Performance Analysis of the IEEE n Block-ACK Mechanism in an Error-Prone Channel Xue-ping CHEN, Wen-da LI and Hong-yuan CHEN*

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1 2016 International Conerence on ustainable nergy, nvironment and Inormation ngineering (I 2016) IBN: Perormance Analysis o the I n Block- Mechanism in an rror-prone Channel Xue-ing CHN, Wen-da LI and Hong-yuan CHN* chool o lectronic and Otical ngineering, Nanjing University o cience and Technology, Nanjing Jiangsu, China, *Corresonding author Keywords: Anomalous slots, I N, Block-. Abstract. A Block- mechanism is adoted to imrove the erormance o WLAN in I n, through Block- mechanism stations can transmit more MPDUs at one-time and receiver only resonds to a single Block- rame, thus the mechanism eectively imroves the eiciency o the MAC layer. In this aer, we analyze the saturation throughut o Block- mechanism by considering the reezing o backo counter, anomalous slots and non-ideal channel, the accuracy o our model is veriied by the N-2 simulation results. Introduction With the WLAN aearing on many emerging alications and services, the demands or the I are higher and higher, articularly in terms o seed. In order to meet the demands, I n [1] in October 2009 became the oicial standard. The rate in which can reach 600 Mbs due to MIMO and OFDM technology be adoted in the hysical layer. However, that is not well imrove the throughut o system because o the high MAC overhead. In order to reduce the MAC overhead, I n introduces the Block- mechanism that is enhanced rom the I e standard [2] to imrove the throughut o MAC layer signiicantly by shrinking the rames. Many articles have analyzed rame aggregation mechanism and Block- mechanism. Wang C Y [3], Kloa J [4] and elvam T [5] gave the detailed descrition o I n rotocol and simulation results, but they did not roose an analytical model. Daldoul Y [6] roosed an analytical model to calculate the imact o the rame aggregation o the multicast traic, however they did not consider the backo overhead. Liu [7] roosed a mathematical model o Block- mechanism in an ideal channel, although Li T [8], Chen Y [9] and Lee [10] roosed an analytical model in a noisy channel, but they did not consider the anomalous slots, the reezing o backo counter and these models were based on I e rotocol. Chen H [11] roosed a Markov model by considering anomalous slots, but the result about saturation throughut was inaccurate, and he ignored the error robability o the BAR rame and the BA rame. These articles [7-10] have enhanced the two-dimensional Markov model which was roosed by Bianchi G [12] by considering a Block- case. But they have ignored some details in the I rotocol, such as the reezing o backo counter and anomalous slots. Tinnirello [13] gave a detailed exlanation about those anomalous slots. Here we briely introduce anomalous slots: backo counter start to decrease only under the idle slots, when a TA successul transmission and the backo value equals to zero the TA occuies the channel again. In [13] a more accurate model was roosed to consider the reezing o backo counter and the anomalous slots in an ideal channel. For research erormance o the Block-, it is necessary to consider bit error rate o the channel. Chen H [14] roosed an analytical model in an erroneous channel, but it is the study o immediate mechanism not Block- mechanism. In this aer, we combine the mathematical model in [14] with Block- mechanism and take into account the anomalous slots. We derive the saturation throughut ormula o Block- by the model and use N-2 veriy the accuracy o the model. The ollowing contents are arranged as ollows: the second art introduces Block- mechanism in details, the third art gives the model 313

2 and analyze saturation throughut, the ourth art gives the simulation results and the ith art summarize the article. The Block- o n Block- mechanism has been used in the I e irstly and exanded in the I n that ut orward the comressed Block- mechanism and immediate Block- mechanism. When sender and receiver want to use the Block- mechanism, sender sends an add Block- request rame (add BA-RQ) to the receiver, receiver which suort Block- mechanism will resonds to an add Block- resonse rame (add BA-RP), so they can use Block- mechanism or data transmission. Channel access rocedure o Block- mechanism as shown in Figure 1. Ater the initialization, the sender sends a MPDU to contend channel, the TA can sends a data block that is comosed o multile MPDUs and each MPDU between IF interval once it receives the rame correctly. When the TA inishes the data block transmission, it sends a Block- request rame (BAR) that tell the receiver data block are sent over to request the BA rame. Receiver resonds a Block- rame (BA) to the sender once it receives one o MPDUs o the data block or the BAR rame correctly. BA rame is an aggregated rame that use bitma to store conirm inormation o these MPDUs. Due to a BA rame can conirm the maximum number o MPDUs which is 64, so a data block can not more than 64 MPDUs. Figure 1. An illustration o a burst transmission or the basic access. [10] Figure 1 illustrates multile MPDUs, BAR rame and BA rame are all in the same backo rocedure and only a BA rame be used to acknowledge the data block. o Block- mechanism greatly reduces the MAC layer overhead. In this article, we discuss the Block- mechanism with a basic access channel mechanism in a noisy channel. In the case o collision, at least two TAs start transmission in a slot, each o them sends out the irst MPDU and then waits or the rame, the senders can t receive the rame because collisions, so the senders have to retry their data again. In the incorrect case, only one TA start transmission, here we assume that BAR rame, rame and BA rame have the error robability. The sender sends the irst MPDU but it can t receive the rame due to the MPDU or rame transmits error, then the contention window is doubled and retry its data. I the TA successul receives the rame indicates it wins the channel and can transmits the data block. The TA can t receive the BA rame due to the data block and the BAR rame all errors or the BA rame error, then the contention window is doubled too and retry its data. Once the receiver receive one o MPDUs o the data block or the BAR rame correctly, it will resonds the BA rame in a IF interval. Once receiving the BA rame correctly, the sender should waits a DIF interval and starts a new backo rocedure. Taking into account anomalous slots, when the next backo value equals to zero the TA occuies the channel again. Meanwhile, all the other TAs should be rozen their backo counter with a DIF interval and when the channel is idle they begin to decrease their backo counter. o it can be seen that the Block- mechanism oerates in a similar way to the [14]. o it is ossible to extend the analysis [14] to study the Block- mechanism. 314

3 Analytical Model o Block- Chen H [14] has roosed a two-dimensional Markov chain (s(t),b(t)) to model the immediate mechanism backo behavior o considering anomalous slots and the reezing o backo counter in a noisy channel. o it is very suitable or Block- mechanism, but the robability o a TA double the contention window need to be comuted again due to the BAR rame and the BA rame can suer errors too. The model is based on the discrete time and the wireless channel model is divided into a series o slot times. The deinition o model slot as shown in Figure 2. Figure 2. The deinition o model slot time. [12] The Markov Chain In this aer, the Markov chain model is extended rom [14], the model considers the wireless channel is a Gaussian channel, in which each acket has the same bit error robability (BR), let ber reresents the BR and each TA is always ready to send MPDU. Let denotes the robability o the each MPDU transmits error. We assume each MPDU has the same size data, and each TA sends L BA MPDUs, so the data block is comosed o L BA MPDUs. reresents the robability o one TA double its contention window, may be collision or errors. stands or the robability that a TA transmits in a randomly chosen slot time. c reresents the robability o collision, N is the number o contend TAs. e reresents the robability that the TA double its contention window because o transmission errors, let, BAR, BA, BAR, BA,, ALL reresent the size o the rame, the size o the BAR rame, the size o the BA rame, the robability o the BAR error, the robability o the BA error, the robability o the error, the robability o these MPDUs o the data block all errors, resectively. o: ALL BA 1 1 BAR 1 ber LBA ber 1 1 data BA ber BAR ber (1) The robability e is related to the transmission situation o the MPDU, the, the data block, the BAR, the BA. o these robabilities c, and e can be exressed as ollows: N 1 c 1 1 e ALL BAR BA ALL BAR BA c e c e (2) In this model ater errors occur the contention window is doubled and R is the number o maximum retransmission. According to the regular o the Markov chain, the robability can be solved, [14] has the detailed derivation or the model. Deine = e /(W + e 1), where W = CW min + 1, W k = CW k + 1, CW k denotes the contention window in the kth retry, CW min is the minimum contention window, the inal result is derived as ollows: 315

4 R1 21 R k1 k R1 1 W k 1 * 1 W k1 aturation Throughut Beore analyzing the saturation throughut we deine some arameters, Let T MPDU, T, T BA, T BAR, T TIMOUT, T DIF, T IF, T IF denote the duration o an idle slot time, the time to transmit one MAC data acket (including MAC header, PHY header, and/or tail), an Immediate- rame, a Block- rame, a Block- request rame, the rame timeout, the DIF time, the IF time, the IF time, resectively. By the model slot time deinition o the Figure 2 we know T IF = T TIMOUT T DIF, and we can get T TIMOUT T T IF according to the I rotocol. Throughut ormula is given here: P (4) T Which deined as the ayload size o the successully transmitted rame P in an exected slot duration [T]. We irstly comute the exected slot duration [T], there are our kinds o situations need to be discussed searately. First, none o the TAs transmit any rames, the duration called idle slot, let T I denotes the length o the duration, so it is natural to know T I, where is an idle slot duration. econd, this is collision case, at least two TAs start to send data block at the same time, let T C denotes the collision duration. Ater the collision, all TAs need to delay the IF interval to begin the next backo rocedure and their backo counter is keeing the last value. As Figure 2 describes the deinition o model slot time. o T C = T MPDU + T IF +. Third, this is error case, only one TA in sending data. Here we consider the error robability o the BAR rame and the BA rame, so in this case we discuss sub-two cases searately: 1) the irst MPDU error or the rame error; 2) the irst MPDU and the rame are transmitted correctly, but the data block and the BAR rame all errors or the BA rame error. Let T FM and T denote the duration o the sub-two cases searately: 1) sender ater waiting or T TIMOUT does not receive the rame correctly shows that it contends ailure o channel and then deer T DIF interval, so T FM = T MPDU + T TIMOUT + T DIF. 2) sender ater receiving the rame correctly sends the data block and the BAR rame but can t receive the BA rame correctly, so T LBA TMPDU TIF T TIF TBAR TIF (5) Fourth, only one TA in sending data and successul accesses the channel, so it starts to transmit L BA MPDUs and each MPDU between IF slot interval. Ater the transmitter receives the BA rame correctly it starts the next backo rocedure and when the randomly backo value equal to zero it directly occuies the channel to send the next MPDU. Considering anomalous slots and bit error rate, in ourth case this sub-three cases to be discussed searately: 1) there are multile successul transmission. Maybe there are some MPDUs transmit errors in the L BA MPDUs, and as the next backo value is not zero the transmission be terminated; 2) there are multile successul transmission, as the next backo value is zero but the transmission be terminated due to the irst case o error cases; 3) the multile successul transmission be terminated due to the second case o error cases. Let T BLOCK denotes the duration o a successul transmission that is comosed o L BA MPDUs, three control rames, each them between IF time interval, so TBLOCK LBA T MPDU TIF T 2 TIF TBAR TBA T (6) DIF We assume there are i successul transmission consecutive, the duration or the above sub-three cases can be exressed as ollows: 1) i data blocks transmit time lus a backo slot, that is it BLOCK + ; 2) i data blocks transmit time lus an duration o the MPDU or the rame transmits error, 316 (3)

5 that is it BLOCK + T FM ; 3) i data block transmit time lus the second error case time, that is it BLOCK + T. Next, we are going to calculate the robability o each case. In the irst case, none o TAs transmit any rames, the robability that one TA is not transmitting data is, so the robability that N TAs are all not transmitting any rames is P I = (1) N. Where P C denotes the robability o collision, P denotes the robability o successul contend channel, P FM denotes the robability o the irst MPDU error or the rame error. P denotes the robability o the data block and the BAR rame all errors or the BA rame error. o these robabilities can be calculated as ollows: N N e N N PI 1 P N PFM N P N PC 1 PI P P e P FM (7) The ourth case can be regarded as a category o contending channel successul. o we discuss these sub-three cases searately. We take into account anomalous slots, or the irst sub-case, the robability that a TA randomly choose the backo value zero ater transmitting the data block over is 1/W, the robability o a TA randomly choose the backo value nonzero is (W)/W. Thereore, the robability that the TA choose the backo value nonzero ater isuccessul transmission is: i1 1 e 1 sn 1 W W (8) Let FM = + (1 ), = e FM, or the second sub-case, the TA ater i 1successul transmission randomly chooses backo value zero, but contend ailure o the channel by the MPDU error or the error, the robability can be exressed as: i1 1 e FM sm W W For the third sub-case, the robability can be exressed as: (9) i1 1 e sa (10) W W Thereore, taking into account the anomalous slots, the average successul transmission time T can be exressed as: T i T i T T i T T sn BLOCK sm BLOCK FM i1 i1 i1 so simliication it can be obtained: W T T BLOCK W 1 W 1 (11) FM e T FM (12) Thereore, the average time o a model slot can be exressed as: T T PI TI PC TC PFM TFM P T P T (13) Ater calculating [T], we start calculate [P]. We just need to analyze the ourth situation and assume that these are j MPDUs errors in i data blocks. These j MPDUs transmit errors only in these il BA MPDUs, so the successully transmitted valid rame [] in an erroneous case is: sa BLOCK 317

6 LBA 1 j ( ilba 1 j) 1 i L 1 ilba 1 i BA j data i data (14) j0 j imliication the above ormula can be obtained: [] = i, the exression is: LBA data data 1 1 (15) According to the [T] calculation and taking into account the anomalous slots, the average data be transmitted o the ourth situation can be exressed as: P sn sm sa i1 i1 i1 o simliication the above ormula can be obtained: data (16) W data P (17) W 1 e In the error case, the second sub-case transmit one MPDU successul, so the ayload size o the successully transmit rame [P] is: P P P P data Thereore, by considering anomalous slots and the reezing o backo counter, the saturation throughut can be exressed as: P P P P T P T P T P I I C C FM data (19) Model Validation FM T P T Now, we validate our analytical model via N-2[15] simulations. N-2 is a commonly used oensource network simulator. Our simulation module is modiied based on the TKN module [16]. Our simulated scenario that is comosed o a single AP and a grou o associated TAs that send their data ackets to the AP. We suose that these TAs use the rates o 300Mbs or data ackets, BAR rame and BA rame and the rates o 96Mbs or immediate rame. We also consider a ixed length o one MPDU o 2048 bytes. In this module, the deault values o simulation arameters are T slottime = 20μs, T IF = 10μs, CW min = 15, CW max = 1023, R=7. In our simulation, two dierent bit error rates are designed to examine the erormance o Block- mechanism in the I n, the moderate bit error rate ( ber = 10-6 ) and the very noisy channel ( ber = 10-5 ). Figure 4 shows the throughut both the simulation results and the model results in two dierent bit error rates with the number o stations increase. According to the I n standard, the PHY and MAC layer arameters is exressed as ollows: =14 bytes, MAC sub layer overhead 26 bytes, Block Acknowledge Request 26 bytes, Block Acknowledge 32 bytes, FC 4 bytes and PHY layer overhead 16μs. And we require the numbers o MPDUs at one transmission is ixed to L BA = 10. From the igure we can know the throughut is decline with the number o stations increase because the robability o collision is increasing, and it tells us that our analytical model can accurately redict the throughut o Block- mechanism by consider anomalous slots and the reezing o backo counter. Conclusions In this aer, we introduced an analytical model that takes into account the eects not only collisions and transmission errors but also anomalous slots and the reezing o backo counter or the Block- mechanism. Based on the Markovian techniques, the analytical model or Block- mechanism is established in order to measure the saturation throughut. We imlement a 318 (18)

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