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ABSTRACT The demand for high-speed mobile wireless communications is rapidly growing. Orthogonal Frequency Division Multiplexing (OFDM) technology promises to be a key technique for achieving the high data capacity and spectral efficiency requirements for wireless communication systems of the near future. OFDM is a bandwidth efficient multicarrier modulation where the available spectrum is divided into subcarriers, with each subcarrier containing a low rate data stream. OFDM has gained a tremendous interest in recent years because of its robustness in the presence of severe multipath channel conditions with simple equalization, robustness against Inter-symbol Interference (ISI), multipath fading, in addition to its high spectral efficiency. In order to improve spectral efficiency, different modulation techniques are employed to modulate the parallel carriers. This work investigates the bit error rate performance of OFDM for different modulation techniques and compared them. Matlab is used to find bit error rate of a transmission when Signal to Noise Ratio and Multi-propagation effects are changed. This work also investigates high peak-to-average power ratio (PAPR) problem of OFDM for large number of sub-carriers, which result in many restrictions for practical applications. Coding, phase rotation and clipping are many PAPR reduction schemes that have been proposed to overcome PAPR. In this thesis, PAPR algorithms are studied and simulate two PAPR reduction methods: partial transmit sequence (PTS) and selective mapping (SLM).

Ϯ

ACKNOWLEDGEMENT Firstly, I wish to express my deepest sense of gratitude to almighty Allah who gave me the strength and power to complete this thesis work. I would like to express my whole-hearted gratitude to my honorable supervisor Ibrahim Abdullah, Assistant Professor, Dept. of Computer Science & Engineering, Islamic University, Kushtia for his continuous guidance, moral support, and valuable suggestions throughout my research work. Without his invaluable co-operation, it would not be possible to complete this thesis work. I am also grateful to my respectable teacher Md. Shamim Hossain, Muntashir Rahman Lecturer, Dept. of Computer Science and Engineering, Islamic University, Kushtia for their fruitful help and advice throughout the time of thesis and my education life in Islamic University. I am thankful to all of my teachers who have assisted to increase my knowledge and cultivated my talents so far. Without their invaluable help, it would never be possible for me to reach at this stage of education. I am greatly thankful to some of my honorable brother, Mahfuzur Rahman Lecturer Dept. of CSE, Comilla University for his kind cooperation in completing the thesis. I am greatly indebted to my family members for their love, sympathy, mental and economical support throughout my life. I want to express my heartiest love to Sumon, Nazrul and Rebina Ferdous for their unforgettable love and help throughout my studentship in Islamic University, Kushtia. July, 2010 Islamic University, Kushtia

The Author

ϯ

Contents Chapter Title

Page No.

List of Figures ««««««««««««««««««««

vii

List of Tables«««««««««««««««««««««

ix

Chapter One

10

Introduction

1.1wireless &RPPXQLFDWLRQ««««««««««««

11

1.2 History of Mobile Wireless CRPPXQLFDWLRQV«« ««««

14

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19

1.4 Objectives of the Book «««««««««««««««

21

1.5 Organization of Book «««««««««««««

21

Chapter Two

Basic Principles of OFDM

23

2.1 Introduction«««««««««

24

2.2 OFDM ««««««««««««««««««««

24

2.3 Evolution of OFDM ««««««««««««««

26

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27

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2.3.3 Orthogonal Frequency Division Multiplexing.

27

2.4 Orthogonal Frequency Division Multiplexing Technology «««. 28 2.5 2UWKRJRQDOLW\«««««««««««««««««

28

2)'0*HQHUDWLRQDQG5HFHSWLRQ«««««««

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2.7 Transmission Protocol «««««««««««««

32

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2.9 Protection against 7LPH2IIVHW«««««««««

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2.10 Protection against ,6,«««««««««««««

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2.12 Band-Limiting of OFDM and :LQGRZLQJ«««««

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2.13 Band Pass FiltHULQJ««««««««««««««

48

2.14 Effect of Band Pass Filtering on OFDM Performance..

49

2.16 Raised Cosine Guard 3HULRG«««««««««««

53

2.17 Effect of Additive White Gaussian Noise on OFDM ...

54

(IIHFWRI'LVWRUWLRQRQ2)'0«««««««

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2.19 Modulation 6FKHPHV«««««««««««««

58

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59

2.21 OFDM Simulation parDPHWHUV««««««««««

61

2.22 Advantages of OFDM ««««««««««««««

62

2.23 Limitations of OFDM «««««««««««««

63

&RQFOXVLRQ««««««««««««««««««

63

Chapter Three:

Modulation Techniques And Transmission Factors

Of OFDM

64

3.1 Modulation «««««««««««««««««««

65

3.2 Digital Modulation «««««««««««««««

65

3.3 Basic Modulation Methods««««««««««««

66

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68

3.4.1 3RZHU(IILFLHQF\««««««««««««««

68

3.4.2 %DQGZLGWK(IILFLHQF\««««««««««««

69

3.4.3 System Complexity «««««««««««««

69

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70

3.6 Factors of OFDM 7UDQVPLVVLRQ«««««««««

73

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3.6.1.1 Bit Error Rate BER Definition and Basics

74

3.6.1.2 BER and EB/12«««««««««««

75

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Chapter Four

PAPR Problem In OFDM And Reduction

Techniques

80

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81

4.2 PAPR Definition ««««««««««««««««

82

4.3 Influencing Factors of PAPR ««««««««««

83

4.4 Why PAPR Reduction in OFDM System ««««««

84

4.5 PAPR Reduction Techniques ««««««««

85

4.5.1 Signal Scrambling Techniques««««««««

86

4.5.1.1 %ORFN&RGLQJ7HFKQLTXHV««««««

86

4.5.1.2 Block Coding Scheme with Error &RUUHFWLRQ«««

87

4.5.1.3 6HOHFWHG0DSSLQJ««««««««««

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4.5.1.4 Partial Transmit Sequence ««««««

88

4.5.1.5 Interleaving 7HFKQLTXH«««««««

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Chapter Five BER of OFDM for Different Modulation Techniques 94 5.1 ,QWURGXFWLRQ««««««««««««««««««

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102

5.3.2.3 Bit Error Rate for 16-36.««««««««

103

5.3.2.3.1 Simulation Result «««««««

105

5.3.2.4 Bit Error Rate for 4-3$0«««««««

106


107

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109

5.3.2.6 Bit Error Rate for 16-QAM «««««««

110


111

5.3.2.7 64-4$0««««««««««««««««

112


113

5.4 Comparison of BER in different modulation techniques ««

114

&RQFOXVLRQ«««««««««««««««««««115 Chapter Six Analysis And Simulation Of PAPR Reduction Techniques

116

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122

3DUWLDO7UDQVPLW6HTXHQFH376 «««««««««««

125

6.4.1 PrinFLSOHRI376««««««««««««««««

125

6.4.2 Simulation of PTS 6FKHPH«««««««««««

127

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128

Chapter Seven

130

Conclusion

7.1 Conclusion ««««««««««««««««««««

131

7.2 Further Improvement For This Work «««««««««

133

7.3 Future Research ««««««««««««..«««««

133

References ««««««««««««««««..««««

134

List of Figure

Figure1.1: Basic multi-carrier transmitter.

12

Figure 1.2: Family tree of the GIMCV. Branches and leaves of the GIMCV family tree are not shown in chronological order.

18

Figure 2.1: Time domain construction of an OFDM signal.

29

Figure 2.2: Block diagram showing a basic OFDM transceiver.

32

Figure 2.3: Frame Structure, showing the null symbol between frames21 Figure 2.4: Frame Structure used for the OFDM transmission

32

Figure 2.5: Example IQ modulation constellation of 16-QAM, with gray Coding of the data to each location.

34

Figure 2.6: IQ plot for 16-QAM data with added noise.

35

Figure 2.7: OFDM generation, IFFT stage

36

Fig2.8: RF modulation of complex OFDM signal in analog techniques. 36 Figure 2.9: RF modulation of complex base band OFDM signal using digital techniques.

37

Figure 2.10: DC offset OFDM signal w- bandwidth fo- frequency offset from DC, fc centre frequency

38

Figure 2.11: Construction of the subcarriers for generating a real output time domain waveform.

39

Figure 2.12: Construction of the subcarriers for complex signal Representation of OFDM signals.

40

ϴ

Figure 2.13: Addition of a guard period to an OFDM signal

41

Figure 2.14: Function of the guard period for protecting against ISI

43

Figure 2.15: Effectiveness of adding a guard period for removal of ISI 46 Figure 2.16: Time waveform of a single carrier OFDM signal, showing symbols.

47

Figure 2.17: Spectrum of a 52 subcarrier OFDM signal with no bandlimiting.

48

Figure 2.18: Spectrum of a 1536 subcarrier OFDM signal with no band.48 Figure 2.19: Effective SNR as a function of the time offset for a band pass filtered 52 subcarrier OFDM signal.

50

Figure 2.20: Section of the waveform that the receiver FFT is taken from depending on the time offset.

51

Figure 2.21: Construction of a RC guard period.

52

Figure 2.22: Envelope of OFDM symbols with a flat guard period and an overlapping raised cosine guard period

53

Figure 2.23: Side-lobe power for an OFDM signal with 20 subcarriers as the length of the RC guard period is varied.

54

Figure 2.24: Effect of distortion on a 2 tone signal, showing harmonics and IMD

56

Figure 3.1: Baseband digital modulation examples.

66

Figure 3.2: Three basic band-pass modulation schemes.

67

Figure 3.3: Power spectral density of ASK.

69

Figure 3.4: Digital Modulation Tree. After 4G.

71

Figure 4.1: An OFDM signal waveform in time domain.

82

Figure 4.2: High PAPR when sub-carriers are modulated by same symbols.

83

Figure 5.1: Constellation diagram example for BPSK.

98

Figure 5.2: Bit Error Rate for BPSK using OFDM for 8-bit FFT size. 100 Figure 5.3: Bit Error Rate for BPSK using OFDM for 16-bit FFT size.100

ϵ

Figure 5.4: Bit Error Rate for BPSK using OFDM for 64-bit FFT size.101 Figure 5.5: Constellation plot for QPSK

101

Figure 5.6: Bit Error Rate for QPSK (4QAM) modulation

103

Figure 5.7: PSK constellation plot

103

Figure5.8: Distance between constellation points

104

Figure 5.9: Bit Error rate curve for 16PSK modulation

105

Figure 5.10: Bit Error rate curve for 4-PAM modulation

107

Figure 5.11: Transmit-Receive block diagram for BFSK

108

Figure 5.12: Bit Error Rate of FSK

109

Figure 5.13: 16-QAM constellation

110

Figure 5.14: Bit Error Rate curve for 16QAM modulation

112

Figure 5.15: Constellation plot for 64-QAM

112

Figure 5.16: Symbol error rate for 64-QAM modulation

113

Figure 5.17: Comparison of BER for Different Modulation Techniques.

114

Figure 6.1: Basic principles of selected mapping.

120

Figure 6.2: 7KHRUHWLFDO3$35¶V&&DF curves using SLM method.

122

Figure 6.3: PAPR reduction performances with different values of M. 124 Figure 6.4: Block diagram of PTS algorithm.

125

Figure 6.5: PAPR reduction performances with different values of W. 128

List of Tables TABLE I: OFDM System Parameters Used for the Simulations

62

TABLE II: Simulation Parameter for BPSK

99

TABLE III: Simulation Parameter for 16-PSK

105

TABLE IV: Simulation Parameter for BFSK

109

TABLE V: Simulation Parameter for 16-QAM

111

TABLE VI: Simulation Parameter for BPSK

113

TABLE VII: Comparison of PAPR Reduction Techniques.

118

ϭϭ

CHAPTER ONE INTRODUCTION

1.1 WIRELESS COMMUNICATION Wireless communication is not a new concept. Smoke signals and lighthouses are all forms of wireless communication that have been around for years. In our era, wireless communication refers to accessing information without the need of a fixed cable connection [2]. Wireless communication continues to grow rapidly as the need for reaching data anywhere at any time rises. The increasing demand for high-rate data services along with the requirement for reliable connectivity requires novel technologies [4]. As wireless communication systems are usually interference limited, new technologies should be able to handle the interference successfully. Interference can be from other users, e.g. Co-channel Interference (CCI) and Adjacent Channel Interference (ACI), or it can be due to users own signal (self-interference), e.g. Inter-symbol Interference (ISI). ISI is one of the major problems for high data rate communications which is treated with equalizers in conventional single-carrier systems. However, for high data rate transmission, complexity of equalizers becomes very high due to the smaller symbol time and large number of taps needed for equalization. This problem is especially important for channels with large delay spreads [14].

ϭϮ

Multi-carrier modulation is one of the transmission schemes which is less sensitive to time dispersion (frequency selectivity) of the channel. A basic multi-carrier transmitter diagram is shown in Fig. 1. In multi-carrier systems, the transmission bandwidth is divided into several narrow subchannels and data is transmitted parallel in these sub-channels. Data in each sub-channel is modulated at a relatively low rate so that the delay spread of the channel does not cause any degradation as each of the subchannels will experience at a response in frequency. Although, the principles are known since early sixties [1][2] multi-carrier modulation techniques, especially Orthogonal Frequency Division Multiplexing (OFDM), gained more attention in the last ten years due to the increased power of digital signal processors.

Figure1.1: Basic multi-carrier transmitter. OFDM is a multi-carrier modulation technique that can overcome many problems that arise with high bit rate communication, the biggest of which is the time dispersion. In OFDM, the carrier frequencies are chosen in such a way that there is no influence of other carriers in the detection of the information in a particular carrier when the orthogonality of the carriers are maintained. The data bearing symbol stream is split into several lower rate streams and these streams are transmitted on different carriers. Since this

ϭϯ

increases the symbol period by the number of non-overlapping carriers (sub-carriers), multipath echoes will affect only a small portion of the neighboring symbols. Remaining ISI can be removed by cyclically extending the OFDM symbol. The length of the cyclic extension should be at least as long as the maximum excess delay of the channel. By this way, OFDM reduces the effect of multipath channels encountered with high data rates, and avoids the usage of complex equalizers. OFDM is used as the modulation method for Digital Audio Broadcasting (DAB)[3] and Terrestrial Digital Video Broadcasting (DVB-T) [5] in Europe, and in Asymmetric Digital Subscriber Line (ADSL) [5]. Wireless Local Area Networks (WLANs) use OFDM as their physical layer transmission technique. Different WLAN standards are developed in Europe, USA, and Japan. The European standard is ETSI Hyper LAN/2 [6], American standard is IEEE 802.11a/g [7], and Japanese standard is ARIB HiSWANa [8]; all of which has similar physical layer specifications based on OFDM. OFDM is also a strong candidate for IEEE Wireless Personal Area Network (WPAN) standard [9] and for fourth generation (4G) cellular systems (see e.g. [10]). Although OFDM has proved itself as a powerful modulation technique, it has its own challenges. Sensitivity to frequency offsets caused when a receiver's oscillator does not run at exactly the same frequency of transmitter's oscillator is one of the major problems. This offset perturbs the orthogonality of the sub-carriers, reducing the performance. Another problem is the large Peak-to-average Power Ratio (PAPR) of the OFDM signal, which requires power amplifiers with large linear ranges. Hence, power amplifiers require more back-off which, in turn, reduces the power efficiency. Some other problems include phase distortion, time-varying channel and time synchronization.

ϭϰ

Most standards employing OFDM do not utilize the available resources effectively. Most of the time, systems are designed for the worst case scenarios. The length of the cyclic prefix, for example, is chosen in such a way that it is larger than the maximum expected delay of the channel, which introduces a considerable amount of overhead to the system. However, it can be changed adaptively depending on the channel conditions, instead of setting it according to the worst case scenario, if the maximum excess delay of the channel is known. The information about the frequency selectivity of the channel can also be very useful for improving the performance of the wireless radio receivers through transmitter and receiver adaptation. OFDM symbol duration, subcarrier bandwidth, number of sub-carriers etc. can be changed adaptively, if the frequency selectivity is estimated. Bandwidth of the interpolation filters for channel estimation can be adapted depending on the distortion in the environment [11]. While OFDM solves the ISI problem by using cyclic prefix, it has another self-interference problem: Inter-carrier Interference (ICI), or the crosstalk among different sub-carriers, caused by the loss of orthogonality due to frequency instabilities, timing offset or phase noise. ISI and ICI are dual of each other occurring at different domains; one in time domain and the other in frequency-domain. ICI is a major problem in multi-carrier systems and needs to be taken into account when designing systems [12]. ICI can be modeled as Gaussian noise and results in an error or if it is not compensated for [15]. Therefore, efficient cancellation of ICI is very crucial, and different methods are proposed by many authors in the literature.

1.2 HISTORY OF MOBILE WIRELESS COMMUNICATIONS The history of mobile communication can be categorized into 3 periods:

ϭϱ

the pioneer era the pre-cellular era the cellular era In the pioneer era, a great deal of the fundamental research and development in the field of wireless communications took place [2]. The postulates of electromagnetic (EM) waves by James Clark Maxwell during the 1860s in England, the demonstration of the existence of these waves by Heinrich Rudolf Hertz in 1880s in Germany and the invention and first demonstration of wireless telegraphy by Guglielmo Marconi during the 1890s in Italy were representative examples from Europe. Moreover, in Japan, the Radio Telegraph Research Division was established as a part of the Electro technical Laboratory at the Ministry of Communications and started to research wireless telegraph in 1896. From the fundamental research and the resultant developments in wireless telegraphy,

the

application

of

wireless

telegraphy

to

mobile

communication systems started from the 1920s. This period, which is called the pre-cellular era, began with the first land-based mobile wireless telephone system installed in 1921 by the Detroit Police Department to dispatch patrol cars, followed in 1932 by the New York City Police Department. These systems were operated in the 2MHz frequency band. Unfortunately, during World War II, the progress of radio communication technologies was drastically stimulated. In 1946, the first commercial mobile telephone system, operated in the 150MHz frequency band, was set up by Bell Telephone Laboratories in St. Louis. The demonstration system was a simple analog communication system with a manually operated telephone exchange. Subsequently, in 1969, a mobile duplex communication system was realized in the 450MHz frequency band. The telephone exchange of this modified system was operated automatically. The new system, called the

ϭϲ

Improved Mobile Telephone System (IMTS), was widely installed in the United States. However, because of its large coverage area, the system could not manage a large number of users or allocate the available frequency bands efficiently. The cellular zone was concept was developed to overcome this problem by using the propagation characteristics of radio waves. The cellular zone concept divided a large coverage area into many smaller zones. A frequency channel in one cellular zone is used in another cellular zone. However, the distance between the cellular zones that use the same frequency channels is sufficiently long to ensure that the probability of interference is quite low [18]. The use of the new cellular zone concept launched the third era, known as the cellular era. The first generation of cellular mobile communication was developed from 1980 to 1990. In this period, research and development (R&D) centered on analog cellular communication systems. In the United States, an analog cellular mobile communication service called Advanced Mobile Phone Service (AMPS) was started in October 1983 in Chicago. In Europe, several cellular mobile communication services were started. In Norway, Nordic Mobile Telephone (NMT) succeeded in the development of an analog cellular mobile communication system. In the United Kingdom, Motorola developed an analog cellular mobile communication system called the total access communication system (TACS) based on AMPS in the 1984-1985 periods. In 1983, NMT started a modified NMT-450 called NMT-900. Moreover, C-450, RTMS and Radiocom-2000 were, respectively, introduced in Germany, Italy and France. Meanwhile, in Japan, Nippon Telephone and Telegraph (NTT) developed a cellular mobile communication system in the 800 MHz

ϭϳ

frequency band and started service in Tokyo in December 1979. Furthermore, a modified TACS that changed the frequency band to adjust for Japanese frequency planning and was called JTACS was also introduced in July 1989. Subsequently, narrowband TACS (NTACS), which introduced the required frequency band in half, started service in October 1991. So far, the evolution of the analog cellular mobile communication system is described. There were many problems and issues, for example, the incompatibility of the various systems in each country or region, which precluded roaming. In addition, analog cellular mobile communication systems were unable to ensure sufficient capacity for the increasing number of users, and the speech quality was not good [17]. To solve these problems, the R&D of cellular mobile communication systems based on digital radio transmission schemes was initiated. These new mobile communication systems became known as the second generation (2G) of mobile communication systems, and the analog cellular era is regarded as the first generation (1G) of mobile communication systems [18] . In Europe, the global system for mobile communication (GSM), a new digital communication system that allowed international roaming and using 900 MHz frequency band had been introduced in 1992 [8]. The generation of wireless communication is depicted in fig 1.2:

ϭϴ

First Generation (1G) is described as the early analogue cellular phone technologies. Actually, 1G is a hybrid of analog voice channels and digital control channels. The analog voice channels typically used Frequency Modulation (FM) and the digital control channels used simple Frequency Shift keying (FSK) modulation. NMT and AMPS cellular technologies fall under this categories [8]. Second Generation (2G) described as the generation first digital widely used cellular phones systems. 2G digital systems use digital radio channels for both voice (digital voice) and digital control channels. GSM technology is the most widely used 2G technologies. This gives digital speech and some limited data capabilities (circuit switched 9.6kbits/s). Other 2G technologies are IS-95 CDMA, IS-136 TDMA and PDC. Two and Half Generation (2.5G) is an enhanced version of 2G technology. 2.5G gives higher data rate and packet data services. GSM systems

ϭϵ

enhancements like GPRS and EDGE are considered to be in 2.5G technology. The so-called 2.5G technology represent an intermediate upgrade in data rates available to mobile users. Third Generation (3G) mobile communication systems often called with names 3G, UMTS and WCDMA promise to boost the mobile communications to the new speed limits. The promises of third generation mobile phones are fast Internet surfing advanced value-added services and video telephony. Third-generation wireless systems will handle services up to 384 kbps in wide area applications and up to 2 Mbps for indoor applications. Fourth Generation (4G) is intended to provide high speed, high capacity, low cost per bit, IP based services. The goal is to have data rates up to 20 Mbps. Most probable the 4G network would be a network which is a combination of different technologies, for example, current cellular networks, 3G cellular network and wireless LAN, working together using suitable interoperability protocols.

1.3 IMPAIRMENTS OF OFDM OFDM has several properties which make it an attractive modulation scheme for high speed transmission links. Powerful channel equalization is not needed to combat ISI and if differential modulation is applied, no channel estimation is required at all. Thus, the complexity of OFDM systems can be much lower compared with a single carrier transmission system. One major difficulty about OFDM is its large peak-to-average (PAP) ratio which distorts the signal if the transmitter contains nonlinear components such as power amplifiers (PAs) [25]. The nonlinear effects on the transmitted OFDM symbols are spectral spreading, inter modulation and changing the signal constellation. In other words, the nonlinear distortion causes both in-band and out-of-band interference to signals. The

ϮϬ

in-band interference increases the BER of the received signal through warping of the signal constellation and inter-modulation while the out-ofband interference causes adjacent channel interference through spectral spreading. The latter is what prevents the usage of OFDM in many systems even if the in-band interference is tolerable. Therefore the PAs requires a back off which is approximately equal to the PAPR for distortion-less

transmission.

This

decreases

the

efficiency

for

amplifiers. Therefore, reducing the PAPR of practical interest [21]. Coding, phase rotation and clipping are among many PAPR reduction schemes that have been proposed to overcome this problem. In this thesis, we will mainly investigate the PAPR reduction performance with different PAPR reduction methods. In addition, several corresponding modified algorithms are studied with respect to balanced performance and applicability. Mobile wireless systems operate under harsh and challenging channel conditions. The wireless channel is distinct and much more unpredictable than the wireless channel because of factors such as multipath and shadow fading, Doppler spread, and delay spread or time dispersion. These factors are all related to variability that is introduced by the mobility of the user and the wide range of environments that may be encountered as a result [17]. In wireless communications, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric, ducting, ionospheric reflection and refraction and reflection from terrestrial objects such as mountains and buildings. The reflected signals arrive at the receiver with random phase offsets, because each reflection generally follows a different SDWKWRUHDFKWKHXVHU¶VUHFHLYHU7KHUHVXOWLVUDQGRPVLJQDOIDGHVDVWKH reflections destructively (and constructively) superimpose on one another,

Ϯϭ

which effectively cancels part of the energy signal for brief periods of time [12]. The degree of cancellation or fading will depend on the delay spread of the reflected signals, as embodied by their relative phases and their relative power [13]. 1.4 OBJECTIVES OF THE BOOK This works studies the Bit Error Rate (BER) for Orthogonal Frequency Division Multiplexing under different modulation techniques and PAPR reduction techniques in OFDM. Digital multimedia applications as they are getting common lately create an ever increasing demand for broadband communications systems. Orthogonal Frequency Division Multiplexing (OFDM) has grown to be the most popular communications system in high speed communications in the last decade. In fact, it has been said by many industry leaders that OFDM technology is the future of wireless communications. Objectives of the proposed research work are: Study and measure the BER of OFDM for different modulation techniques Surveying different techniques to reduce PAPR problem Reducing PAPR using SLM technique under different FFT size.

1.5 ORGANIZATION OF BOOK This is a simulation project which studied the BER performance for Orthogonal Frequency Division Multiplexing (OFDM) under different modulation techniques. This study involves four main procedures to achieve its objectives. The procedures involved modeling and simulations of the modulation techniques between ideal and worst case, OFDM transmission system calculation and comparison of BER. Then the major problem of OFDM system PAPR is analyzed and different techniques for

ϮϮ

reducing this problem is studied and summarize those among various comparison. The second chapter, more concentrate on the subject matter which is Orthogonal Frequency Division Multiplexing (OFDM). Extensive research is carried out on the existing wireless communications system and its underlying modulation schemes. In Chapter 3, concept of the digital modulation scheme is discussed. In this chapter, concentrate more on basics of different modulation has been chosen as a digital modulation in OFDM. Subsequently, the next chapter, Chapter 4, we will focus on PAPR that exists in OFDM communication, how the PAPR contribute in the performance of OFDM. The fifth chapter outlines the modeling and simulation of BER OFDM under different modulation techniques such as BPSK, QPSK, 16-QAM, 64-QAM etc. In chapter 6, outlines the modeling and simulation of SLM technique for different FFT size and simulation of comparison between SLM and PTS and conclude an overall comparison between several PAPR techniques. While in chapter 7, Discussions and analysis on the results are included in this section.

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CHAPTER 2 BASIC PRINCIPLES OF OFDM

2.1 INTRODUCTION Orthogonal Division Multiplexing (OFDM) has grown to be the most popular communications systems in high speed communications in the last decade. In fact, it has been said by many industry leaders that OFDM technology is the future of wireless communications [2]. Late 1997, Lucent and NTT submitted proposals to the IEEE for a high speed wireless standard for local area networks (LAN). Eventually, the two companies combined their proposals and it was accepted as a draft standard in 1998 and as a standard now known as IEEE802.11a standard, in 1999. 2.2 OFDM Orthogonal Frequency Division Multiplexing (OFDM) is very similar to the well-known and used technique of Frequency Division Multiplexing (FDM). OFDM uses the principles of FDM to allow multiple messages to be sent over a single radio channel. It is however in a much more controlled manner, allowing an improved spectral efficiency [1]. A simple example of FDM is the use of different frequencies for each FM

Ϯϱ

(Frequency Modulation) radio stations. All stations transmit at the same time but do not interfere with each other because they transmit using different carrier frequencies. Additionally they are bandwidth limited and are spaced sufficiently far apart in frequency so that their transmitted signals do not overlap in the frequency domain. At the receiver, each signal is individually received by using a frequency tunable band pass filter to selectively remove all the signals except for the station of interest. This filtered signal can then be demodulated to recover the original transmitted information. OFDM is different from FDM in several ways. In conventional broadcasting each radio station transmits on a different frequency, effectively using FDM to maintain a separation between the stations. There is however no coordination or synchronization between each of these stations [1]. With an OFDM transmission such as DAB, the information signals from multiple stations are combined into a single multiplexed stream of data. This data is then transmitted using an OFDM ensemble that is made up from a dense packing of many subcarriers. All the subcarriers within the OFDM signal are time and frequency synchronized to each other, allowing the interference between subcarriers to be carefully controlled. These multiple subcarriers overlap in the frequency domain, but do not cause Inter-Carrier Interference (ICI) due to the orthogonal nature of the modulation. Typically with FDM the transmission signals need to have a large frequency guard-band between channels to prevent interference. This lowers the overall spectral efficiency. However with OFDM the orthogonal packing of the subcarriers greatly reduces this guard band, improving the spectral efficiency. All wireless communication systems use a modulation scheme to map the information signal to a form that can be effectively transmitted over the communications channel. A wide range of modulation schemes has been

Ϯϲ

developed, with the most suitable one, depending on whether the information signal is an analog waveform or a digital signal. Some of the common analogue modulation schemes include Frequency Modulation (FM), Amplitude Modulation (AM), Phase Modulation (PM), Single Side Band (SSB), Vestigial Side Band (VSB), Double Side Band Suppressed Carrier (DSBSC)[2]. Common single carrier modulation schemes for digital communications include, Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK), Phase Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM)[1]. Each of the carriers in a FDM transmission can use an analogue or digital modulation scheme. There is no synchronization between the transmission and so one station could transmit using FM and another in digital using FSK. In a single OFDM transmission all the subcarriers are synchronized to each other, restricting the transmission to digital modulation schemes. OFDM is symbol based, and can be thought of as a large number of low bit rate carriers transmitting in parallel. All these carriers transmit in unison using synchronized time and frequency, forming a single block of spectrum. This is to ensure that the orthogonal nature of the structure is maintained. Since these multiple carriers form a single OFDM WUDQVPLVVLRQWKH\DUHFRPPRQO\UHIHUUHGWRDVµVXEFDUULHUV¶ZLWKWKHWHUP RI µFDUULHU¶UHVHrved for describing the RF carrier mixing the signal from base band. 2.3 EVOLUTION OF OFDM The evolution of OFDM [2] can be divided into three parts. There are consists of Frequency Division Multiplexing (FDM), Multicarrier Communication (MC) and Orthogonal Frequency Division Multiplexing.

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2.3.1 FREQUENCY DIVISION MULTIPLEXING (FDM) Frequency Division Multiplexing (FDM) has been used for a long time to carry more than one signal over a telephone line. FDM is the concept of using different frequency channels to carry the information of different users. Each channel is identified by the center frequency of transmission. To ensure that the signal of one channel did not overlap with the signal from an adjacent one, some gap or guard band was left between different channels. Obviously, this guard band will lead to inefficiencies which were exaggerated in the early days since the lack of digital filtering is made it difficult to filter closely packed adjacent channels [2].

2.3.2 MULTICARRIER COMMUNICATION (MC) The concept of multicarrier (MC) communications uses a form of FDM technologies but only between a single data source and a single data receiver. As multicarrier communications was introduced, it enabled an increase in the overall capacity of communications, thereby increasing the overall throughput. Referring to MC as FDM, however, is somewhat misleading since the concept of multiplexing refers to the ability to add signals together. MC is actually the concept of splitting a signal into a number of signals, modulating each of these new signals over its own frequency channel; multiplexing these different frequency channels together in an FDM manner; feeding the received signal via a receiving antenna into a demultiplexer that feeds the different frequency channels to different receivers and combining the data output of the receivers to form the received signal [18].

2.3.3 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING OFDM is the concept of MC where the different carriers are orthogonal to each other. Orthogonal in this respect means that the signals are totally

Ϯϴ

independent. It is achieved by ensuring that the carriers are placed exactly at the nulls in the modulation spectra of each other. Source for OFDM spectral efficiency is the fact that the drop off of the signal at the band is primarily due to a single carrier which is carrying a low data rate. OFDM allows for sharp rectangular shape of the spectral power density of the signal.

2.4 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING TECHNOLOGY Orthogonal Frequency Division Multiplexing (OFDM) also known as discrete multitude modulation (DMT), is based upon the principle of frequency division multiplexing (FDM), but it utilized as a digital modulation scheme. The bit stream that is to be transmitted is split into several parallel bit streams, typically dozens to thousands. The available frequency spectrum is divided into sub-channels and each low rate bit stream is transmitted over one sub channel by modulating sub-channel by modulating a sub-carrier using a standard modulation scheme, for example: PSK, QAM. The sub-carrier frequencies are chosen so that the modulated data streams are orthogonal to each other, meaning that cross talk between the sub-channels is eliminated. Channel equalization is simplified by using many slowly modulated narrowband signals instead of one fastly modulated wideband signal. The primary advantage of OFDM is its ability to coop with severe channel conditions, for example multipath and narrowband interference without complex equalization filters.

2.5 ORTHOGONALITY Signals are orthogonal if they are mutually independent of each other. Orthogonality is a property that allows multiple information signals to be transmitted perfectly over a common channel and detected, without interference [1]. Loss of orthogonality results in blurring between these

Ϯϵ

information signals and degradation in communications. Many common multiplexing

schemes

are

inherently

orthogonal.

Time

Division

Multiplexing (TDM) allows transmission of multiple information signals over a single channel by assigning unique time slots to each separate information signal. During each time slot only the signal from a single source is transmitted preventing any interference between the multiple information sources. Because of this TDM is orthogonal in nature. In the frequency domain most FDM systems are orthogonal as each of the separate transmission signals are well spaced out in frequency preventing interference. Although these methods are orthogonal the term OFDM has been reserved for a special form of FDM. The subcarriers in an OFDM signal are spaced as close as is theoretically possible while maintain orthogonality between them. OFDM achieves orthogonality in the frequency domain by allocating each of the separate information signals onto different subcarriers. OFDM signals are made up from a sum of sinusoids, with each corresponding to a subcarrier. The baseband frequency of each subcarrier is chosen to be an integer multiple of the inverse of the symbol time, resulting in all subcarriers having an integer number of cycles per symbol [2]. Thus the subcarriers are orthogonal to each other. Figure 2.1 shows the construction of an OFDM signal with four subcarriers.

Figure 2.1: Time domain construction of an OFDM signal.

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(1a), (2a), (3a) and (4a) show individual subcarriers, with 1,2,3 and 4 cycles per symbol respectively. The phase on all these subcarriers is zero. Adding a copy of the symbol to the end would result in a smooth join between symbols. (1b), (2b), (3b) and (4b) show the FFT of the time waveforms in (1a), (2a), (3a) and (4a) respectively. (4a) and (4b) shows the result for the summation of the 4 subcarriers. Sets of functions are orthogonal to each other if they match the conditions in equation (2.1)[1]. If any two different functions within the set are multiplied, and integrated over a symbol period, the result is zero, for orthogonal functions.. The results from all other functions in the set integrate to zero, and thus have no effect.

Equation (2.2) shows a set of orthogonal sinusoids, which represent the subcarriers for an unmodulated real OFDM signal.

Where fo is the carrier spacing, M is the number of carriers, T is the symbol period. Since the highest frequency component is Mfo the transmission bandwidth is also Mfo. These subcarriers are orthogonal to each other because when we multiply the waveforms of any two subcarriers and integrate over the symbol period the result is zero. Multiplying the two sine waves together is the same as mixing these subcarriers. This results in sum and difference frequency components, which will always be integer subcarrier frequencies, as the frequency of the two mixing subcarriers has integer number of cycles. Since the system is linear we can integrate the result by taking the integral of each frequency component separately then combining the results by adding the two subintegrals. The two frequency components after the mixing have an integer

ϯϭ

number of cycles over the period and so the sub-integral of each component will be zero, as the integral of a sinusoid over an entire period is zero. Both the sub-integrals are zeros and so the resulting addition of the two will also be zero, thus we have established that the frequency components are orthogonal to each other.

2.6 OFDM GENERATION AND RECEPTION OFDM signals are typically generated digitally due to the difficulty in creating large banks of phase lock oscillators and receivers in the analog domain. Figure 2.2 shows the block diagram of a typical OFDM transceiver [1]. The transmitter section converts digital data to be transmitted, into a mapping of subcarrier amplitude and phase. It then transforms this spectral representation of the data into the time domain using an Inverse Discrete Fourier Transform (IDFT). The Inverse Fast Fourier Transform (IFFT) performs the same operations as an IDFT, except that it is much more computationally efficiency, and so is used in all practical systems. In order to transmit the OFDM signal the calculated time domain signal is then mixed up to the required frequency. The receiver performs the reverse operation of the transmitter, mixing the RF signal to base band for processing, then using a Fast Fourier Transform (FFT) to analyze the signal in the frequency domain [2]. The amplitude and phase of the subcarriers is then picked out and converted back to digital data. The IFFT and the FFT are complementary function and the most appropriate term depends on whether the signal is being received or generated. In cases where the signal is independent of this distinction then the term FFT and IFFT is used interchangeably.

ϯϰ

destroyed, resulting in a clustering of the bit errors in each symbol. Most Forward Error Correction (FEC) schemes tend to work more effectively if the errors are spread evenly, rather than in large clusters, and so to improve the performance most systems employ data scrambling as part of the serial to parallel conversion stage. This is implemented by randomizing the subcarrier allocation of each sequential data bit [4]. At the receiver the reverse scrambling is used to decode the signal. This restores the original sequencing of the data bits, but spreads clusters of bit errors so that they are approximately uniformly distributed in time. This randomization of the location of the bit errors improves the performance of the FEC and the system as a whole. 2.7.2 SUBCARRIER MODULATION Once each subcarrier has been allocated bits for transmission, they are mapped using a modulation scheme to a subcarrier amplitude and phase, which is represented by a complex In-phase and Quadrature-phase (IQ) vector. Figure 2.5 shows an example of subcarrier modulation mapping [1]. This example shows 16-QAM, which maps 4 bits for each symbol. Each combination of the 4 bits of data corresponds to a unique IQ vector, shown as a dot on the figure. A large number of modulation schemes are available allowing the number of bits transmitted per carrier per symbol is varied.

Figure 2.5: Example IQ modulation constellation of 16-QAM, with gray coding of the data to each location.

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Subcarrier modulation can be implemented using a lookup table, making it very efficient to implement. In the receiver, mapping the received IQ vector back to the data word performs subcarrier demodulation. During transmission, noise and distortion becomes added to the signal due to thermal noise, signal power reduction and imperfect channel equalization. Figure 2.6 shows an example of a received 16-QAM signal with a SNR of 18 dB. Each of the IQ points is blurred in location due to the channel noise. For each received IQ vector the receiver has to estimate the most likely original transmission vector. This is achieved by finding the transmission vector that is closest to the received vector.

Figure 2.6: IQ plot for 16-QAM data with added noise. 2.7.3 FREQUENCY TO TIME DOMAIN CONVERSION After the subcarrier modulation stage each of the data subcarriers is set to an amplitude and phase based on the data being sent and the modulation scheme; all unused subcarriers are set to zero. This sets up the OFDM signal in the frequency domain. An IFFT is then used to convert this signal to the time domain, allowing it to be transmitted [4]. Figure 2.7 shows the IFFT section of the OFDM transmitter.

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Figure 2.7: OFDM generation, IFFT stage In the frequency domain, before applying the IFFT, each of the discrete samples of the IFFT corresponds to an individual subcarrier. Most of the subcarriers are modulated with data. The outer subcarriers are unmodulated and set to zero amplitude. These zero subcarriers provide a frequency guard band before the nyquist frequency and effectively act as an interpolation of the signal and allows for a realistic roll off in the analog anti-aliasing reconstruction filters. 2.7.4 RF MODULATION The output of the OFDM modulator generates a base band signal, which must be mixed up to the required transmission frequency. This can be implemented using analog techniques as shown in Figure 2.7 or using a Digital Up Converter as shown in Figure 2.9.

Figure 2.8: RF modulation of complex base band OFDM signal in analog techniques.

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Figure 2.9: RF modulation of complex base band OFDM signal using digital techniques. (DDS = Direct Digital Synthesis) Both techniques perform the same operation, however the performance of the digital modulation will tend to be more accurate due to improved matching between the processing of the I and Q channels, and the phase accuracy of the digital IQ modulator.

2.7.5 REAL VERSES COMPLEX OFDM GENERATION For most wireless applications the OFDM signal is generated at base band using complex samples, and then modulated up to the required frequency using an IQ modulator, as shown in Figure 2.7 and Figure 2.8. The IQ modulator frequency shifts the OFDM signal from DC to the required RF frequency, and converts the complex signal into a real signal. A transmitted RF signal is always a real signal as it is just a variation in field intensity. It is however possible to directly generate a real OFDM signal. This is useful in wired applications, such as ADSL. In these applications the transmitted signal is generally from just above DC to an upper limit determined by the required signal bandwidth. The required transmission signal is a real signal as only a single cable is used. If a complex signal were used then two wires would be needed, one for the real signal and one for the imaginary signal. A real signal is equivalent to a complex base band

ϯϴ

signal, centred on DC, mixed to the new centre frequency using an IQ modulator: ݂ܿ ൌ

‫ݓ‬ ʹ

൅ ݂‫ ««««« ݂݂݋‬

where fc is the frequency translation required to shift the complex base band signal to form the real OFDM signal, W is the signal bandwidth and foff is the offset from DC, also see Figure 2.9. In wired applications such as ASDL, the lower most subcarrier is offset from DC by a small amount compared with the signal bandwidth. This means that the real signal can be generated directly using the IFFT stage instead of requiring the use of an IQ modulator for frequency translation.

Figure 2.10: DC offset OFDM signal w- bandwidth fo- frequency offset from DC, fc centre frequency Figure 2.11 shows the set up of the OFDM signal in the frequency domain for the generation of a real waveform. With a real waveform the useable bandwidth of the signal is only half the sampling frequency and so to generate a real OFDM signal only one half of the available subcarriers can be used for data modulation. To create a real waveform the upper frequency bins of the IFFT must be set to the complex conjugate of the mirror of the lower half[1]. This can be contrasted with the construction of a complex base band OFDM signal as shown in Figure 2.12. In this case all of the frequency bins can be used for subcarrier modulation, with the main limitation being that the outer bins must be kept as zero to allow reconstruction of the analog signal, without aliasing occurring. In most applications the subcarrier corresponding to DC is not used. Its removal

ϯϵ

simplifies the implementation hardware. Most OFDM system currently using an analog base band the same as shown in Figure 2.7. In order for the DC subcarrier to be use it requires that the IQ outputs are DC coupled to the IQ mixer. This is difficult to achieve in hardware as offset errors result in large errors in the generated IQ vector. Using AC coupling reduces the complexity of the implementation and so the DC subcarrier is usually not used. If digital modulation is used as shown in Figure 2.9 then the DC subcarrier can be used.

Figure 2.11: Construction of the subcarriers for generating a real output time domain waveform.

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Figure 2.12: Construction of the subcarriers for complex signal representation of OFDM signals 2.8 GUARD PERIOD For a given system bandwidth the symbol rate for an OFDM signal is much lower than a single carrier transmission scheme. For example for a single carrier BPSK modulation, the symbol rate corresponds to the bit rate of the transmission. However for OFDM the system bandwidth is broken up into Nc subcarriers, resulting in a symbol rate that is Nc times lower than the single carrier transmission. This low symbol rate makes OFDM naturally resistant to effects of Inter-Symbol Interference (ISI) caused by multipath propagation [1]. Multipath propagation is caused by the radio transmission signal reflecting off objects in the propagation environment, such as walls, buildings, mountains, etc. These multiple signals arrive at the receiver at different times due to the transmission distances being different. This spreads the

ϰϭ

symbol boundaries causing energy leakage between them. The effect of ISI on an OFDM signal can be further improved by the addition of a guard period to the start of each symbol. This guard period is a cyclic copy that extends the length of the symbol waveform. Each subcarrier, in the data section of the symbol, (i.e. the OFDM symbol with no guard period added, which is equal to the length of the IFFT size used to generate the signal) has an integer number of cycles. Because of this, placing copies of the symbol end-to-end results in a continuous signal, with no discontinuities at the joins. Thus by copying the end of a symbol and appending this to the start results in a longer symbol time [2]. Figure 2.13 shows the insertion of a guard period.

Figure 2.13: Addition of a guard period to an OFDM signal The total length of the symbol is Ts=TG + TFFT, where Ts is the total length of the symbol in samples, TG is the length of the guard period in samples, and TFFT is the size of the IFFT used to generate the OFDM signal [11]. In addition to protecting the OFDM from ISI, the guard period also provides protection against time-offset errors in the receiver.

2.9 PROTECTION AGAINST TIME OFFSET To decode the OFDM signal the receiver has to take the FFT of each received symbol, to work out the phase and amplitude of the subcarriers. For an OFDM system that has the same sample rate for both the transmitter and receiver, it must use the same FFT size at both the receiver and

ϰϮ

transmitted signal in order to maintain subcarrier Orthogonality. Each received symbol has TG + TFFT samples due to the added guard period. The receiver only needs TFFT samples of the received symbol to decode the signal. The remaining TG samples are redundant and are not needed. For an ideal channel with no delay spread the receiver can pick any time offset, up to the length of the guard period, and still get the correct number of samples, without crossing a symbol boundary. Because of the cyclic nature of the guard period changing the time offset simply results in a phase rotation of all the subcarriers in the signal. The amount of this phase rotation is proportional to the subcarrier frequency, with a subcarrier at the nyquist frequency changing by 1800 for each sample time offset. Provided the time offset is held constant from symbol to symbol, the phase rotation due to a time offset can be removed out as part of the channel equalization. In multipath environments ISI reduces the effective length of the guard period leading to a corresponding reduction in the allowable time offset error.

2.10 PROTECTION AGAINST ISI In an OFDM signal the amplitude and phase of the subcarrier must remain constant over the period of the symbol in order for the subcarriers to maintain orthogonality. If they are not constant it means that the spectral shape of the subcarriers will not have the correct sinc shape, and thus the nulls will not be at the correct frequencies, resulting in Inter-Carrier Interference [10]. At the symbol boundary the amplitude and phase change suddenly to the new value required for the next data symbol. In multipath environments ISI causes spreading of the energy between the symbols, resulting in transient changes in the amplitude and phase of the subcarrier at the start of the symbol. The length of these transient effects corresponds to the delay spread of the radio channel. The transient signal is a result of

ϰϯ

each multipath component arriving at slightly different times, changing the received subcarrier vector. Figure 2.14 shows this effect. Adding a guard period allows time for the transient part of the signal to decay, so that the FFT is taken from a steady state portion of the symbol [10]. This eliminates the effect of ISI provided that the guard period is longer than the delay spread of the radio channel. The remaining effects caused by the multipath, such as amplitude scaling and phase rotation are corrected for by channel equalization.

Figure 2.14: Function of the guard period for protecting against ISI The addition of guard period removes most of the effects of ISI; however in practice, multipath components tend to decay slowly with time, resulting in some ISI even when a relatively long guard period is used. Figure 2.15 shows the simulated performance of an OFDM system in the presence of static multipath. In this case the multipath impulse response followed an exponential decay with a time constant of 8 samples, resulting in an RMS delay spread of 3.5 samples. Each sample in the impulse response was complex and Gaussian distributed. The RMS delay spread is a common parameter to estimate the spread of the multipath energy in time, and used to estimate the level of ISI in single carrier communications. Section 3.4 provides a more detailed description of RMS delay spread with typical values for a range of environments. A more

ϰϰ

appropriate measure is the time over which 99% of the total accumulated impulse energy arrived, which in this simulation was 16 samples. The results shown in Figure 2.15 plot the effective SNR of the demodulated OFDM signal as a function of the channel SNR. Effective SNR is used extensively though out this thesis as a measure of the performance of the communications link. It is a measure of the signal to noise ratio as seen by the OFDM receiver after demodulation, where the signal power is the magnitude of the wanted signal, and the noise is the combined error in the received signal due to all the detrimental effects in the system including channel noise, IMD, filtering, ISI, ICI, frequency errors, time offset errors, channel equalization errors, etc [12]. The effective SNR provides a measure of the OFDM performance, independent of the modulation scheme. Traditionally the BER is used to measure the performance of a link, however in this thesis OFDM is considered the work with a large number of modulation schemes making BER a poor method of measurement. The BER of any particular modulation scheme can be estimated from the effective SNR by finding the BER of the modulation scheme in an AWGN channel with a SNR equal to the effective SNR. Figure 2.15 shows the effect of multipath on the OFDM transmission. Ideally the effective SNR should follow the channel SNR, however detrimental effects such as ISI lead to degraded performance. We can see from the results that as the length of the guard period is increased the maximum effective SNR improves. For example, the effective SNR of the OFDM signal only reaches a maximum of 15 dB when the guard period length is 4 samples in length, but reaches 25 dB when a guard period of 16 samples is used. This is a result of more of the ISI energy being removed by the guard period. This shows that having a guard period (16 samples)

ϰϱ

that is more than four times the multipath RMS delay spread (3.5 samples) still results in significant IS [16]. The low effective SNR for when the guard period was a similar length to the channel RMS delay spread is fine for robust modulation schemes such as BPSK and QPSK, but is insufficient for higher spectral efficiency modulation schemes such as 64-QAM and 256-QAM. Traditionally the RMS delay spread has been used as a measure of ISI and the allowable symbol rate in a multipath environment. However if a higher spectral efficiency is required a more appropriate measure is needed. To achieve very high spectral efficiencies an effective SNR of greater than 35 dB must be able to be reached. In this case it required a guard period of at least 64 samples in length. This length of the guard period corresponds to the time it took for the impulse energy to decay to ±35 dBc. Thus if we require a SNR of 25 dB then we have a guard period that is at least long enough to remove all impulse reflections that are stronger than ±25 dBc. In order for the OFDM carriers to remain orthogonal to each other, the channel response must be approximately flat over the bandwidth of each subcarrier. The simulation using 320 subcarriers divides the channel response using finer subcarriers, and hence the variation of the channel fading over their bandwidth of each subcarrier is more constant, improving the performance. The effective SNR for the 128 IFFT size is not limited by the guard period, but instead by poor channel equalization caused by an insufficient number of subcarriers [21]. For OFDM to operate effectively, the frequency response must be approximately flat over the bandwidth of a subcarrier [12]. If insufficient subcarriers are used then the frequency response changes too rapidly, leading to degraded performance.

ϰϲ

Figure 2.15: Effectiveness of adding a guard period for removal of ISI 2.11 GUARD PERIOD OVERHEAD AND SUBCARRIER SPACING Adding a guard period lowers the symbol rate, however it does not affect the subcarrier spacing seen by the receiver [11]. The subcarrier spacing is determined by the sample rate and the FFT size used to analyze the received signal. ο݂ ൌ

‫ݏܨ‬ ܰ‫ܶܨܨ‬

««««

,Q(TXDWLRQ ¨f is the subcarrier spacing in Hz, Fs is the sample rate in Hz, and NFFT is the size of the FFT. The guard period adds time overhead, decreasing the overall spectral efficiency of the system.

2.12 BAND-LIMITING OF OFDM AND WINDOWING OFDM in the time domain is equivalent to a sum of modulated sinusoidal carriers that are each windowed in time with a rectangular window function, also known as a boxcar window function (see Appendix A for more details). This window defines the boundary of each OFDM symbol, and determines the frequency response of the generated OFDM signal. Figure 2.16 shows an example time waveform for a single carrier OFDM

ϰϳ

transmission using Phase Shift Keying (PSK). The amplitude of the subcarrier is fixed and the phase is varied from symbol to symbol to transmit the data information. The subcarrier phase is constant for the entire symbol, resulting in a step in phase between symbols. These sharp transitions between symbols result in spreading in the frequency domain. Figure 2.17 shows the spectrum of a 52 subcarrier OFDM signal (same as HiperLAN2, or IEEE802.11a) with no band-pass limiting. The out of band components only fall off slowly due to the sinc roll off of each subcarrier. Figure 2.18 shows the spectrum of a 1536 subcarrier OFDM signal (same as Type I DAB). The side-lobes roll off faster than the 52-subcarrier case, as a fraction of the system bandwidth. However the side-lobes are still significant (> -40 dBc) even far away from the edge of the OFDM main signal block. These side-lobes increase the effective bandwidth of the OFDM signal, degrading the spectral efficiency. There are two common techniques for reducing the level of the side-lobes to acceptable limits; these are band pass filtering the signal, or adding a RC guard period.

Figure 2.16: Time waveform of a single carrier OFDM signal, showing 3 symbols.

ϰϴ

Figure 2.17: Spectrum of a 52 subcarrier OFDM signal with no bandlimiting. This is the same frequency response as an un-filtered HiperLAN2 signal. For HiperLAN2 the subcarrier spacing corresponds to 312.5 kHz. The DC subcarrier has not been used, making the signal symmetrical around DC.

Figure 2.18: Spectrum of a 1536 subcarrier OFDM signal with no bandThis is the same frequency response as an un-filtered Type I DAB signal. For DAB the subcarrier spacing corresponds to 1 kHz.

2.13 BAND PASS FILTERING Whenever signals are converted from the digital domain to an analog waveform for transmission, filtering is used to prevent aliasing occurring. This effectively band pass filters the signal, removing some of the OFDM

ϰϵ

side-lobes. The amount of side-lobe removal depends on the sharpness of the filters used. In general digital filtering provides a much greater flexibility, accuracy and cut off rate than analog filters, making them especially useful for band limiting of an OFDM signal [1]. These signals have been filtered with a Finite Impulse Response (FIR) filter developed using the windowing method. A low number of subcarriers were used in these plots so that the roll off of the FIR filtering could be seen. The filtering removes virtually all of the side lobes, but does so at the cost of the computational expense of implementing the FIR filtering, and it reduces the effective SNR of the OFDM channel [8]. The act of filtering the OFDM signal, chops off significant energy from the outer subcarriers, distorting their shape and causing ICI. Very sharp cut off filters allow separate blocks of OFDM signals to be packed very closely in the frequency domain, improving the spectral efficiency. But this tight filtering can result in a degraded effective SNR, and so its effects must be taken into consideration when designing a system. Filtered results were band pass filtered using an FIR filter, which was developed using the windowing method with a Kaiser Window function.

2.14 EFFECT OF BAND PASS FILTERING ON OFDM PERFORMANCE In the time domain, an OFDM symbol is rectangular in shape, which corresponds to a sinc decay in the frequency domain, as shown in Figure 2.17. If we were to band pass filter an OFDM signal with a brick wall filter then the signal would become rectangular in the frequency domain, causing the time domain waveform to have a sinc decay between symbols. This in turn results in ISI degrading the performance [4]. The ISI caused by the filtering can be removed by using a guard period of sufficient length, and by choosing the time offset to synchronize in the middle of the guard period, so that most of the ISI energy is removed.

ϱϬ

Figure 2.18 shows the simulated performance of a band pass filtered OFDM signal, with different transition widths for the filter, in a channel with no channel noise. This plot shows the performance of the OFDM transmission when the time synchronization offset was varied. The guard period used in this simulation was of the same length as the IFFT section of the symbol. This very long guard period was used so that the effect of the time offset could be varied over a large range, while still maintaining a time offset within the guard period. The effective SNR was calculated by averaging effective SNR over all the subcarriers in the transmission. When the time offset is 0 this corresponds to the receiver taking the FFT of the IFFT section of the transmitted signal. When the time offset is negative this corresponds to the receiver taking the FFT over the IFFT section and part of the symbol guard period. The lowest ISI is achieved when the time offset is negative and half the guard period length. The sharper the filter cuts off the signal (in the figure the sharpest filter removes the side-lobes down to below ±100 dBc within 2 carrier spacings), the longer the ISI. The residual capping of the SNR at 85 dB is caused by ICI, and distortion of the subcarriers at the edges of the signal [14].

Figure 2.19: Effective SNR as a function of the time offset for a band pass filtered 52 subcarrier OFDM signal.

ϱϭ

The guard period in this test was 50% of total symbol time, thus guard period length = useful symbol time [1]. Carr. cutoff corresponds to the WUDQVLWLRQZLGWKRIWKHILOWHULQVXEFDUULHUVSDFLQJ¶V

Figure 2.20: Section of the waveform that the receiver FFT is taken from depending on the time offset The effective SNR of a band pass filtered OFDM signal depends on the effects of both ISI and ICI. The effective SNR varies with subcarrier number as the filter distorts the response of the outer subcarriers the most. The highest modulation scheme used in HiperLAN2 and IEEE802.11a systems is 64-QAM, which requires an effective SNR of greater than 26 dB. We can see from the results in Figure 2.20 that the effective SNR exceeds 26 dB for all carriers even when using a very sharp band pass filter that cuts off within one half of a subcarrier spacing. An odd number of subcarriers were simulated to make the signal symmetrical about DC. The band pass filtering was implemented using an FIR filter based one the windowing method using a Kaiser window. Each result shows five different sharpness of the filter. We can see that for each halving of the guard period length the transition width of the band pass filter must be approximately doubled in order to maintain the same effective SNR. Subcarriers more than 10 subcarrier spacing from the signal boundary have an effective SNR of greater than 30 dB regardless of the sharpness of the filtering provided some guard period is present. This effective SNR is sufficiently high to support a modulation scheme up to 128-QAM with a low error rate, providing that there are no

ϱϮ

other detrimental effects. For subcarriers on the edge of the OFDM signal, their effective SNR can be as low as 20 dB, which may pose a small problem for modulation schemes above 32-QAM. Band pass filtering of OFDM signals allows the side-lobes to be removed from an OFDM signal, effectively reducing its bandwidth, and improving the spectral efficiency.

2.16 RAISED COSINE GUARD PERIOD One of the simplest methods for suppressing the side-lobes of an OFDM signal is to round the guard period of the OFDM signal, tapering it smoothly to zero before the next symbol. This tampering smoothes the transition between symbols, resulting in reduced side-lobe power [1]. Figure 2.21 shows the makeup of a single OFDM symbol with a Raised Cosine (RC) guard period. This section of the guard period is windowed with a squared cosine shape (cos(q)2), hence the name raised cosine.

Figure 2.21: Construction of a RC guard period. The raised cosine section of a guard period can be overlapped with the previous and next symbol as this section of the guard period only provides minimal protection against multipath and timing errors, and is ignored at the receiver. Because this section tapers to zero it results in minimal additional ISI. The main advantage of overlapping is that the length of the raise cosine section can be made double in length without incurring

ϱϯ

additional time overhead [8]. Figure 2.22 shows a diagram of overlapping symbols.

Figure 2.22: Envelope of OFDM symbols with a flat guard period and an overlapping raised cosine guard period The effect of adding a RC guard period to an OFDM signal was simulated to determine the level of the out of band side-lobes. Figure 2.26 shows the spectrum of OFDM signals with an RC guard period. The spectrum shown has been shifted to the left so that just the upper edge of the OFDM signal is shown. The results were presented in this manner to normalize them so that the side-lobes could be compared regardless of the number of subcarriers used in the signal. In Figure 2.26 the lower edge of the OFDM signal can also be seen. The frequency axis has been normalized to units of VXEFDUULHUVSDFLQJ¶V The spectrum of an OFDM signal only varies slightly as the number of subcarriers is increased. The main difference occurs for the side-lobe level when little or no RC guard period is used [13]. In Figure 2.26 the RC guard period length has been specified as a percentage of the flat section of the OFDM symbol, that is: ܴ‫ ܥ‬ൌ ͳͲͲǤ

ܶ‫ܥܴܩ‬ ܶ‫ ܶܨܨ‬൅ܶ‫ܨܩ‬

Ψ «««

Where RC is the raised cosine percentage, TGRC is the length of the RC guard period, TFFT is the length of the FFT section of the symbol and TGF is the length of the flat guard period, see Figure 2.21. For example: The IEEE802.11a standard recommends a RC guard period of 100 ns. The useful symbol period (TFFT) is 3.2 ìs and the total guard period is 800 ns.

ϱϰ

The flat section of the guard period is the total guard period (800 ns) minus the RC section of the symbol (100 ns), thus TGF = 700 ns. The RC section is thus: ܴ‫ ܥ‬ൌ ͳͲͲǤ

ͳͲͲ ൌ ʹǤͷ͸Ψ ͹ͲͲ ൅ ͵ʹͲͲ

Since HiperLAN2 uses 52 signal subcarriers (spaced at intervals of 312.5 kHz) the total system bandwidth using a threshold of ±40 dBc is (2*30+52)*312.5 kHz = 35 MHz. The spacing of the HiperLAN2 channels is 20 MHz, and so a bandwidth of 35 MHz is too high[7]. This indicates that the addition of the RC guard period is insufficient to reduce the sidelobes sufficiently, thus additional band pass filtering is required.

Figure 2.23: Side-lobe power for an OFDM signal with 20 subcarriers as the length of the RC guard period is varied.

2.17 EFFECT OF ADDITIVE WHITE GAUSSIAN NOISE ON OFDM Noise exists in all communications systems operating over an analog physical channel, such as radio. The main sources are thermal background noise, electrical noise in the receiver amplifiers, and inter-cellular interference. In addition to this noise can also be generated internally to the communications system as a result of Inter-Symbol Interference (ISI), Inter-Carrier Interference (ICI), and Inter- Modulation Distortion (IMD).

ϱϱ

These sources of noise decrease the Signal to Noise Ratio (SNR), ultimately limiting the spectral efficiency of the system. Noise, in all its forms, is the main detrimental effect in most radio communication systems. It is therefore important to study the effects of noise on the communications error rate and some of the tradeoffs that exists between the level of noise and system spectral efficiency. Most types of noise present in radio communication systems can be modeled accurately using Additive White Gaussian Noise (AWGN). This noise has a uniform spectral density (making it white), and a Gaussian distribution in amplitude (this is also referred to as a normal distribution or bell curve). Thermal and electrical noise from amplification, primarily have white Gaussian noise properties, allowing them to be modeled accurately with AWGN. Also most other noise sources have AWGN properties due to the transmission being OFDM. OFDM signals have a flat spectral density and a Gaussian amplitude distribution provided that the number of carriers is large (greater than about 20 subcarriers), because of this the inter-cellular interference from other OFDM systems have AWGN properties. For the same reason ICI, ISI, and IMD also have AWGN properties for OFDM signals.

2.18 EFFECT OF DISTORTION ON OFDM One of the problems with OFDM is that the signal has a high peak power compared with its average power. When an RF carrier is modulated with an OFDM signal it results in a similar variation in power of the carrier envelope. This results in the requirement that the signal is amplified and transmitted in a linear way. It is very difficult to maintain a high degree of linearity at high power levels and so most of the distortion in a radio transmission usually occurs in the power amplifier of the transmitter. Some additional distortion can occur in the receiver if it is not designed properly, but in general it is relatively easy to keep the level of distortion in the

ϱϲ

receiver significantly lower than the transmitter. Distortion in the transmitter causes the most problems in the transmission chain, as it can result in spectral spreading, which can cause interference to neighboring systems in RF frequency.

Figure 2.24: Effect of distortion on a 2 tone signal, showing harmonics and IMD Non-OLQHDULW\¶VLQWKHWUDQVPLVVLRQUHVXOWLQWZRPDLQGLVWRUWLRQSURGXFts, Inter- Modulation Distortion (IMD) and harmonics. Figure 2.33 shows the effect of clipping distortion on a 2-tone signal. OFDM signals are made up from a large number of subcarriers resulting in many distortion products. Harmonics result in frequency components at X times the RF carrier frequency, where X is an integer. Thus if we have a 900 MHz RF carrier the harmonics will occur at 1800 MHz, 2.7 GHz, etc. Harmonics can easily be removed using a relatively simple low pass filter on the output of the transmitter. IMD is much more of a problem as it results in distortion components, which are in band and out of band but close to the main transmission. These components are a result of mixing between each of the harmonics of the system, and subsequent mixing between the IMD products. In-band components result in added noise to the OFDM signal at the receiver, effectively limiting the SNR of the system, even in the absence of other

ϱϳ

sources of noise. Out of band components spread the signal in bandwidth, resulting in potential interference with other radio communications in neighboring frequency bands. Even if the signal is perfectly band-limited before going to the transmitter power amplifier, spectral spreading will occur if the power amplifier is non-linear. Spectral spreading can be slightly reduced by using analog band pass filters after the power amplifier. The amplifier models compared are a Solid State Power Amplifier (SSPA), a Travelling Wave Tube Amplifier (TWTA) and a perfectly linearized amplifier. The results show that the optimal Output power Back Off (OBO) for DAB is approximately 2 - 3 dB, with only a small difference of 0.6 dB due to the different amplifier models. These results are however limited to OFDM transmissions using QPSK, which is a very robust modulation scheme, and hence robust against effects of distortion. Modulation schemes that have a higher spectral efficiency (such as 16QAM, 256-QAM, etc) are more susceptible to the effects of distortion due to the requirement of a higher effective SNR. In [55] the performance of both a QPSK and a 16-QAM OFDM system was investigated. The optimal OBO for QPSK transmissions were found to be 3 dB in this study, which compare well with results presented in [5]. For 16-QAM the optimal OBO was found to be higher, approximately 6 dB. The performance of a 64QAM modulated OFDM signal was investigated in [5][6], which showed that the optimal OBO is 6 dB for clipping distortion, and closer to 10 dB for a smooth limiter. Each of these papers show the performance of a fixed system, limiting the usefulness of the results. A more general study is presented showing the performance of an OFDM system as a function of clipping distortion. The effect of distortion causes in-band noise due to IMD, resulting in a lowering of the effective SNR of the channel. The

ϱϴ

results are presented as an effective SNR of the OFDM channel, and so are independent of any particular modulation scheme. 2.19 MODULATION SCHEMES Digital data is transferred in an OFDM link by using a modulation scheme on each subcarrier. A modulation scheme is a mapping of data words to a real (In phase) and imaginary (Quadrature) constellation, also known as an IQ constellation. For example 256-QAM (Quadrature Amplitude Modulation) has 256 IQ points in the constellation, constructed in a square with 16 evenly spaced columns in the real axis and 16 rows in the imaginary axis [20][21]. The number of bits that can be transferred using a single symbol corresponds to log2(M), where M is the number of points in the constellation, thus 256-QAM transfers 8 bits per symbol. Each data word is mapped to one unique IQ location in the constellation. The resulting complex vector I+j.Q corresponds to an amplitude of I2 +Q2 and a phase of (I+j.Q) where jൌ ξെͳ . Increasing the number of points in the constellation does not change the bandwidth of the transmission, thus using a modulation scheme with a large number of constellation points, allows for improved spectral efficiency [22]. For example 256-QAM has a spectral efficiency of 8 b/s/Hz, compared with only 1 b/s/Hz for BPSK. However, the greater the number of points in the modulation constellation, the harder they are to resolve at the receiver. As the IQ locations become spaced closer together, it only requires a small amount of noise to cause errors in the transmission. This results in a direct trade off between noise tolerance and the spectral efficiency of the modulation scheme and was summarized by Shannon's Information Theory, which states that the maximum capacity of a channel of bandwidth W, with a signal power of S, perturbed by white noise of average power N, is given by

ϱϵ

ܵ

‫ ܥ‬ൌ ܹ݈‫ ʹ݃݋‬ሺͳ ൅ ሻ ««« ܰ

The spectral efficiency of a channel is a measure of the number of bits transferred per second for each Hz of bandwidth and thus the spectral efficiency SE is given by ܵ‫ ܧ‬ൌ

‫ܥ‬ ܹ

ܵ

ൌ ݈‫ ʹ݃݋‬ሺͳ ൅ ሻ «««« ܰ

Where both the signal and noise is linear scale and the spectral efficiency is measured in b/s/Hz. If the SNR is significantly higher than one then each doubling of the signal power (a 3 dB increase) the ideal spectral efficiency increases by 1 b/s/Hz. 2.20 OFDM VERSES SINGLE CARRIER TRANSMISSION The BER of an OFDM system is dependent on several factors, such as the modulation scheme used, the amount of multipath, and the level of noise in the signal. However if we look at the performance of OFDM with just AWGN then the performance of OFDM is exactly the same as that of a single carrier coherent transmission using the same modulation scheme [1][3][6]. If we look at just a single OFDM subcarrier (since the subcarriers are orthogonal to each other, this does not affect the performance in any way) then this is exactly the same as a single carrier transmission that is quadrature modulated with no band pass filtering. The transmitted amplitude and phase is held constant over the period of the symbol and is set based on the modulation scheme and the transmitted data. This transmitted vector is then updated at the start of each symbol. This results in a sinc frequency response, which is the required response for OFDM. The optimal receiver for such a single carrier transmission is to use a coherent matched receiver, which can be implemented by mixing the signal to DC using an IQ mixer. This results in an IQ output that describes the amplitude and phase of the received modulated carrier. The amplitude

ϲϬ

and phase of the transmitted signal is constant over the symbol period, and so the optimal method of removing the most noise from the signal is to use an integrate-and-dump filter. This filter averages the received IQ vector over the entire symbol, and then performs IQ demodulation on the average. The demodulation of an OFDM signal is performed in exactly the same manner. In the receiver a FFT is used to estimate the amplitude and phase of each subcarrier. The FFT operation is exactly equivalent to IQ mixing each of the subcarriers to DC then applying an integrate-and-dump over the number of samples in the FFT. From this we can see that the FFT performs the same operation as the matched receiver for the single carrier transmission, except now for a bank of subcarriers. From this we can conclude that in AWGN, OFDM will have the same performance as a single carrier transmission with no band limiting. However, most propagation

environments

suffer

from

the

effects

of

multipath

propagation[12]. For a given fixed transmission bandwidth, the symbol rate for a single carrier transmission is very high, where as for an OFDM signal it is N times lower, where N is the number of subcarriers used. This lower symbol rate results in a lowering of the ISI. In addition to lowering of the symbol rate, OFDM systems can also use a guard period at the start of each symbol. This guard period removes any ISI shorter than its length. If the guard period is sufficiently long, then all the ISI can be removed. Multipath propagation results in frequency selective fading that leads to fading of individual subcarriers. Most OFDM systems use Forward Error Correction to compensate for the subcarriers that suffer from severe fading. The adaptive modulation scheme proposed in section 4.2 matches the modulation scheme of each subcarrier to its SNR. The additional spectral efficiency of those subcarriers that have a SNR greater than the average (due to constructive interference) tends to compensate for subcarriers that are subjected to fading (destructive interference) [1][6]. As a result of this

ϲϭ

the performance of such an OFDM system in a multipath environment is similar to its performance in an AWGN channel. The performance of the OFDM system will be primarily determined by the noise seen at the receiver. However, the performance of a single carrier transmission will degrade rapidly in the presence of multipath. 2.21 OFDM SIMULATION PARAMETERS Table 9 shows the configuration used for most of the simulations performed on the OFDM signal. An 800-carrier system was used, as it would allow for up to 100 users if each were allocated 8 carriers. The aim was that each user has multiple carriers so that if several carriers are lost due to frequency selective fading that the remaining carriers will allow the lost data to be recovered using forward error correction. For this reason any less than 8 carriers per user would make this method unusable. Thus 400 carriers or less was considered too small. However more carriers were not used due to the sensitivity of OFDM to frequency stability errors. The greater the number of carriers a system uses, the greater it required frequency stability [1]. For most of the simulations the signals generated were not scaled to any particular sample rate, thus can be considered to be frequency normalized. Three carrier modulation methods were tested to compare their performances. This was to show a trade off between system capacity and system robustness. DBPSK gives 1 bits/Hz spectral efficiency and is the most durable method, however system capacity can be increased using DQPSK (2 bits/Hz) and D16PSK (4 bits/Hz) but at the cost of a higher BER. The modulation method used is shown as BPSK, QPSK, and 16PSK on all of the simulation plots, because the differential encoding was considered to be an integral part of any OFDM transmission.

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TABLE I OFDM System Parameters Used for the Simulations Parameter

Value

Carrier

DBPSK, DQPSK, D16PSK

Modulation used FFT size

2048

Number

of 800

carrier used Guard Time Guard

512 samples (25%)

Period Half zero signal, half a cyclic

Type

extension of the symbol

For BPSK the SER equals the BER, however for QPSK the BER will be approximately half the SER[1]. This is because two bits of information are transferred for each QPSK symbol and typically only single bit errors occur when suitable mapping is used and the noise level is low. 2.22 ADVANTAGES OF OFDM Can easily be adopted to severe channel conditions without complex equalization. It is spectrally efficient and can effectively reduce the narrowband interference. Robust to inter symbol interference and fading caused by multipath propagation. High spectral efficiency. Efficient implementation by FFTs. Low sensitivity to time synchronization errors.

ϲϯ

Tuned sub channel receiver filter are not required. Facilitates Single Frequency Network; i.e.: transmitter macro diversity. OFDM effectively can lessen the computation complexity. When the delay spread of OFDM system exceeds its maximum limit, it can degrades if performance gracefully and it is convenient for modulation and coding. OFDM is robust in multipath environment. OFDM system can easily estimates the proper channel for data transmission. 2.24 LIMITATIONS OF OFDM Sensitive to Doppler shift. Sensitive to frequency synchronization problems. Inefficient transmitter power consumption since linear power amplifier is required. It is highly sensitive to inter channel interference. High peak to average ratio OFDM signal causes the clipping distortion. OFDM is very sensitive to phase noise and frequency. 2.25 CONCLUSION Orthogonal frequency division multiplexing (OFDM) technology is one of the most attractive candidates for fourth generation (4G) wireless communication. It effectively combats the multipath fading channel and improves the bandwidth efficiency. At the same time, it also increases system capacity so as to provide a reliable transmission. In this chapter we try to describe all the features of OFDM. For its high data rate, law interference, lower complexity and such many other properties it is very popular in modern wireless communication system especially in WiMax.

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CHAPTER 3 MODULATION TECHNIQUES AND TRANSMISSION FACTORS OF OFDM

3.1 MODULATION Modulation is the process of facilitating the transfer of information over a medium. Voice cannot be sent very far by screaming. To extend the range of sound, we need to transmit it through a medium other than air, such as a phone line or radio. The process of converting information (voice in this case) so that it can be successfully sent through a medium (wire or radio waves) is called modulation. There are 2 types of modulations: Analog modulation and digital modulation [20]. In analog modulation, an information-bearing analog waveform is impressed on the carrier signal for transmission whereas in digital modulation, an information-bearing discrete-time symbol sequence (digital signal) is converted or impressed onto a continuous-time carrier waveform for transmission. 2G wireless systems are realized using digital modulation schemes.

3.2 DIGITAL MODULATION Nowadays, digital modulation is much popular compared to analog modulation. The move to digital modulation provides more information capacity, compatibility with digital data services, higher data security,

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better quality communications, and quicker system availability [20][21]. Developers of communications systems face these constraints: available bandwidth permissible power inherent noise level of the system Digital modulation schemes have greater capacity to convey large amounts of information than analog modulation schemes.

3.3 BASIC MODULATION METHODS Digital modulation is a process that impresses a digital symbol onto a signal suitable for transmission. For short distance transmissions, baseband modulation is usually used. Baseband modulation is often called line coding. A sequence of digital symbols are used to create a square pulse waveform with certain features which represent each type of symbol without ambiguity so that they can be recovered upon reception. These features are variations of pulse amplitude, pulse width and pulse position [21].

Figure 3.1: Baseband digital modulation examples. Figure 3.1 shows several baseband modulation waveforms. The first one is the non-return to zero-level (NRZ-L) modulation, which represents a symbol 1 by a positive square pulse with length T and a symbol 0 by a negative square pulse with length T. The second one is the unipolar return

ϲϳ

to zero modulation with a positive pulse of T/2 for symbol 1 and nothing for 0. The third is the biphase level or Manchester, after its inventor, modulation which uses a waveform consisting of a positive first-half T pulse and a negative second-half T pulse for 1 and a reversed waveform for 0. For long distance and wireless transmissions, band pass modulation is usually used. Band pass modulation is also called carrier modulation. A sequence of digital symbols is used to alter the parameters of a highfrequency sinusoidal signal called carrier. It is well known that a sinusoidal signal has three parameters: amplitude, frequency, and phase. Thus amplitude modulation, frequency modulation, and phase modulation are the three basic modulation methods in pass band modulation [20]. Figure 3.2 shows three basic binary carrier modulations. They are amplitude shift keying (ASK), frequency shift keying (FSK) and phase shift keying (PSK). In ASK, the modulator puts out a burst of carrier for every symbol 1 and no signal for every symbol 0. This scheme is also called on-off keying (OOK). In a general ASK scheme, the amplitude for symbol 0 is not necessarily 0. In FSK, for symbol 1 a higher frequency burst is transmitted and for symbol 0 a lower frequency burst is transmitted, or vice versa

Figure 3.2: Three basic band-pass modulation schemes. In PSK, a symbol 1 is transmitted as a burst of carrier with 0 initial phase while a symbol 0 is transmitted as a burst of carrier with 1800 initial phase.

ϲϴ

Based on these three basic schemes, a variety of modulation schemes can be derived from their combinations. For example, by combining two binary PSK (BPSK) signals with orthogonal carriers a new scheme called quadrature phase shift keying (QPSK) can be generated. By modulating both amplitude and phase of the carrier, we can obtain a scheme called quadrature amplitude modulation (QAM) etc [20][22].

3.4 CRITERIA OF CHOOSING MODULATION SCHEMES The essence of digital modem design is to efficiently transmit digital bits and recover them from corruptions from the noise and other channel impairments[20]. There are three primary criteria of choosing modulation schemes: power efficiency, bandwidth efficiency, and system complexity.

3.4.1 POWER EFFICIENCY The bit error rate, or bit error probability of a modulation scheme is inversely related to Eb/No, the bit energy to noise spectral density ratio[20]. For example, Pb of ASK in the AWGN channel is given by ൌ ሺට

ʹ

ሻ

«««««««««

Where Eb is the average bit energy, No is the noise power spectral density (PSD), and Q(x) is the Gaussian integral, sometimes referred to as the Qfunction. It is defined as ͳ

ሺሻ ൌ ‫׬‬

ξʹɎ

ʹ

െ ««««««««

This is a monotonically decreasing function of x. Therefore the power efficiency of a modulation scheme is defined straightforwardly as the required Eb/No for a certain bit error probability (Pb) over an AWGN channel. Pb = 10-5 is usually used as the reference bit error probability.

ϲϵ

3.4.2 BANDWIDTH EFFICIENCY The determination of bandwidth efficiency is a bit more complex. The bandwidth efficiency is defined as the number of bits per second that can be transmitted in one Hertz of system bandwidth. Obviously it depends on the requirement of system bandwidth for a certain modulated signal. For example, the one-sided power spectral density of an ASK signal modulated by an equiprobable independent random binary sequence is given by Ȳ ሺሻ ൌ

ʹ Ͷ

ʹ ȁሺ െ ሻȁ ൅

ʹ Ͷ

Ɂሺ െ ሻ

««««

and is shown in Figure 3.3, where T is the bit duration, A is the carrier amplitude, and fc, is the carrier frequency. From the figure we can see that the signal spectrum stretches from -WR7KXVWRSHUIHFWO\WUDQVPLWWKH signal an infinite system bandwidth is required, which is impractical. The practical system bandwidth requirement is finite, which varies depending on different criteria. For example, in Figure 3.3, most of the signal energy concentrates in the band between two nulls, thus a null-to-null bandwidth requirement seems adequate [22]. Three bandwidth efficiencies used in the literature are as follows:

Figure 3.3: Power spectral density of ASK. 3.4.3 SYSTEM COMPLEXITY System complexity refers to the amount of circuits involved and the technical difficulty of the system. Associated with the system complexity is the cost of manufacturing, which is of course a major concern in

ϳϬ

choosing a modulation technique. Usually the demodulator is more complex than the modulator. Coherent demodulator is much more complex than noncoherent demodulator since carrier recovery is required. For some demodulation methods, sophisticated algorithms like the Viterbi algorithm are required.

3.5 OVERVIEW OF DIGITAL MODULATION SCHEMES To provide an overview, It is listed the abbreviations of digital modulations that will cover in a relationship tree diagram in Figure 3.4. Some of the schemes can be derived from more than one "parent" scheme. The schemes where differential encoding can be used are labeled by letter D and those that can be noncoherently demodulated are labeled with a letter N. All schemes can be coherently demodulated. The modulation schemes listed in the tree are classified into two large categories: constant envelope and non-constant envelope. Under constant envelope class, there are three subclasses: FSK, PSK, and CPM. Under non-constant envelope class, there are three subclasses: ASK, QAM and other non-constant envelope modulations. Among the listed schemes ASK, PSK and FSK are basic modulations and MSK, GMSK, CPM, MHPM and QAM, etc.[20] are advanced schemes. The advanced schemes are variations and combinations of the basic schemes. The constant envelope class is generally suitable for communication systems whose power amplifiers must operate in the nonlinear region of the input-output characteristic in order to achieve maximum amplifier efficiency. An example is the TWTA (traveling wave tube amplifier) in satellite communications. However, the generic FSK schemes in this class are inappropriate for satellite application since they have very low bandwidth efficiency in comparison with PSK schemes. Binary FSK is

ϳϭ

used in the low-rate control channels of first generation cellular systems, AMPS (advance mobile phone service of US.) and ETACS (European total access communication system). The data rates are 10 Kbps for AMPS and 8 Kbps for ETACS. The PSK schemes, including BPSK, QPSK, OQPSK, and MSK have been used in satellite communication systems. 7KH ʌ-QPSK is worth special attention due to its ability to avoid 1800 abrupt phase shift and to enable differential demodulation[20]. It has been used in digital mobile cellular systems, such as the United States digital cellular (USDC) system.

Figure 3.4: Digital Modulation Tree. After 4G. The PSK schemes have constant envelope but discontinuous phase transitions from symbol to symbol. The CPM schemes have not only constant envelope, but also continuous phase transitions. Thus they have

ϳϮ

less side lobe energy in their spectra in comparison with the PSK schemes. The CPM class includes LREC, LRC, LSRC, GMSK and TFM. Their differences lie in their different frequency pulses which are reflected in their names. For example, REC means the Frequency pulse is a rectangular pulse with a length of L symbol periods. MSK and GMSK are two important schemes in CPM class. MSK is a special case of CPFSK, but it also can be derived from OQPSK with extra sinusoidal pulse-shaping. MSK has excellent power and bandwidth efficiency. Its modulator and demodulator are also not too complex. MSK has been used in NASA's Advanced Communication Technology Satellite (ACTS). GMSK has a Gaussian frequency pulse. Thus it can achieve even better bandwidth efficiency than MSK. GMSK is used in the US cellular digital packet data (CDPD) system and European GSM (global system for mobile communication) system. MHPM is worth special attention since it has better error performance than single-h CPM by cyclically varying the modulation index h. The generic nonconstant envelope schemes, such as ASK and QAM, are generally not suitable for systems with nonlinear power amplifiers. However QAM, with a large signal constellation, can achieve extremely high bandwidth efficiency. QAM has been widely used in modems used in telephone networks, such as computer modems. QAM can even be considered for satellite systems. In this case, however, back-off in TWWs input and output power must be provided to ensure the linearity of the power amplifier. The third class under nonconstant envelope modulation includes quite a few schemes. These are primarily designed for satellite applications since they have very good bandwidth efficiency and the amplitude variation is minimal. All of them except QPSK are based on 2Ts amplitude pulse

ϳϯ

shaping and their modulator structures are similar to that of OQPSK. The scheme QPSK is based on four orthogonal car.

3.6 FACTORS OF OFDM TRANSMISSION 3.6.1 BIT ERROR RATE In a digital transmission, the bit error rate or bit error ratio (BER) is the number of received bits that have been altered due to noise, interference and distortion, divided by the total number of transferred bits during a studied time interval.[16] BER is the percentage of bits with errors divided by the total number of bits that have been transmitted, received or processed over a given time period. The rate is typically expressed as 10 to the negative power. For example, four erroneous bits out of 100,000 bits transmitted would be expressed as 4 x 10 -5, or the expression 3 x 10-6 would indicate that three bits were in error out of 1,000,000 transmitted. BER is the digital equivalent to signal-to-noise ratio in an analog system. In digital transmission, BER is a unitless performance measure, often expressed as a percentage number. As an example, assume this transmitted bit sequence: 0 1 1 0 0 0 1 0 1 1, and the following received bit sequence: 0 0 1 0 1 0 1 0 0 1, The BER is in this case 3 incorrect bits (underlined) divided by 10 transferred bits, resulting in a BER of 0.3 or 30%. The bit error probability pe is the expectation value of the BER. The BER can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long studied time interval and a high number of bit errors.

ϳϰ

3.6.1.1 BIT ERROR RATE (BER) DEFINITION AND BASICS As the name implies, a bit error rate is defined as the rate at which errors occur in a transmission system [17]. This can be directly translated into the number of errors that occur in a string of a stated number of bits. The definition of bit error rate can be translated into a simple formula: BER

=

number of errors / total number of bits sent

If the medium between the transmitter and receiver is good and the signal to noise ratio is high, then the bit error rate will be very small - possibly insignificant and having no noticeable effect on the overall system. However if noise can be detected, then there is chance that the bit error rate will need to be considered. The main reasons for the degradation of a data channel and the corresponding bit error rate, BER is noise and changes to the propagation path (where radio signal paths are used). Both effects have a random element to them, the noise following a Gaussian probability function while the propagation model follows a Rayleigh model. This means that analysis of the channel characteristics are normally undertaken using statistical analysis techniques. For fiber optic systems, bit errors mainly result from imperfections in the components used to make the link. These include the optical driver, receiver, connectors and the fiber itself. Bit errors may also be introduced as a result of optical dispersion and attenuation that may be present. Also noise may be introduced in the optical receiver itself. Typically these may be photodiodes and amplifiers which need to respond to very small changes and as a result there may be high noise levels present [18]. Another contributory factor for bit errors is any phase jitter that may be present in the system as this can alter the sampling of the data.

ϳϱ

3.6.1.2 BER AND EB/NO Signal to noise ratios and Eb/No figures are parameters that are more associated with radio links and radio communications systems. In terms of this, the bit error rate, BER, can also be defined in terms of the probability of error or POE. The determine this, three other variables are used. They are the error function, erf, the energy in one bit, Eb, and the noise power spectral density, No.[19] It should be noted that each different type of modulation has its own value for the error function. This is because each type of modulation performs differently in the presence of noise. In particular, higher order modulation schemes (e.g. 64QAM, etc) that are able to carry higher data rates are not as robust in the presence of noise. Lower order modulation formats (e.g. BPSK, QPSK, etc.) offer lower data rates but are more robust. The energy per bit, Eb, can be determined by dividing the carrier power by the bit rate and is a measure of energy with the dimensions of Joules. No is a power per Hertz and therefore this has the dimensions of power (joules per second) divided by seconds). Looking at the dimensions of the ratio Eb/No all the dimensions cancel out to give a dimensionless ratio. It is important to note that POE is proportional to Eb/No and is a form of signal to noise ratio.

3.6.1.3 FACTORS AFFECTING THE BER It can be seen from using Eb/No, that the bit error rate, BER can be affected by a number of factors. By manipulating the variables that can be controlled it is possible to optimize a system to provide the performance levels that are required. This is normally undertaken in the design stages of a data transmission system so that the performance parameters can be adjusted at the initial design concept stages.[16]

ϳϲ

In a communication system, the receiver side BER may be affected by transmission channel noise, interference, distortion, bit synchronization problems, attenuation, wireless multipath fading, etc. The BER may be improved by choosing a strong signal strength (unless this causes cross-talk and more bit errors), by choosing a slow and robust modulation scheme or line coding scheme, and by applying channel coding schemes such as redundant forward error correction codes. The transmission BER is the number of detected bits that are incorrect before error correction, divided by the total number of transferred bits (including redundant error codes). The information BER, approximately equal to the decoding error probability, is the number of decoded bits that remain incorrect after the error correction, divided by the total number of decoded bits (the useful information). The interference levels present in a system are generally set by external factors and cannot be changed by the system design. However it is possible to set the bandwidth of the system. By reducing the bandwidth the level of interference can be reduced. However reducing the bandwidth limits the data throughput that can be achieved. It is also possible to increase the power level of the system so that the power per bit is increased. This has to be balanced against factors including the interference levels to other users and the impact of increasing the power output on the size of the power amplifier and overall power consumption and battery life, etc. It is necessary to balance all the available factors to achieve a satisfactory bit error rate. Normally it is not possible to achieve all the requirements and some trade-offs are required. However, even with a bit error rate below what is ideally required, further trade-offs can be made in terms of the levels of error correction that are introduced into the data being transmitted.

ϳϳ

Since BER is the main criteria of choosing a modulation technique. BER for different modulation techniques are simulated in chapter 5.

3.6.2 PAPR Theoretically, large peaks in OFDM system can be expressed as Peak-toAverage Power Ratio, or referred to as PAPR, in some literatures, also written as PAR. It is usually defined as [25]: ൌ

ൌ ͳͲͳͲ

ሾȁ ȁʹ ሿ ሾȁ ȁʹ ሿ

«««««

Where ܲ‫ ݇ܽ݁݌‬represents peak output power, ܲܽ‫ ݃ܽݎ݁ݒ‬means average output power. ‫ ܧ‬Â GHQRWHV WKH H[SHFWHG YDOXH ‫ ݊ݔ‬represents the transmitted OFDM signals which are obtained by taking IFFT operation on modulated input symbols ܺ݇.[26] Mathematical, ‫ ݊ݔ‬is expressed as: ൌ

ͳ ξ

σെͳ ൌͲ

««««««

For an OFDM system with N sub-carriers, the peak power of received signals is N times the average power when phase values are the same. The PAPR of baseband signal will reach its theoretical maximum at (݀‫)ܤ‬ =10log ܰ. For example, for a 16 sub-carriers system, maximum PAPR is 12 dB. Nevertheless, this is only a theoretical hypothesis. In reality the probability of reaching this maximum is very low. The special case happens when signal sub-carriers are modulated by symbols which have the same initial phase. Another commonly used parameter is the Crest Factor (CF), which is defined as the ratio between maximum amplitude of OFDM signal ‫ ݐ ݏ‬and root-mean-square (RMS) of the waveform. The CF is defined as [25]: ൫ሺሻ൯ ൌ

༌ሾȁሺሻȁሿ ሾȁȁሺሻȁʹ ȁሿ

ൌ ξ

«««««««

ϳϴ

In most cases, the peak value of signal ‫ ݐ ݔ‬is equals to maximum value of its envelope (‫ )ݐ‬. Therefore, PAPR performance of OFDM signals is commonly measured by certain characterization constants which are related to probability. Since PAPR is the main bottleneck OFDM technique. The broad description about PAPR and its reduction techniques are given in chapter 4 and most efficient PAPR reduction technique SLM is simulated in chapter 6. 3.6.3 ISI In an OFDM signal the amplitude and phase of the subcarrier must remain constant over the period of the symbol in order for the subcarriers to maintain orthogonality. If they are not constant it means that the spectral shape of the subcarriers will not have the correct sinc shape, and thus the nulls will not be at the correct frequencies, resulting in Inter-Carrier Interference. At the symbol boundary the amplitude and phase change suddenly to the new value required for the next data symbol. In multipath environments ISI causes spreading of the energy between the symbols, resulting in transient changes in the amplitude and phase of the subcarrier at the start of the symbol. The length of these transient effects corresponds to the delay spread of the radio channel. The transient signal is a result of each multipath component arriving at slightly different times, changing the received subcarrier vector. 3.6.4 PHASE NOISE Phase noise effects introduced by the local oscillator in any receiver can only be ameliorated by improving the performance of the oscillator itself, with the associated cost increase. Hence the importance of determining how much phase noise a receiver can withstand while maintaining the required performance [12].

ϳϵ

Phase noise can be interpreted as a parasitic phase modulation in the RVFLOODWRU¶V VLJQDO ZKLFKLGHDOO\ ZRXOG EH D XQLTXH FDUULHU ZLWK FRQVWDQW amplitude and frequency. It has been modeled for simulation purposes as a phase modulation of the carrier [12]. The modulating signal is a zero mean white Gaussian random process ࢥw (n), with variance ߪ ʹ ‫ ݓ‬. Its autocorrelation function is given by: ܴ߶ ‫ ݓ‬ሺ݇ሻ ൌ ߪ ʹ ‫ ݓ‬Ǥ ߜͻ݇ሻ

««««

And its power spectral density: െ݆ ʹߨ݂݇ ൌ ߪ‫ʹݓ‬ ܵ߶ ‫ ݓ‬ሺ݂ሻ ൌ σ ݇ൌെ ܴ߶ ‫ ݓ‬ሺ݇ሻ Ǥ ݁

««««

It has been low pass filtered with an impulse response h LPF(n), so that its power spectral density becomes: ܵ߶ ሺ݂ሻ ൌ ܵ߶ ‫ ݓ‬ሺ݂ሻǤ ȁ‫ ܨܲܮܪ‬ሺ݂ሻȁʹ «««« In this way we can analyze the influence of the phase noise bandwidth (given by 3 dB-bandwidth of the filter) and its correlation characteristics in the signal quality. We have found it useful to compare this phase noise bandwidth and the OFDM inter-FDUULHU VSDFLQJ ¨I % » N, Where is the number of OFDM sub-carriers and the total available bandwidth. 3.7 CONCLUSION There are several modulation techniques for OFDM. In this chapter we try to give an overall idea about those. In chapter 5 we will discuss broadly along with their mathematical analysis and simulate the BER for each of them. In this chapter we also give an idea about the transmission factors of OFDM on which the performance of OFDM is depend longer. In this chapter we briefly discuss about the major problem of OFDM that is PAPR. In chapter 4 and chapter 6 we give extensive discussion about PAPR and the reduction techniques of PAPR problem along with simulation.

ϴϭ

CHAPTER 4 PAPR PROBLEM IN OFDM AND REDUCTION TECHNIQUES

4.1 INTRODUCTION OFDM has several properties which make it an attractive modulation scheme for high speed transmission links. Powerful channel equalization is not needed to combat ISI and if differential modulation is applied, no channel estimation is required at all. Thus, the complexity of OFDM systems can be much lower compared with a single carrier transmission system. One major difficulty about OFDM is its large peakto-average (PAP) ratio which distorts the signal if the transmitter contains nonlinear components such as power amplifiers (PAs) [25]. The nonlinear effects on the transmitted OFDM symbols are spectral spreading, intermodulation, and changing the signal constellation. In other words, the nonlinear distortion causes both in-band and out-of-band interference to signals. The in-band interference increases the BER of the received signal through warping of the signal constellation and inter-modulation while the out-of-band interference causes adjacent channel interference through spectral spreading. The latter is what prevents the usage of OFDM in many systems even if the in-band interference is tolerable. Therefore the PAs requires a back off which is approximately equal to the PAPR for distortion

less

transmission. This

decreases

the

efficiency

amplifiers. Therefore, reducing the PAPR of practical interest.

for

ϴϮ

4.2 PAPR DEFINITION Theoretically, large peaks in OFDM system can be expressed as Peak-toAverage Power Ratio, or referred to as PAPR, in some literatures, also written as PAR. It is usually defined as [25]: ܲ‫ ܴܲܣ‬ൌ

ܲ ‫݇ܽ݁݌‬ ܲܽ‫݁݃ܽݎ݁ݒ‬

ൌ ͳͲ݈‫Ͳͳ݃݋‬

݉ܽ‫ ݔ‬ሾȁ‫ ݊ ݔ‬ȁʹ ሿ ‫ܧ‬ሾȁ‫ ݊ ݔ‬ȁʹ ሿ

««««««««

Where ܲ‫ ݇ܽ݁݌‬represents peak output power, ܲܽ‫ ݁݃ܽݎ݁ݒ‬means average output power. ‫ ܧ‬Â GHQRWHV WKH H[SHFWHG YDOXH ‫ ݊ݔ‬represents the transmitted OFDM signals which are obtained by taking IFFT operation on modulated input symbols ܺ݇. Mathematical, ‫ ݊ݔ‬is expressed as: ‫ ݊ݔ‬ൌ

ͳ ξܰ

ܰെͳ σ‫ܭ‬ൌͲ ܺ݇ ܹܰ݊݇

«««««

For an OFDM system with N sub-carriers, the peak power of received signals is N times the average power when phase values are the same. The PAPR of baseband signal will reach its theoretical maximum at (݀‫)ܤ‬ =10log ܰ. For example, for a 16 sub-carriers system, maximum PAPR is 12 dB. Nevertheless, this is only a theoretical hypothesis. In reality the probability of reaching this maximum is very low [41]. Fig. 4.1 shows the amplitude characteristic of an OFDM system with 16 sub-carriers. According to the graph, it can be seen that the maximum magnitude of the OFDM signals is less than the upper limit value 16 and corresponding PAPR is also lower than the theoretical maximum12dB.

Figure 4.1: An OFDM signal waveform in time domain. The special case happens when signal sub-carriers are modulated by symbols which have the same initial phase. Assuming that input binary sequence contains 1 for the whole sequence. After PSK constellation mapping and IFFT operation, instant power reaches its theoretical

ϴϯ

maximum [41]. Fig. 4.2 shows the result when input binary sequence contains 16 1, denoted by [1111111111111111]. In this scenario, the maximum amplitude reaches the value of 16. The PAPR can be calculated from (݀‫= )ܤ‬10log ܰ and in this case it is 12dB.

Figure 4.2: High PAPR when sub-carriers are modulated by same symbols. By observing the simulation result in Fig. 4.2, we can make a conclusion that the amplitude of OFDM signal reaches its peak value when the input data sequence has a larger consistency. At the same time, the maximum PAPR value will be reached as well. Another commonly used parameter is the Crest Factor (CF), which is defined as the ratio between maximum amplitude of OFDM signal ‫ ݐ ݏ‬and root-mean-square (RMS) of the waveform. The CF is defined as [26]: ‫ܨܥ‬൫‫ݏ‬ሺ‫ݐ‬ሻ൯ ൌ

༌ ሾȁ‫ݏ‬ሺ‫ݐ‬ሻȁሿ ‫ܧ‬ሾȁȁ‫ݏ‬ሺ‫ݐ‬ሻȁʹ ȁሿ

ൌ ξܲ‫ܴܲܣ‬

««««««

In most cases, the peak value of signal (‫ )ݐ‬is equals to maximum value of its envelope (‫ )ݐ‬. Therefore, PAPR performance of OFDM signals is commonly measured by certain characterization constants which are related to probability. 4.3 INFLUENCING FACTORS OF PAPR From the previous sections, it was shown that PAPR is closely related to modulation schemes, number of sub-carriers and oversampling rate. 1. Modulation schemes

ϴϰ

Different modulation schemes produce different PAPR performance. From CCDF curves which are processed by several commonly used modulation schemes like BPSK, QPSK, 16QAM and 64QAM with the number of subcarriers N=128. Results show that there is only small difference between different modulation schemes. Thus, different modulation schemes have minimum influence on PAPR performance [25]. 2. Number of sub-carriers Different number of sub-carrier results in different PAPR performances due to the varying information carried. When the number of sub-carriers increases, the PAPR also increase. When modulation scheme set as QPSK mode, the PAPR exceeds 10 dB accounts for only 0.1% of transmitted OFDM signals when the sub-carrier number is 64, approximately. But when the sub-carrier number rises up to 256, the PAPR exceeds 10 dB accounts for almost 1% of transmitted OFDM signals. Therefore, the number of sub-carrier is a very important influence factor on the PAPR [25]. 3. Oversampling rate In real implementation, continuous-time OFDM signal cannot be described precisely due to the insufficient N points sampling. Some of the signal peaks may be missed and PAPR reduction performance is unduly accurate [16]. To avoid this problem, oversampling is usually employed, which can be realized by taking L·N point IFFT/FFT of original data with (L-1)·N zero-padding operation. Over-sampling plays an important role for reflecting the variation features of OFDM symbols in time domain. For a fixed probability, higher over-sampling rate leads to higher PAPR value and good PAPR reduction performance. 4.4 WHY PAPR REDUCTION IN OFDM SYSTEM The OFDM technique divides the total bandwidth into many narrow subchannels and sends data in parallel. It has various advantages, such as high

ϴϱ

spectral efficiency, immunity to impulse interference and, frequency selective fading without having powerful channel equalizer [32] [41]. But one of the major drawbacks of the OFDM system is high PAPR. OFDM signal consists of lot of independent modulated subcarriers, which are created the problem of PAPR. It is impossible to send this high peak amplitude signals to the transmitter without reducing peaks. So we have to reduce high peak amplitude of the signals before transmitting.

4.5 PAPR REDUCTION TECHNIQUES There have been many new approaches developed during the last few years. Several PAPR reduction techniques have been proposed in the literature. These techniques are divided into two groups [25] [32]. These are signal scrambling techniques and signal distortion techniques. The signal scrambling techniques are: Block coding Selective Level Mapping (SLM) Partial Transmit Sequences (PTS) Signal scrambling techniques work with side information which minimized the effective throughput since they commence redundancy. Signal distortion techniques introduce band interference and system complexity also. Signal distortion techniques minimize high peak dramatically by distorting signal before amplification. The signal distortion techniques are: Clipping Peak windowing Peak cancellation Peak power suppression Weighted multicarrier transmission

ϴϲ

4.5.1 SIGNAL SCRAMBLING TECHNIQUES 4.5.1.1 BLOCK CODING TECHNIQUES Coding techniques can be applied for signal scrambling, M sequences, Golay complementary sequences, Shapiro-Rudin sequences codes can be used to reduce the PAPR efficiently [29]. The basic premise is that of all possible message symbols, only those with low peak power will be chosen by coding as valid code-words for transmission. By doing so, we do not introduce any distortion to the signals. If we have N subcarriers, they are represented by 2N bits using QPSK modulation and thus 22N messages. Using the whole message space corresponds to zero bits of redundancy. Using only half of the messages corresponds to one bit of redundancy. The remaining message space is then divided in half again and this process continues until N bits of redundancy have been allocated which corresponds to a rate one-half code for N carriers. When the number of carriers is high, increasing the redundancy beyond a rate onehalf code yield a diminishing return and the absolute limit on peak power improvement is when 2N ± 4 bits are allocated to redundancy and only 16 messages, which have the lowest PAPR, are left to be transmitted. The PAPR for up to 15 carriers for different bits of redundancy have been tabulated and the table is included below (note: in the graph, the maximum PAPR is set to N instead of 2N). Large PAPR reduction can be achieved if the long information sequence is separated into different sub blocks, and all sub block encoded with System on a Programmable Chip (SOPC) [29]. There are many likely spaces, where the odd parity checking bits can be put into each frame to minimize PAPR. For further minimization of PAPR, redundant bit location optimized sub-block coding (RBLO-SBC) optimizes these locations redundant Combination optimized sub-block coding scheme (COSBC) optimizes the combination of the coded sub-blocks,

ϴϳ

where two coding schemes instead of one is used to encode the same information source.

4.5.1.2 BLOCK CODING SCHEME WITH ERROR CORRECTION This Block coding scheme with Error Correction has been proposed by Ahn and et.al in [29] to introduce a new block coding proposal for minimization of peak to average power ratio (PAPR) of an Orthogonal Frequency Division Multiplexing (OFDM) system. Block coding has error correction capability. In block coding method, the OFDM symbol can be reduced by selecting only those code words with lower PAPR. In this paper, the key object of the method is proposed that properly designed block codes can not only minimize the PAPR, but also give error correction capability. A k bit data block (e.g. 4-bit data) is encoded by a (n, N EORFNFRGHZLWKDJHQHUDWRUPDWUL[µ*¶LQWKHWUDQVPLWWHURIWKHV\VWHP Followed by the phase rotator vector b to produce the encoded output x=a.G+b(mod 2). To achieve the accurate generator matrix and phase rotator vector that make sure the minimum PAPR for the OFDM system, check all the 2n codes and choose only 2k codes that obtain the minimum 3$35$IWHUWKDWJHQHUDWRUPDWUL[µ*¶DQGWKHSKDVHURWDWRUYHFWRUµE¶DUH produced; which are used mapping between these symbols combination DQG LQSXW GDWD YHFWRU µD¶ 7KH FRQYHUVH IXQFWLRQV RI WKH WUDQVPLWWHU DUH H[HFXWHG LQ WKH UHFHLYHUV\VWHP 7KH SDULW\ FKHFN PDWUL[ µ+¶ LV DFKLHYHG from the generator matrix µ*¶ ZLWK DQ H[FHSWLRQ WKDW WKH HIIHFW RI WKH phase rotator vector b is removed before calculations of syndromes. Contrasting the method in [32], which only presents error detection; this method can improve the overall system performance and provides error correction capability.

ϴϴ

4.5.1.3 SELECTED MAPPING 7KH &&') RI WKH RULJLQDO VLJQDO VHTXHQFH¶V 3$35 DERYH D WKUHVKROG PAPR0 is written as ܲ‫ܴܲܣܲ > ܴܲܣܲ ݎ‬0. Thus for K statistical independent signal waveforms, CCDF can be rewritten as [{ܲ‫> ܴܲܣ‬ ܲ‫ܴܲܣ‬0}], so that the probability of PAPR that exceeds the same threshold will drop to a small value [36]. SLM is very efficient technique for PAPR reduction. The broad description and simulation of SLM is given in chapter 6.

4.5.1.4 PARTIAL TRANSMIT SEQUENCE Partial Transmit Sequence (PTS) algorithm was first proposed by Müller S H, Huber J B [28][29], which is a technique for improving the statistics of a multi-carrier signal. The basic idea of partial transmit sequences algorithm is to divide the original OFDM sequence into several subsequences, and for each sub-sequence, multiplied by different weights until an optimum value is chosen. The details of PTS technique is given in chapter 6.

4.5.1.5 INTERLEAVING TECHNIQUE Interleaving technique has been proposed by Jayalath and Tellambura [32], for reduction peak to average power ratio of an OFDM transmission. The notion that highly correlated data structures have large PAPR can be reduced, if long correlation pattern is broken down. The basic idea in adaptive interleaving is to set up an initial terminating threshold. PAPR value goes below the threshold rather than seeking each interleaved sequences. The minimal threshold will compel the adaptive interleaving (AL) to look for all the interleaved sequences. The main important of the scheme is that it is less complex than the PTS technique but obtains

ϴϵ

comparable result. This method does not give the assurance result for PAPR reduction.

4.5.1.6 TONE RESERVATION (TR) Tone Reservation (TR) method is proposed for PAPR reduction [32]. The main idea of this method is to keep a small set of tones for PAPR reduction. This can be originated as a convex problem and this problem can be solved accurately. The amount of PAPR reduction depends on some factors such as number of reserved tones, location of the reserved tones, amount of complexity and allowed power on reserved tones. This method explains an additive scheme for minimizing PAPR in the multicarrier communication system. It shows that reserving a small fraction of tones leads to large minimization in PAPR ever using with simple algorithm at the transmitter of the system without any additional complexity at the receiver end. Here, N is the small number of tones, reserving tones for PAPR reduction may present a non±negligible fraction of the available bandwidth and resulting in a reduction in data rate. The advantage of TR method is that it is less complex, no side information and also no additional operation is required at the receiver of the system. Tone reservation method is based on adding a data block and time domain signal. A data block is dependent time domain signal to the original multicarrier signal to minimize the high peak. This time domain signal can be calculated simply at the transmitter of system and stripped off at the receiver.

4.5.1.7 TONE INJECTION (TI) Tone Injection (TI) method has been recommended by Muller, S.H., and Huber, J.B. [34]. This technique is based on general additive method for PAR reduction. Using an additive method achieves PAPR reduction of

ϵϬ

multicarrier signal without any data rate loss. Note that Tone injection (TI) uses a set of equivalent constellation points for an original constellation points to reduce PAPR. The main idea behind this method is to increase the constellation size. Then, each point in the original basic constellation can be mapped into several equivalent points in the extended constellation, since all information elements can be mapped into several equivalent constellation points. These additional amounts of freedom can be utilized for PAPR reduction. This method is called Tone Injection method because of replacing the points in the basic constellation for the new points in the larger constellation which corresponds to injecting a tone of the proper phase and frequency in the multi-carrier symbol. The drawbacks of this method are; need to side information for decoding signal at the receiver side, and cause extra IFFT operation which is more complex.

4.5.2 SIGNAL DISTORTION TECHNIQUES 4.5.2.1 PEAK WINDOWING The peak windowing method has been suggested by Van Nee and Wild [37]. This method, proposes that it is possible to remove large peaks at the cost of a slight amount of self interference when large peaks arise infrequently. Peak windowing reduces PAPRs at the cost of increasing the BER and out-of-band radiation. Clipping is a one kind of simple introduces PAPR reduction technique which is self interference. The technique of peak windowing offers better PAPR reduction with better spectral properties. (Peak Windowing technique provides better PAPR reduction with better spectral properties than clipping). In peak windowing method we multiply large signal peak with a specific window, for example; Gaussian shaped window, cosine, Kaiser and Hamming window. In view of the fact that the OFDM signal is multiplied with several of these windows, consequential spectrum is a convolution of

ϵϭ

the original OFDM spectrum with the spectrum of the applied window. Thus, the window should be as narrow band as possible, conversely the window should not be too long in the time domain because various signal samples are affected, which results an increase in bit error rate (BER). Windowing method, PAPRs can be obtained to 4dB which from the number of independent subcarriers. The loss in signal-to-noise ratio (SNR) due to the signal distortion is limited to about 0.3dB.

4.5.2.2 ENVELOPE SCALING The Envelope Scaling technique has been proposed by Foomooljareon and Fernando in [18]. They proposed a new algorithm to reduce PAPR by scaling the input envelope for some subcarriers before they are sent to IFFT. In this paper, they used 256 subcarriers with QPSK modulation technique, so that envelopes of all the subcarriers are equal. The key idea of this scheme is that the input envelope in some sub carrier is scaled to achieve the smallest amount of PAPR at the output of the IFFT. Thus, the UHFHLYHURIWKHV\VWHPGRHVQ¶WQHHGDQ\VLGHLQIRUPDWLRQIRUGHFRGLQJWKH receiver sequence. This scheme is appropriate for QPSK modulation; the envelopes of all subcarriers are equal. Results show that PAPR can be reduced significantly at around 4 dB. Finally the system of single scaling factor and number of clusters equal to number of sub carriers is recommended.

4.5.2.3 PEAK REDUCTION CARRIER Peak Reduction Carrier has been proposed by Tan and Wassell to use of the data bearing peak reduction carriers (PRCs) to reduce the effective PAPR in the OFDM system [29]. This scheme includes the use of a higher order modulation scheme to represent a lower order modulation symbol. This permits the amplitude and

ϵϮ

phase of the PRC to be positioned within the constellation region symbolizing the data symbol to be transmitted. For example, to use a PRC that employs a 16-PSK constellation to carry QPSK data symbol, the 16phases of the 16-PSK constellations are divided into four regions to represent the four different values of the QPSK symbol. This scheme is appropriate for PSK modulation; where the envelopes of all subcarriers are equal. When the QAM modulation scheme will be implemented in the OFDM system, the carrier envelope scaling will result in the serious BER degradation. To limit the bit error rate (BER) degradation, amount of the side information would also be excessive when the number of subcarriers is large.

4.5.2.4 CLIPPING AND FILTERING One of the simple and effective PAPR reduction techniques is clipping, which cancels the signal components that exceed some unchanging amplitude called clip level. However, clipping yields distortion power, which called clipping noise, and expands the transmitted signal spectrum, which causes interfering [30]. Clipping is nonlinear process and causes inband noise distortion, which causes degradation in the performance of bit error rate (BER) and out-of-band noise, which decreases the spectral efficiency [32]. Clipping and filtering technique is effective in removing components of the expanded spectrum. Although filtering can decrease the spectrum growth, filtering after clipping can reduce the out-of-band radiation, but may also cause some peak re-growth, which the peak signal exceeds in the clip level [33]. The technique of iterative clipping and filtering reduces the PAPR without spectrum expansion. However, the iterative signal takes long time and it will increase the computational complexity of an OFDM transmitter [30]. But without performing interpolation before clipping

ϵϯ

causes it out-of-band. To avoid out-of-band, signal should be clipped after interpolation. However, this causes significant peak re-growth. So, it can use iterative clipping and frequency domain filtering to avoid peak regrowth.

4.6 CONCLUSION In this chapter we discuss mathematics of PAPR and various PAPR reduction techniques. The techniques are not same efficient for all case. Each technique is efficient for each type of system. In chapter 6 we will discuss the simulation result of two major techniques. These are SLM and PTS.

ϵϱ

CHAPTER 5 BER OF OFDM FOR DIFFERENT MODULATION TECHNIQUES 5.1 INTRODUCTION The BER can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long studied time interval and a high number of bit errors. In this chapter we introduce the mathematics of BER. We also represent simulation techniques and discuss the simulation results of BER for modulation techniques used in OFDM. For simulation we have used MATLAB.

5.2 MATHEMATICAL DRAFT OF BER The BER is the likelihood of a bit misinterpretation due to electrical noise w(t). Considering a bipolar NRZ transmission, we have x1(t) = A + w(t) for a "1" x0(t íA + w(t) for a "0".

And

Each of x1(t) and x0(t) has a period of T. Knowing that the noise has a bilateral spectral density, x1(t) is ሺǡ And

ʹ

x0(t) is ሺെǡ

ሻ ʹ

ʹ

«««««««« ሻ

«««««««

ϵϲ

We have the likelihood of a bit misinterpretation pe = p(0 | 1)p1 + p(1 | 0)p0. ሺͳȁͲሻ ൌ ͲǤͷሺ

൅Ȝ

ඥ Τ

ሻ

ሺͲȁͳሻ ൌ ͲǤͷሺ

And

««« െȜ

ඥ Τ

ሻ

«««

:KHUHȜLVWKHWKUHVKROGRIGHFLVLRQVHWWRZKHQp1 = p0 = 0.5. We can use the average energy of the signal E = A2T to find the final expression :

ൌ ͲǤͷሺට ሻ

««««««««

5.3 BER FOR DIFFERENT TYPES OF MODULATION In this section we BER for different modulation technique and compare between them. There are several type of modulation technique. 5.3.1 DEFINITIONS For determining error-rates mathematically, some definitions will be needed:

x

Eb = Energy-per-bit

x

Es = Energy-per-symbol = kEb with k bits per symbol

x

Tb = Bit duration

x

Ts = Symbol duration

x

N0 / 2 = Noise power spectral density (W/Hz)

x

Pb = Probability of bit-error

x

Ps = Probability of symbol-error

ϵϳ

Q(x) will give the probability that a single sample taken from a random process with zero-mean and unit-variance Gaussian probability density function will be greater or equal to x. It is a scaled form of the complementary Gaussian error function΀Ϯϭ΁:

««« (5.6) The error-rates quoted here are those in additive white Gaussian noise (AWGN). These error rates are lower than those computed in fading channels, hence, are a good theoretical benchmark to compare with. 5.3.2 PHASE-SHIFT KEYING (PSK) Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave) [23]. PSK uses a finite number of phases; each assigned a unique pattern of binary digits. Usually, each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular phase [23][24]. The demodulator, which is designed specifically for the symbolset used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. This requires the receiver to be able to compare the phase of the received signal to a reference signal ² such a system is termed coherent (CPSK). 5.3.2.1 BINARY PHASE-SHIFT KEYING (BPSK) BPSK (also sometimes called PRK, Phase Reversal Keying, or 2PSK) is the simplest form of phase shift keying (PSK). It uses two phases which

ϵϵ

In Binary Phase Shift Keying, the symbols {-1,+1}are used for transmitting information. From the post, Bit error probability for BPSK modulation [37]. The bit error rate (BER) of BPSK in AWGN can be calculated as: ͳ

‫ܧ‬

ʹ

ܰ‫݋‬

ܲ‫ ܭܵܲܤ ݏ‬ൌ ݁‫݂ܿݎ‬ሺට ‫ ݏ‬ሻ

«««««

Since there is only one bit per symbol, this is also the symbol error rate.

5.3.2.1.1 SIMULATION RESULT The BER of BPSK modulation techniques are varied according to the FFT size. For different FFT size it represents different BER [24]. Table 1 summarizes the important simulation parameter used. These parameters are taken from various research work and change the as needed [16][19][39][40]. TABLE II Simulation Parameter for BPSK FFT Size

8,16,64(For different size)

Number of Data Subcarriers

52

Number of Bits Per OFDM

52

Symbol Number of Symbols

10^5

Bit to Noise Ratio

[0:10]

The BER of BPSK for different FFT size is shown in following figure:

ϭϬϬ

Figure 5.2: Bit Error Rate for BPSK using OFDM for 8-bit FFT size.

Figure 5.3: Bit Error Rate for BPSK using OFDM for 16-bit FFT size.

ϭϬϭ

Figure 5.4: Bit Error Rate for BPSK using OFDM for 64-bit FFT size. From the figure 5.2, 5.3 and 5.4 we have found that the BER rate is decrease with the increasing of signal to noise ratio but it is not fully linear. For different size of FFT the BER is different and the change is very sharp. In 8-FFT size the variation between theoretical and simulation is large. With the increasing of FT size the theoretical and simulation gap is decreased and for 64-FFT size the value of BER in simulation and theoretical is almost aligned. 5.3.2.2 BIT ERROR RATE FOR QPSK Consider that the alphabet used for a QPSK (4-4$0 LV ĮQPSK= {±1, ±1j}[37]

Figure 5.5: Constellation plot for QPSK

ϭϬϮ

Assuming that the additive noise n follows the Gaussian PDF ‫݌‬ሺ‫ݔ‬ሻ ൌ

ͳ ξʹߨߪ

݁ ʹ

െሺ‫ݔ‬െߤ ሻʹ ʹߪ ʹ

ZLWKȝ DQGߪ ʹ ൌ

ܰ‫݋‬ ʹ

Probability of real component of y rather than 0, given s2 was transmitted is where the complementary error function, ݁‫݂ܿݎ‬ሺ‫ݔ‬ሻ ൌ

ʹ െ‫ݔ݀ ʹ ݔ‬ ‫݁ ׬‬ ξߨ ‫ݔ‬

‫ܧ‬

For higher values of ‫ ݏ‬, the probability of error can be approximated as: ܰ‫݋‬

ܲܳܲܵ‫ ܭ‬ൎ ݁‫ ݂ܿݎ‬ሺට

‫ݏܧ‬ ʹܰ‫݋‬

ሻ

««««

Typical communication systems use Gray coded modulation mapping, i.e. bits represented in adjacent symbols differ by bit only [19]. When a symbol is incorrectly decoded, it typically falls into the adjacent the symbol bit. Hence, each symbol error causes one bit out of ݇ ൌ ݈‫ ʹ݃݋‬ሺ‫ܯ‬ሻ bits to be in error. So, the relation between symbol error and bit error is,ܾܲ ൌ

ܲ‫ݏ‬ ݇

With this approximation, the bit error rate equations are: ͳ

‫ܧ‬

ʹ

ܰ‫݋‬

ܾܲǡܳܲܵ‫ ܭ‬ൌ ݁‫݂ܿݎ‬ሺට ܾ ሻ

««««««

5.3.2.2.1 SIMULATION RESULT The BER for QPSK is estimated for both theoretical and simulation. For simulation here we use the number of symbol 10 5, the Es /No is[-3:20]. These parameters are taken from various research work and change the as needed [16][19][39][40]. The BER of QPSK is shown in following graph:

ϭϬϯ

Figure 5.6: Bit Error Rate for QPSK (4QAM) modulation From figure 5.6, we can easily infer that the value of BER in theoretical and simulation is not alike. The value of simulation BER is larger than that of theoretical value. We also found that with the increasing of signal to noise ratio the value of BER is decreased but not properly linear.

5.3.2.3 BIT ERROR RATE FOR 16-PSK Consider a general M-PSK modulation, where the alphabets are used. The 16-PSK constellation plot is shown in figure 5.7.

Figure 5.7: PSK constellation plot Where the additive noise n follows the Gaussian probability distribution function [23],

ϭϬϱ

5.3.2.3.1 SIMULATION RESULT The BER for 16-PSK is estimated for both theoretical and simulation. Table 2 shows the values of different parameter used for simulation. TABLE III Simulation Parameter for 16-PSK Constellation Size

16

Bits Per Symbol

4

Number of Symbols

10^6

Signal to Noise Ratio

[0:25]

Reference Phase values

[0:0.3927:5.8905]

The BER of 16-PSK is shown in figure 5.9

Figure 5.9: Bit Error rate curve for 16PSK modulation From the figure 5.9, we see that the value of BER in 16-PSK modulation is changed with the change of signal to noise ratio but the change is

ϭϬϵ

5.3.2.5.1 SIMULATION RESULT The BER for BFSK is estimated for both theoretical and simulation. Table 3 shows the values of different parameter used for simulation. These parameters are taken from various research work and change the as needed [16][19][39][40]. TABLE IV Simulation Parameter for BFSK Symbol duration

8

Sampling Instants

[0:0.125:0.99]

Number of Symbols

10^8


[0:11]

The BER probability of BFSK is shown in figure 5.12:

Figure 5.12: Bit Error Rate of FSK From the figure 5.12, we can easily infer that the value of BER in theoretical and simulation are approximately alike. In this case the BER value is not reach to lowest level with increasing Es /No. At the highest Es /No value BER is not reach to ground level. We also found that with the

ϭϭϮ

The BER for 16-QAM is depicted in the following graph:

Figure 5.14: Bit Error Rate curve for 16QAM modulation From the figure 5.14, we can easily infer that the value of BER in theoretical and simulation are approximately alike. In this case the BER value is reach to lowest level with increasing Es /No. At the highest Es /No value BER is reach to ground level. We also found that with the increasing of signal to noise ratio the value of BER is decreased non-linearly. 5.3.2.7 64-QAM To compute the symbol error rate for an M-QAM modulation, consider the 64-QAM constellation as shown in the figure below and extend it to the MQAM case.

Figure 5.15: Constellation plot for 64-QAM

ϭϭϯ

The symbol error rate for M-QAM ܲ‫ݏ‬ǡ‫ ܯܣܳܯ‬ൌ ʹ ቀͳ െ

ͳ ξ‫ܯ‬

͵

‫ܧ‬

ቁ ݁‫݂ܿݎ‬ሺටʹሺ‫ܯ‬െͳሻ ܰ‫ ݏ‬ሻ െ ቀͳ െ ‫݋‬

ʹ ξ‫ܯ‬

ͳ

͵

‫ܧ‬

‫ݏ‬ ൅ ቁ ݁‫ ʹ ݂ܿݎ‬ሺට ሻ« ‫ܯ‬ ʹሺ‫ܯ‬െͳሻ ܰ ‫݋‬

(5.25) By using this equation and substituting the value of m=64 5.3.2.7.1 SIMULATION RESULT The BER for 16-QAM is estimated for both theoretical and simulation. Table 5 shows the values of different parameter used for simulation. TABLE VI Simulation Parameter for BPSK Constellation Size

64

Normalizing Factor

0.1543

Number of Symbols

7*106


[0:30]

QAM alphabets

[-7 -1 1 7]

The BER of 64-QAM is depicted in figure 5.16.

Figure 5.16: Symbol error rate for 64-QAM modulation

ϭϭϰ

From the figure 5.16, we can found that the value of BER in theoretical and simulation are approximately alike. In this case the BER value is reach to lowest level with increasing Es /No. At the highest Es /No value BER is reach to ground level. The performance of this modulation is better than other. We also found that with the increasing of signal to noise ratio the value of BER is decreased non-linearly. 5.4 COMPARISON OF BER IN DIFFERENT MODULATION TECHNIQUES From the above discussion the comparison of BER for different modulation techniques is clear. The simulation of them is shown in figure 5.17.

Figure 5.17: Comparison of BER for Different Modulation Techniques. From the figure 5.17 we have found that the BER of OFDM for different modulation technique is different. The value of BER is higher for 32-PSK and at a minimized level in 64-QAM. The BER for 16-QAM and BPSK are approximately equal.

ϭϭϱ

5.5 CONCLUSION Bit error rate BER is a parameter which gives an excellent indication of the performance of a data link such as radio or fibre optic system. As one of the main parameters of interest in any data link is the number of errors that occur, the bit error rate is a key parameter. Knowledge of the BER also enables other features of the link such as the power and bandwidth.

ϭϭϳ

CHAPTER 6 ANALYSIS AND SIMULATION OF PAPR REDUCTION TECHNIQUES 6.1 INTRODUCTION There are several PAPR reduction techniques in OFDM. By comparing among them it is found that the SLM technique is one which is very efficient reduction techniques which can be efficiently work in large number of subcarriers. In this chapter the overall discussion of different PAPR reduction techniques is described. Also as the candidate of reduction techniques the SLM and PTS techniques are simulated using matlab codes.

6.2 OVERALL ANALYSIS OF DIFFERENT TECHNIQUES There are several techniques has been proposed in literature. Thus, it is possible to reduce the large PAPR by using the different techniques. Note that the PAPR reduction technique should be chosen with awareness according to various system requirements. From the study of different PAPR reduction techniques an overall conclusion can be drawn according to different performance parameters such as distortion, power, data rate etc, [25][28][32][41]. The overall analysis is of these techniques are given in following table which give a sharp comparison between all techniques.

ϭϭϴ

TABLE VII Comparison of PAPR Reduction Techniques Name Of

Name Of parameters

Operation required at

Schemes

Transmitter (TX) / Receiver (RX)

Clipping and

Distortion

Power

Data

less

increases

rate loss

No

No

No

Filtering Coding

TX: Clipping RX: None

Yes

No

Yes

TX: Coding or table searching RX: Decoding or table searching

Partial Transmit

Yes

No

Yes

Sequence(PTS)

TX: V times IDFTs operation RX: Side information extraction, inverse PTS

Selective

Yes

No

Yes

Mapping(SLM)

TX: M times IDFTs operation RX: Side information extraction, inverse SLM

Interleaving

Yes

No

Yes

TX: D times IDFTs operation, D-1 times interleaving RX: Side information extraction, de-

ϭϭϵ

interleaving Tone

Yes

Yes

Yes

Yes

Yes

No

Reservation (TR) Tone Injection(TI)

6.3 SELECTED MAPPING 6.3.1 PRINCIPLE OF SLM The probability of PAPR larger than a threshold z can be written as (ܲ‫ܴܲܣ‬ > ‫ ݖ‬í íH[S í] N [34] Assuming that M OFDM symbols carry the same information and that they are statistically independent of each other. In this case, the probability of PAPR greater than z is equals to the product of each independent candidDWH¶V SUREDELOLW\ >@ 7KLV SURFHVV FDQ EH written as ܲሼܲ‫ ݓ݋݈ܴܲܣ‬൐ ‫ݖ‬ሽ ൌ ሺܲሼܲ‫ ܴܲܣ‬൐ ܼሽሻ‫ ܯ‬ൌ ሺሺͳ െ ሺെ‫ݖ‬ሻሻܰ ሻ‫ܯ‬ «««««« In selected mapping method, firstly M statistically independent sequences which represent the same information are generated, and next, the resulting M statistically independent data blocks ࡿm=[ܵ݉,0,ܵ݉«ܵ݉,ܰí1]T, ݉ «‫ ܯ‬are then forwarded into IFFT operation simultaneously. Finally, at the receiving end, OFDM symbols ࢞m=[‫ݔ‬1,‫]ܰݔ«ݔ‬T

in

discrete time-domain are acquired, and then the PAPR of these M vectors are calculated separately. Eventually, the sequences ࢞ࢊ with the smallest PAPR will be elected for final serial transmission. Fig. 6.1 illustrates the basic structure of selected mapping method for suppressing the high PAPR [34].

ϭϮϬ

Figure 6.1: Basic principles of selected mapping. This method can significantly improve the PAPR performance of OFDM system.

The

reasons

behind

that

are:

Data

blocks

ࡿm=[ܵ݉,0,ܵ݉«ܵ݉,ܰí1] , ݉ «‫ ܯ‬are statistical independent, T

assuming that for a single OFDM symbol, the CCDF probability of PAPR larger than a threshold is equals to ‫݌‬. The general probability of PAPR larger than a threshold for k OFDM symbols can be expressed as ‫݌‬K . It can be verified that the new probability obtained by SLM algorithm is much smaller compared to the former. Data blocks ࡿm

are obtained by

multiplying the original sequence with M uncorrelated sequence ࡼm. The key point of selected mapping method lies in how to generate multiple OFDM signals when the information is the same. First, defined different pseudo-random sequences ࡼm=[ܲ݉,0,ܲ݉«ܲ݉,ܰí1]T, ݉ «‫ܯ‬, where ܲ݉,݊=݆݁߮݉,݊ and stands for the rotation factor, is also known as the weighting factor, is uniformly distributed in [0 2ߨ]. The N different subcarriers are modulated with these vectors respectively so as to generate candidate OFDM signals. This process can also be seen as performing dot product operation on a data block Xm with rotation factor Pm [35]

ϭϮϭ

In the reality, all the elements of phase sequence ܲ1 are set to 1 so as to make this branch sequence the original signal. The symbols in branch m is expressed as ܵ݉ ൌ ሾܺͲ ܲ݉ ǡͲ ǡ ܺͳ ܲ݉ ǡͳ ǡ ǥ ǥ Ǥ Ǥ ǡ ܺܰെͳ ܲ݉ ǡ݊ െͳ ሿܶ

m=1,2««0

«««« and then transfer these M OFDM frames from frequency domain to time domain by performing IFFT calculation. The entire process is given by ‫ ݉ݔ‬ሺ‫ݐ‬ሻ ൌ

ͳ ξܰ

σܰെͳ ܺ݊ ܲ݉ ǡ݊ Ǥ ݁ ݆ ʹߨ݊ ο݂‫ ݐ‬ǡͲ ൑ ‫ ݕ‬൑ ܰܶǡ ݉ ൌ ͳǡʹǡ ǥ ǥ Ǥ Ǥ ‫ܯ‬ Ͳ «««

Finally, the one which possess the smallest PAPR value is selected for transmission. Its mathematical expression is given as ‫ ݀ݔ‬ൌ ܽ‫ͳ݊݅݉݃ݎ‬൑݉ ൑‫ ܯ‬ሺܲ‫ܴܲܣ‬ሺ‫ ݉ݔ‬ሻሻ

««««

Where argmin (‫ )ڄ‬represent the argument of its value is minimized. At the receiver, in order to correctly demodulate the received signal, it is necessary to know which sequence is linked to the smallest PAPR among M different candidates after performing the dot product. Hence, the receiver is required to learn information about selected phase vector sequence and ensure that the vector sequence is received correctly [34]. An intuitive approach is to select the whole sequence of branch number m as side information transmitted to the receiving end. However, in practice, the process does not necessarily require the delivery of the entire vector sequence. It can be realized by sending the route number of the vector sequence instead. This is only possible when the receiving end is able to restore the random phase sequence ܲ݉ by means of look-up table or any other method. Since the side information plays a vital role for signal restoration at the receiver, channel coding is used to guarantee a reliable transmission. Once channel coding technique is adopted during the data transmission process, sending of any additional side information is not

ϭϮϮ

required. In this way, all possible routes are detected at the receiving end from which the most likely one is chosen as the optimum. Considering that the emphasis of this chapter is to explore the principle of SLM algorithm and evaluate different related factors, the recovery process of original sequence will not be discussed in detail. 6.3.2 SIMULATION OF SLM SCHEME In this part, an evaluation of factors which could influence the PAPR reduction performance is performed using Matlab simulation. Based on the principles of SLM algorithm, it is apparently that the ability of PAPR reduction using SLM is affected by the route number M and subcarrier number N. Fig. 6.2 shows the theoretical CCDF curves as a function of PAPR distribution when SLM method is used. The number of N sub-carriers is 128. M takes the value of 1 (without adopting SLM method), 2, 8, 32 and 128. It is seen in Fig. 6.2 that with increase of branch number M3$35¶V CCDF distribution gets smaller and smaller.

Figure 6.2: 7KHRUHWLFDO3$35¶V&&')FXUYHVXVLQJ6/0PHWKRG

ϭϮϯ

Therefore, simulation with different values of M and N will be conducted, and the results exhibits some desired properties of signals representing the same information [35]. 1. Comparison of PAPR reduction performance with different values of M while N is fixed at 128. Firstly from the perspectives of complexity and practicability, rotation factor is defined as ܲ݉, ‫[א‬±1,±݆]. This reduces calculation

complexity

dramatically

compared

to

performing

miscellaneous complex multiplication. The algorithm executes 10000 times, over-sampling factor is 8 and QPSK mapping is adopted as modulation scheme in each sub-carrier. Route numbers M=2, M=4, M=8, M=16 and M=32 are used. From Fig. 6.3, it can be observed that the proposed SLM method displays a better PAPR reduction performance than the original OFDM signal which is free of any PAPR reduction scheme. The probability of high PAPR is significantly decreased. Increasing M leads to the improvement of PAPR reduction performance. If the probability is set to 1% and then the CCDF curves with different M values are compared. The PAPR value of case M=2 is about 1dB smaller than the unmodified one M=1. Under the same condition, the PAPR value of case M=16 is about 3dB smaller than the original one M=1. However, from the comparison of the curve M=8 and M=16, we learned that the performance difference between these two cases is less than 0.5dB. This proves that we will not be able to achieve a linear growth of PAPR reduction performance with further increase the value of M (like M>=8), the PAPR reduction performance of OFDM signal will not be considerably improved. Furthermore, from the perspective of execution time, we can see that execution time will last longer with the increase of M. Therefore, in practical application, we usually take M=8, thereby not only improve the

ϭϮϰ

system performance, but also avoid introducing too much computational complexity so as to save the limited resource successfully.

Figure 6.3: Comparison of PAPR reduction performances with different values of M. The following conclusions can be drawn after the analysis and comparison of above groups of simulation results: 1. SLM proposal can significantly improve the PAPR distribution of OFDM system, that is, significantly reduce the presenting probability of large peak power signal. The increasing of the number of OFDM signal frames M will raise the complexity dramatically, but with benefit of small improvement of PAPR reduction performance. 2. SLM algorithm adapted to any length of FFT frame that means it can be used for different OFDM systems with different number of carriers. It is particularly suitable for the OFDM system with a large number of subcarriers (more than 128). 3. SLM can significantly improve the performance of OFDM system by reducing the PAPR, but at the same time, the price is also very clear that is

ϭϮϱ

the complexity of its implementation. Every time when applying SLM algorithm, requires calculating the M group IFFTs at the transmitter compared to only one on ordinary OFDM system, and its M of N points ܰ

IFFTs operation needs ݊݉‫ ݈ݑ‬ൌ ‫ܯ‬Ǥ ݈‫ ܰ ʹ݃݋‬complex multiplication and ʹ

ܰ

݊ܽ݀݀ ൌ ‫ܯ‬Ǥ ݈‫ ܰ ʹ݃݋‬addition, separately. ʹ

These problems pose a very heavy burden on real OFDM implementation; we need to reduce the computational complexity. Therefore, in practical application, compromise the computing complexity and improvement of performance, we usually take M@ µ'LJLWDO 9LGHR %URDGFDVWLQJ '9% )UDPLQJ 6WUXFWXUH &KDQQHO &RGLQJDQG0RGXODWLRQIRU'LJLWDO7HUUHVWULDO7HOHYLVLRQ¶(76,(XURSHDQ Telecommunications Standards Institute Std. EN 300 744, Rev. 1.4.1, Jan. 2001.

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[26] Oh-Ju Kwon and Yeong-+R+D³0XOWL-carrier PAP reduction method using sub-2SWLPDO 376 ZLWK WKUHVKROG´ IEEE Transactions on Broadcasting, June. 2003, vol. 49, no. 2, PP. 232-53 >@0RKLQGHU-DQNLUDPDQµ3HDN7R$YHUDJH3RZHU5DWLR,QSpace-Time Codes And MIMO SystemV¶$UWHFK+RXVHpp. 201. >@ / :DQJ DQG @ /HRQDUG - &LPLQL -U 1HOVRQ 5 6ROOHQEHUJHU ³3HDN-to-Average power ratio reduction of an OFDM signal using partial transmit VHTXHQFHV´IEEE Electronic Letters, vol. 4, no. 3, Mar 2000, pp. 88-86. >@%DXPO5:)LVFKHU5)+DQG+XEHU-%³5HGXFLQJ7KH3HDN-To$YHUDJH 3RZHU 5DWLR 2I 0XOWLFDUULHU 0RGXODWLRQ %\ 6HOHFWHG 0DSSLQJ´ IEEE Electronic Letters, vol. 32, no. 22, Oct 1996, pp. 2056-2057.

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chapter 5 ber of ofdm for different modulation

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