Efﬁcient Coupled PHY and MAC use of Physical Bursts by

ARQ-Enabled Connections in IEEE 802.16e/WiMAX Networks

Oran Sharon

1

, Amit Liron

2

and Yaron Alpert

3

1

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

2

Department of Computer Science, Haifa University, Israel

3

LANTIQ, Ra’anana, 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 networks. In

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

integral number of ﬁxed size Data Blocks. PDUs are transmitted over PHY Bursts, which are divided into FEC

Blocks. We suggest an algorithm that computes the best way to deﬁne PDUs in a Burst in order to maximize

the Burst Goodput. We also give guidelines on how to choose the best Modulation/Coding Scheme (MCS) to

use in the Burst, given the SNR of the channel.

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, mo-

bility and QoS support from wireless networks.

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

WiMAX(Worldwide Interoperability for Microwave

Access) 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 to 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/location of the MAC layer frames de-

noted as MAC PDUs, in the Uplink and Downlink of

IEEE 802.16e systems, 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 as 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

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 a sub-

191

Sharon O., Liron A. and Alpert Y..

Efﬁcient Coupled PHY and MAC use of Physical Bursts by ARQ-Enabled Connections in IEEE 802.16e/WiMAX Networks.

DOI: 10.5220/0004490201910198

In Proceedings of the 10th International Conference on Signal Processing and Multimedia Applications and 10th International Conference on Wireless

Information Networks and Systems (WINSYS-2013), pages 191-198

ISBN: 978-989-8565-74-7

Copyright

c

2013 SCITEPRESS (Science and Technology Publications, Lda.)

set of MSs for their transmissions. In the most com-

mon case a Burst is designated to a single MS, and this

is the case that we consider in this paper. 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 details behind the

FEC technology is unnecessary so we will not elabo-

rate 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 receiver.

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

iterations 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., 2013), 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

probabilities 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.

1

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

is transmitted within X FEC Blocks, holds Q = p

X

.

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.

In this paper we focus on the following question:

Given the Signal-to-Noise Ratio (SNR) of the chan-

nel, a Burst and a MCS, which determines the size

and number of FEC Blocks in the Burst, and the suc-

cess probability of a FEC Block, what is the most ef-

ﬁcient way to transmit PDUs in the Burst so that the

Burst Goodput is maximized. We then suggest an-

other performance criteria which counts the number

of Data Blocks that are transmitted successfully in a

Burst. Finally, we give guidelines on how to choose

the MCS to use in the Burst according to the two per-

formance criteria. All that is described in Section 2.

As far as we know, the problem considered in this pa-

per has not been investigated before.

There are many papers that deal with the efﬁ-

ciency of WiMAX networks. Due to space limits we

only include in the References section the papers that

we use directly in the current paper.

1

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 dam-

aged. 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

single 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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2 MAXIMIZING THE BURST’S

GOODPUT

2.1 Problem Description

We are given an SNR, a Burst of S slots, an inﬁnite

set of Data Blocks of length B bits each and the num-

ber of PDU overhead bits. The problem that we want

to solve is as follows: Given a Modulation/Coding

Scheme (MCS), how to divide the Burst into PDUs

such that the Burst Goodput is maximized. The given

MCS determines the number and the length of the

FEC Blocks in the Burst, and their success probabil-

ity.

2.2 Deﬁnition of the Burst’s Goodput

We are given:

1. A Burst of L FEC Blocks

2. Every FEC Block contains F bits

3. Every FEC Block has probability p to arrive suc-

cessfully at the receiver

4. An inﬁnite number of Data Blocks. Each has a

length of B bits.

5. Every PDU has O overhead bits. We as-

sume that O < F since according to the IEEE

802.16e/WiMAX standard (IEEE, 2005) the to-

tal length of the overhead ﬁelds in a PDU is most

likely to be smaller than one FEC Block.

We want to transmit as many Data Blocks as pos-

sible in the Burst such that the Burst Goodput (B-

Goodput) is maximized. The B-Goodput is deﬁned

as follows: Let D be the number of Data bits that

are transmitted successfully in the Burst. Then, B-

Goodput=

D

L·F

. D is computed as follows: Assume

that a PDU is deﬁned over k FEC Blocks. Then, the

success probability of the PDU is p

k

and every Data

Block in the PDU contributes B · p

k

bits to D. D is the

summation of the contributions of all the Data Blocks

in the Burst.

2.3 Characteristics of the Optimal

Location of PDUs

Since Data Blocks are transmitted in PDUs, we need

to decide on how many PDUs shall be allocated in the

Burst, their length and their location. We call these

decisions the division of the Burst into PDUs.

In principle a PDU can start at any bit position

within a FEC Block. We design a dynamic program-

ing algorithm that checks all these possibilities within

a FEC Block. However, for the case where 2B−1 < F

we show that a PDU can begin only at the ﬁrst B bits

of a FEC Block, or at the last B − 1 bits of a FEC

Block and thus the algorithm does not need to go over

all the bit positions in a FEC Block.

Consider a Burst of L FEC Blocks as shown in

Figure 1. We number the FEC Blocks in the Burst

from right to left, such that the right most FEC Block

is FEC Block 1 and the left most FEC Block is FEC

Block L.

In view of the above, we divide the discussion into

two cases, 2B − 1 < F and 2B − 1 ≥ F.

2.3.1 The Case 2B − 1 < F

Theorem 1. There is an optimal division of the Burst

in which the ﬁrst PDU begins at the beginning of the

left most FEC Block (left edge of the Burst in Figure 1)

and every other PDU either begins immediately after

the previous one ( back to back ) or at the beginning of

the next FEC Block following the end of the previous

PDU (towards the right edge of the Burst).

Proof. Consider an optimal division S of the Burst. If

S fulﬁlls the Theorem then we are done. Otherwise,

we show how to change S so that the new optimal di-

vision fulﬁlls the Theorem. Notice that in general, if

we move a PDU in the Burst towards the left edge of

the Burst, then as long as the beginning of the PDU

does not cross a FEC Block boundary, we either do

not change the number of FEC Blocks over which the

PDU is deﬁned, or we decrement this number by one.

If the PDU crosses a FEC Block boundary, then if it

returns to the same position within a FEC Block as

its original position, then the number of FEC Blocks

over which it is deﬁned is not changed. Therefore, if

the ﬁrst PDU in S is not allocated from the left edge

of a Burst, one can move it to this location without

increasing the B-Goodput. We now consider the sec-

ond PDU in S, from the left, and move it an integral

number of F bits until it reaches a point where there

is at most one FEC Block boundary between its start

position and the end of the ﬁrst PDU. Now, the second

PDU can be moved to reach the end of the ﬁrst PDU,

if it does not cross the boundary of a FEC Block, or

otherwise to the beginning of the FEC Block immedi-

ately following the ﬁrst PDU. By following this pro-

cess for every PDU, one can generate a division that

fulﬁlls the Theorem.

From now on we consider only divisions that fulﬁll

Theorem 1. We also denote the ﬁrst (B-1) bits in a

FEC Block as the Starting edge of the FEC Block,

and the last B bits as the Ending edge.

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Theorem 2. In an optimal division of a Burst, every

PDU ends either within the Starting edge or within

the Ending edge of a FEC Block.

Proof. Consider an optimal division of the Burst. If

all the PDUs end within the above edges of a FEC

Block then we are done. Otherwise, let the k

th

PDU

from the left of the Burst, denoted PDU

k

, to be the

ﬁrst PDU from the left that ends at a bit of a FEC

Block which is outside the above edges. If PDU

k+1

begins at the next FEC Block boundary, or in the case

that PDU

k

is the last PDU in the Burst, one can add

at least one Data Block to the Burst, at the end of

PDU

k

, without changing the success probabilities of

the existing PDUs, thus increasing the B-Goodput and

contradicting the optimality of the given division.

Therefore, assume that PDU

k+1

begins imme-

diately after PDU

k

. If the success probability of

PDU

k+1

is larger than that of PDU

k

then one can

move one Data Block from PDU

k

to PDU

k+1

, thus

increasing the B-Goodput, contradicting the optimal-

ity of the given division. If the success probability of

PDU

k

is larger than that of PDU

k+1

then again one

can move one Data Block from PDU

k+1

to PDU

k

.

The success probability of PDU

k

is not changed. The

success probability of PDU

k+1

can only increase (we

shorten PDU

k+1

), and again the overall B-Goodput in-

creases, contradicting the optimality of the given di-

vision.

It turns out that the success probabilities of PDU

k

and PDU

k+1

must be equal. One can now move Data

Blocks from PDU

k

to PDU

k+1

until one of the follow-

ing occurs: there are Data Blocks left in PDU

k

but the

movement of one more Data Block will cause the be-

ginning of PDU

k+1

to cross a FEC Block boundary,

or there are no Data Blocks left in PDU

k

. In the ﬁrst

case PDU

k

ends within the Starting edge of a FEC

Block. In the second case we can omit PDU

k

from

the division and move PDU

k+1

to begin at either the

beginning of a FEC Block or after PDU

k−1

.

Repeating the above process ends with a division

as claimed in the Theory.

2.4 An Algorithm to Compute the

B-Goodput

Theorems 1 and 2 establish the theoretic basis for

a dynamic programming algorithm to ﬁnd the op-

timal division of a Burst. We denote this algo-

rithm by Division-Find. Algorithm Division-Find

builds a table T of L rows, as the number of FEC

Blocks in the Burst. The ﬁrst row of T refers to

FEC Block 1 of the Burst and so on. Row num-

ber k shows the optimal use of FEC Blocks 1 to

k of the Burst, as it is explained in the following.

Every row has (2B − 1) entries, corresponding to

the places within a FEC Block where a PDU can

start, following Theorem 2. These entries of row k

are numbered T [k, 1],T [k,2], ...,T [k, B],T [k,F − (B −

2)],...,T [k, F].

The entries in T contain an average number of

successfully transmitted data bits, and not Goodputs.

The Goodput can be received by dividing the value in

an entry by the Burst size. The entries are computed

as follows. In row 1 we ﬁll entries T [1, 1], ...,T [1,B]

only. Entry T[1, j],1 ≤ j ≤ B is computed assuming

that a PDU begins at bit number j in the FEC Block

and it contains as many Data Blocks as possible. Say

for entry T [1, j] one can allocate a PDU of X FEC

Blocks, starting from bit number j in the FEC Block.

Then T [1, j] = X · B · p.

We now move to row k,2 ≤ k ≤ L − 1. In each

of these rows we ﬁrst compute entries T [k, F − (B −

2)],...,T [k, F] and then entries T [k,1],...,T [k , B]. We

ﬁrst handle row 2 and consider entries T [2, j ], F −

(B − 2) ≤ j ≤ F. We want to ﬁnd how the section

of the Burst, starting from bit j of the second FEC

Block, and ending at the end of the Burst, is most ef-

ﬁciently used, i.e. how one shall divide this section

into PDUs such that the maximal average number of

data bits are transmitted successfully. One needs to

consider 3 cases, derived from Theorems 1 and 2, as

shown in Figure 2, and choose the maximum among

the 3. Notice that not all the cases in Figure 2 always

exist. This depends on the relation between O + B to

F, e.g. if O + B is larger than 2B − 1 in case B in

Figure 2 then this case actually does not exist. Also

notice that in cases B and C one uses entries from row

1.

We now move to entries T [2,1],..., T [2, B]. Con-

sider entry T [2, j] in this set. We assume that a PDU

begins at bit j of the FEC Block and consider all the

possibilities to allocate PDUs at the section of the

Burst that begins at bit j of the second FEC Block

and that ends at the end of the Burst. We have 3 cases,

as shown in Figure 3, again derived from Theorems 1

and 2. The value of T [2, j] is the maximum among all

the cases. Notice that in case C we use an entry in row

2 that was already computed, and in case B we use an

entry in row 1. Again, not all the 3 cases always exist.

Concerning row L notice that at most two en-

tries need to be computed. From Theorem 1 entry

T [L,1] must be computed. Also, let X ≥ 1 be the

largest integer such that O +X · B +1 ≤ F. Then entry

T [L,O + X · B + 1], if exists, must also be computed.

As in the previous rows entry T [L,O + X · B + 1] is

computed before entry T [L, 1] and notice that entry

T [L,1] is the result of the algorithm that we are look-

ing for.

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Figure 1: Numbering the FEC Blocks in a Burst.

Figure 2: Computing entry T [2, j],F − (B − 2) ≤ j ≤ F in the table of algorithm Division-Find.

Figure 3: Compuing entry T [2, j],1 ≤ j ≤ B in the table of algorithm Division-Find.

EfficientCoupledPHYandMACuseofPhysicalBurstsbyARQ-EnabledConnectionsinIEEE802.16e/WiMAX

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195

Lemma 1. The value of every entry in row k of T ,

2 ≤ k ≤ L − 1, is computed in O(k)

Proof. Consider an entry T [k, j],F − (B−2) ≤ j ≤ F.

In order to compute this entry one needs to consider

two possibilities. The ﬁrst one corresponds to the case

that the next PDU begins at the start of FEC Block

number k − 1. This case has the value T [1,k − 1]. The

other possibility corresponds to the case where a PDU

begins at bit j of FEC Block k. This PDU can end,

according to Theorem 2, at 2(k − 1) different Starting

and Ending edges. Thus, we need to choose the max-

imum among 2(k − 1) + 1 = 2k − 1 cases, where each

case is computed in O(1), possibly using entries from

previous rows.

Considering an entry T [k, j],1 ≤ j ≤ B, the argu-

ments are similar to the case above.

Theorem 3. The time complexity of Division-Find is

O(L

2

B).

Proof. First consider the computation of the entries

in row k, 2 ≤ k ≤ L − 1. In such a row there are 2B − 1

entries and each one is computed in O(k)(Lemma 1).

Thus, row k is computed in O(B · k). Summing over

all the rows k we get that their entries are computed

in O(L

2

B). In row 1 we compute only B entries, each

in O(1), and in row L we compute entries T (L,1) and

T [1,O + X · B] (see above) in O(L). The Theorem fol-

lows.

2.4.1 The Case 2B − 1 ≥ F

Notice that if 2B − 1 ≥ F then a PDU can end at every

position within a FEC Block. Therefore, algorithm

Division-Find is changed to contain only F entries in

any row, and its time complexity is O(L

2

F).

Remark 1. It is sometimes possible to receive the

same optimal B-Goodput in a Burst in different divi-

sions, such that the divisions contain different num-

ber of Data Blocks. For example, for L = 2 FEC

Blocks, F = 480 bits, B = 45 bits, O = 45 bits and

p = 0.9 there are two divisions that yield the maxi-

mum B-Goodput. In one division there is one PDU

with 20 Data Blocks and in another division there

are 2 PDUs, each being deﬁned over a separate FEC

Block, with 9 Data Blocks each. Our algorithm is im-

plemented to choose the division with the largest num-

ber of Data Blocks.

2.5 Modulation/Coding Scheme (MCS)

Selection

IEEE 802.16e/WiMAX enables the use of the fol-

lowing Modulation/Coding schemes (MCSs) (IEEE,

2005): QPSK-1/2, QPSK-3/4, 16QAM-1/2, 16QAM-

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

64QAM-5/6. 64QAM-1/2 is practically not used

and so we will not consider this scheme any fur-

ther (Alpert et al., 2010).

Recall that when a Burst is deﬁned, actually it uses

slots in the Physical layer. In any MCS the set of

slots in a Burst is divided into groups such that any

group is a FEC Block. In every MCS it is possible to

deﬁne groups of slots of different sizes, resulting in

FEC Blocks of different sizes. Here we only consider

the largest FEC Blocks that are possible in the MCSs.

We denote by j the number of slots, in every MCS,

needed to deﬁne the largest FEC Block. We show the

value of j for every MCS in Table 1, together with

F, the number of bits that the largest FEC Block con-

tains. We also show the success probability p of the

largest FEC Block in every MCS and in several values

of the SNR (Signal-to-Noise-Ratio). An entry with ∗

stands for N/A, which means that the success prob-

ability of a FEC Block in the considered MCS and

SNR is 0 . These probabilities are taken from (Jum,

2010). The input from (Jum, 2010) contains graphs

that address, for every MCS allowed in WiMAX, and

for many realistic SNR values, the success probabil-

ity for all possible length FEC Blocks in the consid-

ered MCS. We see from Table 1 that for low SNRs

(bad channels) only few MCSs are applicable, while

in high SNRs all the MCSs are applicable.

We also see that there is a trade-off in using the set

of slots of a Burst. On one hand it is possible to decide

on a reliable MCS to be used in the Burst. However,

the number of FEC Blocks, and so the number of bits

in the Burst, is low. On the other hand, a less reli-

able MCS results in more FEC Blocks and bits in the

Burst, but with a smaller success probability of the

FEC Blocks.

2.6 Performance Results

One criteria to decide on the best MCS is the B-

Goodput. In Table 2 we show the B-Goodput for ev-

ery MCS in every SNR value between 2 to 12 dB, for

the case of S = 900 slots, B = 128 bits and O = 104

bits. B = 128 bits is the smallest Data Block size

that is possible in IEEE 802.16e (IEEE, 2005). With

O = 104 bits we assume that a PDU contains the

GMH and the CRC ﬁelds of 6 and 4 bytes respec-

tively as overhead, and one Fragmentation SubHeader

(FSH) of 3 bytes, which is used when a PDU contains

Data Blocks (IEEE, 2005). The results in Table 2 are

received by using algorithm Division-Find. Accord-

ing to the B-Goodput criteria QPSK-1/2 can be cho-

sen as the best MCS to use in every SNR. However,

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196

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

2 2.5 3 3.5 4 4.5 5 5.5 6

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

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

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

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

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

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

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

MCS SNR

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

Table 2: The number of slots j, the number of data bits F and the B-Goodput in various MCSs and SNR values, for the case

S = 900 slots, B = 128 bits and O = 104 bits.

MCS j F SNR

2 2.5 3 3.5 4 4.5 5 5.5 6

QPSK 1/2 10 480 0.957 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969

QPSK 3/4 6 432 0.225 0.589 0.791 0.955 0.969 0.969 0.969 0.969 0.969

16QAM-1/2 5 480 * * 0.254 0.548 0.847 0.957 0.970 0.970 0.970

16QAM-3/4 3 432 * * * * * * 0.249 0.511 0.781

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

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

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

MCS SNR

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

QPSK 1/2 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969

QPSK 3/4 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969

16QAM-1/2 0.970 0.970 0.970 0.970 0.970 0.970 0.970 0.970 0.970 0.970 0.970 0.970

16QAM-3/4 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969 0.969

64QAM-2/3 * * * 0.373 0.527 0.741 0.897 0.967 0.967 0.967 0.967 0.967

64QAM-3/4 * * * 0.196 0.273 0.453 0.911 0.920 0.969 0.969 0.969 0.969

64QAM-5/6 * * * * * 0.172 0.241 0.267 0.519 0.800 0.925 0.970

Table 3: The number of slots j, the number of data bits F and the average integral number of successfully transmitted Data

Blocks in various MCSs and SNR values, for the case S = 900 slots, B = 128 bits and O = 104 bits.

MCS j F SNR

2 2.5 3 3.5 4 4.5 5 5.5 6

QPSK 1/2 10 480 323 327 327 327 327 327 327 327 327

QPSK 3/4 6 432 114 298 400 483 490 490 490 490 490

16QAM-1/2 5 480 * * 172 370 572 646 655 655 655

16QAM-3/4 3 432 * * * * * * 252 517 790

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

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

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

MCS SNR

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

QPSK 1/2 327 327 327 327 327 327 327 327 327 327 327 327

QPSK 3/4 490 490 490 490 490 490 490 490 490 490 490 490

16QAM-1/2 655 655 655 655 655 655 655 655 655 655 655 655

16QAM-3/4 981 981 981 981 981 981 981 981 981 981 981 981

64QAM-2/3 * * * 503 711 1000 1210 1305 1305 1305 1305 1305

64QAM-3/4 * * * 297 414 687 1383 1410 1471 1471 1471 1471

64QAM-5/6 * * * * * 290 406 451 875 1350 1560 1636

in QPSK-1/2 the Burst contains only 90 FEC Blocks

of 480 bits each. On the other hand, 64QAM-5/6 con-

tains 450 FEC Blocks of 480 bits each. This enables

the transmission of more bits in the Burst, although

with a reduced success probability.

Therefore, in Table 3 we show the average number

of Data Blocks that are transmitted successfully in the

Burst, again for every MCS in every SNR. The results

in Table 3 are received again by algorithm Division-

Find. This time we divide the number of successfully

transmitted Data bits by a Data Block size. Accord-

ing to this criteria, the best MCS can change from one

SNR to another. As the channel becomes better, i.e.,

higher SNR values, the MCS that enables to trans-

mit a larger number of bits in a Burst is becoming

the best MCS to use. For example, in SNR=12 dB

the best MCS is 64QAM-5/6 because the B-Goodput

of all the MCSs are about the same, but 64QAM-5/6

enables the largest number of bits in the Burst. For

SNR= 9 dB , 64QAM-2/3 enables to transmit suc-

EfficientCoupledPHYandMACuseofPhysicalBurstsbyARQ-EnabledConnectionsinIEEE802.16e/WiMAX

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197

cessfully the largest number of Data Blocks, although

its B-Goodput is only the 5

th

in size. The larger num-

ber of bits in a Burst with 64QAM-2/3 enables to

compensate for the lower B-Goodput.

3 CONCLUSIONS

We suggest two performance criteria for the division

of a given Burst into PDUs that contain Data Blocks.

The ﬁrst criteria measures the relation between the

number of successfully transmitted Data bits to the

Burst size. The second criteria measures the abso-

lute number of successfully transmitted Data bits in

the Burst. The two criteria lead to different choices

of the optimal MACS to use in the Burst, given an

SNR. From the user perspective it seams that the sec-

ond criteria is more important. In this case, as a rule

of thumb, the best MCS in a given SNR is one of the

two MCSs that enable to transmit the largest number

of Data Blocks in the Burst.

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Huang, F. H. (1997). Evaluation of soft output decoding

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