Optimal MAC PDU Size in ARQ-enabled Connections

in IEEE 802.16e/WiMAX Systems

Oran Sharon

and Yaron Alpert

Department of Computer Science, Netanya Academic College, 1 University St., Netanya 42365, Israel

Intel Corporation, Haifa, Israel

Keywords:

WiMAX, Bursts, FEC Blocks, Data Blocks, Goodput.

Abstract:

In this paper we address an aspect of the mutual inﬂuence between the PHY layer budding blocks (FEC

blocks) and the MAC level allocations in the Uplink and Downlink of IEEE 802.16e/WiMAX systems, In

these systems it is possible to transmit MAC level frames, denoted MAC PDUs, such that a PDU contains

an integral number of ﬁxed size Data Blocks. We compute the optimal size of a PDU that maximizes the

Goodput of the PDU. The Goodput depends on the success probability of the PDU, which in turn depends

on the FEC blocks over which the PDU is allocated. We then compare among the maximum PDU Goodputs

in different sizes of the FEC blocks and the Data Blocks. The main outcome is that the PDU Goodput is

sensitive only in the case where Data Blocks are very large. We also give guidelines on how to choose the best

Modulation/Coding Scheme (MCS) to use in a scenario where the Signal-to-Noise Ratio (SNR) can change

signiﬁcantly during transmissions, in order to maximize the PDU Goodput.

1 INTRODUCTION

Broadband Wireless Access (BWA) networks consti-

tute one of the greatest challenges for the telecom-

munication industry in the near future. These net-

works fulﬁll the need for range, capacity, mobil-

ity and QoS support from wireless networks. IEEE

802.16e (IEEE, 2005), also known as WiMAX (

Worldwide Interoperabilityfor MicrowaveAccess ) is

the industry name for the standards being developed

for broadband access.

IEEE 802.16e is a cell based, Point-to-MultiPoint

(PMP) technology, providing high throughput in

Wireless Metropolitan Area networks (WMANs) .

The IEEE 802.16e standard reference model includes

the Physical and Medium Access Control (MAC) lay-

ers of the OSI protocol stack. Multiple physical layers

are supported, operating in the 2-66 GHz frequency

spectrum and supporting single and multi-carrier air

interfaces, each suited to a particular environment.

For IEEE 802.16e to be able to fulﬁll the promise

for high speed service, it must efﬁciently support ad-

vanced Modulation and Coding schemes (MCSs) and

progressive scheduling and allocation techniques.

In this study we focus on the inﬂuence between

the PHY layer budding blocks (FEC blocks) and the

length of the MAC layer frames denoted MAC PDUs,

in the Uplink and Downlink of IEEE 802.16e sys-

tems, assuming that Data Blocks are transmitted in

the PDUs, as will be explained later.

1.1 The IEEE 802.16e/WiMAX

Network Structure

IEEE 802.16e/WiMAX is a standard for a Broadband

Wireless Access (BWA) network (IEEE, 2005) which

enables home and business subscribers high speed

wireless access to the Internet and to Public Switched

Telephone Networks (PSTNs). The system is com-

posed of a Base Station (BS) and subscribers, de-

noted Mobile Stations (MSs), in a cellular architec-

ture. The transmissions in a cell are usually Point-to-

Multipoint, where the BS transmits to the subscribers

on a Downlink channel and the subscribers transmit

to the BS on an Uplink channel.

A common PHY layer used in IEEE 802.16e

is Orthogonal Frequency Division Multiple Access

(OFDMA) in which transmissions are carried in

transmission frames (IEEE, 2005). Every frame is a

matrix in which one dimension is a sub-channel (band

of frequencies) and the other dimension is time. A

cell in the matrix is denoted as a slot. The number of

data bits that can be transmitted in a slot is a function

315

Sharon O. and Alpert Y..

Optimal MAC PDU Size in ARQ-enabled Connections in IEEE 802.16e/WiMAX Systems.

DOI: 10.5220/0003974903150322

In Proceedings of the International Conference on Signal Processing and Multimedia Applications and Wireless Information Networks and Systems

(WINSYS-2012), pages 315-322

ISBN: 978-989-8565-25-9

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

of the Modulation and Coding scheme (MCS) that is

used in the slot.

A Burst in a frame is a subset of consecutive slots

sharing the same MCS, which is designated to the

MSs and to the BS for their transmissions. In this

paper we assume that the Convolutional Turbo Code

(CTC) is used as the coding scheme, and in this case

a Burst also maps Forward Error Correction (FEC)

blocks to the slots. In this paper knowing the de-

tails behind the FEC technology is unnecessary so we

will not elaborate on this subject. The only property

needed is that all the data bits in a FEC block have

some probability p to arrive successfully at the re-

ceiver.

1.2 Transmissions in IEEE 802.16e

Systems

The BS and the MSs transmit Protocol Data Units

(PDU) within Bursts. The MAC layer of IEEE

802.16e is connection oriented and PDUs, which are

the MAC level frames, thus belong to MAC connec-

tions (IEEE, 2005). Within PDUs the BS and the

MSs transmit their application packets that are de-

noted Service Data Units (SDU). An SDU can be an

IP packet, ATM cells, etc. The PDUs are used to

map SDUs into the MAC connections, to protect the

SDUs from transmission errors, to enable encryption

of the SDUs, etc. Each PDU has a ﬁxed header, de-

noted Generic MAC Header (GMH). This header is

mainly used to associate a PDU to a MAC connec-

tion. Optionally, a PDU also has a CRC ﬁeld. Any of

the other aforementioned functions performed on the

PDU payload requires an additional subheader. All

the (sub)headers within a PDU are considered to be

PDU overhead.

Let p be the probability that all the bits of a FEC

block, after decoding, arrive correctly at the receiver.

This probability is a function of several parameters

such as the Coding rate, the number of decoding iter-

ations in the case of Turbo codes (Huang, 1997), the

Signal-to-Noise Ratio (SNR) of the channel and the

length, in bits, of the FEC block (Huang, 1997). p

is bigger for longer FEC blocks. In this paper, based

on (Alpert et al., b), we assume that all the FEC blocks

are of the same size and that p is similar for all the

FEC blocks of a transmission frame, i.e. there is no

correlation dependency between the success probabil-

ities of FEC blocks of the same size in a transmission

frame.

The probability Q that a PDU arrives correctly at

the receiver is the probability that all its bits arrive

correctly. This is also the probability that all the FEC

blocks that contain a part of the PDU arrive correctly

. Thus, in view of the above assumption on p, if a

PDU is transmitted within X FEC blocks, holds Q =

In this paper we concentrate on one type of MAC

connections, ARQ-enabled connections. In such con-

nections the SDUs are divided into Blocks, denoted

Data Blocks, of the same size. This size is deﬁned at

the time when a connection is established. In the case

where the length of an SDU is not an integral number

of the Data Block size, the last Data Block of the SDU

is shorter, but it is not padded.

The purpose of the division into Data Blocks is to

enable the transmitter to know whether the SDUs it

transmits arrive successfully at the receiver. This is

accomplished by ARQ Feed-backs that are transmit-

ted back from the receiver to the transmitter. The re-

ceiver notiﬁes the transmitter about every Data Block

whether it arrived successfully or not. In the case

where a Data Block is not received successfully, it

is retransmitted by the transmitter. The only correct-

ness check that a receiver is performing is in the PDU

level. Thus, the receiver considers all the Data Blocks

in a PDU as either arriving correctly or not.

1.3 Problem Deﬁnition

In view of the inﬂuence that FEC blocks have on the

success probability of PDUs, in this paper we con-

sider one aspect of this inﬂuence and we compute the

optimal length of PDUs in ARQ-enabled connections.

The optimal length is deﬁned as the PDU length that

maximizes the PDU Goodput. The PDU Goodput is

deﬁned as the ratio between the number of data bits

in a PDU that arrive correctly at the receiver, to the

total number of bits of the PDU. The PDU Goodput

is computed as follows.

We assume that every PDU contains the Generic

MAC Header (GMH), the CRC ﬁeld and one addi-

tional subheader which is used to number the Data

Blocks in the connection. In addition there might be

bits that are a remainder, as will become clear later.

All the overhead and remainder bits are not counted

in the Goodput computation.

This is actually an approximation. It can happen that

the bits of a FEC block that are contained in a PDU arrive

correctly, and thus also the PDU, while other bits of the FEC

block arrive damaged. However, we use this approximation

following the WiMAX radio performance testing (WiMAX,

2008). In this testing it was found that the bursty nature of

errors in the air IF, and the operation of the interleaver in

CTC codes, tend to disperse the bit errors ( after decoding )

over the FEC block, so that there is usually more than a sin-

gle error, and the errors would be distant from one another.

The result is that all the PDUs, with bits in a FEC block,

would most likely suffer.

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Assume that every PDU contains X equal sized

FEC blocks. Every FEC block contains F data bits

and has a probability p to arrive correctly at the re-

ceiver. Thus, as mentioned, the probability that the

PDU arrives correctly at the receiver is p

. If a PDU

does not arrive correctly at the receiver all the Data

Blocks in the PDU are considered to be lost and are

all retransmitted.

Thus, a PDU is transmitted/retransmitted until

success ( Actually, there is a limit on the number of

retransmissions. When this limit is reached without

a positive ack, the PDU is dropped). If the success

probability is p

, and successive transmissions are in-

dependent, then the average number of transmissions

Let H be the total number of overhead bits in

the PDU, and R the number of bits in the remainder.

Then, the PDU Goodput is

(F·X−H−R)p

F·X

. In this pa-

per we ﬁnd the optimal X such that the PDU Goodput

is maximized, for different values of F and different

Data Blocks’ sizes, which have a direct relation on the

amount of remainder bits in the PDU.

1.4 Related Work

The performance of IEEE 802.16e/WiMAX systems

has been extensively investigated. The interested

reader can ﬁnd in (So-In et al., 2009) and (Seker-

cioglu et al., 2009) a very good survey on WiMAX

performance. Most of the papers deal with scheduling

methods and the efﬁciency of transport layer proto-

cols in IEEE 802.16e systems. These papers assume

the assignment of Bursts to MSs. However, they do

not consider the issue of efﬁcient transmissions in the

Bursts. The only works that we are aware of, and that

deal with the mutual inﬂuence between the PHY layer

budding blocks (FEC blocks) and the MAC layer

PDUs in IEEE 802.16e/WiMAX systems are (Mar-

tikainen et al., 2008), (Alpert et al., b), (Alpert et al.,

2010) and (Alpert et al., a). In (Martikainen et al.,

2008) the optimal size of PDUs is computed, given

ﬁxed length FEC blocks and the transmission of a Bit

stream. However, the PDU size in (Martikainen et al.,

2008) is not accurate because it should have been

rounded off to an integral number of FEC blocks, as

was shown later in (Alpert et al., b). (Alpert et al.,

2010) and (Alpert et al., a) consider the division of

Bursts into PDUs in a way that maximizes the utiliza-

tion of the Burst. However, they do not deal with the

issue of MAC connections carrying ﬁxed length Data

Blocks.

In this paper we ﬁnd the optimal length of PDUs,

given that only ﬁxed size Data Blocks are transmitted

in the PDUs. We are not aware of works that deal with

this optimality scenario.

1.5 Our Results

We suggest an algorithm to compute the optimal

length of PDUs, given that only ﬁxed size Data

Blocks are transmitted in the PDUs. We generalize

the results from (Martikainen et al., 2008) and (Alpert

et al., b) which deal with the optimal size of PDUs as-

suming the transmission of a Bit stream.

We then compare among the maximum PDU

Goodputs in all the FEC blocks’ sizes and Data

Blocks’ sizes that are allowed in the IEEE

802.16e/WiMAX standard, and ﬁnd that unless the

Data Blocks are not very large, the optimal PDU

Goodput is not sensitive to the above sizes.

We also assume various FEC blocks’ success

probabilities p, p = 0.999, p = 0.99 and p = 0.9, and

give guidelines on how to choose the proper MCS,

which determines the FEC block size, in cases where

the estimation of p is not accurate.

The rest of the paper is organized as follows: In

Section 2 we compute the optimal PDU length for a

data stream, i.e. every Data Block is one bit. We omit

the algorithm that computes the optimal PDU length

for the case of Data Blocks of length larger than one

bit. In Section 3 we compare between the PDU Good-

puts in various FEC Blocks’ and Data Blocks’ sizes,

and give guidelines on how to determine the proper

MCS.

2 THE OPTIMAL LENGTH OF

PDUs WITH A BIT STREAM

We compute the maximum PDU Goodput assuming

a Bit stream, i.e. we assume that the length of the

Data Blocks is one bit. Let G(X) be the Goodput of

a PDU with X FEC Blocks. Thus, G(X) =

FX−H

·FX

(1−

), where H is the total number of overhead

bits in the PDU. In order to maximize the Goodput we

derive the expression of the Goodput according to X

and ﬁnd that the optimal X, denoted X

∗

, equals

∗

(1+

1−

Hln(p)

) (1)

Notice that X

∗

must be an integer. Therefore, we

need to check which of the two values, ⌊X

∗

⌋ or ⌈X

∗

⌉

yields a better Goodput.

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3 GOODPUT RESULTS AND

DISCUSSION

In IEEE 802.16e/WiMAX there are 8 possible Mod-

ulation/Coding Schemes (MCS) (IEEE, 2005). See

Table 1. We only consider 7 of them since 64QAM-

1/2 is practically not used (Alpert et al., 2010). In

every MCS there can be various size FEC blocks.

In the following discussion we only consider the

longest ones. We denote the number of bits in the

longest FEC block in every MCS by F. In QPSK-1/2,

16QAM-1/2 and 64QAM5/6 holds F=480. In QPSK-

3/4, 16QAM-3/4, 64QAM-1/2 and 64QAM-3/4 holds

F=432. In 64QAM-2/3 holds F=384. See Table 1

under column F.

The IEEE 802.16e/WiMAX also allows the fol-

lowing Data Blocks’ sizes only : 128, 256, 512, 1024,

2048, 4096 and 8192 bits. Recall that we denote by B

the size of a Data Block.

In Figure 1 we assume three FEC block success

probabilities p: 0.999, 0.99 and 0.9 . In the ﬁgure we

show, for the three success probabilities and for all the

possible values of B and F, the maximum PDU Good-

puts. We assume that the PDU contains the GMH and

CRC ﬁelds of 6 and 4 bytes respectively, and one sub-

header of 3 bytes which contains the serial numbers of

the Data Blocks. Thus, the total number of the PDU

overhead bits is 104. Notice that every PDU size can

also have remainder bits, which are not used for the

transmission of data. This happens when the PDU

size, minus the overhead bits, is not divided by the

Data Block size. There is a trade-off in determining

the optimal PDU length: on one hand adding another

FEC block to a PDU reduces its success probability.

However, on the other hand, it adds data bits to the

PDU, which contribute to the Goodput. Recall that

the use of ﬁxed size Data Blocks only, results with re-

mainders which reduce the Goodput. Also, especially

for long Data Blocks, their size mandates a minimum

number of FEC blocks in a PDU, in order to accom-

modate at least one Data Block.

We see for p = 0.999 that the Goodputs for all

the possible values of B and F are almost the same,

and very high, due to the high value of p. There is

some reduction in the Goodput for B=8192 because

many FEC blocks are needed to accommodate one

such Data Block, with somewhat low PDU success

probability.

For p = 0.99 and 512 ≤ B ≤ 2048, F=432 is

slightly better than the other two values of F. For

512 ≤ B ≤ 2048 and F=432, the optimal PDU sizes

are all 5 FEC blocks. For F=480 the optimal sizes are

11,11 and 9 FEC blocks respectively, and for F=384

they are 7,11 and 11 respectively. For all the consid-

ered values of B, F=432 has a remainder of 8 bits after

5 FEC blocks, and thus it uses the ﬁrst 5 FEC blocks

very efﬁciently. In F=480 the remainders in the short

PDUs are quite large, over 200 bits, and therefore

the optimal PDU size is relatively large compared to

F=432, and the Goodput, therefore, is slightly lower.

For F=384 the addition of one Data Block to the PDU

sometimes requires the addition of two FEC blocks.

On one hand this addition contributes to the Goodput

because there are more data bits. On the other hand

it causes the optimal PDU length to be slightly larger

than for F=432, with a smaller success probability,

and therefore with a small reduction in the Goodput.

In summary, compared to F=480 the case of F=432

is better because of smaller remainders in the short

PDUs. Compared to F=384 it is better because in the

later the PDU size sometimes has ”jumps” in order to

accommodate an additional Data Block.

Notice that for B=4096 and B=8192 the large

number of FEC blocks that is needed to accommo-

date at least one Data Block causes a low PDU suc-

cess probability. This is the dominant parameter and

the FEC blocks’ sizes F and the remainders are less

important. Therefore, the Goodputs are almost the

same for all the values of F.

For p = 0.9 every additional FEC block reduces

the Goodput signiﬁcantly and therefore, for B=128,

256, 512, 1024 the best F is the one where a low

remainder is received ﬁrst. For B=128 and F=384

a remainder of 24 bits happens after 2 FEC blocks,

resulting with F=384 having the best Goodput. For

B=256 both F=384 and F=480 have low remainders

after 3 FEC blocks while in F=432 there is a small re-

mainder only after 4 FEC blocks. For B=512, B=1024

and F=384, a low remainder is received after 3 FEC

blocks while for F=432 and F=480 the ﬁrst three FEC

blocks have a large remainder. Therefore, F=384 has

the highest Goodput. For B=2048, 4096 and 8192 the

large number of FEC blocks that is needed to accom-

modate at least one Data Block makes all the Good-

puts low, with a lower impact to the remainders.

In Figure 2 we compare the Goodput in the case

of a PDU with a Bit stream (Eq.1) to the Goodput of

PDUs with Data Blocks. Figures 2(A),(B) and (C)

show the results for F=480, 432 and 384 respectively.

Since the results are similar in all the cases of F, we

only concentrate in the case of F=480.

We again consider p = 0.999, p = 0.99 and p =

0.9. For p = 0.999 the high FEC success probability

makes the number of FEC blocks in the optimal size

PDUs less dominant. The Goodput in Bit stream is

slightly better than in the case of Data Blocks only

due to the remainders in the later. For B=8192 the

optimal size of a PDU is 35 FEC blocks and it con-

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Table 1: The number of slots j, the number of data bits F and the success probability p in various SNR values of the largest

FEC block in various MCSs.

MCS j F

SNR(dB)

2 2.5 3 3.5 4 4.5 5 5.5 6

QPSK 1/2 10 480 48 0.998 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

QPSK 3/4 6 432 72 0.38 0.85 0.96 0.998 0.999 0.999 0.999 0.999 0.999

16QAM-1/2 5 480 96 * * 0.43 0.82 0.976 0.998 0.999 0.999 0.999

16QAM-3/4 3 432 144 * * * * * * 0.42 0.79 0.957

64QAM-2/3 2 384 192 * * * * * * * * *

64QAM-3/4 2 432 216 * * * * * * * * *

64QAM-5/6 2 480 240 * * * * * * * * *

MCS SNR(dB)

6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12

QPSK 1/2 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

QPSK 3/4 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

16QAM-1/2 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

16QAM-3/4 0.995 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

64QAM-2/3 * * * 0.56 0.79 0.941 0.991 0.999 0.999 0.999 0.999 0.999

64QAM-3/4 * * * 0.33 0.46 0.73 0.92 0.990 0.999 0.999 0.999 0.999

64QAM-5/6 * * * * * 0.3 0.41 0.45 0.8 0.959 0.994 0.999

Figure 1: The Goodput of the optimal size PDUs in various FEC Block sizes and success probabilities, H=104 bits.

tains two Data Blocks. This large number of FEC

blocks reduces the PDU success probability, and to-

gether with the remainder, makes the difference be-

tween the Goodputs of the Bit stream and the Data

Blocks the biggest in this case.

For p = 0.99 and B=128 or B=256 the optimal

PDU sizes for Data Blocks are 4 FEC blocks, com-

pared to 5 FEC blocks in the case of a Bit stream.

However, the remainders in the case of Data Blocks

make their Goodputs slightly lower than that of a Bit

stream.

For 512 ≤ B ≤ 4096 the optimal size PDUs are

between 9 to 11 FEC blocks. Since there are large

remainders in the short PDUs, the optimal size PDUs

are relatively long. The relatively big size of the op-

timal PDUs results with a low success probability of

the PDUs and therefore, compared to p = 0.999, the

Goodput of the Bit stream is relatively much better

OptimalMACPDUSizeinARQ-enabledConnectionsinIEEE802.16e/WiMAXSystems

319

Figure 2: Comparison between the Goodput of a Bit stream and PDUs with Data blocks for various FEC blocks’ sizes and

success probabilities, H=104 bits.

than those of the Data Blocks. This effect becomes

much more dominant for p = 0.9 where the Goodput

of the Bit stream is now much better than those of

Data Blocks.

In Figure 3 we show the same results as in Fig-

ure 2, but from a different view point. In Figure 3 we

show, for every optimal size PDU, how many data bits

are transmitted successfully, on average, in a single

FEC block. E.g., for F=480, p = 0.999 and B=8192,

the optimal PDU size is 35 FEC blocks and the Good-

put is 0.9416 . Thus, the number of data bits that are

transmitted successfully in the PDU is 15427, or 440

bits/FEC block.

For every possible FEC blocks’ and Data Blocks’

sizes, and for p = 0.999, p = 0.99 and p = 0.9, we

show the average number of data bits that are trans-

mitted in a FEC block. Above each marker we also

show the number of FEC blocks in the optimal PDU

size. Thus, e.g. for F=480, B=8192 and p = 0.999,

440 data bits are transmitted, on average, in a FEC

block, and the optimal size PDU contains 35 FEC

blocks. The results follow those in Figure 2. For

p = 0.999 and p = 0.99 the data bits that are transmit-

ted successfully per a FEC block are about the same

for all the Data Blocks’ sizes. For p = 0.9 and for the

large Data Blocks this number is smaller dramatically,

following the signiﬁcant drop in the Goodputs, as it is

shown in Figure 2.

We also checked the results for H = 184. This

amount of overhead assumes two additional ﬁelds in

the PDU which are used for encryption. The results

are about the same as for the case H = 104.

The following outcomes can be derived from Fig-

ures 1- 3:

1. For p = 0.999 and p = 0.99 the Goodput results

are not sensitive to the FEC block size F. For

p = 0.9 this is not the case. This outcome is

important due to the following aspect. In IEEE

802.16e/WiMAX the BS decides, for every Burst,

on the MCS to be used. This decision is based,

among other parameters, on the Signal-to-Noise-

Ratio (SNR) of the channel, which can change

during the connection life time. The change in the

MCS can result with a different F. However, the

Data Block size is determined once, when a con-

nection is established, and it is not changed later.

Consider Table 1 again. In this table we show, for

every MCS, the number j of slots that the largest

FEC block occupies in the transmission frame, the

number F of bits in every such FEC block, and the

success probability p of the FEC blocks in var-

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320

Figure 3: The average number of Data bits that a FEC block transfers successfully for various FEC blocks’ sizes and success

probabilities. H=104 bits.

ious SNR values. The success probabilities are

received from (Jum, 2010). The input from (Jum,

2010) contains graphs that show, for every MCS,

the success probabilities for all possible size FEC

blocks in the considered MCS, in different SNR

values.

Consider SNR=12dB. In this SNR the largest

FEC blocks in all the MCSs have p = 0.999. In

this SNR it is most efﬁcient to use either 64QAM-

2/3, 64QAM-3/4 or 64QAM-5/6. These MCSs

have the same PDU Goodputs as all the other

MCSs, and in all the possible values of B (Fig-

ure 1). Also, the FEC blocks in all the MCSs

transfer the same average number of data bits

(Figure 3). However, the above 3 MCSs use the

lowest number of transmission slots, j =2. There-

fore, in these MCSs the transmission slots are

used most efﬁciently, i.e. transfer the largest num-

ber of data bits. But what happens if the measure

of the SNR is not accurate, and the actual success

probability of the FEC blocks is little lower than

0.999 ? Assume that B=512. Then, it is better

to use 64QAM-3/4 with F=432 because, on one

hand, for p = 0.999, this F has a PDU Goodput

equal to that of the other values of F, but, on the

other hand, for p = 0.99, it is better than the oth-

ers. Therefore, if according to the measured SNR

holds p = 0.999, but actually it is 0.99, F=432 is

the best in both cases. If the measured SNR is

far from the actual one, and instead of p =0.999

holds p =0.9, then it is better to choose 64QAM-

2/3 with F=384 because this is the best F for both

p =0.999 and p = 0.9.

2. For p = 0.999 and p = 0.99 there is no signif-

icant difference between the Goodputs received

for a Bit stream and for Data Blocks, except for

B=8192. This conclusion is important because it

shows that the division into Data Blocks, in or-

der to increase the reliability of the transmissions,

does not effect the efﬁciency in using the trans-

mission channel.

3. For p = 0.999 and p = 0.99 all the Data Blocks’

sizes between 128 and 4096 have about the same

Goodput results. For B=8192 the Goodput results

are lower.

4. For p = 0.9 it is signiﬁcantly more efﬁcient to use

Data Blocks of sizes between 128 to 1024 bits.

OptimalMACPDUSizeinARQ-enabledConnectionsinIEEE802.16e/WiMAXSystems

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4 CONCLUSIONS

In this paper we compute the size of a PDU that

maximizes its Goodput where only Data blocks are

transmitted. We then compare among the maximum

PDU Goodputs in different sizes of the FEC blocks

and the Data Blocks. The main outcome is that the

PDU Goodput is sensitive only in the case where Data

Blocks are very large. We also show that it is possible

to give guidelines on how to choose the best Mod-

ulation/Coding Scheme (MCS) to use in a scenario

where the Signal-to-Noise Ratio (SNR) can change

signiﬁcantly during transmissions, in order to maxi-

mize the PDU Goodput.

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