Analytical Study of Frame Aggregation inError-prone Channels

Nasreddine Hajlaoui∗, Issam Jabri†, Maher Ben Jemaa‡∗‡ ReDCAD Research Unit, National school of Engineers of Sfax, University of Sfax - 3038 Sfax, Tunisia†Department of Networks and Communications National School of Engineers of Gabes - 6029 Gabes, Tunisia

Email: ∗hajlaoui.ing@gmail.com, †issam.jabri@enig.rnu.tn, ‡maher.benjemaa@enis.rnu.tn

Abstract—With many improvements in both the physical andMAC layers, the IEEE 802.11n standard aims to achieve a datatransmission rate of up to 600 Mbps. The most important 802.11nMAC enhancement is frame aggregation which significantlyreduces the headers overheads of the legacy MAC by aggregatingmultiple frames into a single large frame. In this paper we drivean analytical model to study the impact of the frame aggregationon the saturation throughput and access delay under error-pronechannels. We describe the throughput as a function of physicaldata rate, and Frame Error Rate(FER). The analytical resultsshow that the throughput and delay depend significantly onMPDU subframes size in high FER channels. Thus, We proposean algorithm which can dynamically adjust the MPDU subframesize based on the maximum FER tolerable by frame’s accesscategory. We use the feedback Block Acknowledgement (BACK)frame to compute the next MPDU subframe size which can takesinto account the FER and the delay QoS requirements for thecorresponding access category traffic.

I. INTRODUCTION

The IEEE 802.11n [1] standard, ratified on September 2009,aims to enhance the functionalities of WLAN by providinghigher throughput and further range. Many PHY and MACfeatures have been proposed to enhance the physical data rateand to reduce the MAC/PHY overhead. These features makeIEEE 802.11n a promising technology for building WLANs[2].In the physical layer, 802.11n uses a MIMO technologywhere multiple antenna elements can be combined to achieveeither higher PHY data rates (in Spatial Division Multiplex-ing (SDM) mode) or higher range (in Space Time BlockCoding (STBC) mode). This technology provides the abilityto receive and/or transmit simultaneously through multipleantennas. 802.11n PHY layer uses also channel bondingmechanism, where two 20 MHz channels of legacy 802.11can be combined to a single 40 MHz channel, thus increasingthe PHY data rate. In the MAC layer, 802.11n introducesthree key enhancements: the frame aggregation that consistsof combining multiple data frames into a large aggregate oneto reduce the overhead, block acknowledgment mechanismwhere a single-block acknowledgment (BACK) frame is usedto acknowledge several received frames and reverse directionmechanism which allows the channel reservation during thetransmission opportunity of the sender by the receiver thustransmission in both directions to increase the network effi-ciency.The frame aggregation mechanism can increase the efficiency

of MAC layer under ideal channel conditions. In previous work[3], we have investigated the effect of frame aggregation onthe support of voice and video applications in wirelessnetworks. We have proposed a new frame aggregation sched-uler that considers specific QoS requirements for multimediaapplications. However, we do not know much about their per-formance under error-prone channels. In fact, in high Bit ErrorRate (BER) channels, the loss rate increases. Thus, corruptinga large aggregated frames can greatly affect the performancedue to their retransmission cost. So, there is a need to examinethe effect of frame aggregation feature on the performance un-der different channel error conditions.In this work, we drive an analytical model to study the impactof the frame aggregation on the saturation throughput and ac-cess delay under lossy channels. We describe the throughput asa function of physical data rate, and Frame Error Rate(FER).The analytical results show that the throughput and delay dependsignificantly on MPDU subframes size in high FER channels.Based on these results, we propose an algorithm which can dy-namically adjust the MPDU subframe size based on the max-imum FER tolerable by frame’s access category. We use thefeedback Block Acknowledgement (BACK) frame to computethe next MPDU subframe size which can takes into accountthe FER and the delay QoS requirements for the correspondingaccess category traffic.The rest of the paper is structured as follows. In Section II wegive a short overview of 802.11n MAC enhancements. SectionIII presents related work. In Section IV we describe the analyt-ical model. The obtained results are presented and discussed insection V. The dynamic frame size adaptation algorithm is ex-plained in section VI. Finally, conclusions are given in SectionVII.

II. OVERVIEW OF 802.11N MAC ENHANCEMENTS

1) Frame Aggregation: In order to reduce MAC layer over-head caused by inter-frame spacing and preamble and avoidthe wasted time due to backoff and collisions of the 802.11MAC protocol, new 802.11n devices have the option ofbundling frames together for transmission. This mechanism iscalled frame aggregation. 802.11n supports two different formsof aggregation: A-MSDU and A-MPDU.

• MAC Service Data Unit Aggregation (A-MSDU) MS-DU refers to the payload that is carried by the802.11 MAC layer frame. It consists of an LLC header,

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IP header and the IP packet payload. The A-MSDUaggregation technique combines multiple MSDUs withthe same 802.11e access category into a single MACframe (MPDU). The maximum A-MSDU size allowedby 802.11n is 8192 bytes. 802.11n receivers can ac-knowledge an A-MSDU frame by sending a single ACKframe, thus reducing the acknowledgement overhead. Thedisadvantage of A-MSDU technique is that an error inreceiving an A-MSDU transmission incurs the overheadof having to retransmit the entire A-MSDU again.

• MAC Protocol Data Unit Aggregation (A-MPDU) A-MPDU occurs later, after MAC headers are added to eachMSDU. It groups multiple MPDUs frames as a singleframe. The maximum A-MPDU size allowed by 802.11nis 65535 bytes. A-MPDU does not have the limitation thatall MSDUs must be destined to the same MAC addressas A-MSDU technique.

2) Block Acknowledgment: In legacy 802.11 MAC pro-tocol, each of the frames transmitted to an individual ad-dress (not multicast or broadcast frames) is immediatelyacknowledged by the recipient. In order to reduce the over-head, 802.11n introduced the Block Acknowledgment (BACK)scheme. This is achieved by collecting many individual ACKsinto a single BACK frame to acknowledge the receipt ofmultiple MPDUs. The BACK uses a bit map to efficientlyacknowledge each individual subframe within the aggregatedframe. The BACK mechanism must be used with A-MPDUaggregation in order to distinguish between lost and successfulMPDUs, thus allowing the selective retransmission. This canbe very useful in environments which have a high number ofcollision or transmission errors. Fig. 1 shows the structure ofa BACK frame.

Fig. 1. BACK frame format.

III. RELATED WORK

In the literature, several works have studied the performanceof 802.11n frame aggregation using analytical models underideal channel conditions. Bianchi [4] presented an analyticalmodel to compute the IEEE 802.11 DCF throughput underideal channel conditions, finite number of terminals andsaturated traffic. Li et al.[5] proposed an analytical modeldescribing the effective throughput, optimal frame andfragment sizes for single-hop links. In [6] the authorsinvestigates a theoretical analysis of the aggregation withfragment retransmission, based on computing the saturationthroughput for DCF and AFR mechanisms. In [7] Frohnet al. derived an analytical model to examine the effectsof frame aggregation and block acknowledgements on the

effective throughput for multi-hop paths in IEEE 802.11nbased wireless mesh networks. Kim et al. [8] proposed ananalytical model based on a discrete time Markov chainmodel in order to describe the post-backoff behavior due toframe aggregation, and evaluated the throughput performance.In [9] Hoefel et al. designated MAC and PHY analyticalcross-layer model to estimate the saturation net throughputof IEEE 802.11n WLANs. [10] provide an analytical modelto evaluate the impact of the frame aggregation on the MACthroughput for the multicast transport.In addition, many papers have analyzed the frame aggregationperformance under different channel error conditions. Yuxia[11] proposed an analytical model to evaluate the performanceof the 802.11n protocol for uni-directional and bi-directionaldata transfer and also proposed an optimal frame sizeadaptation. In [12] a path loss model for IEEE 802.11n inlarge conference rooms is proposed. Yin et al. [13] studythe effects of packet size in an error-prone channel for IEEE802.11 DCF and conclude that there is an optimal packet sizeunder a certain bit error rate (BER) to achieve the maximumthroughput.

Opposed to these works, we drive an analytical model tostudy the impact of the frame aggregation on the saturationthroughput and access delay under variable Frame Error Rate(FER) channels. We describe the throughput as a functionof physical data rate, and the channel frame error rate. Theanalytical results show that the throughput and delay dependgreatly on the subframes size. In error-prone channels, theuse of large aggregations can degrade the network’s saturationthroughput and eventually becomes worse than that of smalleraggregations. Thus, based on the analytical results we havedesigned an algorithm which can dynamically adjust theMPDU subframe size in order to enhance the the throughputand to reduce the FER. We use the feedback Block Acknowl-edgement (BACK) frame to compute the next MPDU subframesize which can takes into account the maximum FER and delaytolerable by the frame’s access category.

IV. THE ANALYTICAL MODEL

A. Model Assumptions

To study the performance of frame aggregation under dif-ferent channel conditions, we extend Bianchis model [4] tobe suitable with 802.11n enhancements. We assume that wehave n wireless stations competing to access to the mediumand operating in saturated conditions. Each station always hasa traffic available for transmission. To transmit aggregatedframes we consider the RTS/CTS access scheme (Fig. 2) whichis more robust than the basic access scheme in error-pronechannels. The technique used to sense the medium is CarrierSense Multiple Access with Collision Avoidance (CSMA/CA)scheme with binary slotted exponential backoff. The minimumcontention window size is w and the maximum backoff stageis m. The system time can be slotted into virtual time slotswhere each slot is the time interval between two consecutivecountdown of backoff timers by non-transmitting stations [11].

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A station is allowed to transmit only at the beginning of eachtime slot. Since the size of the control frames (RTS, CTS,BACK) are much smaller compared to the aggregated frameand because they are transmitted at the basic rate, we do notconsider the error probabilities for these control frames andalso for the PLCP (Physical Layer Convergence Procedure)preamble. Finally, the data frame represents an A-MPDUframe.

Fig. 2. RTS/CTS Access Mechanism.

B. Model Description

The probability τ that a station transmits in a randomlychosen time slot can be expressed as:

τ =2(1− 2p)

(1− 2p)(w + 1) + pw(1− (2p)m(1)

where p is referred to unsuccessful transmission probability,caused by collisions and errors transmission [4], [11].If we have a transmitted frame, in a time slot, a conditionalcollision can occur wit the probability pc when at least one ofthe n− 1 remaining stations transmit.

pc = 1− (1− τ)n−1 (2)

Corresponding to the error case in Fig. 2(b), the error proba-bility per frame pf is the frame-error-rate (FER). A frame isconsidered erroneous if at least one of the bits in the frameis detected incorrectly. On condition that there is a successfulRTS/CTS transmission, pf is function of the channel bit-error-rate (BER) pb and the frame size FS.

pf = 1− (1− pb)FS (3)

From (3) given pf and FS, the pb can be calculated as,

pb = 1− 10log(1−pf )

FS (4)

and given pf and pb , we derive the FS as,

FS =log(1− pf )

log(1− pb)(5)

Using the equations (2) and (3) we can deduct the probabilityof unsuccessful transmission caused by either collisions ortransmission errors,

p = 1− (1− pc)(1− pf ) (6)

Let us first consider pemp the probability that a time slot isempty.

pemp = (1− τ)n (7)

Let ptr be the probability that at least one station transmits ina chosen time slot.

ptr = 1− pemp = 1− (1− τ)n (8)

The probability for having a transmission without collisionsis the probability that exactly one station transmits on thechannel, conditioned by having at least one transmission,

ps =nτ(1− τ)n−1

ptr=nτ(1− τ)n−1

1− (1− τ)n(9)

The probability for having an erroneous transmission (withoutcollisions) is:

perr = ptrpspf = nτ(1− τ)n−1pf (10)

Finally, the probability that a successful transmission occurswithout collisions and errors is:

psucc = ptrps(1− pf ) = nτ(1− τ)n−1(1− pf ) (11)

1) The Saturation Throughput: The network’s saturationthroughput S can be defined as the limit reached by the systemthroughput. S is calculated as the ratio of Ebs the averagenumber of bits being successfully transmitted in a consideredtime slot by the expected average length of a time slot Et. LetEf be the average frame payload size,

S =Ebs

Et=psuccEf

Et=ptrps(1− pf )Ef

Et(12)

Et can be calculated as,

Et = Temppemp + Tcpc + Terrperr + Tsuccpsucc (13)

where Temp is the duration of an empty time slot. Tc, Terr, andTsucc are the average time the channel is sensed busy becauseof respectively a collision, an erroneous transmission and asuccessful transmission. In the case of an RTS/CTS accessmechanism (Fig. 2), they are determined as follows:

Tc = TRTS + EIFS

Terr = TRTS + TCTS + TDATA + 2SFIS + EIFS

Tsucc = TRTS + TCTS + TDATA + TBACK + 3SFIS +DIFS

where TRTS , TCTS , TDATA, and TBACK are the transmissiontime for respectively RTS, CTS, the aggregated DATA, BACKframes.Let us examine what happens when we have an A-MPDUaggregated data frame. We consider that pf is the probabilitythat a subframe is erroneous. The hole A-MPDU frame isconsidered corrupted only when all subframes are erroneous.Assuming independent errors, the number of erroneous sub-frames Nerr follows a binomial distribution b(Nfr, pf ), whereNfr denotes the total number of subframes in an A-MPDUaggregated frame. The probability that k of Nfr are erroneousis given by

P [Nerr = k] =

(Nfr

k

)pkf (1− pf )

Nfr−k (14)

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Therefore the average number of erroneous subframes is

E[Nerr] = Nfrpf (15)

In this case the variable number of bits successfully transmit-ted Ebs can be expressed as

Ebs = Nfr(FS − Lsubhdr)−Nfrpf (FS − Lsubhdr)

= Nfr(FS − Lsubhdr)(1− pf ) (16)

where Lsubhdr the total size of each subframes header (MACheader , delimiter, and FCS).

2) The Access Delay: We also study the average accessdelay which is defined as the required time for an aggregatedframe to reach the receivers MAC. Using the network satura-tion throughput S, each A-MPDU frame takes an average ofNfrFS

S to be transmitted. Since, we have n stations competingfor the channel we can derive the average access delay as

d = nNfrFS

S(17)

V. ANALYTICAL RESULTS

The analytical results reported in this section are obtainedusing the system parameters in Table. 1 [7].

TABLE IPARAMETERS USED IN THE ANALYSIS

Basic rate 54 MbpsData rate 300 MbpsSIFS 10µsDIFS 28µsTime slot 9µsEIFS TACK + SIFS +DIFS

TRTS , TCTS , TACK , TBACK = length of RTS, CTS, ACK, BACK frameBasic rate

TDATA = length of DATA frameData rate

PLCP Header 6 bytesMAC Header 34 bytesFCS 4 bytes

Fig. 3. Throughput versus the transmission probability τ .

Fig. 3 shows the maximum throughput reached by the802.11n protocol in the case of RTS/CTS access mechanismversus τ the transmission probability in a chosen time slot.

We remark that the maximum throughput reached is inde-pendent of the number of wireless stations. It is reached withdifferent values of τ . In fact, when we have a few number ofstations (ie. n = 1..5) increasing the transmission probabilitycan greatly enhance the saturation throughput. However, risingthe transmission probability rapidly decreases the saturationthroughput when the number of stations is large. This isjustified by analyzing the equations (2) and (8). We can seethat a small variation in the value of τ leads to a high collisionprobability thus increasing the expected average length of atime slot Et and a great decrease in the saturation throughput.Furthermore, we investigated the effect of frame aggregationon the system performance under different channel conditions.Fig. 4 and Fig. 5 show the average saturation throughputversus respectively the MPDU subframe size and the numberof aggregated subframes. From these figures, we remark that

Fig. 4. Saturation throughput versus the subframe size.

the saturation throughput depends greatly on the channelconditions. In fact,under good channel conditions (i.e., fromFER= 0 to 0.05), it is improved as the payload informationincreases either by the number of aggregated subframes or thesubframe size. Also we observe that the saturation throughputstays almost flat when the payload information becomes verylarge (for example starting from 30 subframes of 1000B).However, under high FER channels, first there is a gradualthroughput improvement, and then it rapidly decreases withincreasing the aggregated frame payload size. This is becausethe number of corrupted subframes is large under error-pronechannels, thus their retransmission will waste lots of mediumtime and deteriorates the efficiency produced by an increasedsubframe size. We can conclude that as the frame error rateincreases, the use of large aggregations degrades the network’ssaturation throughput and eventually becomes worse than thatof smaller aggregations. Therefore, in this case, the use ofsmaller MPDU subframe size can reduce the chance of framecorruption and can be more beneficial.

Fig. 6 and Fig. 7 show respectively the effect of varying theMPDU subframe size and the number of aggregated subframes

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on the the access delay under different frame error rates.Remarkably, we can observe that the delay increases with a

Fig. 5. Saturation throughput versus the subframe size.

large aggregated frames. This degradation in access delay isfaster in high FER channels than in low FER ones. This isdue to the the additional time introduced by the large numberof retransmitted subframes with the payload increasing.As a conclusion from these analytical results, we can observethat the effect of frame aggregation on the system performanceis very sensitive to the channels conditions. The maximumthroughput is achieved under different FER and with differentMPDU subframe sizes. Thus there is an optimal value ofsubframe size which depends greatly on the channel FER.

Fig. 6. Access delay versus the number of aggregated subframes.

In the next section, we will focus our attention on theoptimization of the MPDU subframe length. We propose anadaptive frame aggregation scheme allowing: first to enhancethe system performance and second to meet the applicationQoS requirements such as the maximum delay and frame errorrate tolerance for Voice/Video multimedia traffic.

VI. FRAME SIZE DYNAMIC ADAPTATION

The aim goal of the proposed algorithm is to improve theeffectiveness of using frame aggregation mechanism underdifferent channel conditions. We have shown that it does not

Fig. 7. Access delay versus the the number of aggregated subframes.

provide a good performance in high FER channels whenusing large frame aggregation size. Several works suggestedsome propositions to enhance the use of frame aggregationmechanism. However, most of these suggestions do not takeinto account the QoS requirements for multimedia traffic invarious FER channels.The 802.11e standard have introduced the concept of AccessCategories (AC) to provide service differentiation. Thestandard defines four ACs as shown in Table 2 [14]. EachAC has a specific handling in the access mode depending onthe QoS requirements. Prioritization is ensured by assigningdifferent values of contention parameters such as arbitrationinterframe space (AIFS), contention window (CW), andtransmission opportunity duration (TXOP). For example,VoIP traffics are delay-sensitive and they should tolerateless than 1-2% of packets with delays greater than 30ms.Streaming video traffic is sensitive to the loss rate of the802.11n network and the loss rate should be no more than5%; it is more tolerable to the delay where the latency shouldbe no more than 4 to 5 seconds .

TABLE IIPRIORITY TO ACCESS CATEGORY MAPPINGS

802.1D Priority Access Category(AC) Designation0 0 Best Effort1 1 Background2 2 Video3 3 Voice

In order to meet the QoS requirements for the Voice/Videotraffic, we propose an adaptive frame aggregation schemethat can dynamically adjust the size A-MPDU subframesbased on the maximum FER tolerable by the correspondingapplication’s access category. We use the real time feedbackfrom the block acknowledgement frame to update the value ofthe subframe size for the next aggregated frame.

This update can be either by increasing or decreasingthe subframe size. It depends on the result of comparingthe measured FER (mFER) from the BACK frame with themaximum FER tolerable by the application’s access category.

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Algorithm. 1 presents a pseudocode implementation of theproposed algorithm. In the following, we explain the stepsinvolved in our algorithm:Firstly, when receiving a BACK frame, we compute themeasured FER as

mFER =the number of corrupted A-MPDU subframes

the total number of A-MPDU subframes(18)

Then we get the access category of the aggregated frame andthe current subframe size. We obtain the measured BER in thenetwork by substituting mFER and current subframe size intoequation (4)

mBER = 1− 10log(1−mFER)

currentFS (19)

After that, we compare the mFER with the maximumFER tolerable by the corresponding frame access categoryFERmax AC.If mFER ≥ FERmax AC we have to use smaller frameaggregation size to meet the AC QoS requirements. Thus thesubframe size is reduced using the following equation

FS =log(1− FERmax AC)

log(1−mBER)(20)

Else if mFER < FERmax AC we can increase thesubframe size to enhance the throughput. However, the stepsize X AC of this increase is variable corresponding to theaccess category parameters. For example we can not use largesize for voice traffics. That’s why we have fixed a maximumsubframe size for each AC (FSmax AC).

Algorithm 1 Frame size dynamic adaptation algorithmInput: p := receive block ack frame()Output: aggregate frame to transmit

var :AC i := access category iMFER AC i := measured FER of the AC iFERMAX AC i := max FER tolerable by AC iFS:= the sub frame sizeFSMAX AC i := frame size max tolerable by the AC iCURRENTFS AC i := the MPDU sub frame sizeof the current trafic of the AC iX AC i := the step size increase for the AC iAC i := get frame access category()MFER AC i := compute FER(p)if MFER AC i >= FERMAX AC i then

FS := compute subframe size(FERMAX AC i)CURRENTFS AC i := FS

elseif FSMAX AC i >= (CURRENTFS AC i + X AC i)then

CURRENTFS AC i+ = X AC iend if

end ifconstruct AMPDU frame(CURRENTFS AC i)transfert aggregeted frame()

VII. CONCLUSION

In this paper, we derived an analytical model capturingthe effect of frame aggregation on the saturation throughputand the access delay under different channels conditions.The results showed that the network performance dependssignificantly on the subframe size. Thus we designed anadaptive frame aggregation size algorithm. In this algorithm,the MPDU subframe size is dynamically adjusted accordingto the measured FER value from the block acknowledgementframe. In low FER channels, larger frame size is used toincrease the throughput. And in error-prone channels smallerframe aggregation size is used to meet applications QoSrequirements.To evaluate the performance of dynamic adaptation of sub-frame size, we are actually working on the implementation ofthe proposed algorithm in NS2 simulator.

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