CREATING AND PERFORMING WIMAX PHYSICAL LAYER SIMULATIONS IN MATLAB

A Project work

By

Khalid Taher Mohammed Al-Hussaini Matriculation No: 27203864

Submitted to

Communications Laboratory

Faculty of Electrical Engineering and Computer Science

at the University of Kassel

In partial fulfilment of the requirements for

M.Sc. degree in Electrical Communications Engineering

WS 2008/2009

Supervisor: Thomas Edlich

1

Acknowledgements This report is carried out in the Communications Laboratory. Faculty of Electrical

Engineering and Computer Science, University of Kassel, Kassel, Germany.

I would like to take the opportunity to express my sincere gratitude to Prof. Dr. sc.techn. Dirk

Dahlhaus for offering me the opportunity to work on this project work, as well as for his

valuable suggestions and discussions.

I would like to take the opportunity to thank my supervisor Dipl.-Ing. Thomas Edlich and I

appreciate his sincere help and advices during this work.

Khalid Taher Mohammed Al-Hussaini

2

Abstract This project describes the mandatory features of the WiMAX OFDM physical layer (PHY)

based on IEEE 802.16. These mandatory features are implemented by using Matlab. The

project also studies the performance of a WiMAX transceiver.

Chapter 1 introduces an overview about WiMAX standard and briefly explains its PHY and

also its medium access control (MAC). Chapter 2 describes the mandatory blocks of WiMAX

transmitter. Chapter 3 describes the mandatory blocks of WiMAX receiver. Chapter 4

presents the simulation test and results of our model. Perfect synchronization is assumed and

AWGN channel is implemented. Chapter 5 presents the conclusion and future work.

3

Table of Contents 1. Introduction .................................................................................................................. 4

1.1 Fixed Wireless Access ............................................................................................ 4 1.1.1 Point to point FWA .............................................................................................. 4 1.1.2 Point to Multipoint (PMP) ................................................................................... 5 1.1.3 Multipoint to Multipoint (mesh network) .......................................................... 5

1.2 WiMAX .................................................................................................................. 6 1.3 The IEEE 802.16 Standard Family ........................................................................ 7 1.4 The WiMAX MAC Layer ...................................................................................... 8 1.5 The WiMAX Physical Layer .................................................................................. 9

1.5.1 WiMAX OFDM PHY .......................................................................................... 9 1.5.2 Adaptive Modulation ......................................................................................... 10 1.5.3 Forward Error Correction (FEC) ..................................................................... 11

2. WiMAX Transmitter .................................................................................................. 12 2.1 Randomizer .......................................................................................................... 12 2.2 Channel Encoder .................................................................................................. 14

2.2.1 Outer Reed Solomon Encoder .......................................................................... 14 2.2.3 Puncturing ......................................................................................................... 17 2.2.4 Interleaver ......................................................................................................... 18

2.3 Modulation Mapper ............................................................................................. 19 2.4 OFDM modulation .............................................................................................. 20

2.4.1 Pilot modulation ............................................................................................ 20 2.4.2 Inverse Fast Fourier Transform (IFFT)....................................................... 21

3. WiMAX Receiver........................................................................................................ 22 3.1 OFDM Demodulation........................................................................................... 22

3.1.1 Removal of CP ............................................................................................... 23 3.1.2 Fast Fourier Transform (FFT) ..................................................................... 23 3.1.3 Disassemble OFDM Frame ........................................................................... 23

3.2 Demapping............................................................................................................ 24 3.3 Channel Decoder .................................................................................................. 24

3.3.1 Deinterleaving ............................................................................................... 24 3.3.2 Depuncturing ................................................................................................. 25 3.3.3 Convolutional decoder .................................................................................. 25 3.3.4 Reed Solomon Decoder ................................................................................. 26

3.4 De-randomizer...................................................................................................... 26 4. WiMAX Simulation .................................................................................................... 27

4.1 OFDM Symbol Parameters and Transmitted Signal .......................................... 27 4.2 Modulation Schemes and Coding Rates .............................................................. 29 4.3 Simulation Test and Result .................................................................................. 29

5. Conclusion and Future Work..................................................................................... 31 Bibliography ....................................................................................................................... 32

4

1. Introduction

1.1 Fixed Wireless Access Fixed wireless access (FWA) is promising solution for last mile access. It is also called

wireless local loop or radio fixed wireless. In FWA system the sender and receiver are both

stationary instead of mobile, hence the name fixed. There are three different types of FWA

topologies [4]:

1.1.1 Point to point FWA It consists of two base stations with the communication statically configured for a link

between these two base stations only as shown in figure 1.1. These types of systems are often

used as backhaul.

Fig. 1.1: Point to point FWA

5

1.1.2 Point to Multipoint (PMP) It consists of access network with one more powerful base station and many smaller

subscriber stations as shown in figure 2.1. Here the subscriber station can deploy directed

antennas towards the base station.

Fig. 1.2: Point to multipoint FWA

1.1.3 Multipoint to Multipoint (mesh network) It consists of access network (mesh network) where there is no centralized base station as

shown in figure 1.3. As result the covered area is increased.

Fig. 1.3: Multipoint to multipoint FWA

6

The FWA can work outdoors over Metropolitan Area Network (MAN) or smaller areas, thus

the signal can undergo interference, fading, multipath propagation, radio noise, pathloss and

many other factors.

Fig. 1.4: Different network sizes

1.2 WiMAX

The word WiMAX is an acronym for “Worldwide Interoperability for Microwave Access”, It

is a broadband FWA system with the goal of delivering ”last mile” fixed, nomadic, portable

and mobile wireless connections on a metropolitan scale. It has been designed for point-to-

multipoint operation, between one base station (BS) and several subscriber stations (SS). It

provides specifications for both fixed Line of sight (LOS) communication in the range of 10-

66 GHz (IEEE 802.16c), and fixed, portable, non-LOS communication in the range of 2-11

GHz (IEEE 802.16a & IEEE 802.16d). WiMAX is not truly new; rather, it is unique because

it was a bottom-up design to deliver maximum throughput to maximum distance while

offering 99.999 percent reliability. The IEEE 802.16 standard specifies the Physical (PHY)

Layer and Medium Access Control (MAC) layer for BWA within MAN.

WAN

MAN

LAN

PAN

IEEE 802.16 Wireless MAN

IEEE 802.11 Wireless LAN

IEEE 802.20 (proposed)

IEEE 802.15 Bluetooth

WiMAX

7

1.3 The IEEE 802.16 Standard Family

The 802.16 standards appeared in 1998 and aim to deal with the (PMP) BWA system, the

main functionalities described in table 1.1. Standards 802.16a, 802.16c and 802.16d contain

upgrades to the original standard and have been integrated into the 802.16-2004 standards [1].

Table 1.1: Basic Data on IEEE 802.16 Standards. [1]

8

1.4 The WiMAX MAC Layer

The main task of the WiMAX MAC protocol is to provide an interface between the higher

transport layers and the physical layer. and it consist of three sublayers.

• The Service Specific Convergence Sublayer (SSCS): provides transformation and

mapping into MAC Service Data Unit (SDU1).

• MAC Common Part Sublayer (MAC CPS): is the core of the WiMAX MAC. It

provides bandwidth allocation, connection management, connection establishment and

connection maintenance.

• Privacy Sublayer: provides authentication, secure key exchange and encryption.

Fig. 1.5: OSI 7-layer model - IEEE 802.16 Standard scope

1 Service Data Unit: the data units exchanged between two adjacent protocol layers.

Application Layer

Presentation Layer

Session Layer

Transport Layer

Network Layer

Data Link Layer

Physical Layer

Service Specific Convergence Sublayer (SSCS)

MAC Common Part Sublayer (MAC CPS)

Physical Layer

Privacy Sublayer

9

1.5 The WiMAX Physical Layer

The PHY in WiMAX is based on orthogonal frequency division multiplexing (OFDM). It

defines duplexing techniques, frequency division duplex and time division duplex (TDD,

FDD) and supports multiple RF bands 10-66 GHz for LOS and below 11GHz for NLOS also

it supports flexible bandwidths up to 134 MHz in 10-66 GHz band and up to 20 MHz below

11 GHz band. It defines multiple PHYs for different applications described in table 1.2:

Table 1.2: Variants of WiMAX PHY. [3]

1.5.1 WiMAX OFDM PHY OFDM is a multicarrier transmission scheme where the information is transmitted on multiple

subcarriers, which can be divided to three types of carriers:

• Data carriers for data transmission.

• Pilot carriers for various estimation purpose.

• Null carriers no transmission at all, for guard bands and DC carrier.

Figure 1.6 shows the OFDM frequency description.

10

The WiMAX have slightly different implementations of the OFDM PHY. Fixed WiMAX,

which is based on IEEE 802.16-2004, uses a 256 FFT-based OFDM PHY. Mobile WiMAX,

which is based on the IEEE 802.16e-2005 standard, uses a scalable OFDMA-based PHY. In

the case of mobile WiMAX, the FFT sizes can vary from 128 to 2048.

Fig. 1.6: OFDM frequency description. [4]

1.5.2 Adaptive Modulation WiMAX system utilizes adaptive modulation to improve the throughput based on the

propagation conditions. It is obvious from figure 1.7, if good SNR ratio is achieved system

can switch to highest throughput modulation (64QAM). If there is fading, the system is

switched to low throughput modulation (BPSK) without the need to drop the connection.

Fig 1.7. Adaptive modulation. [2]

11

1.5.3 Forward Error Correction (FEC) WiMAX system doesn't need the transmitter to retransmit any additional information which

receiver uses for correcting errors which occurred during the transmission over channel.

WiMAX utilizes Forward Error Correction techniques to detect and correct errors. It use Reed

Solomon FEC, convolutional encoding and interleaving algorithms. WiMAX is using all

these techniques to recover the errors that occurred due to fading or burst errors.

12

2.WiMAX Transmitter This chapter describes the mandatory parts of WiMAX transmitter. The functional blocks

which compose the WiMAX transmitter are shown in figure 2.1. The MAC Payload Data

Units (PDUs2) are fed into the randomizer which randomize the data. Afterwards, the

randomized data is coded by using channel encoder as, which consist of Reed Solomon,

convolutional encoder and puncture. The coded data is interleaved by interleaver and mapped

into QAM symbol . Afterwards, the mapped data enter into the OFDM modulation which

consist of assemble OFDM frame, 256 IFFT and cyclic prefix insertion. Then the data is

transmitted over AWGN channel. Through the rest of chapter the individual block of the

WiMAX transmitter will be explained.

Fig. 2.1: The mandatory parts of WiMAX Transmitter.

2.1 Randomizer The information bits are randomized before the transmission. The randomizer, which is the

first block in the transmitter, performs randomization of input data on each burst on each

allocation to prevent a long sequence of 1's and 0's. This is implemented by using a Pseudo

2 The MAC PDU is the data unit exchanged between the MAC layers of BS and its SSs.

MAC PDU

Transmitter Randomizer

Channel

Encoder

Modulation

Mapper

Cyclic Prefix Insertion

Reed Solomon Encoder

Convolutional Encoder Puncture Interleaver

OFDM

Modulation

256 IFFT

Assemble OFDM Frame

13

Random Binary Sequence (PRBS) generator, which is made of a 15 bits shift register and two

XOR gates as shown in figure 2.2. [4]

Fig. 2.2: Point PRBS for data randomization. [4] For downlink burst the initial vector for the shift register (Linear-Feedback Shift Register

(LFSR) possessing characteristic polynomial (1 + + ) is 100101010000000 and the

scrambler should be reset at the start of each burst. The vector, which is shown in figure 2.3,

is placed at the start of subsequent bursts. We utilize frame number for referring to the frame

in which the downlink burst is transmitted. [4]

Fig. 2.3: OFDM randomizer downlink initialization vector for burst #2...N. [4]

14

2.2 Channel Encoder The channel encoder consists of an FEC scheme (i.e. a concatenation of an outer RS code and

an inner CC), puncturing and interleaving as shown in figure 2.1. The randomized data passes

to the RS encoder and then passes to CC encoder. After this, the encoded data is punctured

and interleaved.

2.2.1 Outer Reed Solomon Encoder The RS code is special kind of linear block codes, which is suitable for correcting burst errors.

The RS encoder add redundancy to the data sequence in order to correct the errors, which

occurred during transmission. This RS code is derived from a systematic RS ( = 255, = 239, = 8) code using a Galois field specified as (2 ), with is the number of

bytes after encoding, is the number of data bytes before encoding and is the number of

data byte that can be corrected.

The following polynomials are used for the systematic code: [4]

Code Generator Polynomial: ( ) = ( + )( + )( + ) … . ( + ) (2.2)

Field Generator Polynomial: ( ) = + + + + 1 (2.1)

Fig. 2.4: The Reed Solomon code.

Data Bytes Redundant Bytes

2

15

In WiMAX RS code is shortened and punctured to enable variable block sizes and variable

error-correction capability. We can obtain a shortened block of bytes by adding 239 − zero bytes before the data block, these 239 − zero bytes are discarded after encoding. RS

code can correct up to symbols, where can be expressed as = ( − )/2. When a

codeword is punctured to permit ′ bytes to be corrected. Only the first 2 ′ of the total 16

parity bytes shall be employed as shown in figure 2.5. For instance, QPSK with (5 6⁄ ) CC

code rate, the RS code is (( = 40), ( = 36), ( = 2)) as shown in table 2.1. The

bit/byte conversion has to be MSB first3. [4]

Fig. 2.5: Shortening and puncturing process of the RS code.

3 Matlab expects the first bit to be the most significant bit in the symbol (for more detail, see Matlab help).

239 - K' Data Bytes K' Data Bytes

239 - K' Data Bytes

K' Data Bytes

K' Data Bytes

16 parity Bytes

Encoding process

Final code

K' Data Bytes 2T'

16

2.2.2 Inner Convolutional Encoder

The random errors which occurred during the transmission over channel can be corrected by

using the convolutional encoder. Unlike a block coder, convolutional coder is not a

memoryless device. The RS encoded bits are encoded by the binary convlutional encoder,

which has native rate of 1/2, a constraint length equal to 7 and a polynomial description [171 133] as shown in equation (2.3), (2.4) to produce its two code bits. The generator is

shown in figure 2.6. [4]

1 = 171 (2.3) 2 = 133 (2.4) Fig. 2.6: Convolutional encoder of rate 1/2. [4]

In WiMAX, after the randomized data is encoded by RS encoder, the encoded bits are

forwarded to convolutional encoder. The block sizes and the code rates, which are used for

the different types of modulation and code rates, are given in table 2.1.

17

Table 2.1: Mandatory channel coding per modulation. [4] .

2.2.3 Puncturing Puncturing is a technique that is utilized on the output of the convolutional encoder. It allows

the encoding and decoding of higher code rates using standard rate 1/2 encoders and decoders.

The purpose of using puncturing is to achieve variable code rate. This is done by deleting bits

from the output stream of a low rate encoder. The bits are deleted according to the table 2.2.

In this table, “1” means a transmitted bit and “0” denotes a removed bit, whereas and are

in reference to figure 2.6. [4]

Table 2.2: The inner convolutional code with puncturing configuration. [4]

18

2.2.4 Interleaver The interleaver is the final part of channel encoder used to randomize the coded bits in order

to make the possible errors at the receiver uncorrelated. All encoded bits coming from RS-CC

encoder are interleaved by a block interleaver with a block size, which depends on the number

of coded bits per allocated subchannels per OFDM symbol . The number of coded bits

depend on modulation scheme as shown in table 2.3. The interleaver in WiMAX is defined by

a two step permutation. The first permutation ensures that adjacent coded bits are mapped

onto non adjacent carriers and is defined by equation (2.5): [4] [1]

12⁄ ∙ + ( 2⁄ ) (2.5)

The second permutation ensures that adjacent coded bits are mapped alternately onto less or

more significant bits of the constellation and is defined by Equation (2.6): [4] [1]

= ∙ ( ⁄ ) + + − 12 ∙ ⁄ ( ) (2.6)

With = 2⁄ , and is the number of coded bit per carrier, is number

of coded bits per OFDM symbol, k is index of coded bits before first permutation, is

index of coded bits after first permutation and before the second permutation and is index

of coded bits after second permutation

Table 2.3: Block sizes of the bit interleaver. [4]

.

19

2.3 Modulation Mapper In the modulation mapper, the interleaved bits are converted to a sequence of complex valued

symbols. WiMAX supports different modulation schemes shown in figure 2.7. The

modulation constellation used in WiMAX is two types of phase shift keying (PSK)

modulation (binary (BPSK) and quadrature (QPSK)) and two types of quadrature amplitude

(QAM) modulation (16QAM and 64QAM). The complex constellation value is scaled by

factor (Normalization constant), such that the average transmitted power is unity, c equals 1 √2 ⁄ for QPSK, 1 √10⁄ for 16-QAM, 1 √42⁄ for 64-QAM (if we assume that all symbols

are equally likely).

Fig. 2.7: BPSK, QPSK, 16-QAM and 64-QAM constellations. [4]

20

2.4 OFDM modulation

In WiMAX, each OFDM symbol consists of 256 subcarriers as shown in figure 2.8. They can

be divided into.

1. 192 data subcarriers that are used for conveying data.

2. 8 pilot subcarriers that are used for conveying pilot symbols.

3. 56 null subcarriers that have no power allocated to them, including the DC subcarrier

and the guard subcarriers toward the edge.

Fig. 2.8: Frequency domain representation of OFDM symbol. [1]

2.4.1 Pilot modulation Before inserting a pilot to its specified position, as shown in figure 2.8, it has to be modulated.

Pilots can be generated by Pseudo Random Binary Sequence (PRBS) generator as shown in

figure 2.9.

21

. Fig. 2.9: PRBS for pilot modulation. [4] The polynomial of PRBS generator is: ( ) = + + 1 (2.7)

Pilot subcarriers are used for various estimation purposes.

2.4.2 Inverse Fast Fourier Transform (IFFT)

To convert mapped data, which is assigned to all allocated data subcarriers of the OFDM

symbol, from frequency domain into time domain, the IFFT is used. We can compute time

duration of the IFFT time signal by multiply the number of FFT bins by the sample period.

Zeros are added at the end and beginning of OFDM symbol. These zero carriers are used as

guard band to prevent inter channel interference (ICI).

2.4.3 Cyclic Prefix insertion (CP) To avoid inter symbol interference (ISI) a cyclic prefix is inserted before each transmitted

symbol. That is achieved by copying the last part of an OFDM symbol to the beginning as

shown in figure 2.10. WiMAX supports four different duration of cyclic prefix (i.e. assuming is the ratio of guard time to OFDM symbol time, this ratio is equal to 1/32, 1/6, 1/8 and

1/4).

. Fig. 2.10: OFDM symbol with the cyclic prefix. [4]

22

3.WiMAX Receiver This chapter describes the mandatory parts of WiMAX receiver. The functional blocks which

compose the WiMAX receiver as shown in figure 3.1 are the reverse functional blocks of

WiMAX transmitter. The received data coming from AWGN channel is fed into the OFDM

demodulation, which consist of removal of CP, Fast Fourier Transform (256 FFT) and

disassemble OFDM frame. Then, the data is performed by de-mapper and afterwards the

demapped data enter the channel decoder. Channel decoder consists of de-interleaver, de-

puncture, convolutional decoder and finally RS decoder. The final block in receiver is the de-

randomizer. Through the rest of chapter the individual block of the WiMAX receiver will be

explained.

Fig. 3.1: The mandatory parts of WiMAX Receiver.

3.1 OFDM Demodulation The OFDM demodulation is the reverse operation of OFDM modulation. Here, the signal is

converted back from time domain to frequency domain. The first step in OFDM demodulation

is to remove the CP. Then FFT is performed. Afterwards the OFDM frame is disassembled.

256 FFT

OFDM

Demodulation De-mapper

Channel

Decoder

Removal of CP

De-randomizer AWGN Channel

MAC

Disassemble OFDM Frame

De-interleaver De-puncture Convolutional Decoder

RS Decoder

23

3.1.1 Removal of CP The first step after the arrival of data is to remove CP as shown in figure 3.2. We know that

CP has no effect in case of using AWGN channel. It is useful when the multipath channel is

used. If CP larger than the delay multipath the ISI is completely removed.

Fig. 3.2: Removal of CP

3.1.2 Fast Fourier Transform (FFT) To convert received data from time domain to frequency domain, the FFT is used. Afterward,

the zeros, which were added at the end and beginning of OFDM symbol (guard bands) at the

transmitter are removed from the assigned places.

3.1.3 Disassemble OFDM Frame After doing FFT and removing guard bands, the data and pilots, which is described in section

2.4 should be separated. This is achieved by using the disassembler.

OFDM symbol CP

Received data

Removal of CP

OFDM symbol

24

3.2 Demapping To convert the waveforms created at the modulation mapper to the original transformed bits,

the de-mapper is used. The demapping is used for decision rules with the goal of making a

decision about which bit "zero" or "one", was sent. The decision metric can be hard decision

or soft decision. The minimum distance rule is the optimum decision in case of independent

and identical distributed (iid) Gaussian noise [5].

3.3 Channel Decoder The channel decoder consists of deinterleaving, depuncturing, Viterbi decoder and RS

decoder as shown in figure 3.1. The sequence of bits coming from de-mapper pass to channel

decoder. The channel decoder tries to recover the original bits.

3.3.1 Deinterleaving To remove the effect of interleaving process achieved at the transmitter, the deinterleaving is

used. Deinterleaver in WiMAX is defined by two-step permutation.

The first permutation is defined by equation (3.1): [4]

= ∙ ( ⁄ ) + + 12 ∙ ⁄ ( ) = 0,1, … , − 1 (3.1)

The second permutation is defined by equation (3.2): [4] = 12 ∙ − − 1 ∙ 12 ∙ ⁄ = 0,1, … , − 1 (3.2) With = 2⁄ , and is the number of coded bit per carrier, is number

of coded bits per OFDM symbol (received block), is the index of a received bit before the

first permutation, is the index of that bit after the first and before the second permutation

and is the index of that bit after the second permutation [4]. The number of coded bits

depend on modulation scheme as shown in table 2.3 in previous chapter.

25

3.3.2 Depuncturing

Depuncturing the reverse process of puncturing. Puncturing is done by deleting bits from

certain places which was explained in table 2.2 in the previous chapter. At receiver, the value

of deleted bits are unknown, so the receiver add zeros in those places, which are known for.

These inserted zeros can be seen as erasures from the channel. They have no effect on the

metric measurement of the Viterbi algorithm.

3.3.3 Convolutional decoder To decode the bit stream coming after depuncturing, the convolutional decoder is used. The

Viterbi algorithm is the one of methods, which is commonly used for decoding the convoluti-

onal codes. The Viterbi algorithm performs the maximum likelihood decoding. It is described

by using the trellis diagrams as shown in figure 3.3. The algorithm compute the distance

between the received sequence at certain time and each trellis paths entering each state at the

same time. When two paths met in single state, the algorithm choose the one, whose better

metric (i.e. smaller Hamming distance). And so on, till remain a single path which represents

the received data (the surviving path). Comparing the received sequence with every possible

code sequence is the best way to detect the random errors. [6]

Fig. 3.3: The trellis diagram. [6]

26

3.3.4 Reed Solomon Decoder The RS decoder is the last part in channel decoder. The operation of RS decoder is the reverse

operation of RS encoder. we know that the output data block of RS encoder was ( + 2 )

as shown in figure 2.4 in previous chapter. So, to make the output of convolutional decoder

entering to the RS decoder as the same. The one that output the encoder block, the first step is

this output is reshaped. That means, each 8 bits is converted to byte and rearranged it

according to the table 3.1. For instance, QPSK with (5 6⁄ ) CC code rate, the RS code is

(( = 40), ( = 36), ( = 2)). Afterwards the 239 − zero bytes is added at the

beginning of each block. And the 16 − 2 parity bytes are obtained by add zeros. At the end

we select from the output of RS decoder only original data bytes. Then these bytes are

converted to stream of bits.

Table 3.1: Mandatory channel coding per modulation. [4]

3.4 De-randomizer The stream of bits coming from RS decoder is forwarded to the de-randomizer. The structure

and the operation of the de-randomizer is the same of randomizer. That means, that de-

randomizer is implemented by the PRBS generator, that was explained in previous chapter.

27

4.WiMAX Simulation The aim of our simulation model achieved by this project work is to evaluate performance of

WiMAX, which was built based on the IEEE 802.16 OFDM PHY layer standard [4]. We have

built our simulation model by using only the mandatory blocks, which were explained in

previous chapters. We have used Matlab® R2007b to do so. The model consists of three parts

as shown in figure 4.1 (i.e. transmitter, receiver and AWGN channel), which were described

previously.

Fig. 4.1: Simulation model

4.1 OFDM Symbol Parameters and Transmitted Signal

The OFDM symbol has two types of parameters. The first one is primitive parameters and the

second one is derived parameters as shown in table 4.1 [4]. We have used some of these

parameters in our simulation model. And the parameters of the transmitted OFDM signal is

shown in table 4.2 [4].

AWGN Channel

MAC PDU Transmitter

Randomizer

Channel Encoder

Modulation

Mapper

OFDM Modulation

MAC PDU

Receiver

De-randomizer

Channel Decoder

De-mapper

OFDM

Demodulation

Transmitter components

Receiver components

Channel

28

Table 4.1: OFDM symbol parameters

Table 4.2: Parameters of transmitted OFDM signal

Primitive parameters Derived parameters

Nominal channel bandwidth (BW) NFFT: smallest power of 2 greater than ( ) Number of used subcarriers ( )

Sampling Frequency (Fs =Floor(n.BW/8000) X 8000)

Sampling factor (n)

Subcarrier Spacing (∆ = Fs/NFFT)

The ratio of CP time (G)

Useful Symbol Time (Tb =1/∆ )

CP Time (Tg =G.Tb)

OFDM Symbol Time (Ts = Tb + Tg)

Sampling Time (Tb/NFFT)

parameters Value

NFFT 256

200

n

For channel bandwidths that are a multiple of 1.75 MHz then n = 8/7. G

1/4

Number of lower frequency guard subcarriers 28

Number of higher frequency guard subcarriers 27

29

4.2 Modulation Schemes and Coding Rates

The parameters of simulation model, which is built in this project are [4] :

• Modulation type is QPSK.

• RS code rate is 3/4.

• CC code rate is 5/6.

4.3 Simulation Test and Result After the model simulation is created, we can test each blocks of model. WiMAX standard

document [4] has test vectors for each blocks of model. they make us sure that each block

works correctly. This test vectors are as following :

Input Data (MAC PDU ) (Hex)

45 29 C4 79 AD 0F 55 28 AD 87 B5 76 1A 9C 80 50 45 1B 9F D9 2A 88 95 EB AE B5 2E

03 4F 09 14 69 58 0A 5D.

Randomized Data (Hex)

D4 BA A1 12 F2 74 96 30 27 D4 88 9C 96 E3 A9 52 B3 15 AB FD 92 53 07 32 C0 62 48 F0

19 22 E0 91 62 1A C1.

Reed–Solomon encoded Data (Hex)

49 31 40 BF D4 BA A1 12 F2 74 96 30 27 D4 88 9C 96 E3 A9 52 B3 15 AB FD 92 53 07 32

C0 62 48 F0 19 22 E0 91 62 1A C1 00.

Convolutionally Encoded Data (Hex)

3A 5E E7 AE 49 9E 6F 1C 6F C1 28 BC BD AB 57 CD BC CD E3 A7 92 CA 92 C2 4D BC

8D 78 32 FB BF DF 23 ED 8A 94 16 27 A5 65 CF 7D 16 7A 45 B8 09 CC.

Interleaved Data (Hex)

77 FA 4F 17 4E 3E E6 70 E8 CD 3F 76 90 C4 2C DB F9 B7 FB 43 6C F1 9A BD ED 0A 1C

D8 1B EC 9B 30 15 BA DA 31 F5 50 49 7D 56 ED B4 88 CC 72 FC 5C.

30

For instance, when we completed the implementation of RS encoder. We tested it by entering

the test vector of randomized data (Hex) mentioned above as input. And we found that the

output vector of our RS encoder is similar to the Reed–Solomon encoded Data vector (Hex)

mentioned above. That means that our RS encoder block works correctly. And so on.

After we tested the whole model by using the above tests and made sure that each block

works correctly. The performance of WiMAX was carried out. The figure 4.2 shows us the bit

error rate (BER) versus the signal to noise ratio (SNR) plot for WiMAX with QPSK as a

modulation type and code rate equal 3/4.

Fig. 4.2: Performance of WiMAX with QPSK.

31

5. Conclusion and Future Work In this project work, the mandatory of WiMAX transceiver is described and implemented

based on the IEEE 802.16 OFDM PHY layer standard [4]. Matlab® R2007b is used to do so.

The goal was to calculate the performance of PHY layer under AWGN channel. The model

can support all types of modulation with different code rates. In this model, we have assumed

that the receiver and the transmitter are completely synchronized. This project work can be

extended by using the optional block turbo coding (BTC) in order to improve the performance

of FEC.

32

Bibliography

[1] Jeffrey G. Andrews, Arunabha Ghosh, Rias Muhamed, " Fundamentals of WiMAX

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