simulation on performance of space time block code

First Edition 2008 © SHARIFAH HAFIZAH SYED ARIFFIN & NORULHUSNA AHMAD 2008

Hak cipta terpelihara. Tiada dibenarkan mengeluar ulang mana-mana bahagian artikel, ilustrasi, dan isi kandungan buku ini dalam apa juga bentuk dan cara apa jua sama ada dengan cara elektronik, fotokopi, mekanik, atau cara lain sebelum mendapat izin bertulis daripada Timbalan Naib Canselor (Penyelidikan dan Inovasi), Universiti Teknologi Malaysia, 81310 Skudai, Johor Darul Ta’zim, Malaysia. Perundingan tertakluk kepada perkiraan royalti atau honorarium. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical including photocopy, recording, or any information storage and retrieval system, without permission in writing from Universiti Teknologi Malaysia, 81310 Skudai, Johor Darul Ta’zim, Malaysia.

Perpustakaan Negara Malaysia Cataloguing-in-Publication Data

OFDM and MIMO-OFDM system / editors: Sharifah Hafizah Syed Ariffin, Norulhusna Ahmad. Includes index ISBN 978-983-52-0660-3 1. Wireless communication systems. 2. Broadband communication systems. 3. Wireless LANs. I. Sharifah Hafizah Syed Ariffin. II. Norulhusna Ahmad. 621.382

Editor: Sharifah Hafizah Syed Ariffin & Rakan Pereka Kulit: Mohd Nazir Md. Basri & Mohd Asmawidin Bidin

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Contents

v

CONTENTS

Preface ix

Chapter 1

The PAPR Performance in WLAN-OFDM System Norhafizah Ngajikin Sharifah Kamilah Syed-Yusof

1

Chapter 2 PAPR Reduction of OFDM Signals using Partial Transmit Sequences Sharifah Kamilah Syed-Yusof Norsheila Fisal Tang Sze Yin

9

Chapter 3 Code Repetition Technique in Reducing Papr of WLAN-OFDM System Norhafizah.Ngajikin Norsheila Fisal Sharifah Kamilah Syed-Yusof

18

Chapter 4 Time-Domain Amplitude Manipulative Papr Reduction Techniques on PRS-OFDM System Sharifah K. Syed-Yusof Norsheila Fisal Muladi

29

Contents

vi

Chapter 5 Peak-To-Average Power Ratio Reduction Technique in PRS-OFDM System Sharifah Kamilah Syed-Yusof Norsheila Fisal Muladi

38

Chapter 6 The Evaluation Of ICI Self-Cancellation Techniques in OFDM Systems Sharifah Kamilah Syed Yusof Norsheila Fisal Muladi

49

Chapter 7 Simulation on Performance of Space Time Block Code Norhafizah Ngajikin Wan. N. Ahmad Norsheila Fisal Sharifah Kamilah Syed-Yusof

58

Chapter 8 Iterative Data Detection And Channel Estimation For Single-Parity Check-Product Coded for Wireless MIMO Communications Systems Muladi, Norsheila Fisal Sharifah Kamiah Yusof

70

Chapter 9 Performance of Block Turbo Coded MIMO Systems Muladi Sharifah Kamilah Syed-Yusof Norsheila Fisal

85

Contents

vii

Chapter 10 The Performance of PRS-OFDM in Multiple Antenna System Sharifah Kamilah Syed Yusof Norsheila Fisal Muladi

96

Chapter 11 The Space-Time-Frequency MIMO-OFDM System with Intercarrier Interference Self-Cancellation Anis Izzati Ahmad Zamani Sharifah Kamilah Syed Yusof Norsheila Fisal

106

Index 115

Preface

ix

PREFACE

Wireless communication has become increasingly important not only for professional applications but also for many fields in our daily routine More and more computers use wireless local area networks (WLANs), and audio and television broadcasting has become digital. Many of the above-mentioned communication systems make use of one of sophisticated technique that is known as orthogonal frequency division multiplexing (OFDM). OFDM is a digital multicarrier transmission technique that distributes the digitally encoded symbols over several subcarrier frequencies in order to reduce the symbol clock rate to achieve robustness against long echoes in a multipath radio channel. The concept of orthogonality between subcarriers is a key to the OFDM system. There are two main setback of OFDM system are Peak-to-Average Power Ratio (PAPR) and Intercarrier Interference (ICI).

This book is a compilation of the research work done on OFDM and MIMO-OFDM systems. The book is organized as follows. In Chapter 1 investigates the Peak-to-Average Power Ratio (PAPR) in OFDM system. Chapter 2 to Chapter 5 explore on some techniques to reduce the PAPR in OFDM system. ICI self-cancellation techniques are explored in Chapter 6. MIMO-OFDM systems are discussed in Chapter 7 to Chapter 11. Preliminary study of space-time (ST) block code is covered in Chapter 7. Iterative data detection schemes are discussed in Chapter 8 and Chapter 9. Chapter 10 deals with the performance of partial response signalling (PRS) OFDM technique in multiple antenna system. A preliminary work on space-time-frequency (STF) OFDM system with the employment of ICI self-cancellation is covered in Chapter 11.

Preface

x

We would like to express our greatest gratitude to the authors of the individual chapters, without whom this book would not exist. And to those who have helped in the completion of this book, we greatly appreciate your assistance.

Sharifah Hafizah Syed Ariffin Norulhusna Ahmad Facuty of Electrical Engineering Universiti Teknologi Malaysia 2008

The PAPR Performance in WLAN-OFDM System

1

1

THE PAPR PERFORMANCE IN WLAN-OFDM SYSTEM Norhafizah Ngajikin

Sharifah Kamilah Syed-Yusof

1.1 INTRODUCTION OFDM is a communication technique that divides a communication channel into a number of equally spaced frequency hands. This modulation scheme is derived from multi-carrier modulation (MCM). A subcarrier that carries a portion of the user information is transmitted in each frequency sub-band. In OFDM, every subcarrier is orthogonal to each other subcarrier.

Due to the summation of signals from each subcarrier in OFDM signal, Peak To Average Power Ratio (PAPR) problem arises. Figure 1.1 illustrates the flow of signal in the OFDM transmitter. ScN multiple subcarriers are added coherently and might contribute a peak in signal envelope that can achieve several dB above the average signal power. An example of power spectrum of the transmitted OFDM signal is shown in Figure 1.2

Figure 1.1 Transmitter

OFDM and MIMO-OFDM System

2

Figure 2 Power Spectrum Of Multi Carrier System

Commonly in a complete transmission system, the signal will be amplified before transmitted for example through an antenna. This condition introduced by the summation of the subcarriers will contribute to a high PAPR. A serious problem of large PAPR occurs if cheap and energy-efficient nonlinear power amplifiers are used in the communication system.

Frequent excursions into the nonlinear operating region contribute to the increment of Bit Error Rate (BER) and spectral regrowth outside the intended frequencies of operation. Reduction of PAPR inconsistency behavior might overcome this problem. The mathematical expression for PAPR is given by equation (1).

In order to keep the PAPR small, the max |sc(t)|2 must be minimized.

(1)


3

This chapter is organized as follows. In section 1.2 we described the OFDM communication model. In section 1.3, the performance of PAPR in WLAN OFDM communication system is investigated. Lastly, section 1.4 concludes the finding of this chapter. 1.2 OFDM COMMUNICATION MODEL Figure 1.3 shows the model of basic OFDM transceiver. In this parallel data transmission scheme, the data is transmitted simultaneously over N orthogonal subcarriers with equal space within the desired transmission bandwidth.

Figure 1.3 OFDM Transceiver

The transmitter converts the input data Cn=C0, C1,…,CN-1

from a serial stream to parallel sets. Before performing the Inverse Fast Fourier Transform (IFFT) this parallel data set are arranged on each subcarrier the frequency domain.

The symmetrical arrangement about the vertical axis is necessary when using the IFFT to change the data into time domain. An IFFT converts the frequency domain data set into samples of the corresponding time domain representation of this data. Specifically, the IFFT is useful for OFDM because it generates samples of a waveform with frequency components satisfying orthogonality conditions. Then, the parallel to serial


4

block creates the OFDM signal by sequentially outputting the time domain samples. Mathematical expression of the transmitted signal, sc(t) is

where Ci ~ binary data vector n ~ number of modulated function f0 ~ lowest frequency of the carrier N ~ no of carrier t ~ OFDM symbol duration

The OFDM receivers basically do the reverse operation of the transmitter. First, the OFDM data are split from a serial stream into parallel sets. The Fast Fourier Transform (FFT) converts the time domain samples back into a frequency domain representation. Thus, the magnitudes of the frequency components correspond to the original data. Finally, the parallel to serial block converts this parallel data into a serial stream to recover the original input data.

There are two assumptions to simplify the analysis. First, it is assumed that the transmission is perfect, where the received signal is approximately similar to the transmitted signal. Secondly it is assumed that synchronization for the whole system is also perfect and will not contribute to ISI problem. In this paper, simulation of OFDM system is based on wireless LAN standard. Numerical values for OFDM parameters are given in Table 1.1 [7].

1.3 PAPR FOR WLAN OFDM SYSTEM Figure 1.4 shows the power spectrum for OFDM system based on WLAN standard. By sending 1000 random hit using 52 carriers, it is found that the maximum peak is 26.6 W. The average power is 11. 6 W. Therefore the calculated PAPR for this signal is 3.6 dB.

(2)


5

Table 1.1 OFDM Parameters for Wireless LAN Standard

Figure 1.4 Power Spectrum of WLAN/OFDM System

1.3.1 Codeword effect There are 16 codeword, which are the combination of 4 binary bits. Table 1.2 list the PAPR value for each code. From several simulations using different combination of bit, it is found that certain bits combination contribute to higher PAPR occurrence. As shown from Figure, code 2, 4, 13 and 15 generate higher PAPR (above 16 dB) compared to the other combinations. The lowest PAPR can be achieved through codes 6 and 11.


6

Table 1.2 PAPR for Different Combination

Figure 1.5 PAPR for Different Code

1.3.2 Code length effect Figure 1.6 shows the effect on PAPR value due to the different length code transmitted. Beside that, PAPR is also influence by the number of subcarriers. As shown from the figure, the different length of code resulted in the same trend of performance.


7

Figure 1.6 PAPR For Different Number Of Carrier

1.4 SUMMARY Based on the simulation result, it can be deduced that PAPR depends on combination of bit (code word) and code length. Different combination of bits provides different PAPR value. The length of the transmitted bit also influences the PAPR where longer codes may gives lower PAPR to the system. Further study will be made to develop an optimum code that will produce low PAPR in WLAN-OFDM. REFERENCES [1] K.G. Paterson and V. Tarokh, “On The Existence and

Construction of Good Codes with Low Peak To Average Power Ratio”, IEEE Transsaction on Information Theory, Vol. 46 No.6, 2000.

[2] C.Tellambura, “Computation of the Continous- Time PAR of an OFDM Signal with BPSK Subcarriers”, IEEE Communication Letters, Vol. 5, No. 5,2001.

[3] P.Michae1, “Introduction To Error Correcting Codes”, Artech House, London, 1995.

[4] A.E Jones et al., “Block Coding Scheme For Reduction of Peak to Mean Envelope Power Ratio of Multicamer Transmission Scheme”, Electronics Letter Vol. 30 No. 25, 1994. 125


8

Authorized licensed use limited to: UNIVERSITY TEKNOLOGI MALAYSIA. Downloaded on December 22, 2008 at 00:03 from IEEE Xplore. Restrictions apply.

[5] LA Tassaduq an R.K Rao, “Weighted OFDM With Block Codes for Wireless Communication”, IEEE Pacific Rim Conference on, Page(s): 441 -444 vol. 2, 2001.

[6] K.G. Paterson, “On Codes with Low Peak to Average Power Ratio for Multicode CDMA“, IEEE International Symposium on Information Theory, 2002.

[7] D. Angela and Collegues, “A Comparison of the HIPERLANQ and IEEE 802.11a Wireless LAN Standards”, IEEE Comm. Magazine, May 2002.

[8] L I. Jr. Cimini and N.R. Sollenberger, “Peak to Average Power Ratioreduction of an OFDM signal using Partial Transmit Sequences”, IEEE Comm. Letters, volume:4, issue: 3, March 2000.

[9] D.C Cox and R.P. Leck, “Distribution of Multipath Delay Spread And Average Access Delay For 910MHz Urban Mobile Radio Paths”, IEEE Trans. Vehic. Tech. VolVT-26, Nov 1997.

[10] M. Lobeira and collegues, “Parameter estimation and indoor channel modeling at 17 GHz for OFDM-based broadband WLAN, Proceedings of IST Mobile Communications Summit, 2000.

PAPR Reduction of OFDM Signals using Partial Transmit Sequences

9

2

PAPR REDUCTION OF OFDM SIGNALS USING PARTIAL TRANSMIT

SEQUENCES Sharifah Kamilah Syed-Yusof

Norsheila Fisal Tang Sze Yin

2.1 INTRODUCTION Orthogonal frequency division multiplexing (OFDM) has been a promising candidate for achieving .high data transmission in mobile environment. OFDM, employing multicarriers modulation (MCM) technique, enable it to transmit signals over multiple subcarriers simultaneously. By dividing the total bandwidth into several narrow subchannels, which are transmitted in parallel, the effects of the multipath delay spread can he minimized. The carriers are made orthogonal to each other by precisely choosing the frequency spacing between them. The spectral overlapping among the subcarriers in OFDM thus, provides better spectral efficiency. OFDM scheme has been adopted in several recent digital wireless broadcast and network standards, including Digital Audio Broadcasting (DAB), Digital Video Broadcasting over terrestrial network (DVB-T, HiperLAN/ and IEEE802.11a [l].

One major drawback of the OFDM is the potentially high peak-to-average power ratio (PAPR), results from the nonstable power. envelopes, a consequences of using independently modulated subcarriers. These carriers may add up constructively or estructively and creates the potential for a large variation in the signal power envelopes. In particular, a baseband OFDM signal


10

with N subcarriers could result a peak power, equal to N times the average power. Therefore, the upper bound of the PAPR can be express by PAPR (dB) = 10 log N; for an example, a PAPR of 21 dB results if the phases of all 128 carriers for every channels line up during a symbol period. When passed through nonlinear devices, such as transmit power amplifier the signal may suffer significant spectral spreading and distortion.

In order to avoid the nonlinear distortion to the very high peak power, the power amplifiers must operate with large power back-offs and in turn leads to inefficient amplification [2]. Therefore, it is favorable to study on the methods in overcoming the PAPR issue. Several alternative solutions have ken proposed to reduce the PAPR, such as clipping and filtering, block coding and selective mapping.

This chapter discusses about another promising technique that has been proposed for improving the PAP statistics of an OFDM signal, termed as the Partial Transmit Sequences approach [3]. This chapter is divided into 5 sections. Section 2.2, gives a brief overview of the fundamentals of PTS in OFDM system. In section 2.3, simulation model had been used is presented. Section 2.4 discusses the results obtained. Lastly, Section 1.5 gives the conclusions of this research work. 2.2 PARTIAL TRANSMIT SEQUENCE (PTS) In OFDM, a block of N symbols, {Xn, n = 0.1,,.., N-1} is formed with each symbol modulating one set of N subcarriers, {fn, n = 0,1, ....N –1}.The N subcarriers spacing is chosen to be orthogonal, that is, fnfn Δ= , where NTf /1=Δ and T is the symbol period. Thus, the complex envelope of the transmitted OFDM signal is represented by

(1)


11

The instantaneous envelope power of the signal is the real-

valued function of P(t) where P(t) = |s(t)|2. The PAPR of the transmitted OFDM signal, s(t) can be defined as

where E[|s(t)|2] denotes the expectation of the average power value.

Partial transmit sequences (PTS) technique is proposed by Muller and Huber in 1997 [3]. Figure 1 below depicts a typical PTS transmitter model.

Figure 1 Partial Transmit Sequences (PTS) Technique

In PTS approach, the input data block is partitioned into disjoint subblocks or clusters, which are combined to minimize the PAPR. The input data block is defined as a vector, X = [X0 X1 ...... ]TNX 1− . Then, the X is partitioned into M disjoint sets, represented by {Xm, m = 1, 2 ... M}. Every cluster consists of a set of subcarriers of equal size. Subblock partition scheme (SPS) performs the division of the subcarriers into multiple disjoint

(2)


12

subblocks by choosing the appropriate subcarriers to be allocated in each subblocks [4]. The clusters then converted to time domain using the N-point Inverse Fast Fourier Transform (IFFT).

Since the FFT is a linear transformation, the representation of the cluster in time domain is known as .partial transmit sequences in the PTS approach. Each transmit sequence is then phase rotated with a constant weighting factor, bm. The modified subcarriers vector can be expressed by

∑=

=M

mmm xbx

1'

where {bm, m = 1, 2,…, M). The weighting factors are carefully chosen by the optimization block that performs a specific algorithm .in searching for the optimized combination of the weighted transmit sequences, which produce the lowest PAPR. Then the optimum signal combination will be transmitted.

However, this scheme requires that the receiver to have the knowledge about the generation of the transmitted OFDM signal. Thus, the phase factors must be transmitted as the side information to the receiver so that it can derotate the subcarriers appropriately [3]. The side information is the redundancy introduced by the PTS, resulting in some loss of efficiency. Though, the PTS is the distortionless scheme and it works with arbitrary at any type of modulation on them while insetting only little redundancy. 2.3 SYSTEM DESCRIPTION A simulation model has been constructed by utilizing MATLAB to examine the usefulness of PTS technique in alleviating the PAPR issue. Figure 2 below shows the overall simulation model of OFDM-PTS system. The transmitter and the receiver are assumed to be perfectly synchronized. The effect on frequency offset and phase noise during the data transmission will not be taken into consideration during simulation.

(3)


13

Figure 2 OFDM-PTS Simulation Model

2.4 RESULT AND ANALYSIS As discussed .in the above section, the PAPR is associated with the time-domain OFDM transmit signal: In the result analysis, the complementary cumulative distribution function (CCDF) of the peak-to-average power (PAP) of an OFDM signal is used to analyze the PAPR statistics of an OFDM signal. In the results that follow, random OFDM blocks were generated to obtain the CCDFs. The simulation model is assumed to have 128 subcarriers throughout and employ 4-QAM data symbols.

Figure 3 above shows the CCDF for the unmodified OFDM signal and the OFDM-PTS signal. In particular, the PAP of an OFDM signal exceeds 17 dB for 0.1% of the possible transmitted OFDM blocks. However, by introducing PTS approach with 8 clusters partition with phase factors limited to {+l, -1 ), the 0.1% PAP reduces to 13 dB. In short, PTS can achieve a reduction of PAPR by approximately 4 dB at the 0.1% PAP. The effect of varying several simulation parameters is examined. Figure 4 depicts the effects of varying the number of clusters for the weighting factors chosen from a set of {+l, -1}.


14

Figure 5 shows the comparison by varying size of the possible weighting factors set, for a fixed number of cluster, M =8.

Figure 3 Comparison Of The Unmodified OFDM Signal With The OFDM-PTS Signal

Figure 4 Effect Of Varying The Number Of Clusters

From Figure 4, as expected, the improvement increases as the number of clusters increases. With 16 clusters, it can achieve a reduction of 4.5 dB compared to the unmodified OFDM signal.


15

In Figure 5, for a fixed number of clusters, the phase factors can be chosen from a larger set, specifically, {+l, -1, +j, -j}. It is shown that, the added degree of freedom in choosing the combining phase factors offer an additional 0.8 dB reduction compared to the set size of 2 with phase factor of {+l, -1}.

Besides the simulation parameters that have been discussed above, the PTS-SPS is also studied from the aspect of the PAPR reduction. Figure 6 shows the comparison between the interleaved SPS and the adjacent SPS for 8 clusters and the weighting factors chosen from a set of {+l, -1}. It can be observed that, the adjacent SPS outperforms the interleaved SPS by approximately 0.6 dB at the 0.1% PAP.

Figure 5 Effect Of Varying The Size Of The Set Of The Weighing

Factors 2.5 CONCLUSION In conclusion, OFDM is an attractive technique for achieving broadband wireless data transmission. However, the occurrence of the high PAPR restricts its application. The PTS provides a distortionless technique in eliminating the PAPR at the expense of additional complexity. Based on the simulation results, it is proven that the PTS technique succeed to reduce the PAPR of an


16

OFDM signal. Employing adjacent SPS can reduce PAPR further.

Figure 6 The Effect The Subblock Partition Scheme

REFERENCE [1] A. F. Molisch, Wideband Wireless Digital Communications.

Upper Saddle River, New Jersey: Prentice Hall, 2000. [2] L.J. Cimini Jr. and N.R. Sollenberger, “Peak-lo-average power

ratio reduction of an OFDM signal using partial transmit sequences,” IEEE Commun. Letters, vol. 4 Issue: 3, pp. 86-88. March 2000.

[3] S.H. Muller and J.B. Huber, “OFDM with reduced peak-to-average power ratio by optimum combination of partial transmit sequences,” IEEE Electronics Letters, vol. 33 Issue: 5, pp. 368-369, Feb. 1997.

[4] Seog Geun Kang, Jeong Goo Kim and Eon Kyeong Joo, “A novel subblock partition scheme, for partial transmit sequence OFDM,” IEEE Transactions on Broadcasting, vol. 45 Issue: 3, pp. 333-338, Sept. 1999.


17

[5] C. Tellambura, “Improved phase factor computation for the PAR reduction of an OFDM signal using PTS,” IEEE Commun. Letters, vol. 5, Issue: 4, April 2001, IEEE Transactions on Broadcasting, vol. 45 Issue: 3, pp. 333-338, Sept. 1999.


18

3

CODE REPETITION TECHNIQUE IN REDUCING PAPR OF WLAN-OFDM

SYSTEM N.Ngajikin

N.Fisal Sharifah K. Syed-Yusof

3.1 INTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM) is one of the multi-carrier modulation (MCM) techniques that can reduce the Intersymbol Interference (ISI), delay spread of signal and increase the spectral efficiency of system. Due to the numerous advantages of this system, it has been successfully applied in wide variety of digital communications over the past several years and has been adapted to the wireless LAN standards [1].

However, an OFDM system dynamic range is typically two or four times larger than a single carrier system Increasing value of the dynamic range will lead to an increased the cost, power consumption of transmitter amplifier and also lead to high peak to average power ratio (PAPR). This is one of the major drawbacks of OFDM system.

A serious problem of large PAPR presents when cheap and energy-efficient nonlinear power amplifiers are used. Frequent excursions into the nonlinear operating region contribute to the increment of BER and spectral regrowth outside the intended frequencies of operation. Therefore PAPR reduction techniques are required to overcome this problem.

There are several techniques have been proposed to reduce

Code Repetition Technique in Reducing PAPR of WLAN-OFDM System

19

PAPR in OFDM system. From the literature, clipping is the simplest approach to reduce PAPR. However it results a significant in-band distortion and this technique requires filtering to overcome the weakness. Besides of using clipping and filtering, coding scheme get attention since it can handling both reducing PAPR and error correction at the same time. Therefore, this paper investigates the effectiveness of coding technique in reducing PAPR for OFDM system. In this method a combination of convolutional code and Code Repetition was developed.

This chapter is divided into 6 sections. Section 1.2, gives a brief overview of the fundamentals of PAPR in WLAN/OFDM system. In section 1.3, Channel coding that had been used in this work is presented. This section briefly explains the encoding and decoding process of code repetition, which is the coding that had been proposed to reduce PAPR. Section 1.4 gives the methodologies used for reducing PAPR. Section 1.5 discusses the results obtained in this research and an analysis and discussion of these results are carried out, Lastly, Section 1.6 gives the conclusions of this research work. 3.2 PEAK TO AVERAGE POWER RATIO (PAPR) An OFDM signal is the sum of Ci complex random variables, each of it can be considered as a complex modulated signal at a different frequency. In some cases, all signal components can add up in phase and produce a large output and in some cases, they may cancel each other, producing zero output. Thus, the peak-to-average ratio (PAPR) of an OFDM system is very large. In the transmitter front-end, a power amplifier with a wide linear range to include the peaks in the transmitted waveform is needed. Such amplifier not only consumes a large amount of power but also costly. DAC’s and ADC’s must also have a wide signal range to avoid clipping. The symbols that have a large PAPR are vulnerable to errors.

Peak to Average power Ratio is defined by Muller and Huber (1997) [7];


20

],0[ }|)({||)(|max

2

2

TttS

tSPAPR

x

x ∈=ε

where ε denotes the expectation and S,(t) is the OFDM transmitted signal. This expectation value is the value that we expect to measure most often if repeated measurements were made on the system. The PAPR also can be expressed in dB as in equation (2).

[dB] |)(|

|)(|maxlog10 2

2

NtS

tSPAPR

x

x=

2|)(|max tS x is the maximum power of the OFDM transmitted

signal while N

tS x2|)(|max

is the average power for N number of

carriers. 3.3 CODE REPETITION Code Repetition (CR) is one of the forward error correcting (FEC) codes that have a capability to detect and correct an error bit depends on the number of repetition, k. The encoding process of CR can be achieved by repeating each input bit k times depending on number of repetition. A block CR can be used to detect errors in a u-block. As before, CR will send a few copies of a codeword whenever a codeword is to be sent. Then, it will produce a new block code in which every block is just k repetitions of one of the original codewords. If the original code is an r-block code, then the new code will be a u-block code where u=rk. There are still only 2u codewords, but each block consists of r message digits and (k-l)r check digits.

For example, where r=4, r=2, u=8 the codeword 1100 is in the original 4-block code. The 8-block code will have the codeword 11001100. One error in transmission will destroy the symmetry of

(1)

(2)


21

the block, revealing the presence of an error. Let say the received word is 1 1001 1 10 then we know an error occurred. There is no guarantee that two errors will be detected, since two errors might preserve symmetry. It is clear that repetition causes a decrease in efficiency. We send extra digits with no additional information. For k = 2, only single error can be detected but it does not have capability to correct the error bit, More errors can be detected by repeating the codewords more times. Sending k copies of a codeword enables detection of k-1 errors.

In the case of a binary code (using only 0 and l), the possible received of codeword available using a u-block code is 2u. For example in a 3-block binary code there are 8 possible codeword [000, 001, 010, 100, 011, 101, 110, and 111]. Figure 1 shows the distance for each possible received codeword for 3 times repetition.

Figure 1 Distance between possible received codeword

The CR decoding process can be done using maximum

likelihood by select the nearest neighbor of the received codeword. However, there is a simple way to do it than searching explicitly for the nearest neighbor. In this paper, decoding process is done by select the output bit based on the majority bits in the codewords. For example, if the received codewords is {l01}, the majority bit is 1. Therefore the CR decoder will produce bit 1 as an output.

3.4 OFDM WITH MODIFIED CR


22

The MATLAB simulation model generates the corresponding OFDM transmission, simulates through the channel before attempts to recover input data and performs the analysis to determine the PAPR reduction and BER performance.

In this simulation model, the OFDM sub-carriers are modulated using BPSK modulation technique as a symbol mapper to the FFT point. The sub-carrier signals in OFDM were placed at indexed from -26 to +26 at 64 FFT point except at point 0, which is the direct current (DC) sub-carrier. Spacing between sub-carriers is 0.3125 MHz and total bandwidth for this system is 16.875 MHz. Basic parameters and system configuration used for the simulations are summarized in Table 4.1.

Table 1 OFDM Parameters For Wireless LAN 802.11a Standard

There are seven models have been designed to be analyzed. Each designed model is differentiates at the channel coding part. The conventional COFDM is used as a reference model to be compared with proposed CRk models. The first model is the generation OFDM that represent a basic OFDM without any channel coding technique applied. This model is used to analyzed the characteristic of PAPR in OFDM system based on Wireless LAN physical layer configuration. Second model is coded OFDM (COFDM). This model used convolutional codes as a channel coding with rate of ½ and constraint length equal to 7. I t is used as a reference model in the analysis. The other 5 represent the proposed model with adaptation of code repetition, CRk on the COFDM model where k=3, 4, 5, 6 and 7. The

3.4 OFDM WITH MODIFIED CR


23

repetition, k is chosen to be greater than 3 to allow both error detection and correction. Table 4 shows the parameters for each model.

Table 2 Parameters For OFDM, COFDM, Crk Simulation Models

Figure 2 shows the proposed coded OFDM with additional Code Repetition (CR). This proposed scheme separate channel coding into two parts. They are convolutional codes and code repetition. The purpose of adapting CR before the symbol mapper is to produce codeword with low PAPR value. Therefore it will result in reduction of PAPR for OFDM. transmitted signals. Beside of reducing PAPR, CR also capable to handle error correction and leads to BER improvement.

Some modifications of conventional CR arc needed to further reduce the PAPR. Output from CR encoder is chosen to have low PAPR value besides of choosing the maximum number of repetition to handle error correction. CR for this system can be generated by mapping input bit k times and toggle up the LSB bit. For example, for number of repetition, k = 4, conventional CR will produce output either (1111) if the input bit is 1 or (0000) if the input bit is 0. These codeword have a


24

maximum PAPR value for 4 binary bits, as shown in Table 5.1 in section 5.2.1. Therefore CR will toggle up the LSB bit. Hence, it wili produce output either (1110) or (0001). From the same table, it can be seen that these codeword have the lowest PAPR compared to the others. Table 4.3 shows PAPR value for each possible output from CR with different rate. The increment of k revealed the increase value of PAPR for CR output.

Decoding process for CR is done by toggle up the LSB bit and choosing the majority bits as the output. However, for even number of repetition (k= 4 and 61, it is possible to receive the same number of bit 1 and 0. Therefore, there is no majority bit. In this case, the LSB will be chosen as the output.

Figure 2 CR Transceiver

Table 3 PAPR for CDk Output


25

PAPR calculation is done at the end of the transmitter. In terms of BER performance, AWGN channel is inserted in Monte Carlo BER simulation.

3.5 RESULTS AND DISCUSSION This part discussed all the results obtained. The MATLAB simulated outcomes have been successfully carried out from the simulation model. Several simulations had been done using 1000 random binary bit. The averaging results from those simulations are presented in Table 4.

Table 4 PAPR Performance For All Simulation Models

Model OFDM COFDM CR3 CR4 CR5 CR6 CR7PAPR (dB) 9.64 7.8 9.0 2.0 3.8 3.2 6.8

The uncoded OFDM system is also shown in the graph for

comparison. Basic OFDM Without any coding technique gives PAPR value of 9.6dB while PAPR for COFDM is 7.8dB. The reduction is about 1.8 dB with respect to the basic OFDM. From this simulation, model CR4 yield the optimal performance with 5.8dB reductions regarding to COFDM. This results shows that the combination of bit and length of bit transmitted for CR4 is appropriate combination to reduce PAPR in this system.


26

Figure 3 shows the BER performance of the all simulation models in an AWGN channel with ½ rate convolutional code with constraint length 7 and hard decision Viterbi decoding. The number of repetition, k contribute to the error correction capability of the system. Thus, the increment of repetition, k will decrease the BER performance. The graph in Figure 3 shows that the model with highest repetition number, CR7 gives the best BER performance. The improvement percentage of BER performance is calculated using formulation and gives 96% improvement regarding to COFDM model.

Figure 4 BER Performance For All Simulation Models In AWGN

Channel

3.6 CONCLUSION CR encoder and decoder has been designed based on the PAPR characteristic for different combination bits. The combination that gives low PAPR is considered to be the output for CR encoder. The COFDM system with CR were implement for code rate, r= 1/3, 1/4, 1/5, 1/6 and 1/7. In terms of PAPR reduction, model with r =1/4 gives an optimal performance with PAPR reduction is up to 5 dB. The other models with additional CR also reduced PAPR down to 3 dB with respect to the conventional COFDM. In general, the increases of repetition, k will reasonably increased the


27

data rates and consequently increase the BER. Besides that, BER should be increased with the increment of PAPR. This is due to the frequent excursion into nonlinear operating region of power amplifier. However, this work assumed that the power amplifier operated in linear range. Therefore the results on BER do not totally follow the general principle. It has been found that BER performance increases with increasing number of repetition, k.

In general the proposed technique has achieved the objective to reduce PAPR and improve BER. The adaptation of CR to convolutional codes in WLAN/OFDM system had reduces PAPR with a simple encoding and decoding task. The simulations studies have been carried out to investigate the reduction of PAPR using Code Repetition technique. From the results, it has been found that an addition of CR in WLAN/OFDM system decreases PAPR value up to 5 dB compared to COFDM system. However, this technique contributes to increase data rates k times from conventional COFDM. The increased data rates will somehow affect the bandwidth efficiency. Analysis on this drawback is a possible extension that can be made. REFERENCES [1] D.Angela and Collegues, “A Comparison of the

HIPERLAN/2. and IEEE 802.1 la Wireless LAN Standards”. IEEE Comm. Magazine, May 2002.

[2] Engels and collegues, “design of lOOMbps Wireless Local Area Network”, ISSSE 98, URTS International Symposium on Signals, System and Electronics, pp.253-256, 1998.

[3] Bahai, A b e d R.S., Saltzberg, Burton R. “Multi- Carrier Digital Communications”, New York, NY: Plenum Publishers, 1999.

[4] C. Shurgers, “A systematic Approach to the Peak to Average Power Ratio in Multi Carrier system”, http://www.janet.ucIa.edul-curts/reports/research/PAR-0FDM.pdf


28

[5] I.A Tassaduq an R.K Rao, “Weighted OFDM With Block Codes for Wireless Communication”, IEEE Pacific Rim Conference on, Page(s): 441 -444 vo1.2, 2001.

[6] J. G. Prokis, “Digital Communications”, Mc. Graw Hill Co. Inc., New York, 2000.

[7] Muller, S.H. and Huber, J.B. (1997), “A novel peak power reduction scheme for OFDM“,IEEE conference proceedings PIMRC.

[8] A.E Jones and collegues, “Block Coding Scheme For Reduction of Peak to Mean Envelope Power Ratio of Multicarrier Trabsmission Scheme”, Electronics Letter Vol. 30 No. 25, 1994.

[9] Li, X. and Ritcey, J.A. (1997), ”m-sequences for OFDM PAPR reduction and error correction”, Electronic Letters, Vol. 33, pp. 545-546.

[10] Tellambura, C (1997), “Use of m-sequences for OFDM peak to average power ratio reduction”, Electronics Letters, VoI. 33, No. 15, May, pp 1300- 1301.

[11] Eetvelt, P.V., Wade, G. and Tonilinson, M. (1996) “Peak to Average Power Reduction for OFDM Schemes by Selective Scrambling”. IEE Electronics Letters, August.

[12] Li, X. and Cimini, L.J. (1998), “Effects of Clipping , and Filtering on the Performance of OFDM”, Communication Letters, Vol. 2, No. 5, May, pp. 113-133.

Time-Domain Amplitude Manipulative PAPR Reduction Techniques on PRS-OFDM System

29

4

TIME-DOMAIN AMPLITUDE MANIPULATIVE PAPR REDUCTION

TECHNIQUES ON PRS-OFDM SYSTEM Sharifah K. Syed-Yusof

Norsheila Fisal Muladi

4.1 INTRODUCTION

As a promising technique for high data-rate transmission, OFDM has been successfully used in many environments, such as DAB, DVB, and HiperLAN-II. In a classical OFDM system, the entire channel is divided into many orthogonal subchannels. Information symbols are transmitted in parallel over these subchannels with a long symbol duration in order to deal with frequency-selective fading of wireless environments. However, it has been shown that ICI destroys orthogonality among subchannels and causes ICI to occur. If not compensated for, the ICI will result in an error floor in the OFDM performance. Several methods have been proposed to reduce the effect of the ICI. One of the methods is frequency-domain PRS. Performing PRS in the time domain has been studied for single-carrier systems to reduce the sensitivity to time offset without sacrificing the bandwidth. In the frequency domain, the PRS with correlation polynomial F(D) = 1–D was used to mitigate the ICI caused by carrier frequency offset [1].

Another setback of OFDM system is high PAPR. The summation from the PRS signals resulted in the OFDM signal compression in the time domain [2], hence contributed to the PAPR increment to take place. The maximum peak power of


30

OFDM system occurs when N modulated symbols are added with the same phase. Although the occurrence of these maximum peaks is infrequently, it will seriously hamper practical implementations of both the transmitter and receiver, especially in wireless applications [4].

This chapter is organised as follows. In section 4.2 integer coefficient PRS-OFDM system is described. In section 4.3, the optimum weights of PRS which on maximises the CIR (carrier-to-interference power ratio) of the PRS-OFDM system is used in the PAPR performance. Then, in section 4.4, the simulation results of PAPR clipping techniques on PRS-OFDM system are presented. The clipping techniques being investigated in this work is deliberate clipping and clipping with filtering. Lastly, conclusion is provided in section 4.5. 4.2 INTEGER COEFFICIENT PRS-OFDM SYSTEM

The baseband model of PRS-OFDM is shown in Figure 1.

Figure 1. Baseband Model Of PRS-OFDM System

The transmitted data, Rf will be modulated and divided into

N orthogonal subchannels through the parallel and serial process. Let X(k) be the symbols to be transmitted and c(i) be the integer coefficients for PRS polynomial, the transmitted signal at the k-th subcarrier can be expressed as


31

( ) ( ) ( )ikXickS1K

0i

−= ∑−

=

where k=0, 1, …, N-1. The number of coefficients or length of the polynomial is denoted as K. In this work, E[X2(k)]=1 and E[X(k)X(j)]=0 for k≠j are assumed. By applying the principle of inverse Fourier transform, the general expression for PRS-OFDM transmission system in time domain, y(t) can be expressed as

( ) ( ) stfj

N

k

Tt,ekSty k <≤=∑−

=

021

0

π

where fk = f0 + kΔf is the frequency of the k-th subchannel, Δf = 1/Ts is the subchannel spacing, f0 is the fundamental frequency and Ts is the symbol duration.

The PAPR of PRS-OFDM signal in n-th symbol period is then defined as

( )

( )dB2nsE

2ns10PAPR 10

⎭⎬⎫

⎩⎨⎧

⎭⎬⎫

⎩⎨⎧

=max

log

At the receiver, by performing FFT on the received signal, the demodulated signal can be written as

( ) ∑=m

tfj2-(t)ey~kY m

π

If carrier frequency offset, θ occur at the receiver, then the received signal becomes

( ) ( ) θjetyty =~

In this paper, PRS length up to K=4 is investigated. The following

(1)

(2)

(3)

(4)

(5)


32

listed the coefficient that will be used in the investigation as shown in Table 1.

Table 1: The Optimum PRS-OFDM Polynomial Integer Coefficients

For The Respective K Length

Length, K PRS integer coefficients 2 1, -1 3 1, -2, 1 4 1, -2, 2, -1

4.3 PAPR CCDF OF PRS-OFDM SYSTEM In this comparison study, PAPR complementary cumulative distribution function (CCDF) of integer coefficients PRS-OFDM system is carried out. In the PAPR distribution analysis, the CCDF of an OFDM signal for a given PAPR level is the probability that the PAPR of the OFDM frame exceeds a certain threshold, PAPRo. This can be denoted as Pr(PAPR >PAPRo). The effect of different length of partial response polynomials in reducing the PAPR is studied.

In this measurement, a total of 5 000 OFDM symbols are generated. At every OFDM symbol duration, the PAPR is measured using the formula in equation (3). Figure 2 shows the CCDF of integer coefficient PRS-OFDM system.

At 10-3 probability, K=3 has the highest PAPR with the value of 13.7 dB whereas for the case of K=4 and K=2 the PAPR are 12.6 dB and 10.6 dB respectively. PRS resulted from summation of other subcarriers signals in the frequency domain. This summation causes greater compressed OFDM signals in the time domain [2]. Hence by performing PRS on OFDM symbol, higher peak occurrences are produced as compared to conventional OFDM signals that have about 10-3 probability occurrence at PAPR equals 10 dB. It can be deduced that PRS-OFDM can


33

reduce ICI at the expense of increased PAPR.

Figure 2. CCDF PAPR Comparisons Of PRS-OFDM Systems

Three classes of PAPR reduction techniques that have been proposed in literature are coding, clipping and probabilistic [5]. In this work, in order to preservation the correlation between the subcarriers in PRS-OFDM system, time-domain manipulative PAPR reduction techniques are the most appropriate techniques to be used. Amongst the techniques are clipping and clipping and filtering techniques. In the next section we look into the effect of clipping techniques on integer coefficient PRS-OFDM signal systems.

4.4 CLIPPING TECHNIQUE ON PRS-OFDM SYSTEM Since PRS-OFDM signal resulted in increment of PAPR, deliberate clipping would be an effective and simple approach to reduce or counteract the effect. In this section, investigation on the effects of clipping PRS-OFDM signal is carried out. The effect of clipping on PRS-OFDM signal with N=64 subcarriers is


34

investigated. Figure 3(a) and Figure 3(b) illustrates the block diagram of deliberate clipping and clipping with filtering PRS- OFDM system. In clipping and filtering technique shown in Figure 3(b), the oversampling is accomplished by zero-padding the input before taking a longer IFFT on the oversampled OFDM block [6]. For the purpose of demonstration, an oversampling rate of I=2 is used throughout the simulation. Rotation of the input PRS symbols Sk was carried out so that the carrier frequency is at the middle of the passband bandwidth [7]. Thus the input to the IFFT block is given by

( )

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

−≤≤−⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −−

−−≤≤

−≤≤⎟⎠⎞

⎜⎝⎛ +

=

1INk2NIN,

2NINkS

12NINk

2N,0

12Nk0,

2NkS

kS'

Figure 3(a). Block Diagram Of Deliberate Clipping PRS-OFDM

System

(6)


35

Figure 3(b). Block Diagram Of Clipping And Filtering PRS-OFDM System

The oversampled PRS-OFDM signal after IFFT is presented as,

( ) ( ) ,ekSns1IN

0k

INnk2j'∑−

=

= π 10 −≤≤ INn

In the following discussion, a normalised clipping level of the clipper, which is called clipping ratio (CR) is used in this work. CR is given by

ρA

=CR

where A is the clipping level and ρ is the average power of the partial response OFDM signal. A lower CR results in a lower PAPR, but also causes a larger BER performance degradation due to the clipping process. The purpose of this study is to know the performance of PRS-OFDM at different length of K when clipping is used as a method to reduce the PAPR. For the purpose of analytical work, the target of the system is to achieve BER=10e-4 when the SNR at the transmission channel is set at 25 dB [7]. The procedure searches for the optimum CR that is allowed to be used in order to achieve the defined target PRS-OFDM performance. Suboptimum PRS-OFDM detection technique and CR up to 30 are used in this performance measurement. Table 2 summarises the results of clipping and clipping with filtering PRS-OFDM signal. Without taking into consideration of the frequency offset occurrence, an optimum CR of at least 6.6 is required at 10e-04 BER level of PRS-OFDM signal with length K=2 (see Table 2).

At the respective clipping ratio of 6.6, the PAPR is reduced from 9.4 dB to 1.4 dB a reduction of about 8 dB. However, when oversampled clipping filtering is used, the optimum CR increased to 10.1 in order to satisfy the BER requirement. The PAPR is

(7)

(8)


36

reduced from 9.4 dB to 4.4 dB compared to the normal OFDM. As the length of PRS polynomial is increased to K=3, higher CR is required for both the clipping schemes investigated. A CR of at least 11.1 is required from the clipping technique with PAPR reduced from 6.3 dB to about 3.6 dB. A higher CR of about 20.6 is required for the clipping and filtering technique at the same BER level. In this case, the PAPR reduction of about 1.3 dB is achieved. However, as the length of PRS polynomial is increased to K=4, no CR is applicable that will gratify the BER condition when both the clipping schemes are performed on the PRS-OFDM signal. As known, clipping is a nonlinear process and may cause significant in-band distortion, which degrades the BER performance. As K is higher, the more compact is the time-domain PRS-OFDM signal.

Table 2. PAPR And Optimum CR At BER=10e-04

K=2 K=3 K=4 PAPR of PRS-

OFDM 9.4 dB 6.3 dB 15.8 dB

PAPR of clipped PRS-OFDM

1.4 dB 3.6 dB none

PAPR of clipped & filtered PRS-OFDM

4.4 dB 5 dB none

clipping CR 6.6 11.1 none clipping & filtering

CR 10.1 20.6 none

Hence, clipping the signal at high K resulted in more distortion to occur. In fact, more signal loss is expected form the clipping process. The performance degradation will be worse when frequency offset is present in the system. Therefore, other method that would reduce the PAPR of integer coefficient PRS-OFDM signal should be investigated. In order to preserve the CIR enhancement property of PRS-OFDM signal, a distortionless PAPR reduction would be interesting to be explored in the future.

4.5 SUMMARY


37

It is known that by performing PRS on OFDM system, the CIR is enhanced. In this work, integer PRS polynomial that maximises the CIR are used. However, the PRS-OFDM system suffers PAPR increment due to the partial responsed polynomial functions. Here, the performances of suboptimum PRS-OFDM at different polynomial length, K when clipping is used as a method to reduce the PAPR are investigated. For the purpose of analytical work, the target of the system is to achieve BER=10e-4 when the SNR at the transmission channel is set at 25 dB. From the simulation results, K=2 and K=3 are able to achieve the target while reducing the PAPR. However, K=4 suffers performance degradation. Hence, further BER degradation is expected with the existence of frequency offset in the transmission channel or at the receiver. REFERENCES [1] Y. Zhao and S. G. Haggman, (1998). “Intercarrier interference

compression in OFDM communication systems by using correlative coding,” IEEE Comm. Letters, vol. 2, pp. 214– 216, 1998.

[2] V. Vadde, “PAPR reduction by envelope stabilization using partial response signaling in OFDM systems,” Proceedings of the IEEE RAWCON 2001, 2001, pp. 197-201.

[3] H. Ochiai and H. Imai, (2001). “On the distribution of peak-to-average power ratio in OFDM signals,”. IEEE Trans. on Comm., vol. 49, issue 2, pp. 282-289, 2001.

[4] A. F. Molisch, Wideband Wireless Digital Communications, Upper Saddle River, NJ. Prentice Hall, 2001.

[5] J. Armstrong, “New OFDM Peak-to-Average Power Reduction Scheme,”. Proceedings of the IEEE VTC 2001, , 2001, vol. 1, pp. 756-760.

[6] X. Li and L. J. Cimini Jr., “Effects of clipping and filtering on the performance of OFDM,”. IEEE Comm. Letters, vol. 2, issue 5, pp. 131-133, 1998.

4.5 SUMMARY


38

5

PEAK-TO-AVERAGE POWER RATIO REDUCTION TECHNIQUE IN

PRS-OFDM SYSTEM Sharifah K. Syed-Yusof


5.1 INTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM) has been successfully used in many environments, such as Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), and HiperLAN-II. However, one of the main problems of OFDM signal is intercarrier-interference (ICI). The occurrence of ICI in OFDM system destroys orthogonality among subchannels which will resulted in an error floor in the OFDM performance. Several methods have been proposed to reduce the effect of the ICI. One of the methods is frequency-domain partial response signaling (PRS). Nevertheless the summation from the PRS resulted in OFDM signal compression in the time domain [2]. Hence, this leads to the PAPR increment.

This chapter is organised as follows. In Section 5.2, integer coefficient PRS-OFDM is mentioned. The CIR and PAPR performance of PRS-OFDM are shown. In this paper, PAPR reduction approach known as Fraction Time Selective (FTS) Envelope Modification technique is used to reduce the PAPR of integer coefficients PRS-OFDM system. In Section 5.3, this distortionless technique is described. Then, in Section 5.4, the simulation results of FTS Envelope Modification on PRS-OFDM

Peak-To-Average Power Ratio Reduction Technique in PRS-OFDM System

39

system are presented. The PAPR reduction depends on the modification level and vector size being used. Lastly, section 5.5 concludes the research work.

5.2 INTEGER COEFFICIENT PRS-OFDM SYSTEM

The implementation of PRS in OFDM system is illustrated in Figure 1.

Figure 1. Baseband Model Of PRS-OFDM System

To avoid error propagation to occur in PRS, the binary data is precoded first before performing modulation. The signal sequence before PRS is expressed as X(k) where k is subcarriers’ index with k=0, 1, …, N-1 and N is given as the total number of subcarriers in OFDM system. By considering BPSK modulation, X(k) consists of -1 and 1 values which, fulfill zero mean and independence conditions. Let c(i) be the integer coefficients for PRS polynomial. The transmitted signal at the kth subcarrier can be expressed as

( ) ( ) ( )ikXickS1K

0i

−= ∑−

=

(1)

where k=0, 1, …, N-1.

The number of coefficients or length of the polynomial is denoted as K. Without loss of generality, E[X2(k)]=1 and E[X(k)X(j)]=0 for k≠j is assumed. By applying the principle of inverse Fourier transform, the general expression for PRS-OFDM


40

transmission system in time domain, y(t) can be expressed as

( ) ( ) NnkjN

k

ekSnsπ21

0∑−

=

= (2)

where n=0, 1, …, N-1.

The PAPR of PRS-OFDM signal is defined as

( )

( )dB

maxlog10PAPR

⎭⎬⎫

⎩⎨⎧

⎭⎬⎫

⎩⎨⎧

= 2nsE

2ns10

(3)

In this paper, the integer coefficients of PRS for the respective polynomial length that maximised CIR are determined through exhaustive search. The benefit of using integer coefficients PRS-OFDM is reduced hardware processing complexity compared to using real-valued coefficient [3]. Table 1 listed the integer coefficients that are found in this work and the CIR gain tabulated from the PRS-OFDM compared to the conventional OFDM system [4].

As shown from Table 1, K=2 has the lowest range of CIR gain while K=4 has the highest gain as the frequency offset is increased from 0 to 0.5.

Table 1: PRS-ORDM Integer Coefficients And CIR Gain Compared To Conventional OFDM System

K cK min. CIR gain max. CIR gain

2 1, -1 2.6251 dB 4.0570 dB

3 1, -2, 1 3.0037 dB 4.6577 dB

4 1, -2, 2, -1 3.2056 dB 4.9604 dB

In the PAPR comparison study, complementary cumulative

distribution function (CCDF) measurements of integer coefficients PRS-OFDM system are performed. The CCDF of an OFDM signal


41

for a given PAPR level is the probability that the PAPR of the OFDM frame exceeds a certain threshold, PAPRo. This can be denoted as Pr(PAPR >PAPRo). The effect of different length of partial response polynomials in reducing the PAPR is studied.

In this measurement, a total of 3 000 OFDM symbols are generated. At every OFDM frame, the PAPR is measured using the formula in (3). Figure. 2 shows the CCDF of integer coefficient PRS-OFDM system. Higher PAPR are produced by performing PRS on OFDM symbols as compared to conventional OFDM signals that have about 10-3 probability occurrence at PAPR equals 10 dB. At the same probability, K=4 has the highest PAPR with the value of 14.8 dB whereas for the case of K=3 and K=2 the PAPR are 13.7 dB and 12.6 dB respectively. PRS resulted from summation of other subcarriers signals in the frequency domain. Hence, it can be deduced that PRS-OFDM can reduce ICI or enhance CIR at the expense of increased PAPR

Figure 2. PAPR Comparisons Of PRS-OFDM Systems

In order to preserve the correlation between the subcarriers in

PRS-OFDM system, time-domain manipulative PAPR reduction


42

techniques are the most appropriate techniques to be used. In the next section we look into the development of distortionless PAPR reduction approach known as FTS Envelope Modification on integer coefficients PRS-OFDM system and the effectiveness of the proposed technique in reducing PAPR is elaborated in the following section.

5.3 FRACTION TIME-SELECTIVE (FTS) ENVELOPE

MODIFICATION Figure 3 shows the application of FTS Envelope Modification for reducing the PAPR of PRS-OFDM. The FTS envelope modification is applied at the transmission part after performing IFFT. The details about FTS envelope modification approach in reducing PAPR of PRS-OFDM signal is illustrated in Figure 4. The discrete PRS-OFDM signal, s(n) is firstly partitioned into disjoint subblocks that are combined to minimised the PAPR. Let N be the vectorlength of s(n) which is also equals to the IFFT length and M be defined as the number of disjoint subblocks. This algorithm required the factor of

MN to be integers. For simplicity,

adjacent subblock partitioning is chosen in this work [5]. Therefore, every subblock consists of equal index size of time-domain signal and can be represented as,

s = {s1, s2, ..., sM} = {s0, ..., s

1−MN , s

MN , ..., sN-1} (4)

As seen in Figure 4, each transmit sequence is then modified

with an modification factor, bm, where {bm, m=1, 2, ..., M}. The modified discrete time-domain vector can be computed as s’ = {s1’, s2’, ..., sM’} = {b1 s1, b2 s2, ..., bM sM} (5)


43

The modification factor can be selected from B(v) where v indicate the size of vector B.

Figure 3. Integer Coefficient PRS-OFDM System With FTS Envelope Modification

Figure 4. Time-Domain Disjoint Adjacent Subblock Partitioning In FTS


44

Envelope Modification On PRS-OFDM System

PRS-OFDM signal has a feature of having low magnitudes at both ends of the time domain signal and high amplitudes at the middle range due to time-compression introduced by the PRS [2]. To simplify implementation, these characteristics are taken into considerations when developing FTS envelope modification technique. Therefore, in this technique, modification will only be performed in the middle range as this range has high peaks and not on both ends of the PRS-OFDM signal [2]. The first and last element of the weight factor b in (5) is assigned to 1. This can be interpreted, as no modification on both ends of the time domain signal. This would also mean that only the middle disjoint time-domain subblocks are selected for envelope modification. The magnitudes of the weight factors are set to modification, A where A≤1. In this work, the weight factor for every subblock is chosen based on A= fP , where Pf is the fraction of power to be transmitted. For example if Pf =50%, A=0.7071.

In FTS envelope modification, the information in the PRS-OFDM signal will not be distorted as in the case of clipping [6]. Instead, only a fraction of the total power of the signal will be transmitted depending on the chosen weight factors The weighting factors are carefully chosen by the optimisation function that performs the algorithm to determine the optimised combination of the weighted FTS sequences, which produces the lowest PAPR.

After the modification factor combinations have been determined, the first combination will be applied to the disjoint subblock sequences. The PAPR will then be computed for the particular OFDM block and the iteration continues for every factor combination. Once PAPR has been calculated for all the weight combinations, the combination that gives the transmitted time-domain sequence the lowest PAPR will be selected for transmission.

This scheme requires the receiver to have knowledge about the generation of the transmitted OFDM signal. Thus, the weight factors must be transmitted as side information so that the receiver


45

can correct the subcarriers appropriately. However, sending side information (SI) means introducing redundancy that may reduce system efficiency. Nevertheless, it should be pointed out the modification factor in the middle range are the only ones needed at the receiver as the weight factors at both ends are equal to 1 hence resulted in reduced SI transmission. Additionally, being a distortionless scheme, this technique also works with arbitrary type of modulation. In the next section, the PAPR performance of FTS Envelope Modification on PRS-OFDM system is investigated.

5.4 PAPR PERFORMANCE OF FTS ENVELOPE

MODIFICATION PRS-OFDM SYSTEM

In this study, the proposed FTS envelope modification is explored. Figure 6 shows the PAPR performance when FTS envelop modification with M=4 is employed. Since modification factor at both ends are set to one, therefore, only two subblocks will be involved in the modification procedure. At 10-3 probability, PAPR managed to be reduced by about 0.8 to 2.8 dB depending on the length K. A reduction of 1.5 dB is achieved when K=2 is applied. Meanwhile, K=3 and K=4 has a reduction of 0.8 dB and 2.8 dB respectively. In this case, A has a value of 0.7071 and the PAPR reduction is subjected to magnitude A. The lower the A is, the more PAPR reduction is achieved as shown in Figure 7. With A=0.7, the PAPR is 11.1 dB but lower PAPR is achieved at A=0.5 where the PAPR is 10 dB.

The effects of the subblock numbers, M and the modification factor vector size, v are also investigated in this work. The more M is, the less number of time-index sequence in a subblock. Nevertheless, from the PAPR performance in Figure 8, both M=4 and M=8 has the same performance. It should be mentioned that high peaks occur in the middle portion of the time-index sequence of PRS-OFDM signal. Therefore, only the middle subblocks will be attenuated while the ends subblocks remained the same. Hence, the higher M is will not resulted in significant PAPR reduction.

Figure 9 shows the PAPR performance when different size of


46

vector v is used in FTS envelope modification. The more v is, the more PAPR is reduced. For example, at 10-3 probability, PAPR is reduced about 0.8 dB more when v=4 is employed in reducing PAPR of PRS-OFDM system compare to when v=2 is used. It shows that the added degree of freedom in choosing the combination modification factors provides an additional PAPR reduction. The PAPR reduction from the simulation results is sufficient in ensuring that the OFDM signals are within the dynamic region of the power amplifier (PA) in OFDM applications.

Figure 6. PAPR performance of FTS Envelope Modification PRS-OFDM system

4 5 6 7 8 9 10 11 1210

-4

10-3

10-2

10-1

100

Pr

(PA

PR

> P

AP

Ro)

PAPRo (dB)

FTS PRS-OFDM(A=0.7)FTS PRS-OFDM(A=0.5)

Figure 7. PAPR performance of FTS Envelope Modification PRS OFDM (K=2) system with different envelope modification magnitude, A


47

Figure 8. PAPR performance of FTS Envelope Modification PRS-OFDM system with different subblocks number, M

4 5 6 7 8 9 10 11 12 1310

-4

10-3

10-2

10-1

100

Pr(

PA

PR

> P

AP

Ro)

PAPRo(dB)

FTS PRS-OFDM(v=4)FTS PRS-OFDM(v=2)

Figure 9. PAPR performance of FTS Envelope Modification PRS-

OFDM system with different modification vector size, v 5.5 CONCLUSION

In this paper, PRS-OFDM system has been studied. Firstly, the effectiveness of PRS-OFDM system in enhancing CIR is investigated. Integer coefficient PRS managed to enhance further the CIR of OFDM system by about 2.6 dB up to 5 dB when the length of polynomial, K is 2, 3, 4, and 5 respectively.

However, PRS-OFDM suffers PAPR increment due to the PRS polynomial functions. Fraction Time-Selective (FTS) envelope


48

modification is proposed to reduce PAPR in integer coefficient PRS-OFDM system. This technique is motivated from the PRS-OFDM time-domain characteristics. This distortionless technique is able to reduce the PAPR by 0.8 down to 2.8 dB at 10-3 CCDF. PAPR reduction depends on the modification level and vector size. We conclude that this reduced complexity system is feasible and can be applied in future broadband system development such as MIMO-OFDM system. REFERENCES [1] Y. Zhao and S. G. Haggman, “Intercarrier interference

compression in OFDM communication systems by using correlative coding,” IEEE Comm. Letters, vol. 2, issue 8, pp. 214– 216, 1998.

[2] V. Vadde, “PAPR reduction by envelope stabilization using partial response signaling in OFDM systems,” Proceedings of the IEEE RAWCON 2001, Massachusetts, USA, Aug. 2001, pp. 197-201.

[3] H. Zhuang, Y. Li, “Optimum frequency-domain partial response encoding in OFDM system,” IEEE Transactions on Communications, vol. 51, no. 7, pp. 1054-1068, July 2003.

[4] S. K. Syed-Yusof, N. Fisal, and Muladi, “Integer coefficients partial response signaling in OFDM System,” Proceedings of the 2006 Intl. Conf. on Radio Frequency and Microwave, pp. 326-328, September 2006.

[5] S. G. Kang, J. G. Kim, and E. K. Joo, “A novel subblock partition scheme for partial transmit sequence OFDM.” IEEE Trans. on Broadcasting, vol. 45, issue 3, pp. 333-338, 1999.

[6] S. K. Syed-Yusof, N. Fisal, and Muladi, “The effects of clipping techniques on PRS-OFDM system,” Proceedings of the 2006 Intl. Conf. on Radio Frequency and Microwave, pp. 62-65, September 2006.

The Evaluation of ICI Self-Cancellation Technique in OFDM Systems

49

6

THE EVALUATION OF ICI SELF-CANCELLATION TECHNIQUES IN

OFDM SYSTEMS Sharifah K. Syed Yusof


6.1 INTRODUCTION As a promising technique for high data-rate transmission, Orthogonal Frequency Division Multiplexing (OFDM) has been considered for many emerging wireless applications due to its high spectral efficiency and robustness against frequency selective fading.

However, in time variant mobile radio environment, the relative movement between transmitter and receiver resulted in frequency offset caused by Doppler frequency shifts. Therefore, the carriers cannot be perfectly synchronised. This imperfection destroys the fundamental orthogonality characteristics among subcarriers in OFDM signal. This loss of orthogonality causes intercarrier interference (ICI) to occur in addition to signal rotation and attenuation [1].

Several methods have been proposed to reduce the effect of the ICI. ICI self-ICI-cancellation approach has been proposed, which transmits each symbol over a pair of adjacent or non-adjacent subcarriers with a phase shift of π [2, 3]. In order to improve the PAPR performance of self-cancellation technique, a simple conjugated data allocation of (Xk, Xk+1= -Xk

* ) was proposed [4]. These ICI self-cancellation methods can reduce the ICI


50

significantly in a simple manner but at a price of reduction in bandwidth efficiency.

In single-carrier systems, partial response signaling has been studied to reduce the sensitivity to time offset without sacrificing the bandwidth [5]. In OFDM system, partial response in frequency domain is capable of reducing the sensitivity of multicarrier system towards frequency offset caused by Doppler shift in the channel. The partial response OFDM signal with correlation polynomial F(D) = 1 – D was used to mitigate the ICI occurrence [6]. In partial response OFDM system, ICI is actually deliberately introduced in a controlled manner through the polynomial functions. The optimum weights for partial response coding that minimise the ICI power were derived [7]. However, the usage of integer polynomial coefficients does allow suboptimum detection hence reduces the complexity of the receiver.

So far, no literature on performance evaluation on the ICI self-cancellation techniques and partial response coding has been studied. Therefore in this paper, we study the CIR, BER and PAPR performance of the self-cancellation schemes and partial response coded OFDM (PRC-OFDM) system with integer polynomial coefficients employing a simple symbol-by-symbol suboptimum detection technique 6.2 ICI CANCELLATION TECHNIQUES IN OFDM

SYSTEM Let the received OFDM signal in the presence of frequency offset be

Y(k)=X(k)S(l -k)+ W(k) (1)

for k=0,l,...,N-l where N is the number of subcarriers. X(k) is the transmitted symbol of the k-th subcarrier. W(k) is additive white Gaussian noise (AWGN) with zero mean and variance No/2 and is assumed to be independent and identically distributed. S(l-k) is the ICI effect of the l-th subcarrier to the k-th which can be represented as follows


51

(2)

where ε is the normalised frequency offset with respect to the frequency separation between subcarriers. By ignoring the effect of AWGN, the received signal can be expressed as a sum of desired signal C(k) and undesired ICI signal I(k)

(3) where

(4) The desired signal value C(k) depends only on the signal transmitted on subcarrier k, while I(k) depends on the signals transmitted on all the other subcarriers.

Zhao and Haggman proposed the conevtional ICI self-cancellation scheme in which a pair of complex signals (Xk, Xk+1= -Xk) is assigned in adjacent subcarriers, for k=0, 2, .... N-2. However, such allocation with π phase difference between the subcarrier pair causes high PAPR of OFDM symbol defined as

where max |xn|2 is the maximum value of x. And E|xn|2 denotes the expectation of the average power value. ICI self-cancellation with allocation assignment in the form of (Xk, Xk+1= -Xk

*) was proposed by [4] as a method to reduce high peak signal in the conventional ICI self-cancellation technique.

The baseband model of PR-OFDM is shown in Figure l. In PRC-OFDM, the modulated signal is encoded by partial response polynomial. Precoding is also performed before modulation in

(5)


52

order to avoid error propagation during decoding process. Let Xk be the symbols to be transmitted and ci be the coefficients for partial response polynomial, the transmitted signal at the k-th subcarrier can be expressed as

where K is the number of coefficients or length of the polynomial. In this work, E|Xn|2 =1 and E(Xk,Xj*)=0 for are assumed. In terms of the partial response coding coefficients, the intercarrier interference power can be expressed as

Figure.1 Baseband model of PR-OFDM

(6)

(7)


53

6.3 SIMULATION RESULTS AND PERFORMANCE EVALUATION

In this section, the performance of PRC-OFDM with integer polynomials and ICI self-cancellation system are presented. In PRC-OFDM, different polynomial length (up to K=4) and coefficients are investigated. The coefficients are limited to the value of ±1, ±2 and 0. The number of subcarriers used throughout this simulation study is 64 subcarriers. Our simulation is conducted with the assumption of flat fading channel. Symbol-by-symbol suboptimum detection is used at the receiver.

ICI power level can be evaluated by using the CIR [8]. At each polynomial length, the polynomial that gives the lowest carrier to interference ratio (CIR) is chosen. Table 1 lists the best combination of coefficients for the respective length. The length of polynomial is limited up to 4 as length greater than this gives relatively about the same performance gain [7].

Table 1 PRC coefficients at the respective length, K

For simplicity, K=2 is chosen for comparison with the ICI

cancellation technique. Figure 2 shows the theoretical CIR (in decibels) of the mentioned techniques as a function of the normalised frequency offset, ε. The ICI self-cancellation techniques enhance the CIR of OFDM systems. At ε=0.25, the self-cancellation gives more than 13 dB improvement over the PRC-OFDM and the conjugate signal allocation ICI self-cancellation (cjsc), gives about 7 dB enhancement. However, in terms of spectral efficiency, the PRC-OFDM reduced the bandwidth usage by half compared to the self-cancellation


54

techniques.

Figure 2 Comparison of CIRs with respect to constant frequency

offset

In the PAPR distribution analysis, the complementary cumulative distribution function (CCDF) of an OFDM signal for a given PAPR level, PAPRo dB, is the probability that the PAPR of the OFDM frame exceeds a certain threshold PAPRo dB. This is defined as Prob(PAPR >PAPRo dB).

Figure 3 shows the PAPR for N=64. On the overall, the PAPR of OFDM system is better compared to self cancellations and PRC-OFDM system. It should be mentioned that no envelope stability algorithm was used in this investigation [9]. The conjugate self-cancellation and PRC-OFDM has better PAPR performance compared to self-cancellation scheme. At 10-3 probability, the conjugate data algorithm is almost 2 dB and 1 dB lower than self-cancellation scheme and PRC-OFDM respectively. However, it can be observed from Figure 3 that the PAPR of conjugate data algorithm fluctuates in the range of threshold PAPR. This is due to the fact that the phase difference variations between the two adjacent subcarriers resulting in the occurrence of envelope instability before transmission.


55

Figure 3 Comparisons of PAPR performance

From Figure 4, BER for PRC-OFDM improves at high Es/No.

However, the ICI self-cancellation schemes deteriorate at high SNR. Redundancy criteria in these schemes improve the performance at low Es/No. however the PRC-OFDM outperforms them at higher Es/No.

Figure 4 BER comparison at ε=0.15


56

6.4 CONCLUSION This paper studies the performance of ICI self-cancellation schemes and the PRC-OFDM. Polynomial coefficients with integer values PRC-OFDM system was chosen for this comparison studied in order to reduce the complexity of the receiver. As known, the redundancy property adopted in self-cancellation schemes reduced the bandwidth efficiency by half compared to PRC-OFDM system Although the CIR gain for PRC-OFDM is the lowest compare to the self-cancellation schemes, the BER is better at higher Es/No. From the PAPR point of view, the PRC-OFDM gives a moderate improvement and can be improved further through an envelope stability algorithm.

Therefore, PRC-OFDM with integer polynomial coefficients gives a solution to adverse the effects of both ICI and PAPR in OFDM systems simultaneously in a simple manner. This system is feasible and can be applied in future broadband system development such as MIMO-OFDM system. REFERENCES [1] T. Pollet, M. Van Bladel, and M. Moeneclaey, 'BER sensivity

of OFDM to carrier frequency offset and Weiner phase noise," IEEE Transactions on Communications, 43, 1995, 191-193.

[2] Y. Zhao and S-G Haggman, "Intercarrier interference self-cancellation scheme for OFDM mobile conmnunication systems," IEEE Transactions on Communications, vol. 49, no.7, pp. 1 185-1191, July 2001.

[3] K. Sathananthan, RM.A.P. Rajatheva, S.B. Slimane, "Cancellation technique to reduce intercarrier interference in OFDM," Electronics Letters, vol. 36, no. 25, pp. 2078-2079, Dec. 1999.

[4] Y. Fu, S. G. Kang, C. C. Ko, "A new scheme for PAPR reduction in OFDM systems with ICI self cancellation VTC 2002, vol. 3, pp. 1418-1421, Fall 2002.


57

[5] P. Kabal, S. Pasupathy, 'Partial-response signaling," IEEE Transactions on Communications, com-23(9), 1975, 921-934.

[6] Y. Zhao, J-D. Leclercq and S-G. Haggman, "Intercarrier interference compression in OFDM communication systems by using correlative coding," IEEE Communicafions Letters, 2(8), 1998,214-216.

[7] H. Zhuang, Y. Li, "Optimum frequency-domain partial response encoding in OFDM system," IEEE Transactions on Communicatfions, 51(7), 2003,1054-1068.

[8] P.H. Moose, "A technique for orthogonal frequency division multiplxing frequency offset correction," IEEE Transactions on Communications, vol.42, pp. 2908-2914, Oct. 1994.

[9] V. Vadde and S. Gray, 'Partial response signaling for enhanced spectral efficiency and RF performance in OFDM systems," GLOBECOM 2001, vol. 5, pp. 3120-3124, Nov. 2001.

Simulation on Performance of Space Time Block Code

59

7

SIMULATION ON PERFORMANCE OF SPACE TIME BLOCK CODE

N. Ngajikin W. N. Ahmad

N. Fisal Sharifah K. Yusof

7.1 INTRODUCTION It has been long known that multiple antennas can be used to boost system performance through fading environment. This diversity technique provides the receiver with multiple version of the transmitted signal over independent channel. Therefore the probability of all signals being faded will be less than the probability that just one is faded. This system is often called a multiple-input multiple output (MIMO) system.

MIMO uses antenna arrays at both the transmitter and receiver to offer substantial benefits in terms of rate and reliability. Two standards approaches for communicating in MIMO are spatial multiplexing and transmit diversity [1]. Multiplexing sends independent information streams across the transmit antennas to maximize rate while transmit diversity sends redundant information streams to maximize reliability.

The contents of this paper are divided into five sections. Section 2 covers the literature review with some theories on diversity technique and MIMO system. Section 3 focused on the STBC concept that had been used in this paper. The interleaving and coding process are further discussed in this section. Results for the simulation model have been discussed in section 4. The discussion is on BER and capacity performance for different code rate and different number of antennas. Finally, section 5 concludes


60

this paper and end up with some recommendations for future works. 7.2 DIVERSITY TECHNIQUE One of the most efficient and simple techniques to overcome the destructive effects of fading is diversity. Diversity is an efficient technique to exploit the random nature of radio propagation by finding methods to generate and extract independent signal paths for communication. The concept of diversity is if one signal path undergoes a deep fade at a particular point of time, another independent path may have strong signal. By having more than one path to select from, both instantaneous and average SNR can be improved in the receiver by a large amount. There are various types of diversity, which are Space Diversity, Frequency Diversity, Time Diversity, Polarization Diversity and Multipath Diversity. In this paper we will only look at space diversity and space diversity reception technique, which are the main concept used in this simulation. 7.2.1 Space Diversity Space diversity, also known as antenna diversity, is one of the most popular forms of diversity used in wireless systems. It is a method of transmission or reception, or both, in which the effects of fading are minimized by the simultaneous use of two or more physically separated antennas, ideally separated by one or more wavelengths.

There are two types of space diversity that are the transmitter diversity and receiver diversity. Space diversity - transmitter diversity placed an antenna array at the transmitter. M different numbers of antennas are used to obtain uncorrelated fading signals at the receiver as shown in Figure 1. It has a spacing distance between the antennas whereby the total transmitted power is split between the antennas.


61

Figure 1 Space Diversity-Transmitter Diversity

The space correlation properties of the radio channel of Space Diversity - receiver diversity are used to provide multiple uncorrelated copies of the same signal to the receiver. This is shown in Figure 2. M different numbers of antennas are used at the receiver to obtain independent fading signals. It has a spacing distance between the antennas, with no efficiency loss at the receiver.

Figure 2 Space Diversity-Receiver Diversity

7.2.2 Diversity Reception Technique Diversity reception technique is a method of processing the diversity signals received such that it maximizes the power efficiency of the system. There are several possible diversity reception methods employed in communication receivers. The most common techniques are Selection Diversity, Maximal


62

Ratio Combining (MRC) and Equal Gain Combining (EGC). Selection diversity is the simplest diversity technique. Figure 3 shows a block diagram of selection diversity technique.

Figure 3 Space Diversity-Receiver Diversity)

In this scheme, the receiver simply select the received signal (y1 to yL) with the largest SNR as the output, y. In the case of two-fold diversity, the diversity combining strategy for selective combining is given by equation (1)

⎩⎨⎧

>>

=||||||||

122

211

kkk

kkkk ZZifZ

ZZifZZ

where Z2k and Z2k are decision variable at the first and second diversity paths and Zk is the decision variable at the output of the diversity combiner. 7.3 SIMULATION MODEL-STBC Space-Time codes (STC) method is one of the spatial techniques used to improve system performance in fading environment and increase the capacity. In order to increase the capacity, STC employs multiple antennas at both transmitter and receiver. STC first introduced by Tarokh et al. [2] in 1998 as a novel means of providing transmit diversity for the multiple-antenna fading

(1)


63

channel and it is known as a channel-coding scheme. This scheme maintains high channel capacity of MIMO system along with diversity and coding gain.

Space-Time Block Codes (STBC), which is one of STC families operate on a block of input symbols, producing a matrix output whose columns represent time and rows represent antennas. STBC has the provision of full diversity with a simple encoding and decoding scheme. 7.3.1 2Tx1Rx Model First simulation model in this paper is based on STBC Alamouti’s Diversity Scheme. Diversity scheme that has been introduced by Alamouti [3] in 1998 use two transmit antennas and one receive antenna. This scheme operate using transmit diversity instead of receiver diversity. This is to avoid the remote unit antenna to be larger and more expensive with the use of multiple antenna and radio frequency (RF) chains.

Figure 4 shows the STBC with two transmit and one receive antenna. In this scheme, two signals are simultaneously transmitted from the two antennas. The notation s0 for the signal transmitted from antenna 0 and s1 is the signal transmitted from antenna 1. During the next symbol period, signal (-s1)* is transmitted from antenna 0 and signal s0* is transmitted from antenna 1 where * is the complex conjugate operation.

The first bit s0 is transmitted through antenna 0 at t second while bit s1 is transmitted through antenna 1 at the same time. Then, at t + T, a delayed replica of the transmitted signal s0* is transmitted through antenna 1 and – s1* which is the complex conjugate of s1 is transmitted through antenna 0 instead of antenna 1. This transmission sequence applies the diversity concept where the all the bit transmitted will be transmit using both antenna 0 and 1. Table 1 simplifies the operation of transmit sequence.


64

Figure 4 The Two Branch Transmit Diversity Scheme With One

Receiver Table 1 The Sequence For Two Branch Transmit Diversity

Time Antenna 0 Antenna 1

t S0 S1

t+T (-s1)* S0*

The encoding process is done in space and time diversity (space-time coding). Transmission channel at time t is represent by a complex multiplicative distortion, h0(t) for antenna 0 and h1(t) for antenna 1. Assuming that fading is constant across two consecutive symbols, the transmitted signal can be written as equation (2) and equation (3) [3];

1

0

1111

0000

)()(

)()(θ

θ

α

αj

j

ehTthth

ehTthth

==+=

==+=

where T is the symbol duration. The received signals can then be expressed as [3]

(2)

(3)


65

1101101

0011000

**)()(

rhshshTtrrhshshtr

=++=+=++=

where r0 and r1 are the received signals at time t and t+T respectively while n0 and n1 are complex random variables representing receiver noise and interference. 7.3.2 2Tx2Rx Model 2Tx2Rx simulation model also derived from Alamouti’s transmit diversity scheme. In this model, the random binary bit will be split into 2 message using interleaver. Then, the message will be encoded using cyclic code with 4/5, 4/6 and 4/7 code rate and modulated using BPSK modulation. The received signal is chosen based on Selection Diversity Technique where the strongest and highest signal power is selected. 7.4 RESULTS AND DISCUSSION The BER measurement for the simulation model is done using Monte Carlo simulation [4]. In this method, the difference between input and output bit is calculated to measure BER.

For channel capacity analysis, MIMO channel is measured based on Shannon’s capacity theorem [5]. Equation (6) is used for 1TxlRx Model while equation (7) is used for 2Tx2Rx model.

)1log(,)1log(,

SNRBMCCapacitySNRBCCapacity+=

+=

where B represent bandwidth, SNR as a signal to noise ratio and M is a number of transmit and receive antenna.

(4) (5)

(6)

(7)


66

7.4.1 BER Performance The simulation for BER performance is done for different number of code rate (R=4/5, 4/6 and 4/7). Figure 5 shows the performance for all simulation model with code rate R=4/5. The simulation result shows that the MIMO system with 2 transmit antenna improve almost 90% BER compared to the conventional single transmit antenna system

Figure 5 SNR Vs BER For Code Rate 4/5

Figure 6 and 7 gives the performance for code rate R=4/6 and code rate R=4/7 respectively. The code rate does not much affect the BER performance. However, the results carried out clearly shows a significant improvement in BER performance with changing the number of transmit antenna. It shows that the effects of noise are minimized by the simultaneous use of multiple number of multiple number of transmit antenna.



67


In this simulation, the effect of multiple number of receive antenna is shown by model 2x1 and 2x2. Results in Figure 5. 6 and 7 give the moderate result where the 2x2 model perform better than 2x1 model. The improvement is nearly 10% at SNR greater than 5dB.

7.4.2 Capacity Performance Simulation results for capacity performance are shown in Figure 8 and Figure 9. Figure 8 shows the capacity performances for conventional 1 transmit and 1 receive antenna with different code rate. Simulation model with code rate R=4/5 gives the best capacity performance compared to the R=4/6 and R=4/7. The capacity performance for single antenna system is affected by bandwidth (BW) and SNR of the system. The lowest code rate will contribute to the lowest BW but it has the least capability of error correcting compared to the higher code rate.


68

Figure 8 Capacity Performance For 1 Transmit And 1 Receive

Antenna System Simulation result for 2 transmit and 2 receive antenna system

shows that code rate, R=4/6 gives the ideal toleration between two factors that affect the capacity performance, which are BER and SNR. It is shown in Figure 9

Figure 9 Capacity Performance For 2 Transmit And 2 Receive

Antenna System

7.5 SUMMARY Three simulation models (1TxlRx, 2TxlRx and 2Tx2Rx) have been developed and the result was analyze for BER and capacity performance. The simulation results show that time and space diversity concept increase almost 90% of BER performance in AWGN channel environment. The uses of multiple antennas also improve channel capacity compared to the conventional 1TxlRx


69

system. The increment in capacity is about 73 % using 2Tx2Rx system.

This paper is a preliminary study of Space time Codes. Further research can be done using other types of channel coding or modulation technique such as Minimum Shift Keying (MSK). Therefore the investigations on the effect of channel capacity can be done since different coding and modulation technique contribute to a different bandwidth and error correction capability.

REFERENCE [1] Robert W. Heath Jr, Arogyaswami 1. Paulraj. “Diversity versus

Multiplexing in Nanowband MIMO Channels: A Tradeoff Based on Euclidean Distance”, IEEE Transactions on Communication April 2001, revised December 2002.

[2] V. Tarokh, N. Seshadri, and A.R. Calderbank, “Spacetime codes for high data rates wireless communications: Performance criterion and code construction”, IEEE Trans. Inform. Theory, 1998, vol.44, pp. 744-765.

[3] S. M. Alamouti, “A simple transmit diversity technique for wireless communication”, IEEE Journal on select areas in communications, Oct. 1998, vol. 16, no. 8, pp. 1453-1455.

[4] Duane Bong “Monte Carlo Simulation”, http://www.visionengineer.com.tech/monte_cado_sim dation .shtml.

[5] G. Andrea, and Colleague “Fundamental Capacity of MIMO Channels”, Stanford University, Stanford. CA 94305, November 8, 2002.

[6] G. H. Author, “Title of the conference paper,” in Proceedings of the 2000 IEEE International Symposium on Circuits and System, Geneva, Switzerland, May 2000, pp. 100-105.


70

8

ITERATIVE DATA DETECTION AND CHANNEL ESTIMATION FOR SINGLE-

ITERATIVE DATA DETECTION AND CHANNEL ESTIMATION FOR SINGLE-

PARITY CHECK-PRODUCT CODED FOR WIRELESS MIMO

COMMUNICATIONS SYSTEM Muladi N. Fisal

Sharifah K. Yusof

8.1 INTRODUCTION The joint iterative data-detection and channel estimation appears to be a suitable means to achieve excellent performance in wireless communication system, where the length of the training sequence or pilot symbols is to be kept as small as possible to maintain the data throughput is still high. Basically, iterative schemes (which are usually denoted through the adjective “turbo”), the channel estimator and the data detector recursively exchange information in order to improve the system performance.

The explosive growth of wireless communication services, along with the emerging of new applications, such as mobile computing and wireless Internet, as well as the deployment of wireless local area network (WLAN), has resulted in an in bandwidth-efficient high-data-rate transmission system. Recent results from information theory have shown that capacity of a multiple antennas wireless communication system operating in a

Iterative Data Detection and Channel Estimation for Single-ParityCheck-Product Coded for Wireless MIMO

Communications Systems

71

rich scattering environment grows with a law approximately linear in minimum between the number of transmit and receive antennas [1]. Likewise, high-performance space-time diversity systems have been recently introduced, which permit the system to achieve huge performance gains with respect to single-antenna communication system (see. e.g [2], [3], and [4]).

Some layered space-time architectures have been proposed in order to exploit the benefit of the multiple antenna system promise in theory and their potential gains over single antenna systems. Among these, the most popular one has been termed Bell Labs Layered Space-Time Architecture (BLAST) [5]. This system has attracted much attention in the last ten years and several papers have appeared in the open literature, presenting theoretical finding and/or performance results for BLAST-like system. In our previous work [6], the full-rate space-time diversity scheme have been proposed. Compare to the system using space-time block codes [3], the proposed scheme has the advantage that guarantee the transmission rate always equal to 1 symbol/Hz/s. This paper extends these previous results by increasing the bit rate and develops the channel estimation. One alternative in increasing bit rate uses high rate code as component code of the product code but it provides low error rate. Turbo codes are robust in error-rate performance but are often low rate and the decoding complexity can be high. Low-density-parity-check (LDPC) codes have also been shown to be capable of approaching the AWGN channel capacity. However, the encoding and/or decoding complexity for these codes can be high. In addition, the generally require a large number of decoding iterations (only 50-100 iterations being common) and suitable for very long codeword.

The work in this paper uses the single-parity-check code (SPC) as component code, parallel concatenated, of product code (PC). SPC. is simple, but weak, algebraic code. The SPC-PC codes -are high-rate codes when reasonable block lengths are used. They are simple to encode and decode and have been shown to produce good performance. Maximum a posteriori (MAP) decoded


72

multidimensional SPC-PC were shown to have very good performance in [9].

By taking the output of the SPC-PC encoder into two defined-interleaver and transmitting through multiple transmit antennas, will provide space and time diversity in the system. This scheme would be BLAST-like system. Pilot-symbol aided channel estimation is used to measure the channel impulse response. Following the iteration of the decoding process, the channel impulse response will be updated by employing the extrinsic information output of the decoder. The convergence of this channel impulse response update will investigate.

The paper is organized as follows. System model is described in Section 2. Data recovery and iterative decoding will presented in Section 3, while Section 4 is presenting the channel estimation and pilot sequence design. Simulation results and discussion is elaborated in Section 5 and conclusion is in Section 6. 8.2 SYSTEM MODEL Figure 1 depicts the discrete time model of proposed system diagram. At the transmitter, the data stream is formatted into a block data with size of kr x kc,, where kr, is the data length in rows and kl is the data length in column. Each row and column of data is encoded using single parity check code (SPC) to be a )2,,1( 2kkr + for row and )2,,1( cc kk + for column. The encoding process in rows and columns are to be independent thus the check on check parity bit is not generated [7]. Without lost of generality, in this paper it sets kr=kc=k.

The encoded data stream output to two systematic interleavers, defined by the row-wise reading and column-wise reading (see [6]). These data streams are then mapped into S-symbol of constellation elements, s. The L number of pilot symbols p are inserted at each l data information to provide the channel response measurement. The resulted blocks have the following format:



73

].........[ 3121211 n

l

ll

l

ppsspsspx ++=

These blocks are transmitted through each branch of transmit

antenna. Each transmit antenna uses the same amount of energy and that totally equal to transmitted energy of the single transmit antenna system. It is assumed that the transmit antennas are far-separated enough thus each path between transmit and receive antennas are independent.

Figure 1 (a) Proposed System Diagram (Transmitter)

Figure 1 (b) Proposed System Diagram (Receiver)

Assuming that receiver employs a number of antennas that

equal to the number of antennas at the transmitter. The received complex base-band sample at the received antenna n is presented by:

∑=

+=2

1,

mnmnmn wxhr

(1)

(2)


74

where xm is transmitted block symbols from transmit antenna m While wn is an additive noise, Gaussian distributed with mean zero and variance No/2 when the transmitted bit energy is Eb/No.

Assuming that the transmit antennas are separated enough as well as the receive antennas, thus the link between each transmit and each receive are independent. This link is in a rich scattering environment that consists of multiple paths but no line of sight component. The link can be modeled as a wide-sense-stationary complex Gaussian process with zero mean, which makes the marginal distributions of the phase is uniform and amplitude is Rayleigh at any given time, hence the link can be characterized as Rayleigh fading. 8.3 ITERATIVE DATA DETECTION One block of data information are interleaved by two interleavers and transmitted from two transmit antennas. The receive signal from two receive antennas can be derived from (2) as follows:

⎥⎦

⎤⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

1

2

1

2212

2111

2

1

ww

xx

hhhh

rr

where hmn is channel impulse response of the link between transmit antenna p and receive antenna n, m= 1, 2 and n = 1, 2. By using explicit notation, (3) can be rewritten as:

22221122

12211111

wxhxhrwxhxhr

++=++=

The estimated received symbols are obtained by combining the received signals,

2221212

2121111

**ˆ**ˆ

rhrhxrhrhx

+=+=

(5)

(4)

(3)



75

where (.)* is conjugate operator. Soft-output de-mapping process yields the estimated bit sequences as follow:

)ˆ(ˆ)ˆ(ˆ

21

2

11

1

xMb

xMb−

−

=

= (6)

where (.)-1 is inverse process. Remember that the transmitted bit sequence from transmit antenna one is same with the transmitted bit sequence from antenna two, but interleave at different position prior to mapping process and transmission. Thus, by de-interleaved

1̂b and 2b̂ , into its original position result the measured channel value of the same codeword. Both will be decoded using different SPC-PC decoder, as shown in Fig. 2.

Figure 2 Iterative Double SISO PRC-PC decoder

The decoding process starts by calculating the log-likelihood ratio (LLR) for each received bit of two received sequences,


76

where d represents the transmitted data bits. The computation of (7) and (8) are same, thus it can be presented in general. Using Bayesian rule, (7) and (8) to be:

Assuming all bits are equal likely, the second term can be ignored. The first term can be simplified as:

This will be used as the channel LLR Lc(b). For statistically independent transmission of the dual diversity system, the LLR channel is [7]:

Where )ˆ(dLc is simplified version of )ˆ|( bdL . The LLR output (soft output) of the decoder is equal to [8]:

where )ˆ(dLc is extrinsic LLR obtained from row and column decoding. From [6] and [8], the extrinsic LLR is:



77

Where

where Lc(p) is LLR channel of the parity bit at the same row or column of the dj. The input LLR for the column decoding for the jth data bit can be written as

)ˆ()ˆ( jerj dLdL =

where )ˆ( jer dL is LLR output of row decoding (half iteration). For the next iteration, the LLR for row decoding can be written as:

)ˆ()ˆ( jecj dLdL =

where )ˆ( jec dL is extrinsic information of the column decoding from previous iteration. At the last iteration, the soft output of the decoder is:

)ˆ()ˆ()ˆ()ˆ( jecjerjcj dLdLdLdL ++=

The hard decision value of this data bit can be obtained by applying the sign function to (17). 8.4 PILOT SEQUENCE DESIGN FOR CHANNEL ESTIMATION

(15)

(16)

(17)


78

Eq. (3) can be represented in matrix form as follows:

R = HX+W

This relation gives one possible way to measure the channel response. The transmitted block X consists of a few number of pilot symbol, xp, that the receiver knows the pilot value and its position within the block. A particular pilot symbol will help to measure the channel impulse response and the pilot positions will define the time of those response occurrences. The channel impulse responses will be obtained by inverting the pilot symbol matrix, Xp. that the elements of this matrix are pilot symbol from antenna one and two.

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

MNMM

N

N

p

ppp

pppppp

21

22212

11211

X

where M, N are number of transmit antenna and receive antenna, respectively. In the case of two transmit and two receive antennas employment, M= N= 2, the pilot symbol matrix is:

⎥⎦

⎤⎢⎣

⎡=

2221

21112 pp

pppX

This matrix define the minimum number of pilot symbol that should be inserted into the transmitted data block, thus the channel impulse response measurement can be performed.

In order simplified computation of the channel impulse response, this paper sets the pilot symbol orthogonal in time. In particular, the simplest pilot symbol matrixes are:

(18)

(19)

(20)

8.4 PILOT SEQUENCE DESIGN FOR CHANNEL ESTIMATION



79

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡0

00

0

21

12

22

11

pp

orp

p

Once the channel impulse responses at a particular time are

achieved, the channel response for the whole transmitted block can be obtained by using interpolation, where the number of pilot symbol define the accuracy of the generated samples.

H = X-1(R-W)

As described in the previous section, the iterative data detection gives the extrinsic information of data that will update the received bits value (Lc+Le). Soft-mapping these bit sequence to the constellation elements of S (soft-values). Using equation in (5), the new channel impulse response can be calculated. Thus the channel impulse responses are also updated iteratively together with the data decoding process. 8.5 SIMULATION RESULT AND DISCUSSION Simulation results are presented for the proposed scheme. It begins with comparing the error rate performance of the proposed system with single antenna system. The PC uses SPC with k = 8 and the flat Rayleigh fading channel is assumed. Fig. 3 is shown that the proposed system has 2 dB more power advantage than single antenna system to achieve bit error rate (BER) at 2x10-5. A significant improvement is obtained after iteration number 3. Beyond that the iteration does not improved the BER performance significantly. It has been investigated in [10], that the effective iteration number of two dimensional SPC-PC is three. At Eb/No 6 dB, the second iteration gives BER 5x10-5, while BER 2.4x10-6 gives by the third iteration, and 1.75x10-6 by the forth iteration.

(21)


80

Figure 3 Performance Of The Proposed System With Perfect Channel

Estimation

Figure 4 Performance Of The Proposed System Employing A

Numbers Of Pilots Symbols Compared Transmitted To The Length Of The Transmitted Block

At the second investigation, a number of pilot symbols are inserted into the data information block to provide the channel impulse response measurement. A comb-type insertion is used where the distance between the pilot symbols within the data block is uniform. The channel impulse responses at the pilot’s time position can withdraw directly from the receive signal by



81

divide it with the pilot symbols. This simple process is allowed just because the pilot symbols from transmit antenna one and transmit antenna two were designed orthogonally each other. The complex channel impulse response at the other time position is generated using interpolations through the real part and imaginary part separately, then scale up or down by the samples that generated from interpolating the magnitude (amplitude). This interpolation process is done once just before the iterative decoding is performed. Errors between these samples and the actual values can occur and they are corrected iteratively using extrinsic information of the decoding data process.

Fig. 4 shows error rate performance of the proposed system with different number of pilot symbol within one block of data information. The channel is a Rayleigh distributed flat fading and is assumed to be invariant during one symbol period. Number of pilot symbols compare to the number of symbols in one data block is presented in percentage. The graph shows higher number of pilot symbols in one transmitted block will give better error rate performance. When the number of pilot symbols equal to data symbols (50%), the system experiences BER 2x10-5 at Eb/No 6 dB, while when uses perfect channel estimation 3x10-6 This error performance decreases significantly as the number of pilot symbols is decreased. If half number of pilot symbols is employed, the error performance will decrease to 2x10-5. Furthermore, the error rate performance will decrease to lx10-4 if the number of pilot symbol is a quarter of transmitted block length, and 2x10-3 if the number of pilot is one over eight of the length of transmitted block. These results confirmed that higher number of pilot symbols will give higher error rat performance at the cost of lower rate transmission.

Next, we investigate convergence of the iterative decoding algorithm when the channel is not perfectly measured. In the term of bit error rate performance, the different numbers of pilot symbols are employed to estimate the channel response. As it is shown in Fig. 5, the decoding algorithm will converge after 5


82

iterations. Since more accurate information of channel is available, the algorithm will converge faster. In this case, the information of the channel is brought by pilot symbol in the transmitted block. The algorithm will converge in the second iteration when the number of pilot is equal to the number of data symbol in the transmitted block (50% of block length). Higher number of iteration is required to reach convergence when employing a few number of pilot symbols. Three and five iterations is required when the number of pilot symbols is a quarter and one over eight of the transmitted block, respectively. Although these iteration number are still reasonable but the error rate performances are not significant. Thus, the bound between the error rate and transmission rate is important to define on this system.

8.6 CONCLUDING REMARKS

The application of SPC-PC in multiple antennas system was introduced. Using two different interleavers based on row-reading and column reading [6], the proposed system provided the space-time diversity. Decoding of the received data can be performed iteratively based on MAP criterion.

Pilot symbols are used to estimate the channel impulse responses in the proposed system. Accurate channel estimation will be given by employing large number of pilot symbol in the transmitted block. By using extrinsic information of iterative data decoding-to update the channel impulse response, the decoding process will converge faster.



83

Figure 5 Convergence Curve Of The Iterative Data Decoding And

Channel Estimation; Dash-Line: Without Channel Response Update, Fill-Line: With Channel Response Update

REFERENCE [1] G. J. Foschini and M. J. Gans, “On limits of wireless

communications in a fading environment when using multiple antennas”, in Wireless Personal Conmunications, 1998, vol. 6, pp. 311-335.

[2] V. Tarokh, N. Seshadri, and A. R. Chalderbank, “Spacetime codes for high data rate wireless communication: Performance criterion and code construction”, IEEE Trans. Inform Theory, vol. 44, pp. 744-765, March 1998.

[3] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Spacetime block codes from orthogonal designs,” IEEE Trans. Inform Theory, vol. 45, pp. 1456-1467, July 1999.

[4] G. Raleigh and J.M. Chioffi, “Spatial-temporal coding for wireless communication,” IEEE Trans. Commun., vol. 46, pp. 357-366, March 1999.

[5] G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multiple-


84

elements antenna,” Bell Labs. Tech. Journal, vol. 1, pp. 41-59, 1996.

[6] Muladi, N. Fisal, and S. K. Yusof, “Product coded MIMO system with iterative decoding,” in Proc. Of The IASTED Conf on Network and Computer Systems, Krabi- Thailand, 18-20 April 2005.

[7] J. Hagenauer, “Interative decoding of binary block and convolutional codes”, IEEE Trans. Inform Theory, vol. 42, pp. 429-445, March 1996.

[8] B. Sklar, Digital Communications: Fundamental and Applications, Second Edition, New Jersey: Prentice Hall Inc., 2001, ch. 8.

[9] J. Lodge, P. Hoeher and J. Hagenauer, “The decoding of multidimensional codes using separable map filtering,” in Proc. 16th Queen’s Bienial Symp. Communications, Kingston, ON, Canada, 1992, pp. 343-346.

[10] J. S. K Tee, D. P. Taylor, and P. A. Martin, “Multiple serial and parallel concatenated single parity-check codes,” IEEE Trans. on Comm, vol. 51, pp. 1666-1675, October 2003.

Performance of Block Turbo Coded MIMO Systems

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9

PERFORMANCE OF BLOCK TURBO CODED MIMO SYSTEMS

Muladi Sharifah K. Syed-Yusof

Norsheila Fisal

9.1 INTRODUCTION Wireless communication has been growing explosively in the last two decades according to the growing demand of high capacity and reliability communication link. Unfortunately, the amount of radio spectrum suitable for wireless communication is limited, therefore more sophisticated technologies have to be employed to make better use of the radio spectrum while providing reliable degree of services. One of major problems in wireless communication is its detrimental effects caused by multipath and movement in radio link. Telatar [I] and Foschini and Ganz [2] have been studied the information theoretic that showed the enormous capacity promised by multiple input multiple output (MIMO) systems in such channels. These capacity results have motivated new area in the design of channel codes. In their seminal paper. Tarokh et al [3] have been starting the development of channel codes for multiple antenna system which is called ‘space-time codes’ relied on the fact that these codes provided diversity both in space and time. The code design is based on trellis that it is called space-time trellis codes (STTC). Then Alamouti [4] proposed the full-rate space-time code for two transmit antennas scheme. This result was extended to higher number of transmit antennas based on orthogonal design [5]. But the resulted codes did not provide full rate transmission and coding


86

gain although they were full diversity. In literature, both STTC and STBC were designed for quasi-static fading channels where the channels are constant over a frame of coded symbols. However, this assumption is rarely seen in wireless communication systems.

There are many approaches to solve the drawback of the space-time codes when it is implemented in worse channel characteristic, such as fast fading channel where the channel varies in shorter period than the length of the frame of coded symbol. Some of the famous solutions are concatenated space-time codes with another channel codes, interleaver employment or using other channel codes as space-time codes, e g. space time turbo codes [6], and product turbo code [7,8].

In this paper, block turbo codes is a product code with iterative decoding using sub-optimum MLD algorithm [9]. We proposed a new product coded-MIMO schemes that provides space and time diversity over Rayleigh fading channel. The scheme is similar to [7,8], where the coded symbols are interleaved and converted from serial to parallel. In our scheme, the coded symbols are read in row, column and depth, for three dimension (3-D) product code, then transmitted individually via different transmit antenna. These reading methods provide quasi interleaving to the transmitted symbols. The number of transmit antenna, corresponds to the dimension of the product code. The product code consists of linear block code as constituent codes with the same or different type and size. In particular, we use two transmit and two receive antennas with two-dimensional product code while three transmit and three receive antennas with three-dimensional product code. Performance of the system is analysed through computer simulation and compared to the space-time block coding from orthogonal design [5].

9.2 SPACE-TIME DIVERSITY SYSTEM The space-time diversity system is modeled with nT transmit antennas and nR receive antennas. The received signal at the receive antenna j at time t is:


87

where hi,j is channel impulse response between transmit antenna i and receive antenna j, xt,i is transmitted symbol from transmit antenna i at time t and wj is Gaussian random process of additive white noise with mean zero and variance one at receive antenna j.

It is assumed that the channel response is constant at least over one symbol period and perfectly known at the receiver but not at the transmitter. This channel model is different with assumption used in [4, 5] where channel response is not changed over one period of frame consist of several symbol periods.

9.3 D-DIMENSIONAL PRODUCT CODES Product code is serially concatenated codes and it was introduced by Elias [10]. The product code is built from two, or more, short linear block codes resulting a very long block code. Consider D systematic linear block codes with parameters (Nd, Kd, δd), where Nd is length of codeword Cd, Kd, is length of information bit and δd is minimum Hamming distance of code Cd. The product code built from D linear systematic block codes will result D-dimensional code. The encoding performs by constructing K1 in first dimension (rows), K2 in second dimension (columns), K3 in third dimension (depth), and so on. Then encode K1 rows using C2, K2 columns using C1, K3 depths using C4, K4 forth dimensions using C3, and so on, where C1, C2, ... Cd may come from same or different types of linear block codes. The resulted code has length C = ΠCd with minimum Hamming distance δ = Πδd and code rate R = ΠRd. In this paper, only the two and three dimensional product codes are considered.

The two dimensional (2-D) product codes have been discussed in many papers. Let us consider 3-D product code constructed by

(1)


88

three systematic linear block codes C1 with parameter (N1, K1, δ1), C2 with parameter (N2, K2, δ2) and C3 with parameter (N3, K3, δ3), where Ni, Ki, and δi stand for length of codeword, length of information bits and minimum Hamming distance, respectively. The 3-D code is obtained by placing (K1xK2xK3) information bit in array of K1 rows, K2 columns and K3 depths. Encode K1 rows using C2, K2 columns using C1 and K3 depths using C3. The parameter of the product code P are N = N1xN2xN3, K = K1xK2xK3, δ = δ1xδ2xδ3 and the code rate R is given by R = R1xR2xR3, where Ri is the code rate of code Ci. Thus we have a very long codeword with large minimum Hamming distance by combining short codes with small Hamming distance.

Figure 1 Proposed Scheme


89

9.4 SPACE-TIME SYSTEM WITH ORTHOGONAL TRANSMISSION 9.4.1 System Model We proposed the space-time system with orthogonal transmission using product codes over flat Rayleigh fading channels with several different channel estimation schemes. Later, we compare the performance of our schemes with serially concatenated product code and space-time block codes from orthogonal design. Figure 1 shows the proposed scheme.

At the transmitter, a sequence data bit of length K1xK2xK3 is arranged in three dimensional form consisted of K1 rows, K2 columns and K3 depths. This data are then encoded using same or different type of linear block codes with (Nd-Kd) parity bits, where d = I, 2, and 3. The resulted codeword has a 3-D dimension with size of N1 rows, N2 columns and N3 depths and is read in three different ways corresponding to the three transmit antennas. How to read the codeword will be described in the next sub-section. Each codeword is mapped to M-symbols of M-PSK constellation elements using Gray mapping. The first codeword symbols read in row-direction will be transmitted directly through first transmit antenna. For the second and third transmit antennas, the second and third codeword symbols are converted to its orthogonal values. Transmit antennas use the same power in transmission and assumed it separated enough such that the paths between each transmit antennas and each receive antennas are independent.

At the receiver, the received signals from each receive antenna are combined and estimated utilizing channel state information. It is assumed that the channel impulse response is known at the receiver. Due to the different reading of the 3-D codeword at transmitter, the same symbol will present at three symbol periods in three different times. To obtain a particular symbol, we have to re-order the receive signal according to the symbol position in the transmission time. The arrangements are according to the reading-


90

ways in column and depth direction. This process is similar with de-interleaving process in bit interleaved transmission system. 9.4.2 Reading Mechanism The reading-ways of the 3-D codeword will be explained through the following example. A codeword P has size of three rows, three columns and three depths consisting of 27 symbol elements as shown in Figure 2. Symbol elements are shown as their position in the codeword.

Figure 2 An example of 3-D codeword

There are many methods to read the data from a 3-D codeword, such as in row, column, or depth-wise and also in diagonal-wise as well. Here we use the row, column and depth reading to obtain the diversity in time. Row-wise reading results the following symbol position sequence:

r1=1,2,3,4,5.6.7,8,9,10,11,12,13,14,l5,16,17,18,19,20,21,22,23,24, 25,26,27

Column-wise reading can be performed by read in column wise following by row-wise or depth wise. To obtain long distance and high diversity in time, we choose column-wise, depth-wise and row-wise, consecutively. The resulted sequence of column-wise reading followed by depth-wise and then row wise is: c1=1,4,7,10,13,16,19,22,25,25,8,11,14,17,20,23,26,3,6,9,12,15,18,


91

21,24,27 While column-wise reading followed by row-wise reading and then depth-wise reading yields: c2= 1,4,7,2,5,8,3,6,9,10,13,16,11,14,17,12,15,18,19,22,25,20,23, 26,21,24,27 As column-wise reading, we have two options in depth-wise reading. The depth-wise reading followed by row-wise and then column-wise results: d1 = 1,10,19,2,11,20,3,12,21,4,13,22,5,14,23,6,24,7,16,25,8,17,26, 9,18,27 And when depth-wise reading followed by column-wise and then row-wise will yield the sequence of. d1 = 1,10,19,4,13,22,7,16,25,2,11,20,5,14,23,8,17,26,3,l2,2l,6,15, 24,9,18,27 We have to choose the right combination of r, c, and d to obtain high degree of diversity in time. The number of symbols that transmitted in different time through different transmit antenna for each combination can be calculated and the results are presented in table 1 as number of differences (Nd).

Table 1 Number of Differences

Combinations Nd Combinations Nd r1-c1 24 c1-d1 24 r1-c2 18 c1-d2 18 r1-d1 24 c2-d1 18 r1-d2 18 c2-d2 24

This sequence combination provides long distance and high diversity in time although we still have the same symbols


92

present at the same time. Therefore we call this arrangement as quasi-interleaving because the symbol sequence is not fully interleaved. Estimation values of transmitted symbol are obtained by reordering the received signals following the order of sequences at above.

9.4.3 Iterative Decoding At the receiver, the received signals from NR antennas are combined and processed using orthogonal decoder and inverse channel response combiner. Soft-output values of the received symbol are yielded by using soft-output de-mapping. This codeword is then converted serial-to-parallel to form a product code. Soft-input soft-output product code decoder employs sub-optimum maximum-likelihood decoding [10]. 9.5 SIMULATION RESULTS We show the results of our computer simulation and compare it to serially concatenated product code and space-time block codes from orthogonal design at the same transmission rate over flat Rayleigh fading channel. Based on the number of differences calculation, a consecutive reading r1-c2-d1 has been chosen. At the first investigation, the proposed scheme uses 2-D product codes and compares its performance with PC-STBC scheme using two transmit and two receive antennas.

Figure 3 shows the simulation results of our schemes together with serially concatenated product code and space time block code (PC-STBC) We use the same linear block code to encode rows and column of data to obtain 2-D product codes to be used in two transmit and two receive antennas scheme. A single error correction BCH (7, 4, 1)2 is used, which provides a code rate of 0.33, codeword length of 49 bits and minimum Hamming distance of two. The codeword is mapped using binary phase shift keying and transmitted over flat Rayleigh fading channel.


93

Figure 3 Pe performance of the proposed scheme using 2x2

and 3x3 antennas compare to PC-STBC schemes

It is assumed that the receivers know the channel response value at every symbol period, thus the received symbols can be estimated exactly at every symbol period based on its corresponding channel response. At single iteration decoding (same with hard decision decoding), the results show that the scheme can reach Pe = 10-3 at almost Eb/No = 5 dB which is 2 dB worse than PC-STBC scheme. It is because our scheme is not providing full diversity in time as in PC-STBC. As it is shown at example in section 4.2, the first symbol is transmitted from all transmit antennas at time one, which is also experienced by the last transmitted symbol at the end of frame. We can change the position of first symbol to the last symbol and vice versa to improve the time diversity with the cost of reading complexity.

The single error correction BCH (7, 4, 1)3 is used as product code for three transmit and three receive antennas schemes with BPSK mapping. This code has rate of 0.19, minimum Hamming distance of three and length of codeword 343 bits. To obtain equal transmission rate, we set a PC-STBC scheme with three transmit


94

and three receive antennas using a half rate STBC code G3 [5] and QPSK mapping. As it is shown in Figure 3, our proposed scheme has 0.5 dB worse than PC-STBC scheme at bit error rate 10-5. This is because the time diversity is not always available at the whole frame period as it occurs at the MlMO systems using 2 transmit and 2 receive antennas.

9.6 CONCLUSION We have already utilized product code for space time systems with multiple transmit and multiple receive antennas system that provide diversity both in space and time. Full rate in orthogonal transmission is provided although it employs three or more transmit antenna, which cannot be served by space-time block code from orthogonal design. The rate advantage of the proposed scheme sacrifices the bit error rate performance. The performance of the proposed scheme also highly depends on the channel estimation performance which is required in signal combining at the receiver. Solving these problems could become the tasks of our future work. In this work, soft-input soft-output decoder employs optimum trellis-based decoding using MAP criteria. In order to reduce the complexity of the system, the sub-optimum decoder one [10], multistage decoding [11], etc can be used. The performances of these decoders have not been investigated yet over MIMO channel. REFERENCES [1] I.E. Telatar, “Capacity of multi antenna Gaussian channels,”

Europe Transaction Telecommunication, vol. 10, no. 6, pp. 585-595, November 1999.

[2] G.J. Foschini and M.J. Ganz, “On limits of wireless communications in a fading environment when using a multiple antenna.” Wireless Personal Communications, vol. 6,


95

pp. 311-335,March 1998. [3] V. Tarokh, N. Seshadri, and A.R. Calderbank, “Space-time

codes for high data rate wireless communication: Performance criterion and code constructions,” IEEE Transaction on Information Theory, vol. 44, pp. 774-765, March 1998.

[4] S.M. Alamouti, “A simple Transmitter diversity scheme for wireless communication,” IEEE Journal on Selected Areas in Communication, vol. 16, no. 8, pp. 1451-1458,October 1998.

[5] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space time block coding from orthogonal design,” IEEE Transaction on Information Theory, vol. 45, no. 5, pp. 1456-1467, July 1999.

[6] Y. Liu, M. P. Fitz, and 0. Y. Takeshita, “Full rate space-time turbo codes,’’ IEEE Journal on Selected Areas in Communication, vol. 19, no.5, pp. 969-980, May 2001.

[7] Y. Chen and K. K. Parhi, “On the performance and implementation issues of block turbo code with antenna diversity,” Proceeding of IEEE Globecom 2002, Taipei, Taiwan, November 2002, pp. 604-608.

[8] K. C. Amis and R. M. Pyndiah, “Block turbo codes for space-time systems,” Proceeding of IEEE Globecom 2000, San Fransisco, CA, November2000, pp. 1021-1025.

[9] R. Pyndiah, “Near-optimum decoding of product codes: block turbo codes”. IEEE Transactions on Communications, vol. 46, no. 8, pp. 1003 - 1010,August 1998.

[10] P. Elias, “Error free coding,” IRE Transaction of Information Theory, vol. IT-4, pp. 29-37, September 1954.

[11] A. R. Calderbank, “Multilevel codes and multistage decoding”, IEEE Transactions on Communications, vol. 37, no. 3, pp. 222 - 229, March 1989.


96

10 THE PERFORMANCE OF PRS-OFDM IN

MULTIPLE ANTENNA SYSTEM Sharifah K. Syed Yusof


10.1 INTRODUCTION The main advantage of OFDM transmission comes from the fact that the Fourier basis forms an eigenbasis for time invariant channels [1]. This allows simplification on hardware implementations especially at the receiver. For example, when the channel is time-invariant within one OFDM transmission block, the equalizer is just a single-tap filter in the frequency domain. Combined with multiple-input multiple-output channels (MIMO), MIMO-OFDM has a potential of achieving high data rates. However, the block time-invariance assumption may not be valid at high mobile speeds where impairments such as frequency offset are likely to occur. Such scenario resulted to loss of orthogonality of the OFDM subcarriers that leads to inter-carrier interference (ICI) in addition to signal rotation and attenuation. With the increasing frequency offset occurrence, the degradation of BER performance in OFDM system enhances further [1].

In single-input single output (SISO) OFDM system, several methods have been proposed to reduce the effect of the ICI. One of the methods is frequency-domain equalization [2]. Time-domain windowing is another way to reduce the effect of frequency offset [3]. A self-ICI-cancellation approach has been proposed, which transmits each symbol over a pair of adjacent or non-adjacent subcarriers with a certain phase shift [5, 6, 7].This method can

The Performance of PRS-OFDM in Multiple Antenna System

97

suppress the ICI significantly with a reduction in bandwidth efficiency. In single-carrier systems, partial response signaling has been studied to reduce the sensitivity to time offset without sacrificing the bandwidth [8]. The partial response with correlation polynomial F(D) = 1 - D was used in the frequency domain to mitigate the ICI caused by carrier frequency offset [9]. In this technique, ICI is deliberately introduced in a controlled manner through the polynomial functions. The ICI suppression in multiple-input multiple-output (MIMO) OFDM is studied in [4] by using time-domain filtering based. In this paper, we investigate the performance of partial response signaling OFDM (PRS-OFDM) used by [8] in reducing BER caused by frequency offset in multiple antenna system system. Symbol-by-symbol suboptimum detection technique is used in this study.

This paper is organised as follows. In Section 2 we describe PRS-OFDM in multiple antenna system. The ICI expressions and analysis is included in Section 3. Then, in Section 4, the simulation results are presented and followed by Section 5 for conclusion. 10.2 PARTIAL RESPONSE SIGNALING IN OFDM SYSTEM Let be the symbols to be transmitted and c, be the coefficients for correlation polynomial, the transmitted signal at the k-th subcarrier can be expressed as

where K is the number of coefficients or length of the polynomial. Without loss of loss of generality, and for jk ≠ is assumed.

(1)


98

The transmitted SISO-OFDM signal in time domain is

Where is the frequency of the -th subchannel,

, is the subchannel spacing, and , is the symbol duration.

After passing through a time-varying channel with the impulse response , the received signal is

The channel impulse response for the frequency-selective fading channel can be described by

where v is the total number of non-zeros taps in the channel response, represents the time variant attenuation factor of the -th path and is time varying delay of -th path. The channel

impulse response can also be represented in terms of Doppler frequency shifts, caused by movement of mobile receiver as

(2)

(3)

(4)

(5)


99

where is the amplitude of the -th path. The received OFDM signal can be written as

where is the additive white Gaussian noise (AWGN).

The output of the DFT at the receiver for a time-block where N is the number of carriers can be

written as

for . The gives the desired signal value for subcarrier with an average carrier power of

. While is defined as the subcarrier frequency offset response for the -th subcarrier [5]. It is also the ICI effect of the -th subcarrier to the -th subcarrier with the occurrence of normalised frequency offset, . In the case of time-variant the equation becomes

Therefore, the ICI power on the m-th subcarrier can be expressed into

(6)

(7)

(8)

(9)


100

10.3 ICI ANALYSIS OF PRS-OFDM IN MULTIPLE

ANTENNA SYSTEM In the case when we have transmit and receive diversities with receive and , transmit antennas, we can modify (7) to

where is the subcarrier frequency offset for the -th subcarrier between the -th receiver and -th transmitter for . is the DFT matrix and is the equivalent channel matrix between -th receiver and -th transmitter. Also the received vector for the -th subcarrier frequency is , while the transmitted vector is and the noise vector is

. By ignoring the additive noise, the ICI power on the -th

subcarrier can then be evaluated as

By substituting eq. (1) into (11) becomes

(10)

(11)


101

10.4 SIMULATION RESULT In this section, the performance of correlative coded MIMO-OFDM scheme is compared with the conventional MIMO-OFDM system. The simulation is of limited complexity. OFDM cyclic extension is not considered in this simulation because no delay spread between the transmitter and receiver is assumed. Other parameters considered in the simulation: - Flat channel frequency response in each OFDM subcarrier - Slow changing channel (quasi-static during block time) - Complex path gains are uncorrelated - Perfect channel state information is known at the receiver - Perfect symbol timing synchronization is assumed at the

receiver

Three different types of MIMO channels are investigated in the simulation:

• L transmitter and 2 receive (MRC)

• 2 transmitter and 1 receiver (Alamouti’s transmit diversity)

• 2transmitter and 2 receiver transmitter (MIMO)

Fig. 1 shows the BER performance of MIMO-OFDM system when correlative coding is used. A frequency offset, of 0.15 is introduced in each path of the MIMO-OFDM channels. As seen from the figure, the classic MRC has the best performance while STBC-OFDM has the worst performance. In fig. 2, 3 and 4, correlative coded MIMO-OFDM systems are compared to conventional MIMO-OFDM system. As shown from the figures,

(12)


102

correlative coding improves the BER performance of MIMO-OFDM system when frequency offset is present in the transmission channel. At probability of , The needed by 2x2 and 2xl MIMO configuration is reduced by 2 dB compared to the conventional method. The MRC diversity technique managed to reduce up to 4 dB at the same BER performance.

Figure 1 Correlative Coded MIMO-OFDM Systems

Figure 2 BER Comparison of 2x2 MIMO-OFDM System With Respect

to


103

Figure 3 BER Comparison of MRC-OFDM System With Respect to

Figure 4 BER Comparison of STBC-OFDM System With Respect to

10.5 CONCLUSION In this paper, multiple antenna system with the employment of PRS-OFDM technique was studied. In PRS-OFDM system, ICI was deliberately introduced in a controlled manner through the correlative coding polynomial functions. The effectiveness of correlative coding in improving BER of MIMO-OFDM system with the presence of constant frequency offset was demonstrated.


104

At BER of , the needed managed to be reduced by 2-4 dB when correlative coding was used in MIMO-OFDM with the presence of frequency offset, =0.15 in the channels. REFERENCES [1] T. Pollet, M. Van Bladel, and M. Moeneclaey, "BER sensivity

of OFDM to carrier frequency offset and Weiner phase noise," IEEE Transactionis on Communications, vol. 43, pp 191-193, Feb-Apr. 1995.

[2] J. Ahn and H. S. Lee, "Frequency domain equalization of OFDM signal over frequency non selective Rayleigh fading channels," Electronics Letters, vol. 29, no. 16, pp. 1476-1477, Aug. 1993.

[3] R. Li and G. Stette, "Time-limited orthogonal multicarrier modulation schemes," IEEE Transactions on Communications, vol. 43, pp. 1269-1272, Feb-Apr. 1995.

[4] A. Stamoulis, S. N. Diggavi, N. Al-Dhahir, "Intercarrier interference in MIMO-OFDM," IEEE Transactions. on Signal Processing_, vol. 50, no.10, pp. 2451-2464, Oct. 2002.

[5] Y. Zhao and S-G Haggman, "Intercarrier interference self-cancellation scheme for OFDM mobile communication systems," IEEE Transactions on Communications, vol. 49, no. 7, pp 1185-1191, July 2001.

[6] K. Sathananthan, R.M.A.P. Rajatheva, S.B. Slimane, "Cancellation technique to reduce intercarrier interference in OFDM," Electronics Letters, vol. 36, no. 25, pp. 2078-2079, December 1999.

[7] Y. Fu, S. G. Kang, C. C. Ko, "A new scheme for PAPR reduction in ODM systems with ICI self-cancellation," VTC 2002, vol. 3, pp. 1418-1421, Fall 2002.

[8] P. Kabal, S. Pasupathy, "Partial-response signaling," IEEE Transactions on Communications, vol. Com-23, no. 9, pp. 921-934, Sept. 1975.

[9] Y. Zhao, J-D. Leclercq and S-G. Haggman, "Intercarnier interference compression in OFDM communication systems


105

by using correlative coding," IEEE Communications Leiters, vol. 2, no. .8, pp 214-216, August 1998.

[10] S.M. Alamouti, "A simple transmit diversity technique for wireless communications," IEEE J. Select. Areas Commun., vol. 16, pp. 1451-1458, Oct. 1998.

[11] M. Uysal, N. Al-Dhahir and C. N. Georghiades, "A space-time blockcoded OFDM scheme for unknown frequency-selective fading channels," IEEE Communications Letters, vol. 5, no.10, pp 393-395, Oct. 2001.


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11

THE SPACE-TIME-FREQUENCY MIMO-OFDM SYSTEM WITH INTERCARRIER

INTERFERENCE SELF-CANCELLATION

Anis Izzati A.Z, Sharifah Kamilah S.Y, Norsheila Fisal

11.1 INTRODUCTION In present wireless communication systems, the competition in developing a high data rate communication is becoming obvious due to current demand. OFDM has been the most engaging technique used in high data rate where the high speed data is divided into parallel low rate data streams. This introduces longer symbol duration and high spectral efficiency. OFDM has been used widely in existing systems and standards such as wireless LAN IEEE 802.11a, g, n, wireless MAN IEEE 802.16, wireless PAN IEEE 802.15.3a and terrestrial digital TV (DVB-T).

OFDM goes with the orthogonality principle which requires very accurate synchronization between the transmitter and receiver. This orthogonality feature is very sensitive to carrier frequency offset CFO which exists due to tuning oscillator inaccuracies and Doppler shift. CFO causes ICI to OFDM system whereby the orthogonality between the subcarriers is lost. Additionally, the BER performance decreases rapidly with the increasing of CFO occurrence in OFDM system [1].

Presently, there are five different method to reduce ICI have been developed which are ICI self-cancellation, frequency-domain equalization, time-domain windowing scheme, frequency offset estimation and compensation techniques, and Doppler diversity

The Space-Time-Frequency MIMO-OFDM System with Intercarrier Interference Self-Cancellation

107

[2]. The ICI self-cancellation has been known as a very simple yet effective scheme to combat ICI in OFDM systems. It proposed redundancy by transmitting the same data twice with the same magnitude but different polarization (Xk , Xk+1 = -Xk) over a pair of subcarriers. This is called ICI cancellation modulation (ICM). While ICI cancellation demodulation (ICD) operates by subtracting these 2 signals at the receiver, (Y*k = Yk – Yk+1). The combination of ICM and ICD is ICI self-cancellation [3].

However, by using ICI self-cancellation technique can produces high PAPR after the signal is through inverse Fast Fourier Transform (IFFT). The phase difference between two adjacent subcarriers is fixed to π. A high PAPR could lead to signal distortion. So, a new data allocation is introduced to reduce this effect, (Xk , Xk+1= ) , a pair of complex signals over pair of subcarriers [4]. With this new allocation, the phase difference between two adjacent subcarriers will varies with respect to the signal. 11.2 MIMO-OFDM SYSTEM WITH CFO Consider a MIMO-OFDM system equipped with Nt transmit antennas and Nr receive antennas. The data source produces a single stream of binary input data to the encoder, and the encoder transform the data into N parallel streams. The nth OFDM symbol at transmit antenna i denoted by , and is given by

where m is the number of IFFT input to the transmit antenna i; n = 0,..,N-I, i = 1,.,..,Nt .

At the receiver, after the signal went through the FFT encoders, it is given that the mth FFT output at antenna j is denoted by equation (2), where m = 0,…..,N-1, j=1,….,Nr.

(1)


108

The transmitted signal is received throughout a channel with additive noise. The received OFDM signal of subcarrier k is written as [5]

X(k) represents the transmitted symbol for the kth subcarrier and W(n) is the FFT of an additive white Gaussian (AWGN) noise sample. For this paper, only CFO is considered as the cause of ICI in the MIMO-OFDM system. The ICI coefficient between the l-th and k-th subcarriers, S(l-k) is given by [5] as

where ε is the normalised frequency offset. As discussed earlier, ICI can degrade the performance of an

OFDM system. The same scenario applied to MIMO-OFDM. STF diversity is used as a way to reduce the effect of ICI.

The STF diversity is realised by applying 2 encoders, one represents space-frequency (SF) diversity and the other, space-time (ST) diversity. To reduce the problem of ICI, this paper employs the SF encoder to perform ICI self-cancellation technique.

The concept of an SF code is to introduce redundancy to the data streams. In the process of SF encoding, the data source is two-dimensionally encoded across space and frequency, in this case over the subcarriers of OFDM symbols. The SF code in the frequency domain is denoted in matrix form as [3];

(4)

(3)

(2)


109

The repetition is done with r=2 where r is how many times the

data is repeated. Then, the repeated symbols is sign-reversed from the actual symbols, gives the same allocation as ICM. The new codeword is as follows [3].

Apparently, the data allocation as equation (6) causes high

PAPR of OFDM symbol. As the name state, PAPR is the ratio between the maximum value of transmitted signal x2 to the average energy E of an OFDM symbol which is written as [4]

By submitting conjugate to the repeating signals to reduce

PAPR to its optimum unitary value, the codeword becomes

An allocation of a pair of complex signals results in a signal with phase difference between two adjacent subcarriers that vary

(5)

(6)

(8)

(7)


110

with respect to the signal itself [4]. This method is called conjugate ICI self-cancellation.

As for the ST diversity is performed using ST code where the same data symbols are transmitted through multiple antennas at different times. Unlike SF diversity, ST provides diversity in space and time to the system.

In this paper, the ST diversity employs the Alamouti’s ST code [6] as shown in Table 1 with an assumption that maximum configuration of antennas in MIMO-OFDM system is 2x2.

Table 1 Alamouti’s ST code

Antenna 1 Antenna 2

Time t x1 x2

Time t + T -x2* x1*

By applying maximal-ratio receiver combining (MRRC) scheme, the following explains a way of decoding the received signal to obtain the original data symbols in the ST decoder. The channel is modeled with multiplicative distortion represented by h1 and h2 as given as [6]

The additive noise are then added at time t which resulted in [6]

where T is the symbol duration. The receiver MRRC combining scheme is as follow [6]

(9) (10)

(11)

(12)

(14) (13)


111

where and are the signals received that will go through demodulation process. While at the SF decoder, the symbols are decoded using the formula in the ICD.

The baseband model of STF MIMO-OFDM is shown in Figure 1. The data stream is first encoded in SF encoder before it input the OFDM modulation. Then, the data streams go through the ST decoder before it all transmitted to the channel. The opposite operation is being done at the receiver.

Figure 1 STF MIMO-OFDM Baseband Model

11.3 SIMULATION RESULTS AND PERFORMANCE EVALUATION This section presents the simulation results for the performance of OFDM system that includes ICI self-cancellation technique in STF diversity. Performance of an STF MIMO-OFDM system is compared to the conventional OFDM. In the simulation, 64 OFDM subcarriers is used. The analysis is done wit comparison of the BER performance for each system.

Figure 2 shows an illustration of simulation result for the comparison between a conventional SISO-OFDM system, SISO-OFDM with ICI self-cancellation and SISO-OFDM with conjugate ICI self-cancellation. The simulation is done using quadrature amplitude modulation (QAM-4) with 4 constellations and phase shift of epsilon, ε=0.3.


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Figure 2 Comparison Of Conventional, ICI Self-Cancellation And Conjugate ICI Self- Cancellation SISO OFDM System.

Overall, the system of SISO-OFDM with ICI self-cancellation

shows better performance than the conventional SISO-OFDM with reduction of 5 dB at BER = 0.16. When the system is added with a conjugate ICI self-cancellation technique to reduce the effect of PAPR to it, the BER performance shows the best performance among all three systems. The BER performance for conjugate ICI self-cancellation reduce up to 2dB at BER=0.03 in contrast with ICI self-cancellation OFDM system.

It is proven that there is a significant improvement when a wireless communication system is included with ICI self-cancellation. The system becomes better with conjugate ICI self-cancellation rather than SISO-OFDM system alone. Conjugate ICI self-cancellation not only reduces ICI, but also improves PAPR value to its optimum.

The following Figure 3 depicted the MIMO-OFDM system with and without ICI self-cancellation. MIMO configuration used in this simulation is 2x2. The elimination of ICI self-cancellation in the system is done by the removal of the SF encoder from the system.


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Figure 3 Comparison Of MIMO-OFDM 2x2 With And Without ICI

Self-Cancellation.

The figure shows that the system worsen as the function of ICI self-cancellation was not provided to it. Without ICI self-cancellation, the system seems to be affected greatly by the CFO and simulation result shows an irreducible error rate occurs even as the Eb/No become higher.

At BER=0.03, the BER performance of the system with ICI self-cancellation has reduce up to 5.62dB compared to the system without ICI self-cancellation scheme. 11.4 CONCLUSION

For this paper, it can be concluded that ICI self-cancellation is a reliable method to reduce ICI in MIMO-OFDM system. MIMO-OFDM system can also be improved using the method called conjugate ICI self-cancellation to reduce ICI and the effect of high PAPR at the same time. The STF codes in MIMO-OFDM system perform an effective role to reduce the BER in the system. The BER performance of OFDM system, with the application of ICI self-cancellation is improved as much as 5dB. Conjugate ICI self-cancellation gives the best BER performance with 2 dB of difference with the ICI self-cancellation OFDM system. Overall,


114

the conjugate ICI self-cancellation is the most effective method to reduce ICI in MIMO-OFDM system.

REFERENCES [1] T. Pollet, M. Van Bladel and M. Moeneclaey, “BER sensitivity

of OFDM to carrier frequency offset and Weiner phase noise,” IEEE Trans. on Communications, 43, 1995, 191-193.

[2] Li Zhao and Ping Zhang, “A new ICI self-cancellation scheme based on repeated symbol in OFDM systems,” IEEE, pp. 1216-1220, 2006.

[3] D˜ung Ngo.c Ð`ao, and Chintha Tellambura, “Intercarrier interference self-cancellation space-frequency codes for MIMO-OFDM,” IEEE Trans. Vehicular Technology, vol. 54, pp. 1729-1738, Sept 2005.

[4] Y. Fu, S. G. Kang, C. C. Ko, “ A new scheme for PAPR reduction in OFDM systems with ICI self-cancellation,” VTC 2002, vol. 3, pp. 1418-1421, Fall 2002

[5] Yuping Zhao and Sven-Gustav Häggman, “Intercarrier interference self-cancellation scheme for OFDM mobile communication systems,” IEEE Trans. Commun., vol. 49, pp. 1185-1191, July 2001.

[6] Siavash M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE Journal on Select Areas in Communications, vol.16, pp. 1451-1458, Oct 1998.

INDEX ADC, 21 antenna, 1, 66, 67, 69, 70, 72, 73,

74, 78, 80, 82, 86, 87, 92, 94, 95, 98, 103, 104, 106, 111, 118

AWGN, 24, 27, 57, 76, 78, 107, 118

Bayesian rule, 82 BCH, 101, 102 BER, 1, 20, 24, 27, 29, 37, 41, 56,

60, 63, 64, 66, 72, 73, 74, 76, 87, 106, 111, 117, 123, 125

BLAST, 78 BPSK, 7, 24, 44, 72, 102 capacity, 66, 69, 72, 74, 76, 78, 94 CCDF, 14, 35, 44, 53, 60 CFO, 117, 118, 123 CHANNEL, iv, 78, 86 channel impulse responses, 86, 87,

91 CIR, 32, 37, 41, 43, 44, 53, 56, 60,

63 clipping, 10, 20, 21, 32, 35, 37, 41,

47, 54 Code Repetition, 20, 22, 24, 29 codeword, 6, 22, 24, 78, 82, 96, 98,

101, 102, 118 COFDM, 24, 27, 29 concatenated, 78, 92, 94, 96, 98,

101 constellation, 80, 86, 98 convolutional code, 20, 27 correlation, 32, 35, 44, 56, 67, 106,

107 CR, 22, 24, 29, 37 cyclic code, 72 DAB, 10, 32, 43 DAC, 21 Diversity, 67, 68, 70, 72, 76 DVB-T, 10, 117 EGC, 68 ESTIMATION, iv, 78, 86

fading, 32, 56, 60, 66, 67, 69, 70, 80, 87, 92, 94, 98, 101, 104, 107, 111

FFT, 3, 11, 24, 33, 118 FTS, 11, 43, 44, 47, 51, 53 Hamming, 96, 101, 102 HiperLAN, 10, 32, 43 ICD, 117, 118 ICI, iv, 32, 35, 43, 44, 56, 57, 60,

63, 64, 106, 107, 110, 111, 117, 118, 123, 125

ICI cancellation demodulation, 117 IEEE802.11a, 10 IFFT, 3, 11, 37, 47, 117, 118 in-band distortion, 20, 37 interpolation, 86, 87 ISI, 3, 20 iterative, 78, 86, 87, 91, 92, 94 LDPC, 78 LLR, 82, 85 log-likelihood ratio, 82 Low-density-parity-check, 78 MAN IEEE 802.16, 117 MAP, 78, 91, 103 MATLAB, 14, 24, 27 Maximum a posteriori, 78 maximum-likelihood, 101 MIMO, iv, 53, 63, 66, 69, 72, 73,

76, 78, 92, 94, 103, 106, 111, 117, 118, 123, 125

Minimum Shift Keying, 76 MRC, 68, 111 MSK, 76 multiple-input multiple output, 66 nonlinear, 1, 10, 20, 29, 37 OFDM, iii, iv, 1, 3, 5, 7, 10, 11, 14,

18, 20, 21, 24, 27, 29, 30, 32, 33, 35, 37, 41, 43, 44, 47, 51, 53, 54, 56, 57, 60, 63, 64, 117, 118, 123, 125

Index

116

orthogonal, 1, 3, 10, 11, 32, 33, 64, 86, 92, 94, 98, 101, 103, 104, 111

oversampled, 37 PAPR, iii, 1, 3, 6, 7, 10, 11, 14, 20,

21, 24, 27, 29, 30, 32, 33, 35, 37, 41, 43, 44, 47, 51, 53, 54, 56, 57, 60, 63, 64, 117, 118, 123, 125

partition, 11, 14, 18, 54 PC, 78, 82, 87, 91, 101, 102 pilot, 78, 80, 86, 87, 91 power amplifiers, 1, 10, 20 PRC, 56, 57, 60, 63, 82 Precoding, 57 product code, 78, 94, 96, 98, 101,

102, 103 PRS, iii, iv, 32, 33, 35, 37, 41, 43,

44, 47, 51, 53, 54, 106, 110, 111 QAM, 14, 123 Redundancy, 60 RF, 64, 70 scheme, 1, 3, 10, 11, 18, 20, 24, 30,

47, 54, 57, 60, 64, 68, 69, 70, 72, 78, 87, 94, 98, 101, 102, 103, 104, 111, 117, 118, 123, 125

Selection Diversity, 68

self-cancellation, 56, 57, 60, 63, 64, 111, 117, 118, 123, 125

SF, 118, 123 single-parity-check code, 78 SISO, 82, 106, 107, 123 SNR, 37, 41, 60, 67, 68, 72, 73, 74 Space diversity, 67 space-frequency, 118, 125 Space-Time codes, 69 space-time trellis codes, 94 SPC, 78, 80, 82, 87, 91 SPC-PC, 78, 87 spectral efficiency, 10, 20, 56, 60,

64, 117 SPS, 11, 14 STBC, 66, 69, 70, 94, 101, 102,

111 STC, 69 STF, 118, 123 STTC, 94 Subblock, 11, 14, 47 subcarrier, 1, 3, 33, 44, 57, 107,

110, 111, 118 transmit diversity, 66, 69, 70, 72,

76, 111, 125 turbo codes, 94, 104 WLAN, iii, 1, 3, 5, 7, 20, 29, 78

simulation on performance of space time block code

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