ZCT PRECODING BASED SLM TECHNIQUE FOR PAPR REDUCTION

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ZCT PRECODING BASED SLM TECHNIQUE FOR PAPR REDUCTION

LOO TWAN ZHAN

UNIVERSITI SAINS MALAYSIA

2017

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ZCT PRECODING BASED SLM TECHNIQUE FOR PAPR REDUCTION

By

LOO TWAN ZHAN

Thesis submitted in fulfillment of the requirements for the degree of

Bachelor of Engineering (Electronic Engineering)

JUNE 2017

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ACKNOWLEDGEMENTS

First and foremost, I would like to express my sincere gratitude to my supervisor as well as my thesis advisor, Dr. Aeizaal Azman bin Abd Wahab whose contribute in supporting and doing me a favour in doing researches and studies. Besides that, I would like to appreciate all the efforts, encouragement and contributions provided by him in completion of this thesis. Furthermore, my supervisor always give me advices and guide me throughout the project. Whenever I met any arise problem, he would patiently advise or give me some idea and discuss with me on how to overcome the problem, and this led to completion of the project to be easier and efficient.

In addition, a special thank you to the examiners for their professional evaluation on the final year project and the thesis. I would like to express my deepest appreciation to all the lecturers in Schools of Electrical and Electronic Engineering who provided us the possibility in completion of the project.

Last but not least, I appreciate everyone who help me either directly or indirectly in completion of the project.

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LIST OF TABLES

Table 3.1 Parameters for QAM modulation with N subcarriers ... 27 Table 3.2 Parameters for QPSK modulation with N subcarriers ... 28 Table 4.1 Plots of PAPR performance for conventional OFDM, ZCT precoded OFDM, SLM-OFDM, SLM-ZCT precoded OFDM and ZCT precoded SLM-OFDM with N=64

& V=4, 8, 16 with QPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM modulations ... 38 Table 4.2 Plots of PAPR performance for conventional OFDM, ZCT precoded OFDM, SLM-OFDM, SLM-ZCT precoded OFDM and ZCT precoded SLM-OFDM with N=256 & V=4, 8, 16 with QPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM modulations ... 46

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LIST OF FIGURES

Figure 2.1 Concept of OFDM signal: orthogonal multicarrier technique versus

conventional multicarrier technique.[11] ... 8

Figure 2.2 Multi carriers of OFDM signal[12] ... 10

Figure 2.3 A conventional OFDM system block diagram[13] ... 11

Figure 3.1 Block diagram of ZCT precoding based OFDM system ... 17

Figure 3.2 Block diagram of SLM based OFDM system ... 19

Figure 3.3 Block diagram of SLM-ZCT based OFDM system ... 20

Figure 3.4 Block diagram of ZCT-SLM based OFDM system ... 22

Figure 3.5 Flow Chart of ZCT-SLM-OFDM system... 25

Figure 3.6 Flowchart of ZCT-SLM-OFDM technique in MATLAB programme ... 27

Figure 4.1 CCDF vs PAPRo of conventional OFDM and ZCT-C-SLM-OFDM with 𝑉 = 16 ... 31

Figure 4.2 CCDF vs PAPRo of conventional OFDM and ZCT-R-SLM-OFDM with 𝑉 = 16 ... 31

Figure 4.3 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 4 for QPSK modulation ... 32

Figure 4.6 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 4 for 4-QAM modulation... 34

Figure 4.8 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 16 for 4-QAM modulation ... 35

Figure 4.11 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 16 for 16-QAM modulation ... 37 Figure 4.12 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 4, 8, 16 for 4-QAM modulation . 39

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Figure 4.21 CCDF vs PAPRo with 𝑁 = 256 & 𝑉 = 16 for 16-QAM modulation .... 45

Figure 4.22 CCDF vs PAPRo with 𝑁 = 256 & 𝑉 = 4, 8, 16 for 4-QAM modulation ... 47

Figure A.1 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 4 for 64-QAM modulation ... 51

Figure A.7 CCDF vs PAPRo with 𝑁 = 256 & 𝑉 = 4 for 64-QAM modulation... 54

Figure A.8 CCDF vs PAPRo with 𝑁 = 256 & 𝑉 = 8 for 64-QAM modulation... 54

Figure A.11 CCDF vs PAPRo with 𝑁 = 256 & 𝑉 = 8 for 256-QAM modulation ... 56 Figure A.12 CCDF vs PAPRo with 𝑁 = 256 & 𝑉 = 16 for 256-QAM modulation . 56

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LIST OF ABBREVIATIONS

CCDF : Complementary Cumulative Distribution Function ICI : Inter-carrier Interference

ISI : Inter-symbol Interference

OFDM : Orthogonal Frequency-Division Multiplexing PAPR : Peak-to-Average Power Ratio

QAM : Quadrature Amplitude Modulation

QPSK : Quadratic Phase Shift Keying SLM : Selected Mapping

ZC : Zadoff-Chu sequence

ZCT : Zadoff-Chu matrix Transform

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ABSTRAK

Frekuensi Ortogon Bahagian Pemultipleksan (OFDM) adalah skim modulasi pelbagai pembawa yang digunakan dalam komunikasi digital talian wayar dan tanpa wayar sejak beberapa tahun lalu. Fungsi OFDM ini adalah untuk mengurangkan penyebaran kelewatan, gangguan antara simbol (ISI), gangguan antara saluran (ICI) dan kekerapan pudar terpilih disebabkan oleh pelbagai arah. Walau bagaimanapun, kelemahan utama sistem OFDM adalah Nisbah Kuasa Puncak ke Kuasa Purata (PAPR) yang tinggi. PAPR adalah salah satu parameter penting untuk memastikan kecekapan penghantaran data yang tinggi. Dalam kertas ini, sistem Transformasi matriks Zadoff- Chu (ZCT) diprakodkan pemetaan pilih (SLM) berdasarkan OFDM (SLM-OFDM) dicadangkan untuk pengurangan PAPR. Teknik ini adalah berdasarkan prakod simbol buruj dengan ZCT precoder selepas pendaraban faktor putaran fasa dan sebelum Transformasi Fourier Cepat Songsang (IFFT) dalam Sistem SLM berdasarkan OFDM (SLM-OFDM). Pada peringkat awal projek tersebut, sistem parameter perlu dijelaskan.

Isyarat binari menjalani skim modulasi seperti QPSK, 4QAM, 16QAM, 64QAM dan 256QAM. Isyarat termodulat didarabkan dengan faktor fasa dan melalui ZCT dengan cara baris matriks precoder sebelum memasuki IFFT. Selepas itu, salah satu isyarat mempunyai PAPR yang paling kecil dipilih dan PAPR dinilai dengan menggunakan Pelengkap Fungsi Pengagihan Kumulatif (CCDF). Keputusan simulasi prestasi PAPR dijadualkan. Pada kadar keratan di 10⁻³, keputusan simulasi menunjukkan bahawa sistem yang dicadangkan boleh mengurangkan PAPR sehingga 6.8 dB dengan 𝑁 = 64 atau 256 (subpembawa sistem) dan 𝑉 = 16 (urutan fasa tidak serupa) untuk 4QAM modulasi. Tambahan pula, sistem ZCT berdasarkan SLM-OFDM boleh mengelakkan kemerosotan isyarat dalam prestasi apabila melalui satu Penguat Kuasa Tinggi (HPA) yang tidak linear.

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ABSTRACT

Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation scheme that is being used in wireline and wireless digital communications for several years ago. The function of the OFDM is to reduce delay spread, inter symbol interference (ISI), inter channel interference (ICI) and frequency selective fading due to the multipath. However, the major drawback of OFDM system is high value of Peak to Average Power Ratio (PAPR). PAPR is one of the important parameters to ensure the best transmission efficiency. In this paper, Zadoff-Chu matrix Transform (ZCT) precoded Selected Mapping (SLM) based OFDM (SLM-OFDM) system is proposed for PAPR reduction. This technique is based on precoding the constellation symbols with ZCT precoder after the multiplication of phase rotation factor and before the Inverse Fast Fourier Transform (IFFT) in the SLM based OFDM (SLM-OFDM) Systems. At the beginning of the project, parameters of the system are initialized. The binary signal is undergoes modulation schemes which are QPSK, 4QAM, 16QAM, 64QAM and 256QAM. The modulated signal is multiplied with the phase factor and pass through the ZCT with row wise precoder matrix before entering IFFT. Then select one of the transmitted signal with the least PAPR and PAPR is evaluated by using Complementary Cumulative Distribution Function (CCDF). The simulation results of PAPR performance are tabulated. At the clipping rate of 10⁻³, simulation results show that the proposed system can reduce the PAPR up to 6.8 dB with 𝑁 = 64 or 256 (System subcarriers) and 𝑉 = 16 (Dissimilar phase sequences) for 4QAM modulation.

In additional, ZCT based SLM-OFDM system can avoid signal degradation in performance when passes through a nonlinear High-Power-Amplifier (HPA).

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CHAPTER 1 INTRODUCTION

1.1 RESEARCH BACKGROUND

What is Orthogonal Frequency Division Multiplexing (OFDM)? OFDM is a multicarrier modulation scheme and popularly used for wireless and wireline digital communication systems. For the wireless digital communication system, there are several limitation of wireless channel. To overcome these limitations, how wideband single channel is divided into small subcarriers and increase efficiency by reducing delay spread.

One of the limitations is delay spread. As a consequence of multi path propagation the duration of a symbol gets extended. This may interfere with the next symbol. This is called Inter Symbol Interference (ISI) or Cross-talk. Guard periods are introduced to avoid cross-talk. Another limitation is inter channel interference. Often signal bandwidth of adjacent carrier frequencies overlap with each other giving rise to interchannel interference. Guard bands were introduced to avoid interchannel interference. All these limitations compounded with the scarcity of bandwidth gave rise to multiple access technique OFDM.

To ensure the high transmission efficiency of OFDM, the Peak to Average Power Ratio (PAPR) is a vital factor in this case. The high PAPR requires the digital- to-analog and analog-to-digital convertors with dynamic range to accommodate these peaks. The more complex the convertor, the higher the cost[1]. To overcome this problem, the signal power must be low and power amplifier (PA) operates in the linear region.

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2 In this paper, ZCT precoding based SLM technique for PAPR reduction is proposed. In the proposed technique, the SLM technique is focus on phase rotation.

After that, the ZCT based precoder is applied after the multiplication of phase rotation factor and before the IFFT in the SLM-OFDM systems. However, there is still a problem when reducing more PAPR. According to [2], ZCT with column wise precoder matrix and Quadrature Phase Shift Keying (QPSK) modulation is used. In this project, ZCT with row wise precoder matrix and Quadrature Amplitude Modulation (QAM) will be used to show the improvement in PAPR performance.

In this project, MATLAB is used to do simulation on the ZCT precoding based SLM technique and then do analysis on the simulation result. After that, analyse the effect of the proposed technique towards PAPR reduction and the advantages of the proposed technique compared to other PAPR reduction technique.

1.2 PROBLEM STATEMENT

Nowadays, the Orthogonal Frequency Division Multiplexing (OFDM) has become commonly used modulation scheme. This is due to its high speed date rates, high spectral efficiency, immunity from Intersymbol Interference (ISI) and etc[3]. The OFDM signals is generated by the addition of several independently modulated signals, then it may exhibit very high peaks. The power of these high peaks will be higher compared to the average power of the signal.

The high Peak to Average Power Ratio (PAPR) will deteriorates the performance of the OFDM system and also increase the complexity of the analog-to- digital (A/D) and digital-to-analog (D/A) converters.

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3 There are several ways to approach this problem, either using signal scrambling techniques or signal distortion techniques. In this project, Zadoff-Chu matrix Transform (ZCT) precoding based Selected Mapping (SLM) technique will be the major approach concerned.

1.3 OBJECTIVES OF RESEARCH

The objectives in this project are:-.

i. To develop a system to reduce the Peak to Average Power Ratio (PAPR) by using ZCT code.

ii. To evaluate the system performance in OFDM system.

1.4 SCOPE OF RESEARCH

The scope of this project is to compare the previous results on reducing PAPR with the one using Zadoff-Chu Matrix Transform. The results will be analyzed and discussion will be made.

1.5 THESIS OUTLINE

This report consists of three chapters which are described below:

Chapter 1 introduces the overviews of the OFDM system, problem statement, objectives of research, scope of research and thesis outline. The content of the introduction included brief explanations about PAPR reduction and ZCT precoding based Selected Mapping (SLM) technique.

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4 Chapter 2 summarizes the literature reviews of the project. Concepts of OFDM system will be discussed from the previous works. Research background, principle of OFDM, operation of OFDM, theories of OFDM system and PAPR will be discussed in this chapter.

Chapter 3 discussed the project methodology on how it is being carried out. This project design is an improved ZCT method on PAPR reduction. The flow of the project design will be discussed in this chapter.

Chapter 4 displays the results and discussions carried out during the simulation on the PAPR reduction performance. Comparison of result between the ZCT-SLM- OFDM system and other techniques on PAPR reduction will be discussed.

Chapter 5 summarizes the project with conclusion and to ensure that the objective of this project is accomplished. Suggestions on future work are also proposed.

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CHAPTER 2 LITERATURE REVIEW

2.1 INTRODUCTION

Orthogonal Frequency Division Multiplexing (OFDM) is a digital multi carrier modulation technique and commonly used in wireless communication. This is due to OFDM provides high speed date rates, high spectral efficiency, frequency selective fading and robustness against narrow band interference[4].

With the introduction of OFDM, the Intersymbol Interference (ISI) and the delay spread of the signal can be reduced. This caused the spectral efficiency of system increased. Due to the few advantages provided by OFDM, thus it is widely used in variety of digital communications over the past several years. Several digital communications like Wireless Local Area Networks (WLAN), Wide Area Networks (WAN), Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB) and etc[5].

However, the Peak to Average Power Ratio (PAPR) is still one of the major problems of OFDM signal that restricted the development of OFDM[6]. High PAPR normally produced at transmitter part during the process of modulation. There is a multiple subcarriers added together to form the signal to be transmitted, the large PAPR is given at the same time. When the sinusoids of the subcarriers added together, the peak magnitude will be increased which rely on the amount of sinusoids[7]. So the average magnitude might be quite low as the destructive interference between the sinusoids. High PAPR will result in increased complexity of the analog-to-digital (A/D)

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6 and digital-to-analog (D/A) converters, high power consumption, lower efficiency and expensive devices.

Therefore, several techniques are proposed to improve the performance of OFDM system which in turn reduce PAPR. Nowadays, many techniques have been introduced for PAPR reduction and the techniques are categorized into two groups:

signal scrambling techniques and signal distortion techniques. Examples of scrambling techniques are Block Codes, Tone reservation (TR) and Tone Injection (TI), Partial Transmit Sequence (PTS), Selective Mapping (SLM) and so on. Whereas the examples of signal distortion techniques are Clipping and Filtering, Peak Windowing, Peak Reduction Carrier and etc[8].

According to [9], several important aspects related to the PAPR, its overall effect on the OFDM system and several techniques for PAPR reduction are discussed.

Several advantages on using these techniques such as transmit signal power increase, computational complexity increase and so on. If the computational complexity increased which means the cost will be increased too. Therefore, there is still have some disadvantages although the techniques are efficient for PAPR reduction.

There is another method which known as Zadoff-Chu Matrix Transform (ZCT) precoding based SLM technique. This is the proposed model in this project. According to [2], the technique they used can reduce more PAPR if they increase the value of V number of phase, but the computational complexity is increased. The digital modulation scheme that they used is QPSK modulation. In this project, the 4QAM, 16QAM, 64QAM and 256QAM modulation scheme is used. In the previous work, they used the ZCT with column wise precoder matrix. Then ZCT with row wise precoder matrix will

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7 be the key in this project. The PAPR value will be evaluated and compared it with the result of previous work.

2.2 THEORETICAL BACKGROUND

In this section, the principle of OFDM, operation of OFDM, theories of conventional OFDM system, OFDM signals, PAPR and method of PAPR reduction will be discussed. The concept of OFDM is very important before learning how to reduce the PAPR which is the major drawback of OFDM.

2.2.1 PRINCIPLE OF OFDM

Orthogonal Frequency Division Multiplexing (OFDM) is a multiple carrier modulation technique which splits the free spectrum into numerous carriers each one being modulated by a low data rate stream. OFDM system is identical to Frequency Division Multiple Access (FDMA) system in that the multiple user access is achieved by sub-dividing the accessible bandwidth into various channels, which are then distributed to users. However OFDM utilizes the spectrum much more productively by arranging the channels more close-packed. This is attained by forming all the carriers orthogonal to one another, avoiding interference between the closely spaced carriers.[10] Figure 2.1 explains the dissimilarity between the conventional nonoverlapping multicarrier technique and the overlapping multicarrier modulation technique. Based on Figure 2.1, by making use of the overlapping multicarrier modulation technique, conservation nearly 50% of bandwidth can be make. To accomplish the overlapping multicarrier technique, yet crosstalk between subcarriers

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8 required to be minimize, which means that orthogonality between the varying modulated carriers will be achieved.[11]

Figure 2.1 Concept of OFDM signal: orthogonal multicarrier technique versus conventional multicarrier technique.[11]

The orthogonality of the carriers means that each carrier has a whole number of cycles over a symbol period. Ascribed to this, the spectrum of each carrier has a null at the core frequency of each of the other carriers in the system. This gives rise to no interference between the carriers, letting them to be spaced as packed as hypothetically possible. This prevails over the trouble of overhead carrier spacing required in FDMA.

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9 Each carrier in an OFDM signal has a very confined bandwidth (i.e.1kHz), hence the resulting symbol rate is small. This leads to the signal having a high tolerance to multipath delay spread, since the delay spread must be very long to provoke remarkable inter-symbol interference (e.g. > 500 μsec).

2.2.2 OPERATION OF OFDM

As mentioned before, the OFDM is a multi-carrier modulation scheme where every sub-carrier is orthogonal to each other. The "orthogonal" in the OFDM name states that there is an explicit mathematical correlation between the frequencies of the carriers in the system. It is likely to position the carriers in an OFDM signal in case the sidebands of the individual carriers overlap and the signals can still be accepted without adjoining carriers’ interference. In order to do this the carriers must be mathematically orthogonal. Assuming that the integral of the product of two signals is zero over a time period, then these signals are orthogonal to each other, since the carriers are all sine/cosine wave which fulfil this standard. If a sine wave of frequency,𝑚 is multiplied by a sinusoid (sine or cosine) of a frequency,𝑛 , then the product is shown below:

𝑓(𝑡) = sin 𝑚𝑤𝑡 ∗ sin 𝑛𝑤𝑡 (2.1)

Where both m and n are integers by basic trigonometric correlation, this is equivalent to a sum of two sinusoids of frequencies (𝑛 − 𝑚) and (𝑛 + 𝑚), since these two components are each a sinusoid, the integral is equal to zero after one period. The integral under this product is given as below:

𝑓(𝑡) = ∫ ¹₂cos(𝑚 − 𝑛) −¹

2cos(𝑚 + 𝑛)𝑤𝑡

2𝜋

0 (2.2)

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10 According to the Equation 2.2, the area under the product is zero when a sinusoid of frequency,𝑛 is multiplied by a sinusoid of frequency,𝑚. All integers 𝑛 and 𝑚, sin 𝑚𝑥, cos 𝑛𝑥, sin 𝑛𝑥 are orthogonal to each other. These frequencies are called harmonics.

The spectrum of each carrier has a null at the center frequency of each of the other carriers in the system since the sub-carriers are orthogonal. This allowing them to be located as near as theoretically possible when no interference between the carriers.

The orthogonality enables concurrent transmission on plenty of sub-carriers in a close frequency space without interference from each other. Therefore extract the individual sub-carriers easily on the receiver side. However, overlapping of carriers are not possible in traditional FDM systems. In FDM system, a guard band is supplied between each carrier to prevent inter-carrier interference.[12] Based on Figure 2.2, it shows the multi carriers of OFDM signal.

Figure 2.2 Multi carriers of OFDM signal[12]

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11 2.2.3 CONVENTIONAL OFDM SYSTEM

The Figure 2.3 shows the block diagram of a conventional OFDM system. At the transmitter part, first of all, input binary serial data stream is first handled by channel encoder, constellation mapping and serial to parallel (S/P) conversion. A single signal is then split into N parallel routes after inverse fast Fourier transform (IFFT). Each orthogonal sub-carrier is modulated by one of the N data routes independently. N parallel points form one OFDM symbol and then parallel data sequence is converted to serial sequence. In the end of transmitter, the serial sequence is passed through digital to analog (D/A) conversion and radio frequency (RF) modulation. Then the signal transmitted to channel.

Figure 2.3 A conventional OFDM system block diagram[13]

At the receiver end, initially, demodulate received signals then demodulated signals are converted from analog to digital (A/D) converter, sample output and take time estimation to find an initial position of OFDM symbol. Fast Fourier transforms (FFT) transformation will be carried out on the sample points to recover the data in the

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12 frequency domain. Eventually, the output of baseband demodulation is passed to the channel decoder to recover the original data.

2.2.4 OFDM SIGNALS

An OFDM symbol is generated by summing all the N modulated subcarriers with N corresponding bits by using IFFT. For an instance, there is a group of N bits 𝑋 = (𝑋₀, 𝑋₁, … , 𝑋_𝑁−1) and a group of N subcarriers𝑓_𝑚, 𝑚 = (0,1, … , 𝑁 − 1). Since the N subcarriers are orthogonal to each other, then 𝑓_𝑚 = 𝑚∆𝑓, where ∆𝑓 = 1 (𝑁𝑇)⁄ and T is the original bit period. Thus, the transmitted OFDM signals can be expressed as:

𝑥_𝑛(𝑡) = ¹

√𝑁∑^𝑁−1_𝑚=0𝑋_𝑚𝑒^{𝑗2𝜋𝑓}^𝑚^𝑡, 0 ≤ 𝑡 ≤ 𝑁𝑇 (2.3) Where 𝑗 = √−1

2.2.5 PAPR

PAPR is the total of amplitude fluctuations. PAPR occurs when N signals are summed with the identical phase which means they give a peak power that is equal to N times of average power. Thus, the PAPR of the transmitted signal in OFDM system is indicated as the ratio of the peak power to the average envelope power of the signal.

𝑃𝐴𝑃𝑅 = ^{0≤𝑡≤𝑁𝑇}^max ^[|𝑥^𝑛^(𝑡)|

2]

𝐸[|𝑥𝑛(𝑡)²|] (2.4)

Where 𝐸[. ] denotes expectation.

The PAPR value is rising attributable to the IFFT pre-processing. In the IFFT pre- processing, the dissimilar symbols are randomly filled onto the subcarriers, then they

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13 are fortuitously all sum up across the subcarriers to produce a high peak value which gives rise to the peak power with respect to the mean value.

2.2.6 METHODS OF PAPR REDUCTION

There are some techniques to diminish the high PAPR in OFDM system. These techniques can be divided into two categories such as: Signal Distortion Technique and Signal Scrambling Technique. Signal scrambling techniques are all variations on how to scramble the codes to reduce the PAPR. Examples of methods in respectively techniques are stated below[9]:

1) Signal Distortion Techniques

 Peak Windowing

 Envelope Scaling

 Peak Reduction Carrier

 Clipping and Filtering 2) Signal Scrambling Techniques

 Block Coding Technique

 Block Coding Scheme with Error Correction

 Partial Transmit Sequence (PTS)

 Interleaving Technique

 Tone Reservation (TR)

 Tone Injection

 Selected Mapping (SLM)

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CHAPTER 3 METHODOLOGY

3.1 INTRODUCTION

This project is mainly focus on the Zadoff-Chu matrix Transform (ZCT) precoded Selected Mapping (SLM) based OFDM (SLM-OFDM) system for PAPR reduction in OFDM system by using different phase sequences. The major drawback of OFDM system is high Peak to Average Power Ratio (PAPR), there are several PAPR reduction techniques have been discussed in previous chapter. In this chapter, the implementation of ZCT-SLM-OFDM technique on PAPR reduction will be discussed.

Besides that, ZCT-OFDM, SLM-OFDM, SLM-ZCT-OFDM techniques on PAPR reduction will be discussed too. In addition, system performance of the system will be analysed too. ZCT-SLM-OFDM technique is efficient, distortion less and does not require any complex optimization compare to other techniques[2]. The researches and studies on ZCT-SLM-OFDM system have been made for a better understanding on how to implement it. Therefore, the modulation scheme, project implementation flow, and the conventional ZCT-SLM-OFDM system will be discussed in this chapter.

3.2 PROJECT IMPLEMENTATION FLOW

An OFDM symbol is made of sub-carriers modulated by constellations mapping.

At the transmitter part, a binary data sequence is randomly generated and converted into decimal data sequence. The sequence of data bits are mapped into constellation points of QPSK or QAM and serial-to-parallel conversion to produce the OFDM symbol sequences. These symbol sequences are then divided into blocks of length N, where N represents the number of subcarriers. In SLM-OFDM system, the blocks of

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15 length N and V different phase sequence vectors are multiplied element by element, resulting in V modified data blocks. However, in the ZCT-OFDM system, the blocks of length 𝐿 = √𝑁 is used for element wise multiplication with V different phase sequence vectors.

After that, the V modified data blocks will be pass through ZCT precoder and resulting in ZC precoded data. This means that the V modified data blocks will be multiplied by the Zadoff-Chu (ZC) sequences of length N that formed in the kernel of the ZCT matrix size of 𝑁 = 𝐿 𝑥 𝐿. The IFFT is used to convert the modulated complex data to the time domain. After performing the IFFT operation, the complex baseband ZCT-SLM-OFDM signal is formed. The PAPR is analyzed by using Complementary Cumulative Distribution Function (CCDF). In the end of process, the one with the lowest PAPR is selected for transmission.

Next, Zadoff-Chu (ZC) sequences, Zadoff-Chu matrix Transform (ZCT), ZCT precoding based OFDM (ZCT-OFDM) system, SLM based OFDM (SLM-OFDM) system, SLM-ZCT precoding based OFDM (SLM-ZCT-OFDM) system, and the proposed model ZCT precoded SLM based OFDM (ZCT-SLM-OFDM) system will be discussed in the following sections.

3.2.1 Zadoff-Chu (ZC) Sequences

Zadoff-Chu (ZC) sequences are class of poly phase sequences that having the ideal periodic autocorrelation function and the optimum periodic cross correlation function. Referring to [14], the Zadoff-Chu (ZC) sequences of length N is defined as

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16 𝑒

𝑗2𝜋𝑟 𝑁 (𝑘²

2+𝑞𝑘)

𝑓𝑜𝑟 𝑁 𝐸𝑣𝑒𝑛

𝑎_𝑛 = (3.1)

𝑒

𝑗2𝜋𝑟 𝑁 (𝑘(𝑘+1)

2 +𝑞𝑘)

𝑓𝑜𝑟 𝑁 𝑂𝑑𝑑

Where 𝑘 = 0, 1, 2 … 𝑁 − 1, q is any integer, r is any integer relatively prime to N and 𝑗 = √−1.

3.2.2 Zadoff-Chu matrix Transform (ZCT)

The ZC sequence undergoes matrix transform to form ZCT. The ZC sequence can be reshaping by 𝑘 = 𝑚 + 𝑙𝐿 (column-wise) or 𝑘 = 𝑚𝐿 + 𝑙 (row-wise) to form the ZCT kernel column wise filling and row wise filling respectively, A, of size 𝑁 = 𝐿 𝑥 𝐿 as shown in Eq. (3.2).

𝐴 = [

𝑎₀₀ 𝑎₀₁ ⋯ 𝑎_0(𝐿−1)

𝑎₁₀ 𝑎₁₁ ⋯ 𝑎_1(𝐿−1)

⋮ ⋮ ⋱ ⋮

𝑎_(𝐿−1)0 𝑎_(𝐿−1)1 ⋯ 𝑎_{(𝐿−1)(𝐿−1)}

] (3.2)

Refer to both equations 𝑘 = 𝑚 + 𝑙𝐿 and 𝑘 = 𝑚𝐿 + 𝑙, 𝑚 indicates row variable and 𝑙 represents column variable. In other phrases, the 𝑁 = 𝐿² point long ZC sequence fills the kernel of the matrix column-wise or row-wise. When variables 𝑚 and 𝑙 fulfill the equation 𝑘 = 𝑚 + 𝑙𝐿, the 𝑘 values in the kernel of the matrix column-wise is shown in Eq. (3.3), and the 𝑘 values in the kernel of the matrix row-wise is stated in Eq. (3.4).

𝑘_𝐴𝑐𝑜𝑙𝑢𝑚𝑛−𝑤𝑖𝑠𝑒 = [

0 𝐿 ⋯ 𝐿(𝐿 − 1)

1 𝐿 + 1 ⋯ 𝐿(𝐿 − 1) + 1

⋮ ⋮ ⋱ ⋮

𝐿 − 1 𝐿 + (𝐿 − 1) ⋯ 𝐿(𝐿 − 1) + (𝐿 − 1)

] (3.3)

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17 𝑘_𝐴_{𝑟𝑜𝑤−𝑤𝑖𝑠𝑒} = [

0 1 ⋯ 𝐿 − 1

𝐿 𝐿 + 1 ⋯ 𝐿 + (𝐿 − 1)

⋮ ⋮ ⋱ ⋮

𝐿(𝐿 − 1) 𝐿(𝐿 − 1) + 1 ⋯ 𝐿(𝐿 − 1) + (𝐿 − 1)

] (3.4)

3.2.3 ZCT precoding based OFDM (ZCT-OFDM) system

Figure 3.1 shows the block diagram of ZCT precoding based OFDM system and the flow of process. In this ZCT precoding based OFDM system, a set of binary data sequence undergoes constellation mapping and S/P convertor which generates a complex vector of size L that can be written as 𝑋 = [𝑋₀, 𝑋₁, 𝑋₂… 𝑋_𝐿−1]^𝑇.

Figure 3.1 Block diagram of ZCT precoding based OFDM system

This complex vector,X is then applied by the ZCT with row wise precoder matrix or ZCT with column wise precoder matrix,A of size 𝐿𝑥𝐿 which can transform this complex vector into new vector of same length L. This new vector of length L can be written as 𝑌 = 𝐴𝑋 = [𝑌₀, 𝑌₁, 𝑌₂… 𝑌_𝐿−1]^𝑇. The new vector is also can written as:-

𝑌_𝑚 = ∑^𝐿−1_𝑙=0𝑎_𝑚,𝑙𝑋_𝑙 𝑚 = 0,1 … 𝐿 − 1 (3.5) Variables 𝑚 and 𝑙 in the 𝑎_𝑚,𝑙 are represented 𝑚^𝑡ℎ row and 𝑙^𝑡ℎ column of the ZCT precoder matrix. Eq. (3.5) is expanding by using either column-wise sequence

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18 reshaping 𝑘 = 𝑚 + 𝑙𝐿 or row-wise sequence reshaping 𝑘 = 𝑚𝐿 + 𝑙 and inserting 𝑟 = 1 and 𝑞 = 0 into the Eq. (3.1).

𝑌_𝑚𝑐𝑜𝑙𝑢𝑚𝑛−𝑤𝑖𝑠𝑒 = ∑ (𝑒^𝑗

𝜋(𝑚+𝑙𝐿)² 𝐿² ) 𝑋_𝑙

𝐿−1 𝑙=0

= ∑ (𝑒^𝑗

𝜋[𝑚²+2𝑚𝑙𝐿+(𝑙𝐿)²] 𝐿² ) 𝑋_𝑙

𝐿−1 𝑙=0

= 𝑒^𝑗

𝜋𝑚2

𝐿2 ∑^𝐿−1_𝑙=0𝑋_𝑙𝑒^𝑗𝜋𝑙²𝑒^𝑗^{2𝜋𝑚𝑙}^𝐿 𝑚 = 0,1, … , 𝐿 − 1 (3.6) Or

𝑌_𝑚_{𝑟𝑜𝑤−𝑤𝑖𝑠𝑒} = ∑ (𝑒^𝑗^{𝜋(𝑚𝐿+𝑙)}

2 𝐿² ) 𝑋_𝑙

𝐿−1 𝑙=0

= ∑ (𝑒^𝑗

𝜋[(𝑚𝐿)²+2𝑚𝑙𝐿+𝑙²] 𝐿² ) 𝑋_𝑙

𝐿−1 𝑙=0

= 𝑒^𝑗𝜋𝑚²∑ 𝑋_𝑙𝑒^𝑗𝜋(^𝐿^𝑙⁾

2

𝑒^𝑗^{2𝜋𝑚𝑙}^𝐿

𝐿−1𝑙=0 𝑚 = 0,1, … , 𝐿 − 1 (3.7)

Equation (3.6) and (3.7) represent the ZCT precoded constellations symbols. The complex baseband ZCT-OFDM signal with L subcarriers which undergoes IFFT operation can be written as:-

𝑥_𝑛 = ¹

√𝐿∑^𝐿−1_𝑚=0𝑌_𝑚𝑒^𝑗2𝜋^𝑛^𝐿^𝑚 𝑛 = 0,1, … , 𝐿 − 1 (3.8) The PAPR of ZCT-OFDM signal in Eq. (3.8) is calculated and written as:-

𝑃𝐴𝑃𝑅 = ^[|𝑥^𝑛^|

2] 𝑛=0,1,…,𝑁−1

𝑚𝑎𝑥 1

𝑀∑^𝑁−1_𝑛=0[|𝑥𝑛|²] (3.9)

In this ZCT precoding based OFDM system, there will be two types different system which are Zadoff-Chu matrix Transform with Row wise precoder OFDM (ZCT-R- OFDM) system and Zadoff-Chu matrix Transform with Column wise precoder OFDM

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19 (ZCT-C-OFDM) system. Both systems have the different performance and given different PAPR values. Comparison among these two systems will be carried out to analyze which system has lesser PAPR and decide which system is suitable to use for PAPR reduction technique.

3.2.4 SLM based OFDM (SLM-OFDM) system

Figure 3.2 shows the block diagram of SLM based OFDM system and the process flow. The SLM is one of the PAPR reduction technique which is based on the phase rotations. In this SLM based OFDM system, a complex vector of length N, 𝑋 = [𝑋₀, 𝑋₁, 𝑋₂… 𝑋_𝑁−1]^𝑇 is generated by the constellation mapping and S/P convertor.

Figure 3.2 Block diagram of SLM based OFDM system

There is a set of V dissimilar phase sequences of length N can be defined as 𝐵^(𝑣) = [𝑏_𝑣,0, 𝑏_𝑣,1, … , 𝑏_{𝑣,𝑁−1}]^𝑇(𝑣 = 1,2 … 𝑉). Then, every data block is required to multiply with V dissimilar phase sequences which results in 𝑋^(𝑣)= [𝑋₀𝑏_𝑣,0, 𝑋₁𝑏_𝑣,1, … , 𝑋_𝑁−1𝑏_{𝑣,𝑁−1}]^𝑇(𝑣 = 1,2 … 𝑉) or written as:-

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20 𝑋_𝑛^𝑣 = 𝑋_𝑛𝑏_𝑣,𝑛 𝑣 = 1,2, … , 𝑉 (3.10) The SLM-OFDM signal with N subcarriers which undergoes IFFT operation can be defined as:-

𝑥_𝑛^(𝑣) = ¹

√𝑁∑^𝑁−1_𝑘=0𝑋_𝑘^𝑣𝑒^𝑗2𝜋^𝑁^𝑛^𝑘 𝑛 = 0,1, … , 𝑁 − 1, 𝑣 = 1,2, … , 𝑉 (3.11) The PAPR of SLM-OFDM signal in Eq. (3.11) is calculated and be written as:-

𝑃𝐴𝑃𝑅 = ^{𝑚𝑎𝑥|𝑥}^𝑛

(𝑣)|² 𝐸[|𝑥_𝑛^(𝑣)|²]

(3.12)

3.2.5 SLM-ZCT precoding based OFDM (SLM-ZCT-OFDM) system

Figure 3.3 shows the block diagram of SLM-ZCT precoding based OFDM system and the flow of process. In this SLM-ZCT based OFDM system, a set of binary data sequence undergoes constellation mapping and S/P convertor which result in a complex vector of length L can be written as 𝑋 = [𝑋₀, 𝑋₁, 𝑋₂… 𝑋_𝐿−1]^𝑇.

X X

𝑋0

𝑋₁

𝑋_𝐿−1

𝑌0

𝑌1

𝑌_𝐿−1 𝐵⁽¹⁾

𝐵^(𝑉) 𝑌⁽¹⁾

𝑌⁽²⁾

𝑌^(𝑉)

𝑥⁽¹⁾

𝑥⁽²⁾

𝑥^(𝑉) Zadof

f-Chu Matri

x Transf

orm

IFFT

Select one with the lowest PAPR Input

data

Mappe r

Serial to parallel

or partition

of data in to blocks

𝐵⁽²⁾

𝑥^(𝑢⁾

Figure 3.3 Block diagram of SLM-ZCT based OFDM system

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21 This complex vector is then multiplied with the ZCT precoder matrix,A of size 𝐿𝑥𝐿 to produce a new complex vector of same length L, 𝑌 = 𝐴𝑋 = [𝑌₀, 𝑌₁, 𝑌₂… 𝑌_𝐿−1]^𝑇 or can be written as:-

𝑌_𝑚 = ∑^𝐿−1_𝑙=0𝑎_𝑚,𝑙𝑋_𝑙 𝑚 = 0,1 … 𝐿 − 1 (3.13) After that, a set of V dissimilar phase sequences of length L, 𝐵^(𝑣) = [𝑏_𝑣,0, 𝑏_𝑣,1, … , 𝑏_{𝑣,𝐿−1}]^𝑇(𝑣 = 1,2 … 𝑉). This vector of V dissimilar phase sequences is multiplied by the complex vector 𝑌 which result in 𝑌^(𝑣) = [𝑌₀𝑏_𝑣,0, 𝑌₁𝑏_𝑣,1, … , 𝑌_𝐿−1𝑏_{𝑣,𝐿−1}]^𝑇(𝑣 = 1,2 … 𝑉). The matrix multiplication of 𝑌 and 𝐵^(𝑣) can be written as:-

𝑌_𝑖,𝑘^(𝑣) = ∑^𝐿−1_𝑗=0𝐵_𝑖,𝑗^(𝑣)𝑌_𝑗,𝑘 𝑘 = 0,1,2, … , 𝐿 − 1, 𝑖 = 0,1,2, … , 𝐿 − 1 (3.14) The SLM-ZCT-OFDM signal with L subcarriers which undergoes IFFT operation can be defined as:-

𝑌_𝑛^(𝑣) = ¹

√𝐿∑ 𝑌_𝑘^𝑣𝑒^𝑗2𝜋

𝑛 𝐿𝑘

𝐿−1𝑘=0 𝑛 = 0,1, … , 𝐿 − 1, 𝑣 = 1,2, … , 𝑉 (3.15)

The PAPR of SLM-ZCT-OFDM signal in Eq. (3.11) is calculated and be written as:-

𝑃𝐴𝑃𝑅 = ^{𝑚𝑎𝑥|𝑌}^𝑛

(𝑣)|² 𝐸[|𝑌_𝑛^(𝑣)|²]

(3.16)

3.2.6 ZCT precoded SLM based OFDM (ZCT-SLM-OFDM) system

Figure 3.4 shows the block diagram of the proposed ZCT precoded SLM- OFDM system. Based on the figure 3.3, the operation is different with SLM-ZCT- OFDM system as in the ZCT-SLM-OFDM system, SLM system will be performed first before the ZCT system performed. Whilst the SLM-ZCT-OFDM system is vice-versa.

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22 Figure 3.4 Block diagram of ZCT-SLM based OFDM system

At the beginning of this ZCT-SLM-OFDM system, a set of binary data is passed through constellation mapping and S/P convertor to generate complex vector of length L, 𝑋 = [𝑋₀, 𝑋₁, 𝑋₂… 𝑋_𝐿−1]^𝑇. SLM system based on phase rotations, so there is a set of V dissimilar phase sequences of length L, 𝐵^(𝑣) = [𝑏_𝑣,0, 𝑏_𝑣,1, … , 𝑏_{𝑣,𝐿−1}]^𝑇(𝑣 = 1,2 … 𝑉).

Each data block is multiplied with the set of phase sequences, then it produced 𝑋^(𝑣)= [𝑋₀𝑏_𝑣,0, 𝑋₁𝑏_𝑣,1, … , 𝑋_𝐿−1𝑏_{𝑣,𝐿−1}]^𝑇(𝑣 = 1,2 … 𝑉). The result can be simplified as

𝑋_𝑙^𝑣 = 𝑋_𝑙𝑏_𝑣,𝑙 𝑙 = 0,1 … 𝐿 − 1, 𝑣 = 1,2,3 … 𝑉 (3.17) After that, the signal in Eq (3.17) is passed through the ZCT precoder matrix of size 𝐿𝑥𝐿, thus the new complex vector is

𝑌_𝑚^𝑣 = ∑^𝐿−1_𝑙=0𝑎_𝑚,𝑙𝑋_𝑙^𝑣 𝑚 = 0,1 … 𝐿 − 1 (3.18) The variables 𝑚 and 𝑙 in the 𝑎_𝑚,𝑙 are represented 𝑚^𝑡ℎ row and 𝑙^𝑡ℎ column of the ZCT precoder matrix.

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23 By using either column-wise sequence reshaping 𝑘 = 𝑚 + 𝑙𝐿 or row-wise sequence reshaping 𝑘 = 𝑚𝐿 + 𝑙 and inserting 𝑟 = 1 and 𝑞 = 0 into the equation (3.1), then expand the equation (3.18) and the resultant equation as shown below.

𝑌_𝑚𝑐𝑜𝑙𝑢𝑚𝑛−𝑤𝑖𝑠𝑒

𝑣 = ∑ (𝑒^𝑗

𝜋(𝑚+𝑙𝐿)² 𝐿² ) 𝑋_𝑙^𝑣

𝐿−1 𝑙=0

= ∑ (𝑒^𝑗

𝜋[𝑚²+2𝑚𝑙𝐿+(𝑙𝐿)²] 𝐿² ) 𝑋_𝑙^𝑣

𝐿−1 𝑙=0

= 𝑒^𝑗

𝜋𝑚2

𝐿2 ∑^𝐿−1_𝑙=0((𝑒^𝑗𝜋𝑙². 𝑋_𝑙^𝑣). 𝑒^𝑗^{2𝜋𝑚𝑙}^𝐿 ) (3.19) Or

𝑌_𝑚^𝑣_{𝑟𝑜𝑤−𝑤𝑖𝑠𝑒} = ∑ (𝑒^𝑗^{𝜋(𝑚𝐿+𝑙)}

2 𝐿² ) 𝑋_𝑙^𝑣

𝐿−1 𝑙=0

= ∑ (𝑒^𝑗

𝜋[(𝑚𝐿)²+2𝑚𝑙𝐿+𝑙²] 𝐿² ) 𝑋_𝑙^𝑣

𝐿−1 𝑙=0

= 𝑒^𝑗𝜋𝑚∑ ((𝑒^𝑗𝜋(^𝐿^𝑙⁾

2

. 𝑋_𝑙^𝑣). 𝑒^𝑗^{2𝜋𝑚𝑙}^𝐿 )

𝐿−1𝑙=0 (3.20)

Where 𝑚 = 0,1,2, … , 𝐿 − 1, Eq (3.19) and (3.20) represent the ZC precoded signal.

The complex baseband ZCT-OFDM signal with L subcarriers which undergoes IFFT operation can be written as:-

𝑥_𝑛^(𝑣)= ¹

√𝐿∑^𝐿−1_𝑚=0𝑌_𝑚^𝑣. 𝑒^𝑗2𝜋^𝑛^𝐿^𝑚 𝑛 = 0,1,2 … 𝐿 − 1, 𝑣 = 1,2, … V (3.21) The PAPR of ZCT-SLM-OFDM signal in equation (3.21) can be written as below

𝑃𝐴𝑃𝑅 = ^{𝑚𝑎𝑥[|𝑥}^𝑛

(𝑣)|²] 𝐸[|𝑥_𝑛^(𝑣)|²]

(3.22)

In this ZCT precoding based SLM-OFDM system, the PAPR value is measured at the end of the transmitter. For the PAPR measurement or analysis, the transmitted

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24 signal must be in the form of time domain. Thus, IFFT operation is needed to convert the frequency domain signal into time domain signal. ZCT precoding based SLM- OFDM technique is applicable for any number of subcarriers and all types of modulation techniques such as QAM and QPSK. The PAPR reduction for ZCT-SLM- OFDM system depends on the number of phase sequences V (4,8,16), the output data with lowest PAPR value at transmitter part is selected for transmissions. The number of subcarriers N, modulation techniques, and value of V is varied until the lowest PAPR value is achieved.

Figure 3.5 shows the flow of process of the ZCT-SLM-OFDM system. The PAPR measurement and analysis is at the end of transmitter part.

Figure 3.5 Continues…

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25 Figure 3.5 Flow Chart of ZCT-SLM-OFDM system

3.3 PROJECT REQUIREMENT

This project is software based project. MATLAB with Communication System Toolbox provides algorithms included channel coding, modulation, OFDM and etc.

3.4 PROJECT DESIGN

At the beginning of the project, the parameters used in the OFDM system for ZCT-SLM-OFDM technique are initialized. Then the binary data sequences is randomly generated. The random binary data sequences will pass through the constellations mapping and serial-to-parallel convertor to produce data symbol sequences. The symbol sequence is then multiplied by phase rotations to form a new complex vector. The new complex vector is pass through the ZCT precoder matrix to form ZC precoded data. It then pass through the IFFT to convert into time domain. The

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26 system performance is determined from the comparison with the conventional OFDM and CCDF versus time waveform of transmitted signal for QAM and QPSK modulations. The one with the least PAPR will be selected for further transmission. It will pass through the channel before entering the receiver part. The data then pass through the serial-to-parallel conversion and FFT to form data in frequency domain.

Then the data will pass through the parallel-to-serial convertor and undergoes demodulation operations. Finally the data will be reconstructed to its original form. In this ZCT precoding SLM based OFDM system, the only transmitter part will be discussed. The channel and receiver part will not be discussed in this project as PAPR reduction technique is focused on transmitter part only.

Figure 3.6 shows the flowchart of the ZCT-SLM-OFDM technique in MATLAB programme. This technique is mainly focus on transmitter part as the PAPR value is measure at the end of transmitter part.

Figure 3.6 Continues…

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27 Figure 3.6 Flowchart of ZCT-SLM-OFDM technique in MATLAB programme

Step 1: Initialize parameter for the system

The parameters of the system should be initialized first before start the MATLAB programming. The important parameters required in this project such as total number of subcarriers, modulation format, phase factors, and number of runs.

Table 3.1 Parameters for QAM modulation with N subcarriers

No. Parameter Value

1 Number of subcarriers,N 64,256

2 Modulation format,M 4,16,64,256

3 Number of phase,V 4,8,16

4 Number of runs 10000

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28 Table 3.2 Parameters for QPSK modulation with N subcarriers

No. Parameter Value

1 Number of subcarriers,N 64,256

2 Modulation format,M QPSK

3 Number of phase,V 4,8,16

4 Number of runs 10000

Step 2: Constellation mapping and S/P convertor is undergone after random data is generated

A random binary data streams are generated by using MATLAB. The data will be undergoes QAM or QPSK modulation to ensure that the transmission will be more reliable at the channel.

Step 3: Multiplication of phase factor

In this ZCT precoding SLM based OFDM system, Selected Mapping (SLM) technique is used, one of the sequence will be selected from a number of sequences. This technique focus on the phase rotation and to produce a set of V modified data blocks.

SLM is one of the PAPR reduction technique used to reduce the PAPR.

Step 4: Multiplication of ZCT precoder matrix

The modified data blocks is multiplied by the ZCT precoder matrix to form a ZCT precoded data.

Step 5: Perform IFFT

The complex baseband ZCT-SLM-OFDM signal is passed through IFFT where each sequence convert the frequency domain signal into time domain signal.

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29 Step 6: Calculate and select the lowest PAPR signal for further transmission The plot result obtained from the MATLAB will be analysed and the lowest PAPR signal will be selected for further transmission.

3.5 DATA ANALYSIS

In this project, PAPR is the key to ensure the high transmission efficiency and the performance of OFDM system. Complementary Cumulative Distribution Function (CCDF) is used to evaluate and identify the performance index for the probability of PAPR exceeds a certain threshold 𝑃𝐴𝑃𝑅₀ (𝐶𝐶𝐷𝐹 = 𝑃𝑟𝑜𝑏(𝑃𝐴𝑃𝑅 > 𝑃𝐴𝑃𝑅₀)). CCDF is independent from the transmitter amplifier. Equation for the calculation of CCDF of the PAPR is expressed as

P(𝑃𝐴𝑃𝑅 > 𝑦) = 1 − P (𝑃𝐴𝑃𝑅 < 𝑦) (3.23)

3.6 CONCLUSION

In this chapter, the implementation of Zadoff-Chu matrix Transform (ZCT) precoded Selected Mapping (SLM) based OFDM (SLM-OFDM) system for PAPR reduction is introduced. Parameters for this project are initialized, binary data sequences is randomly generated, undergo modulation scheme and serial-to-parallel conversion, multiplication of phase factor and ZCT precoder, then pass through IFFT to convert into time domain signal. This is due to time domain signal is needed for the evaluation of PAPR. CCDF of the PAPR is used to analyse the probability whether which one is the lowest PAPR selected for the further transmission. In this project, the results will be compared with the previous work.

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30

CHAPTER 4

RESULT AND DISCUSSION 4.1 INTRODUCTION

In this chapter, the simulation results of Zadoff-Chu matrix Transform (ZCT) precoder Selected Mapping (SLM) based OFDM (ZCT-SLM-OFDM) system are being discussed. At first, the simulation results of conventional OFDM signal, ZCT with Row wise precoder SLM based OFDM (ZCT-R-SLM-OFDM) system and ZCT with Column wise precoder SLM based OFDM (ZCT-C-SLM-OFDM) system are being discussed. The result is used to compare which system either row-wise or column-wise is performed better. Then the system that performed better will be used for the following simulations. The result varies with the different parameters used and the simulation results are achieved. The discussion on the result of PAPR performance will be discussed in this section.

4.2 RESULT AND DISCUSSION 4.2.1 16-QAM (Columnwise or Rowwise)

Figure 4.1 and Figure 4.2 displayed the result from the CCDF versus PAPRo by using 16-QAM modulation scheme. From Figure 4.1, at clip rate of 10⁻³, the PAPR is 10.24dB and 5.522dB for conventional OFDM and ZCT-C-SLM-OFDM respectively which means that it can reduce PAPR up to about 4.7dB. From Figure 4.2, at clip rate of 10⁻³, the PAPR is 10.09dB and 3.765dB for conventional OFDM and ZCT-R-SLM- OFDM respectively which indicates that it can reduce PAPR up to about 6.3dB. From both results obtained, it can concluded that ZCT-R-SLM-OFDM system can reduce more PAPR than the ZCT-C-SLM-OFDM system. Thus, ZCT with row-wise precoder is preferred and used for the following simulations.

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31 Figure 4.1 CCDF vs PAPRo of conventional OFDM and ZCT-C-SLM-OFDM with 𝑉 = 16

Figure 4.2 CCDF vs PAPRo of conventional OFDM and ZCT-R-SLM-OFDM with 𝑉 = 16

4.2.2 QPSK (N = 64)

Figure 4.3, Figure 4.4 and Figure 4.5 showed the result of CCDF versus PAPRo of conventional OFDM, ZCT precoded OFDM, SLM-OFDM, SLM-ZCT precoded

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32 OFDM and ZCT precoded SLM-OFDM with 𝑁 = 64 & 𝑉 = 4, 8, 16 for QPSK modulation scheme. There was a remarkable decrease in PAPR when the phase sequence, V was increased.

Figure 4.3 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 4 for QPSK modulation

Figure 4.4 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 8 for QPSK modulation

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33 Figure 4.5 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 16 for QPSK modulation

4.2.3 4-QAM (N = 64)

Figure 4.6, Figure 4.7 and Figure 4.8 showed the result of CCDF versus PAPRo of conventional OFDM, ZCT precoded OFDM, SLM-OFDM, SLM-ZCT precoded OFDM and ZCT precoded SLM-OFDM with 𝑁 = 64 & 𝑉 = 4, 8, 16 for 4-QAM modulation scheme. The results show that there was a notable reduction in PAPR when the phase sequence, V was increased.

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34 Figure 4.6 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 4 for 4-QAM modulation

Figure 4.7 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 8 for 4-QAM modulation

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4.2.4 16-QAM (N = 64)

Figure 4.9, Figure 4.10 and Figure 4.11 showed the result of CCDF versus PAPRo of conventional OFDM, ZCT precoded OFDM, SLM-OFDM, SLM-ZCT precoded OFDM and ZCT precoded SLM-OFDM with 𝑁 = 64 & 𝑉 = 4, 8, 16 for 16- QAM modulation scheme. The results show that there was a significant decline in PAPR when the phase sequence, V was increased.

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Figure 4.10 CCDF vs PAPRo with 𝑁 = 64 & 𝑉 = 8 for 16-QAM modulation

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In addition, the simulation results from 64-QAM (Figure A.1-Figure A.3) and 256-QAM (Figure A.4-Figure A.6) modulation scheme are shown in the Appendix A.

Both of the results showed that there was a significant decrease in PAPR too when the phase sequence, V was increased.

Table 4.1 showed the result of CCDF versus PAPRo plots where this can concluded the PAPR performances from all the results that obtained from Figure 4.1 to Figure 4.11 and from Figure A.1 to Figure A.6. From this table, almost all the techniques with modulation scheme could influence the PAPR result. From all the results obtained, it can be concluded that the Zadoff-Chu matrix Transform (ZCT) precoded Selected Mapping (SLM) based OFDM (ZCT-SLM-OFDM) system with 4QAM modulation and 𝑉 = 16 produced the best PAPR performance.

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38 Table 4.1 Plots of PAPR performance for conventional OFDM, ZCT precoded OFDM, SLM-OFDM, SLM-ZCT precoded OFDM and ZCT precoded SLM-OFDM with 𝑁 = 64 & 𝑉 = 4, 8, 16 with QPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM modulations

Types of

Techniques CCDF vs PAPRo (Y=10^-3)

modulation V=4 V=8 V=16

QPSK

Conventional OFDM 10.25 10.18 10.26

ZCT-OFDM 8.225 8.234 8.244

SLM-OFDM 7.561 6.824 6.214

SLM-ZCT-OFDM 5.063 4.372 3.61

ZCT-SLM-OFDM 4.769 3.941 3.414

4QAM

ZCT-OFDM 8.211 8.249 8.245

SLM-OFDM 7.634 6.823 6.334

SLM-ZCT-OFDM 5.656 4.364 3.609

ZCT-SLM-OFDM 4.67 4.015 3.348

16QAM

ZCT-OFDM 7.837 7.917 7.884

SLM-OFDM 7.569 6.795 6.235

SLM-ZCT-OFDM 5.171 4.321 3.8

ZCT-SLM-OFDM 5.021 3.988 3.514

64QAM

ZCT-OFDM 7.756 7.831 7.833

SLM-OFDM 7.501 6.83 6.258

SLM-ZCT-OFDM 5.389 4.391 3.716

ZCT-SLM-OFDM 5.111 4.391 3.583

256QAM

ZCT-OFDM 7.906 7.719 7.963

SLM-OFDM 7.584 6.736 6.263

SLM-ZCT-OFDM 5.089 4.23 3.429

ZCT-SLM-OFDM 5.278 4.35 3.835

Where y-axis = CCDF, x-axis = PAPRo 4.2.5 Overall 4-QAM (N = 64)

Figure 4.12 showed the result of CCDF versus PAPRo of conventional OFDM, ZCT precoded OFDM, SLM-OFDM, SLM-ZCT precoded OFDM and ZCT precoded SLM-OFDM with 𝑁 = 64 & 𝑉 = 4, 8, 16 for 4-QAM modulation scheme. The simulation result in Figure 4.12 showed all the techniques with different V, it was easier

ZCT PRECODING BASED SLM TECHNIQUE FOR PAPR REDUCTION

ZCT PRECODING BASED SLM TECHNIQUE FOR PAPR REDUCTION

LOO TWAN ZHAN

UNIVERSITI SAINS MALAYSIA

2017

ZCT PRECODING BASED SLM TECHNIQUE FOR PAPR REDUCTION

By

LOO TWAN ZHAN

Thesis submitted in fulfillment of the requirements for the degree of

Bachelor of Engineering (Electronic Engineering)

JUNE 2017

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

LIST OF ABBREVIATIONS

ABSTRAK

ABSTRACT

CHAPTER 1 INTRODUCTION

CHAPTER 2

LITERATURE REVIEW

CHAPTER 3

METHODOLOGY

CHAPTER 4