodes increases even if RTS/CTS is used, making thismode useless. If the slot time is adapted to includethe round-trip propagation time, then DIFS includestwice the round-trip propagation time and RTS/CTStransactions are partially protected against collision fromhidden nodes, with the only adverse effect of possibleearly accesses to the channel by those nodes after theACK.

4.2.5 Coverage ClassThe recent revision of the standard [4] explicitly con-siders that 802.11 may be used for metropolitan areanetworks and introduces a regulatory triplet, consideringaspects such as the transmission power limit and thecoverage class. It is stated that the slot time may bealtered through a Coverage Class parameter. If this op-tional feature is activated, the Coverage Class parametergets an integer value in the range [0,31] and then thestandard slot time gets increased in 3 · CoverageClassmicroseconds.This permits us to adapt DCF to BSS witha maximum radius of 15 Km, as it changes directly theslot time as required for minimizing the vulnerability

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interval, and changes indirectly the ACKTimeout. Longerdistances are not supported by Coverage Class feature.

4.3 The Distance in Previous DCF Analytical ModelsA number of papers propose analytical models of IEEE802.11 DCF, most of them based on the seminal paper byBianchi [16] of a model using a bi-dimensional Markovchain. The model was based on some strong simplifi-cations, such as the limited number of retransmissions,the constant transmission probability and conditionalcollision probability for all stations and all stages, andthe complete visibility among stations. For the rest, themodel captured all the complexity of DCF, hence givingvery good results. After this model, many other authorspublished their own analysis on improving or extendingBianchi’s bi-dimensional Markov chain. In [18], [27],[28], the authors took into account the finite number ofretransmissions. Other models included variable packetsizes [29], or introduced the effects of non-ideal wirelesschannels [19], among other extensions. In 2005, Bianchiand Tinnirello proposed an alternative model only basedon conditional probability, incorporating the correctionsand contributions from other authors to Bianchi’s model[17].

There are also a number of authors that have proposedalternative models that are not based on Bianchi’s ap-proach. None of the previous models can be applied tothe case of long distances among stations, but [17] hassome valuable aspects that have to be taken into accountin this work.

Bianchi and Tinnirello [17] defined a model slot asthe interval between two consecutive decrements ofthe contention window in a non-transmitting station.A station with counter at value b at a given slot willcertainly transmit b slots later. The slot duration dependson what the slot contains, and hence, it can be empty,contain a collision, or contain one or several successfultransmissions. There is a non-null probability that astation having transmitted a frame successfully gets acontention window of zero slots for the next transmis-sion and wins the channel again before the other stationsdecrement their counters. Due to this behaviour, Bianchiand Tinnirello calculate effective values for some param-eters accounting for the probability that a slot containsmore than one successful transmission, as follows:

E[P ]′ = E[P ] +∞∑k=1

Bk0E[P ] =

E[P ]

1−B0(3)

where E[P ]′ is the effective average packet size, P is thepacket size, and B0 = 1

CWmin+1 . The average durationof a successful transmission and that of a collision areredefined in the same way:

T ′s = Ts +

∞∑k=1

Bk0Ts =

Ts

1−B0(4)

T ′c = Tc + σ (5)

These equations will be used later in this paper. Thedefinition of the contention window in [17] is mathe-matically different from previous models. Now, Wi =min(2i(CWmin + 1) − 1, CWmax) for i = (1, ..., R), butW0 = CWmin − 1 because of the new definition of amodel slot.

In these terms, Bianchi and Tinnirello use conditionalprobabilities to obtain a set of two equations with twounknowns. The unknowns are the transmission proba-bility at any slot (τ ) and the conditional collisional prob-ability p for a transmission for a starting transmission,yielding the following expressions:

τ =1

1 + 1−p1−pR+1

∑Ri=0 p

i(1 + CWi

2

) (6)

p = 1− (1− τ)n−1 (7)

Equation 6 represents the internal behaviour of DCFfor any given station, while Equation 7 represents the in-teraction among stations. It is considered that all stationshave the same probabilities τ and p and have the sameperception of the network. It is obvious that Equation 6is true for each station, no matter what the inter-stationdistances are, while Equation 7 assumes a symmetry thatis not necessarily true for wide area networks with morethan two nodes.

Equation 7 also assumes that two stations only collidewhen transmitting in the same slot, which is not truefor long distances, as seen in the previous section. Forany given station EQ, the transmission probability ina given slot is τ , so (1 − τ) is the probability of thatstation not transmitting in any given slot, (1−τ)n−1 is theprobability of all other (n− 1) stations not transmittingin the same given slot (given that all have the sametransmission probability τ , which is not necessarily true),and 1−(1−τ)n−1 would be the probability of at least oneof them transmitting at a given slot. As p is defined as theconditional probability of colliding once a packet is goingto be transmitted in a given slot, Equation 7 impliesthat two transmissions can collide only if they start inthe same slot, which is only true for short propagationtimes. As a consequence, [17] provides a part of a DCFanalytical model that is independent of distances, and anew analysis is required in order to complete that model.

5 A NEW ANALYTICAL MODEL OF IEEE802.11 DCF FOR LONG DISTANCES

In this section we develop an analytical model of IEEE802.11 DCF that takes into account intrinsically the prop-agation times among stations.

5.1 Assumptions

The following assumptions are made:H1.- No hidden nodes will be considered. In real long-

distance WiFi networks, there are hidden nodes

8

in almost all cases, so this could seem a lim-iting assumption. However, a significant part ofthe performance problems of these networks arepresent even if there are not any hidden nodes,and may be better studied and explained with thisassumption. The extreme complexity introduced byhidden nodes will be analysed in a future work.

H2.- The channel is ideal and frames are always ac-knowledged unless they collide. Also, ideal chan-nels do not exist, but real channels may havealmost ideal behaviour, if the received signal isstrong enough (which may be a design criteria).Dong and Varaiya [19], as well as other authors,show how the BER (Bit Error Rate) can be easilytaken into account if necessary just by redefiningp as the probability of a packet that is going to betransmitted in a given slot to be lost, either due toa collision or due to transmission errors.

H3.- Every station always has a frame that is ready fortransmission. Also, the saturation condition is notreal, but gives a worst-case condition.

H4.- The conditional collision probability pQ is constantand stage independent for station EQ. This as-sumption is known to be good enough becauseit is common in analytical models and does notdepend on the distances at all. On the other hand,we have also studied analytically the consequencesof eliminating this assumption, and in this case, themodel quickly becomes unmanageable.

H5.- The probability that a transmission starts and fin-ishes in any single vulnerability interval V IQDX

of the network can be neglected. In other words,the shortest possible transmission is longer than thelongest vulnerability interval in the network.

H6.- Distances among stations can be as long as 100Km. ACKTimeout is supposed to be adjusted asrequired for each distance.

5.2 Model for n Active Stations Without HiddenNodesLet us consider n stations E1, ..., En with full visibilityamong them. Any two stations EQ and ED are separateddQD meters, and the propagation time between them isδQD = δDQ =

dDQ

c .For station EQ, pQ is the conditional collision proba-

bility, and τQ is the transmission probability at any slot.Each station EQ sees the network differently, thus havingits own probabilities τQ and pQ and perceiving time slotsat very different instants. Hence, for the n stations wehave 2n different variables (p1, ..., pn, τ1, ..., τn).

As explained before, Equation 6 is true for each stationas long as H1, H2, H3, and H4 are satisfied. So, we maydefine a set of n equations as (8) with 2n unknowns forstations EQ, where Q ∈ (1, ..., n):

τQ =1

1 +1−pQ

1−pR+1Q

∑Ri=0 p

iQ

(1 + Wi

2

) (8)

Fig. 5. Model of DCF with a bi-dimensional Markov chaincompatible with Bianchi and Tinnirello’s model.

where Wi = min(2i(CWmin + 1), CWmax + 1) for i = (1,..., R), and W0 = CWmin.

We need n additional equations to complete a systemwith the 2n unknowns. The effect of the distance mustbe considered in depth for this purpose. Let us defineξQDX as the probability that station EX collides with atransmission from EQ to ED. Such collision will happenif EX starts a transmission during the correspondingvulnerability interval V IQDX . Let us also define µQD

as the probability that a transmission from station EQ

is destined for ED. In the particular case that all possi-ble destinations have always the same probability, thenµQD = 1

n−1 .The probability that a transmission from EQ collides

may be expressed as

pQ =

n∑D=1,D 6=Q

µQD

1−n∏

X=1,X 6=Q

(1− ξQDX)

(9)

To obtain a convenient expression for ξQDX , we needto calculate the steady state probabilities of a station tobe in any model slot as defined previously. Those prob-abilities can be calculated by defining a bi-dimensionalMarkov chain for each station EQ that must be com-patible with the assumptions and definitions given forthe first part of the model, and must share the samedefinition of a slot and consider the same definition ofWi, i ∈ [0, R]. Such a Markov chain is shown in Fig. 5,and is almost identical to the Markov chain proposedby Chatzimisios et al. in [18]. Equation (8) can also bederived from it.

This chain models the bi-dimensional discrete-timestochastic process bQ[n], sQ[n] where bQ[n] and sQ[n]represent the backoff timer and the backoff stage respec-tively for station EQ at slot n. Let

9

bQ,i,k = limn→∞

P{s[n] = i, b[n] = k} (10)

be the stationary distribution of the Markov chain, wherei ∈ [0, R], and k ∈ [0,Wi−1]. When station EX is at stagei (ith retransmission) and state j (it will transmit withinj slots), it is said to be at eX,i,j .

There are two minor differences between this Markovchain and the one in [18]:

• The conditional probability of collision is now spe-cific for each station, and accordingly, the nomen-clature has changed using pQ instead of p.

• The fist stage now has W0 = CWmin as explainedabove, instead of W0 = CWmin +1 as for Chatzimi-sios et al.

However, similar relationships as in [18] may be ob-tained:

bQ,i,0 = piQbQ,0,0 , i ∈ [0, R] (11)

bQ,i,k =Wi − k

WibQ,i,0 , i ∈ [0, R], k ∈ [0,Wi − 1] (12)

bQ,0,0 = τQ1− pQ

1− pR+1Q

(13)

Let us define the events {AQ,D,X,j} ={EX transits from eX,i,j to eX,i,0 during V IQDX} and{BX,j} = {EX receives nothing in j consecutive slots}.The first could also be defined as {AQ,D,X,j} ={V IQDX contains at least j + 1 starting slots of EX}.

The calculation of ξQDX is strongly based on assump-tion H5. We will consider that EX can only collidewith EQ if it does not receive another frame during thevulnerability interval and before its transmission. Then,ξQDX could be calculated as the sum of all bX,i,j , eachmultiplied by the probability for EX to get from eX,i,j

to transmission state before a time V IQDX elapses. Thisis expressed as

ξQDX =R∑i=0

CWi∑j=0

bX,i,jP{AQ,D,X,j}

= τX +R∑i=0

CWi∑j=1

bX,i,jP{AQ,D,X,j} (14)

If distances are short and stations only collide whenthey transmit in the same slot, the only non-null termsare for j = 0, and then ξQDX = τX because τX =∑R

i=0 bX,i,0. Also the saturation condition implies forshort distances that µXQ = 1

n−1 ,∀EX , EQ. In this case, itis straight forward to see that (9) reduces to (7). Applyingthe Bayes’ Theorem

P{AQ,D,X,j} =P{AQ,D,X,j |BX,j} · P{BX,j}

P{BX,j |AQ,D,X,j}(15)

and considering that P{BX,j |AQ,D,X,j} = 1 due toassumption H5, we may have ξQDX by calculatingP{AQ,D,X,j |BX,j} and P{BX,j}.

The first of those probabilities will be called KQDX,j =P{AQ,D,X,j |BX,j} in the next equations, and is definedby

KQDX,j =

1 int(NV IQDX) > j

(NV IQDX − j) int(NV IQDX) = j

0 int(NV IQDX) < j

(16)

The effect of multiplying a term by KQDX,j has theeffect of preserving it if the vulnerability interval con-tains more than j complete empty slots, to annulate it ifthe vulnerability interval never contains j starting slots,and to multiply the term by the probability of containingexactly j starting slots in the intermediate case.

Regarding the second probability defined above, ne-glecting the previous history of frame exchanges in thenetwork, P{BX,j} is the product of two independentprobabilities:

1) Probability that stations different from EX and EQ

do not transmit during a time jσ, so that all of themmust still transit through j slots before transmitting.

2) Probability that EX gets a contention windowhigher than j, no matter in what stage it is.

Based on this, we define

P{BX,j} =

(1− µXQ

R∑a=0

Wa−1∑b=0

min(

j

Wa, 1)bX,a,b

)·

n∏y=1,y 6=X,Q

R∑l=0

Wl−1∑m=j

by,l,m (17)

Replacing in (15) and then in (14), we obtain (18).We can replace variables by,l,m in (18) using their

definition in (13), and then we have (19) that representsn equations ∀Q ∈ (1, ..., n) with 2n unknowns, thuscompleting the set of 2n equations with 2n unknownsof our model.

5.3 Performance calculation

The total throughput can be calculated as

S =n∑

i=1

Si (20)

where Si is defined as the average number of bitstransmitted per slot divided by the average slot size,

Si = τi(1− pi)E[P ]′

E[Slot](21)

The average slot duration is calculated taking into ac-count the different contents that a station Ei can perceivein a slot. A slot can be empty, busy by a transmissionfrom Ei, busy by another station’s transmission, busyby a collision that involves Ei or busy by a collision thatdoes not involve Ei, this is,

10

ξQDX =R∑i=0

Wi−1∑j=0

KQDX,jbX,i,j

n∏y=1,y 6=X,Q

R∑l=0

Wl−1∑m=j

by,l,m

(1− µXQ

R∑a=0

Wa−1∑b=0

min

(j

Wa, 1

)· bX,a,b

)(18)

pQ =

n∑D=1,D 6=Q

µQD

{1−

n∏X=1,X 6=Q

[1−

R∑i=0

Wi−1∑j=0

KQDX,jWi − j

WipiXτX

1− pX

1− pR+1X

·(n∏

y=1,y 6=X,Q

R∑l=0

Wl−1∑m=j

Wl −m

Wlplyτy

1− py

1− pR+1y

)(1− µXQ

R∑a=0

Wa−1∑b=0

min(

j

Wa, 1)Wa − b

WapaXτX

1− pX

1− pR+1X

)]}(19)

E[Sloti] = (1− Ptr)σ +

n∑j=1

τj(1− pj)Ts,j,i + (22)

Ptr(1− Ps)

(τiPtr

Tc,i +

(1− τi

Ptr

)Tc,not−i

)where

Ptr = 1−n∏

x=1

(1− τx) (23)

is the probability of a slot to be busy by any transmission,

PtrPs =n∑

x=1

τx(1− px) (24)

is the probability of successful transmission,

Ts,j,i =1

1−B0

{Ts,short i 6= j

Ts,short + 2 · E[δi] i = j(25)

is the duration of a successful transmission. In (25), B0 =1

CWmin+1 was already defined in (3),

Ts,short = E[P ]+2 ·PLCP +SIFS+ACK+DIFS (26)

is the average duration of a successful transmission inthe case of neglected propagation time,

Tc,i = σ +E[P ] + PLCP +ACKTimeout+DIFS (27)

is the duration of a collision that involves to station Ei,and

Tc,not−i = σ + E[P ] + PLCP + EIFS (28)

is the duration of a collision that does not involve tostation Ei.

The intuitive values of successful transmission timeand collision time are corrected as in (3) and (4) due tothe definition of a model slot, as explained before. Theaverage propagation time needed for Ts,j,i is defined as

E[δi] =

n∑j=1,j 6=i

µi,jδi,j (29)

The packet dropping probability is calculated follow-ing the expression in (30) and the delay is as in (31).Those definitions are derived from [23] and do notrequire further justification, because the first is distance-agnostic and the second is derived from the throughputand the packet dropping probability through Little’sResult,

Pdrop,Q = τQ(1− pQ)p

R+1Q

1− pR+1Q

R∑i=0

(1 +

Wi − 1

2

)(30)

DQ =E[P ]′

SQ(1− Pdrop,Q) (31)

5.4 PtP link case

It has been already explained in the first sections whylong-distance PtP links are a relevant particular case.Real networks are often based on multi-interface nodeslinked to their neighbours through PtP links. For thoselinks, we want to know what performance may beexpected as a function of the distance covered.

We have two stations EA and EB that communicateover a distance dAB taking a propagation time δAB =

δBA = dAB [Km]c[Km/s] . In this case, there is full symmetry, so

that we have two equations with two unknowns τ =τA = τB , and p = pA = pB . Now (6) is exactly valid,as it is for short distances. For the second equation, wecan also perform some simplifications. First, (9) becomesp = ξ, and we have

p =

R∑i=0

CWi∑j=0

bi,jP{ei,j −→ ei,0 during V IAB} (32)

where Kj is defined as

Kj =

1 int(NV IAB) > j

(NV IAB − j) int(NV IAB) = j

0 int(NV IAB) < j

(33)

Second, the steady-state probabilities derived from theMarkov chain are no longer station dependent:

11

Fig. 6. How the curves representing the PtP model evolveas the distance increases. Equations (6) and (35) arerespectively referred to as 1st Equation and 2nd Equationin the legend.

ba,b =Wa − b

Waba,0 =

Wa − b

Wapaτ

1− p

1− pR+1(34)

and we can also simplify µ = 1, and we finally get

p =∑R

i=0

∑Wi−1j=0 Kj

[Wi−jWi

piτ 1−p1−pR+1

(1−

∑Ra=0∑Wa−1

b=0 min(

jWa

, 1)

Wa−bWa

paτ 1−p1−pR+1

)](35)

We have a system of two equations, (6) and (35), withtwo unknowns (p, τ), each of them taking values inthe range [0,1]. We have checked numerically that thesolution is always unique (see Fig. 6), although we havenot been able to prove this analytically.

The normalised throughput S can be calculated nowwith

S = 2τ(1− p)E[P ]′

E[Slot](36)

where

E[Slot] = (1− Ptr)σ + PtrPsTs + Ptr(1− Ps)Tc (37)Pidle = (1− Ptr) = (1− τ)2 (38)PtrPs = 2τ(1− p) (39)

Ts =E[P ]+2·PLCP+ACK+DIFS+δ

1−B0(40)

Tc = E[P ] +ACKTimeout+DIFS + σ (41)

Packet dropping probability and delay are calculatedas

Pdrop = τ(1− p)pR+1

1− pR+1

R∑i=0

(1 +

Wi − 1

2

)(42)

D =2E[P ]′

S(1− Pdrop) (43)

6 METHODS AND MATERIALS FOR VALIDA-TION

The model receives as inputs the number of nodes, adistance matrix, and several parameters, such as con-tention windows, number of retransmissions, slottimeand packet size. The result is a triplet composed of thesaturation throughput, the average delay and the packetdropping probability for each node. A program namedGenSolver has been developed in C++ implementingexactly the proposed model. GenSolver is used to obtaintheoretical values of performance at different distances.For PtP links, calculations are done for different linklengths, starting at 0 Km and finishing at 100 Km becauselonger links are not feasible with CSMA/CA due to thestrict limitation of ACKTimeout in the available hardware.For more than two nodes, calculations are obtained fordistances up to 40 Km because longer distances donot make sense in PtMP and mesh setups, as shownin Section II. Parameter µQ,D in the model fixes theprobability that a packet being transmitted by a certainstation EQ is intended for another specific station ED,and has always been set to µQ,D = 1

n−1 for all EQ andED, which means that each station transmits equally toall others.

The theoretical values were compared with experi-mental results from three different sources:

• A wireless channel emulator PropSim C8 has beenused to obtain experimental results of the perfor-mance of IEEE 802.11 point to point links as afunction of the propagation time (i.e. the distance).Wireless systems communicating through the em-ulated channel consisted of embedded computersSoekris Net4511 with a long-range Proxim OrinocoSilver b/g WiFi card, with Voyage Linux as theoperating system, and with MadWiFi for controllingthe wireless card. Each of the wireless systems wereenclosed in an anechoic portable chamber Rhode &Schwartz CMU-Z10/Z11, in order to guarantee thatboth systems can see each other only through thechannel emulator. The scheme in Fig. 7 representsthe whole framework.Tests were made by injecting traffic with a soft-ware tool named iperf. Saturation throughput mea-surements have been obtained sending bidirectionalconstant bit rate flows at a rate slightly higher thanthe maximum for each case.

• As the previous framework only provides a meanfor PtP experiments, we also explored network sim-ulators for a better validation. Many network sim-ulators implement the IEEE 802.11 MAC, but sometests run on seven different products showed thatonly NS-2 [30] and OPNET Modeler [31] seemed totake into account the distance (although the resultsdiffered from the experimental observations). NS-2 was modified and recompiled in order to enablethe adjustment of ACKTimeout and the slot timeat simulation time. However, this was not possible

12

Fig. 7. Schema of long-distance point to point wirelesslink with PropSim C8 channel emulator.

Fig. 8. CuzcoSur network: Network topology and dis-tances among nodes.

with OPNET.• We had partial access to a real rural WiFi network

in Cuzco, Peru, for experimental purposes (see Fig.8). This network connects rural health centers to thecity hospital in Cuzco, Peru, using PtP IEEE 802.11links for the backbone and PtMP links with no morethan 4 nodes in each BSS for the access segments.The network is operational, but it supports no trafficat all during the night. We can run performance testson the point-to-point links (i.e. any BSS with only 2active nodes at the moment of the test) using iperf.The 6 links used for the comparisons are those work-ing properly at 2 Mbps, covering distances between1.5 Km and 21 Km. Some qualitative tests are alsorun in the BSS connecting Laykatuyoc, Marcaconga,Sangarara and Acopia, which is the only one with4 nodes and has only partial visibility among them.

TABLE 1Parameters for experiments with IEEE 802.11b.

Nombre del parmetro ValorP 8000 bitsMACHeader 224 bitsPLCPHeader 48 bitsPLCPPreamble 144 bitsBasicBitRate 1 MbpsBitRate 2 Mbpsδ distance / cACKTimeout SIFS + σSTD + 2δ + PLCPSIFS 10µsσSTD 20µsDIFS 50µsACK 112 bits + PLCPHeader + PLCPPreambleR 7CWmin 31CWmax 1023

Using the described tools, 1800 traffic injections havebeen made through the channel emulator at differentdistances and slot time values (saturating the link for 1minute each time) and the same number of simulationshave been run in NS-2. Additionally, around 150 trafficinjections have been performed and measured in theCuzcoSur Network. With these tests, we have measuredthe evolution of the performance in WiFi links undersaturation conditions as the distance among stationschanges. All experiments and calculations were basedon parameter values given in Table 1.

The bit rate has always been kept to 2 Mbps for alltests because that is the maximum speed that may beused in all the scenarios and distances considered, andit was also the speed being used in the PtP links atCuzcoSur network at that time.

7 MODEL VALIDATION IN STANDARD CONDI-TIONS

First of all, the theoretical and experimental perfor-mances of PtP links for different distances have beencompared. In Fig. 9 we compare the theoretical through-put obtained with the model, the experimental resultsobtained with NS-2 and OPNET simulators, and theexperimental results obtained with real 802.11 stationscommunicating through the channel emulator, all understandard conditions4. A discontinuous line shows theprediction by Bianchi & Tinnirello’s model, which givesa reference of the throughput that would be obtainedif the distance increased the times, but not the collisionprobabilities.

We can see in Fig. 9 that the model closely matchesthe experimental results. The systematic tests run onthe channel emulator give very similar values to modelpredictions, and the measurements on real links from

4. By standard conditions we mean that the slot time, CWmin andother parameters are respected as they are defined in the standard,with the exception of ACKTimeout, that must be modified in orderto work over long distances

13

Fig. 9. Normalised througput vs. distance for a point topoint link under standard conditions.

TABLE 2Normalized distances among the 8 nodes used for

calculations and simulations.

CuzcoSur network show that the emulated channel is ef-fectively representing the behaviour of real long-distancelinks very accurately.

On the other hand, NS-2 and OPNET give optimisticresults that diverge from experimental results as thedistance grows. For the case of NS-2, we have tried tofind the reason of this divergence in the simulator sourcecode, but with no conclusive results until now.

For the general case of n > 2 nodes, we have cal-culated the theoretical performance for a mesh networkwith 8 active nodes for which the relative positions have

Fig. 10. Saturation throughput obtained with the modelfor each of 8 nodes at different significant distances.

Fig. 11. Average delay obtained with the model for eachof 8 nodes at different significant distances.

Fig. 12. Packet dropping probability obtained with themodel for each of 8 nodes at different significant dis-tances.

been maintained while increasing the absolute distances.The normalized distances among nodes chosen for thestudy are shown in Table 2. The performance figureshave been calculated for different maximum distancesfrom 0 Km up to 40 Km (the maximum distance isbetween node 1 and node 7 or 8), and the results are pre-sented in Figs. 10, 11, and 12 for throughput, delay andpacket-drop probability, respectively. The three figuresshow how different nodes obtain different performancerates due to the different relative distance to the others.This essentially causes a different collision probabilitythat produces unfairness. Different nodes also sufferdifferently from the impact of the distance on the per-formance. Finally, we can see the catastrophic effect ofthe long distances on the packet-drop probability. Thisis a direct consequence of the high collision probability.

The theoretical results for n > 2 can not be comparedwith simulation results because simulators already gaveuseless results with the PtP case. The channel emulatorcan only emulate PtP links. Finally, the PtMP cells inCuzcoSur network contain hidden nodes, which makesimpossible a quantitative comparison, but experimentalmeasurements demonstrate that different stations getvery different performance figures when all contend forthe channel in saturation conditions. In fact, the unfair-ness is much more important than for the case withouthidden nodes, some nodes not being able to exchangepackets when other more privileged are saturating theBSS. We checked that RTS/CTS does not improve this

14

behaviour, as expected.

8 PERFORMANCE OPTIMIZATION FOR LONGDISTANCES

The model allows the identification of which parameterscould be used to optimize the performance of DCF atlong distances. Tuning some of them may give theoreti-cal benefits that are practically useless, like packet size Por maximum number of retransmissions R. The packetsize impacts on the performance, but there are severalconsiderations at the application level that require someflexibility for that parameter. The number of retransmis-sions has an ambiguous effect: throughput and delaymay be improved by decreasing R, but then the numberof packets dropped is increased.

The parameters that may be tuned to optimize theperformance are slot time and the minimum contentionwindow W0. In Eq. (19) we see that the contentionwindows Wi have a direct effect on the final value ofcollision probabilities pi. Also important is the effect offactor KQDX,j , which depends directly on the slot time(σ). Hence, we look for the optimum values of σ and Wi

at different distances.Intuitively, and consistently with the explanations in

Section IV.B, reducing the number of backoff slots thatmay occur during the vulnerability interval reducesthe collision probability. The limit will come from theconsideration that the slot time contains completely thereal round-trip propagation time plus the CCA time, sothat two stations really cannot collide unless they starta transmission in the same slot. On the other hand, asthe slot time increases, we waste more and more time inthe backoff procedure even though the channel may beavailable, which produces the opposite effect.

Secondly, the increase of maximum contention win-dow size Wmin decreases the transmission probabilityin any given slot, which in turn reduces the collisionprobability just like increasing the slot time. The advan-tage of doing so is the possibility of using any 802.11eEDCA compliant products. On the other hand, changingWmin and letting the slot time with the default valueadapts the backoff to the distance but keeps the differentIFS values unchanged, which may have some negativeconsequences as well.

A detailed study follows about outlining how perfor-mance may be optimized by adjusting one of those twoparameters.

8.1 Optimizing the performance by adjusting σ

The variation of the performance with σ has been stud-ied using the model, the channel emulator and NS-2 forthe PtP case, and then only with the analytical modelfor n > 2. The results of throughput versus distance forthe PtP case are shown in Fig. 13 for different values ofσ. We can see that in all cases the model approaches theexperimental results better than simulations.

Fig. 13. Normalized througput vs. distance calculated,measured and simulated in a point to point link for a) σ =20µs, b) σ = 80µs, c) σ = 120µs, d) σ = 160µs and e)σ = 200µs.

Figures 14 and 15 present the relationship amongthroughput, distance and slot time for n = 2 andfor n = 8 respectively. The figures show how muchthe throughput can be improved for each distance. Forexample, we obtain an improvement of 16% for n = 2at 40 Km, while the improvement for n = 8 is 51% atthe same distance. We can also see that the throughputloss due to the time lost in propagation is also muchmore important for the PtP case (25% at 40 Km) thanfor n = 8 (12% at the same distance), but this is due tothe fact that we are comparing maximum distances, the

15

Fig. 14. Throughput vs distance calculated with the modelat different slot time values for n=2.

Fig. 15. Throughput vs distance calculated with the modelat different slot time values for n=8.

difference disappears if we compare average distances.Figures 16 and 17 present the average delay and

packet-drop probability versus distance for different slottimes. For n = 8, Figures 18 and 19 illustrate whathappens to each of the eight nodes in terms of delayand the packet loss when we adapt the slot time sothat σ ≈ σSTD + 2δMAX . We may appreciate that thisadjustment of σ recovers the long-term fairness of DCF.It can be seen that the values of σ maximizing thethroughput and minimizing the delay and packet-dropprobability are different. Both delay and packet lossobtain optimal values when σ ≈ σSTD+2δMAX , whereasthe optimization for the throughput is achieved withσ ≤ σSTD + δMAX . This effect on the throughput whenthe slot time is increased is due to the trade-off betweenthe throughput loss caused by longer contention win-dows and the throughput gain caused by a reduction inthe collision probability. The delay suffers slightly fromthe increment in the propagation time, but the impactof reducing the collision probability so that most ofthe frames pass through at the first try is much moreimportant. Finally, the packet dropping probability isindependent on the propagation time itself, as it onlydepends on the collision probability.

The optimization of σ = σSTD + 2δMAX has manybenefits. It is not the best for maximizing the throughput,but it recovers the correct behaviour of DCF. In fact, evenRTS/CTS may be used under those conditions becausethe NAV is not set correctly but the subsequent DIFS

Fig. 16. Average delay vs. distance in a network of 8nodes calculated with the model for different values of σin saturation conditions.

Fig. 17. Packet drop probability for each node vs. dis-tance in a network of 8 nodes calculated with the modelfor different values of σ in saturation conditions.

Fig. 18. Average delay for each node vs. distance in a net-work of 8 nodes calculated with the model for σ = 140µs.

16

Fig. 19. Packet drop probability for each node vs. dis-tance in a network of 8 nodes calculated with the modelfor σ = 140µs.

Fig. 20. Throughput versus distance calculated with themodel for different values of CWmin.

(which includes two adapted slot times) protects the op-eration against collisions. This has also been qualitativelyverified in the PtMP cells of CuzcoSur network.

8.2 Optimizing the performance with CWmin

Fig. 20 shows the throughput versus distance calculatedfor different values of CWmin. Only values of the form2i + 1 have been considered. We can see that CWmin

may also be used to optimize the throughput. In fact,Fig. 21 shows that the optimal values obtained with bothmethods are almost the same for all distances. However,increasing the value of CWmin does not modify theDIFS, and then the RTS/CTS mode cannot avoid com-pletely collisions with hidden nodes. This obstacle maybe solved in EDCA-compliant systems by adapting bothCWmin and AIFS accordingly to the distance, but thenthose parameters could not be used for differentiatingtraffic classes.

9 CONCLUSIONS

In developing countries, there are large isolated ruralareas in which IEEE 802.11 DCF can be used for long-

Fig. 21. Comparison between optimization with CWmin

and with the slot time (σ).

distance low-cost wireless networks. However, there waslittle formal knowledge concerning the impact of thedistance on the performance of the protocol, or aboutthe process of optimizing the performance.

This paper has studied formally the real limits of IEEE802.11 DCF and has identified the drawbacks for thedeployment of long-distance WiFi networks. We haveproposed an analytical model of the MAC protocol thataccounts for the effect of long propagation times. Themodel has been used to analyse the performance (interms of throughput, delay, packet drop probability)and to optimize that performance. It has been shownthat a correct adjustment of the ACKTimeout parameter,together with the optimization of the slot time, permitthe use of these technologies at very long distances withexcellent results. As a golden rule, we obtain a correctbehaviour and an acceptable performance in a WiLDnetwork by adding the round-trip propagation time tothe default value of both parameters in all stations.

It has also been found that the CWmin parameter mayalso be used for optimization instead of the slot time,getting similar results. However, in case of the hardwarepermitting the modification of the slot time, this mustbe the first choice, because it adapts more integrally theCSMA/CA protocol.

It has also been proved that network simulators imple-mentations of DCF must be improved in order to behavecorrectly within long distances.

Hence, it has been demonstrated that IEEE 802.11DCF can be used with slight modifications to the valueof the CSMA/CA parameters for wide area rural areanetworks in developing countries. This is specially truefor PtMP cells with maximum distances no longer than40 Km. Longer PtP links are also possible up to 105 Kmwith systems commercially available, but other solutionsnot based on CSMA/CA might be more efficient forthis case, if available. We permit ourselves to suggesta modification to the IEEE 802.11 standard in the senseof allowing higher values of the air propagation timethrough the Coverage Class feature. This would be reallystraight-forward and useful in the context of rural areasat developing countries.

For future works, we will take into account hidden

17

nodes and realistic radio channels (with non-null BER) inour analysis. We will also analyse the possibilities offeredby IEEE 802.11e for QoS (quality of service) support overlong distances, and we will compare the performanceobtained with optimized CSMA/CA to other previouslyproposed alternatives.

ACKNOWLEDGMENTS

The authors would like to thank Prof. Mark Wilby forhis contributions in the development of the GenSolvertool, and also to Prof. Giusseppe Bianchi for his fluidinteraction in the discussion of several aspects of hisanalytical models. We also thank Prof. Jesus Cid forhis help in trying to eliminate the condition H4 of theproposed model.

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Javier Simo-Reigadas received the B.Sc andPh.D degrees from the Universidad Politecnicade Madrid, Spain, in 1997 and 2007 repectively.He was a researcher at the EHAS Foundationbetween 2003 and 2005 in the field of ruralbroadband networks for developing countries.Since 2005, he is an associate professor withthe Department of Signal Theory and Communi-cations at the Universidad Rey Juan Carlos. Hismain fields of research are broadband wirelesstechnologies for rural regions and strategies for

remote network sustainability.

18

Andres Martınez-Fernandez received theTelecommunication Engineer and the Ph.D.degrees from the Universidad Politecnica,Madrid, Spain, in 1994 and 2003, respectively.He is currently an Associate Professor inthe Department of Theory of Signals andCommunications, Universidad Rey JuanCarlos, Madrid. He is also Director of theEHAS Foundation. His current interests aretelemedicine and low-cost telecommunicationsystems for less developed regions.

Javier Ramos-Lopez received the B.Sc andM.Sc. degrees from the Universidad Politecnicade Madrid, Spain. Between 1992 and 1995 hecooperated in several research projects at Pur-due University, Indiana, USA, working in the fieldof Signal Processing for Communications. Hereceived the Ph.D degree on 1995 and receivedthe Ericsson award to the best Ph.D. dissertationon Mobile Communications. During 1996 he wasPost-Doctoral Research Associate at PurdueUniversity. From 1997 to 2003 Dr Ramos was

associate professor at Carlos III University of Madrid. Since 2003 DrRamos is the Dean of the Telecommunications Engineering School atthe Universidad Rey Juan Carlos. His present fields of research areBroadband Wireless Services and Technologies, Wireless NetworksSecurity and distributed sensing.

Joaquın Seoane-Pascual got his telecommuni-cation engineering degree in 1976 and a Ph.Din 1989. He worked briefly for real time con-trol and supervision companies, and finally jointthe Universidad Politecnica de Madrid in 1978where he is currently an associate professorin the Telecommunication Engineering School.Since 2000 he also collaborates with the EHASFoundation in rural telemedicine projects fordeveloping countries. His current interests aredistributed systems administration, internation-

alization and localization, SGML and XML based teaching tools, freesoftware, and low-cost networking for less developed regions.