# High Peak To Mean Envelope Power Ratio Computer Science Essay

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This project report with respect to Techniques to tackle high peak to mean envelope power ratio is the result of the detailed work carried out as a part of BEng in Electronics and digital communication at university of Hertfordshire Faculty of Science, Technology and Creative Arts, at School of Engineering and Technology.

In the design of large and complex digital systems, it is often necessary to have one device communicate digital information faster as possible. Hence the technique of multi-carrier systems has recently been receiving wide interest, especially for high data-rate transmission applications around the world.

There are many recognized obstacles to overcome in multicarrier systems to provide high efficiency. Among, high peak-to-mean-envelope-power ratio (PMEPR) is the one of the major obstacles that is available. It adds up constructively and produced large peaks; therefore power amplifier should be highly linear that significantly hampers its power efficiency of orthogonal frequency division multiplexing (OFDM), digital subscriber lines and other broadband multicarrier systems.

The purpose of this project is to investigate the techniques to tackle high peak to mean envelope power ratio and simulate those techniques on matlab and observe the outputs and evaluate the performances of reduction of high peaks. Apply the improvements to the techniques to achieve faster and efficient transmission in multicarrier systems consider as the future development of this product.

TABLE OF CONTENTS

CHAPTER 1 1

INTRODUCTION 1

INTRODUCTION 2

1.1 Introduction 2

1.2 Project Aim 2

1.3 Report Outline 3

CHAPTER 2 4

MULTI CARRIER SYSTEMS 4

2.1 Introduction 5

2.2 Development of multi carrier systems 6

2.3 Different Form of Multi Carrier Systems. 7

2.3.1 Orthogonal Frequency Division Multiplexing (OFDM) 7

2.3.2 Code Division Multiple Access 7

2.4 PMEPR and Effects 7

2.4.1 Peak to mean average power ratio (PMEPR) 7

2.4.2 Mathematical Definition of PMEPR 9

2.4.3 Effects of PMEPR 10

Chapter 3 12

Orthogonal Frequency Division Multiplexing (OFDM) 12

3.1 Introduction 13

3.2 OFDM System 13

3.3 OFDM Advantages and Disadvantages 15

3.3.1 OFDM Advantages 15

4.3.2 OFDM Disadvantages [14] 17

Chapter 4 18

Techniques to tackle high PMEPR 18

Techniques to Tackle High PMEPR 19

4.1 Introduction 19

4.2 Comparison of methods 21

4.3 Evaluation of PMEPR reduction techniques 21

Chapter 5 23

Implementation and Results 23

Implementation and Results 24

5.1 Introduction 24

5.1 Amplitude Clipping 24

5.1.1 Analysis on Amplitude clipping 27

5.2 Selective Mapping 28

5.2.1 Analysis on Selective Mapping 31

Chapter 6 32

Conclusion 32

Conclusion 33

5.1 Conclusion 33

5.2 Future developments 34

LIST OF FIGURES

Figure 1 Schematics of a multi carrier system transmitter [2] 6

Figure 2 - PMEPR for a 16-channel OFDM signal 8

Figure 3 - Nonlinear behaviour of the PA [7] 11

Figure 4 - Frequency domain distribution of signals [11] 14

Figure 5 - OFDM output wave without clipping 26

Figure 6 - OFDM transmitter with amplitude clipping 26

## GLOSSARY

ADSL - Asymmetric Digital Subscriber Line

BER - Bit Error Rate DAB : Digital Audio Broadcasting

DSP - Digital Signal Processor ICI: Inter Carrier Interference

ISI - Inter Symbol Interference

LAN - Local Area Network Multiplex

OFDM - Orthogonal Frequency multiplexing

PMPER - Peak to Mean Envelope Power Ratio

ADSL - Asynchronous Digital Subscriber

AWGN - Additive White Gaussian Noise

BER - Bit Error Rate

SNR - Signal to Noise Ratio

CDMA - Code Division Multiple Access

DFT - Discrete Fourier Transform

IFFT - Inverse Fast Fourier Transform

FDMA - Frequency Division Multiple Access

AD - Analogue to Digital

DA - Digital to Analogue

## CHAPTER 1

## INTRODUCTION

INTRODUCTION

## 1.1 Introduction

Communication is one of the important aspects of life. With the advancement in age and its growing demands, there has been rapid growth in the field of communications. Signals, which were initially sent in the analogue domain, are being sent more and more in the digital domain these days. For better transmission, even single carrier waves are being replaced by multi carrier systems. CDMA and OFDM are nowadays being implemented commonly and very much popular.

In the OFDM system, orthogonally placed sub carriers are used to carry the data from the transmitter end to the receiver end. Presence of guard band in this system deals with the problem of ISI and noise is minimized by larger number of sub carriers. But the large Peak to Mean Envelop Power Ratio of these signal have some undesirable effects on the system.

In this thesis it is focused on learning the basics of an multi carrier system and has undertaken various methods to reduce the PMEPR in the systems which can be used more commonly and effectively.

## 1.2 Project Aim

The primary aim of this project is to find out different techniques to combat with high peek to mean average power ratio in multi carrier system which is a major drawback in multi carrier systems such OFDM where numbers of subcarriers are available. In order to accomplished the above mentioned objective that the software package that used is matlab R2010a.

## 1.3 Report Outline

Chapter 1 Introduction

This chapter gives a brief introduction of the topic that covers during the project period.

Chapter 2 Multicarrier Systems

In this chapter the theoretical and functional procedures in multicarrier systems and PMEPR as a major issue in such systems has been described.

Chapter 3 Orthogonal Frequency Division Multiplexing

In this chapter, OFDM has been taken as an example and describe the functional procedures and described how PMEPR affect to the OFDM.

Chapter 4 Techniques To Overcome High PMEPR.

This chapter can be considered as one of the most important chapters which

is dedicated to describe the techniques that are proposed and being used to reduce high peak to mean envelope power ratio in multicarrier systems.

Chapter 5 Implementation and results

Chapter 5 is the core of this project. It is described the amplitude clipping and selective mapping, system implementations and described the recorded results were discussed and concluded.

Chapter 6 Future Work

There are few modifications can be done to the system setup for make this two techniques more efficient and effective to employ them to reduce high peak to average power and this chapter is dedicated for that purpose.

## CHAPTER 2

## MULTI CARRIER SYSTEMS

## Multi carrier systems

## 2.1 Introduction

Multi-carrier System is method of transmitting data by splitting it into several components, and sending each of these components over separate carrier signals. The individual carriers have narrow bandwidth, but the composite signal can have broad bandwidth. The advantage of Multi Carrier System is that it has relative immunity to fading which is caused by transmission over more than one path at a time.

This is also referred to as multi path fading. Multi Carrier Systems are less susceptible than single-carrier systems to interference caused by impulse noise, and have enhanced immunity to inter-symbol interference. And provide sufficient transmission [1]

In an orthogonal frequency division multiplexing (OFDM) system, a set of equally spaced carriers are selected with each carrying a portion of the whole transmitted signal, thus resulting in a parallel transmission of different bits at different frequencies. Each individual carrier, commonly called a subcarrier, transmits information by modulating the phase and possibly the amplitude of the subcarrier over the symbol duration. That is, each subcarrier employs a modulation scheme to convey information just as conventional single carrier systems.

Figure 1 shows the schematics of a multi carrier system transmitter. It is seen that the input data stream is first encoded by a modulator and then separated into M parallel sub streams by virtue of a serial-to-parallel converter. Each sub stream of data is modulated by its individual carrier [2]

Figure 1 Schematics of a multi carrier system transmitter [2]and the summed signal is transmitted by the RF part of the transmitter after

## 2.2 Development of multi carrier systems

Multi Carrier System benefited from considerable research due to many applications, certainly to a much lesser extent than direct-sequence (DS) spread spectrum. It was known from experiments with wireless data transmission that the selection of the modulation technique is highly critical. In the early days of mobile communications, many attempts to connect a telephone modem to a cellular phone failed miserably, mainly because of the poor anticipation to the mobile channel anomalies, although entrepreneurs rapidly recognised the demand for wireless data communications. [3]

Experiments and product tests rapidly revealed that the mobile fading channel needed specific solutions for the modulation scheme, bit rate, packet length and other aspects. Among the many proposals, Multi- Carrier Modulation appeared one of the most elegant solutions for wireless digital transmission at high symbol rate. The signal waveform used for Multi- Carrier transmission has intriguing properties. The rapid increase in digital signal processing power in radio receivers has given way for large-scale use of this idea. [3]

## 2.3 Different Form of Multi Carrier Systems.

## 2.3.1 Orthogonal Frequency Division Multiplexing (OFDM)

OFDM uses three transmission principles, multi rate, multi symbol, and multicarrier. OFDM is similar to frequency division multiplexing (FDM). OFDM distributes the data over a large number of carriers that are spaced apart at preÂcise frequencies. The spacing provides the Orthogonality in this technique, which prevents the demodulator from seeing frequencies other than their own.[4]

## 2.3.2 Code Division Multiple Access

CDMA uses spread spectrum techniques and their inherent interference immunity to achieve access to the spectrum by multiple users. Spread spectrum systems take an inforÂmation data stream, including coding and interleaving, and multiply it by a pseudorandom noise (PN) code sequence at a data rate that is much higher than the rate of the informaÂtion data stream. This process, in effect, spreads the signal over a bandwidth that is much greater than the bandwidth of the information signal.[5]

## 2.4 PMEPR and Effects

## 2.4.1 Peak to mean average power ratio (PMEPR)

As an OFDM signal is the result of adding up a number of independently modulated sub-carriers, it can have a very large instantaneous power compared to the average power of the signal. The worst case occurs when the signals on the n subcarriers all have the same phase. When added together, the signal has a peak envelope power that is n (or more) times the average envelope power. This effect, for an OFDM signal using a 4-QAM constellation over 16 subcarriers, is illustrated in Figure 2.

Figure 2 - PMEPR for a 16-channel OFDM signal

Figure 2 - PMEPR effect on 4-QAM constellation over 16 subcarriers [6]

Above figure shows, these high peaks occur rather infrequently, however their presÂence means that somehow it is required to reduce these peaks and have to design RF power amplifiers to deal with the peaks. Even though, most of the time, the amplifiers will be operating in only a fraction of their linear dynamic range.[6]

Other than the reduced effiÂciency of the RF power amplifier, disadvantages of having signals with high PMEPR include the increased complexity required in the analogue-to-digital and digital-to-analogue converters. Other concerns such as regulatory limits on the peak power of transmissions, further motivation to find solutions to control the PMEPR of the transmitted OFDM signal.[6]

## 2.4.2 Mathematical Definition of PMEPR

The PMEPR Defined as follows

Where Pav is the mean envelope power of an OFDM signal, and the average is taken either over all possible OFDM signals, or over all the OFDM signals produced based on some codebook.

Assuming the samples to be mutually uncorrelated, the cumulative distribution function for the Peak Power per OFDM symbol can be given by

This is plotted for different values of N, and as it can be seen from Figure 3 the system is more susceptible to PMEPR when subcarrier size increases. For a baseband OFDM signal with N subcarriers, PMEPR may be as large as N for PSK modulation if N sub channels add coherently.

Reduction of subcarrier is one way to reduce PAPR but not efficient. Also from the Figure 3, we can infer that high PMEPR does not occur often. Considering these infrequent large peaks, a common approach is to perform clipping in order to mitigate the PAPR. These peaks are removed at a cost of self-interference and bandwidth regrowth.

Figure 3 - PMEPR Vs Subcarriers [7]

## 2.4.3 Effects of PMEPR

This distorts the transmitted signal if the transmitter contains nonlinear compoÂnents such as power amplifiers (PAs). Since PA is forced to operate in the nonlinear region. The nonlinear effects may cause in-band or out-of-band distortion to sigÂnals such as spectral spreading, intermodulation, or change the signal constellation. Out-of-band distortion is detrimental even if the in-band distortion is tolerable.

To have distortion less transmission, the PAs require a back off, which is approximately equal to the PMEPR. This decreases the efficiency for amplifiers and increases the cost. High PAPR also requires high range and precision for the analogue-to-digital converter (ADC) and digital-to-analogue converter (DAC), as a result, reducing the PMEPR of practical interest.[7]

Figure 3 - Nonlinear behaviour of the PA [7]

Figure 5 illustrates nonlinear behaviour of the Power amplifier. It is desired to operate the power amplifier in the linear region. To avoid the high peaks, average input power may be decreased. Operating region of the power amplifier is called input back-off and the resulÂtant signal is guaranteed to be in output back-off range.

High input back off reduces the power efficiency and would mandate the cost of the power amplifier higher, since input back off is usually greater than or equal to the PMEPR of the signal. Ideally, the average and peak values should be as close as can be in order to maximize the efficiency of the power amplifier. PMEPR mitigation relaxes the power amplifier back off requirements as well as the high resolution requirements on ADC and DAC. [8]

High PAPR corresponds to a wide power range which requires more complicated analogue-to-digital (A/D) and digital-to-analogue (D/A) converters in order to accommodate the large range of the signal power values. Therefore, high PAPR increases both the complexity and cost of implementation.

## Chapter 3

## Orthogonal Frequency Division Multiplexing (OFDM)

## Orthogonal Frequency Division Multiplexing

## 3.1 Introduction

Orthogonal frequency division multiplexing (OFDM) is a promising technique for achieving high data rate and combating multipath fading in wireless communications. OFDM can be thought of as a hybrid of multi-carrier modulation (MCM) and frequency shift keying (FSK) modulation. MCM is the principle of transmitting data by dividing the stream into several paralÂlel bit streams and modulating each of these data streams onto individual carriers or subcarriers FSK modulation is a technique whereby data is transmitted on one carrier from a set of orthogoÂnal carriers in each symbol duration.

Orthogonality amongst the carriers is achieved by separatÂing the carriers by an integer multiple of the inverse of symbol duration of the parallel bit streams. With OFDM, all the orthogonal carriers are transmitted simultaneously. In other words, the entire allocated channel is occupied through the aggregated sum of the narrow orthogonal sub bands. By transmitting several symbols in parallel, the symbol duration is increased proporÂtionately, which reduces the effects of ISI caused by the dispersive Rayleigh-fading environment.[9]

## 3.2 OFDM System

The block diagram of an OFDM system is shown in Figure 3.1. The transmitter first converts the input data from a serial stream to parallel sets. Each set of data contains one symbol, Si, for each subcarrier. For example, a set of four data would be [S0 S1 S2 S3].

Figure 6 - The block diagram of an OFDM system [10]

Before performing the Inverse Fast Fourier Transform (IFFT), this example data set is arranged on the horizontal axis in the frequency domain as shown in Figure 2. This symmetrical arrangement about the vertical axis is necessary for using the IFFT to manipulate this data [11].

Figure 4 - Frequency domain distribution of signals [11]

An inverse Fourier transform converts the frequency domain data set into samples of the corresponding time domain representation of this data. Specifically, the IFFT is useful for OFDM because it generates samples of a waveform with orthogonal frequency components.

Then, the parallel to serial block creates the OFDM signal by sequentially outputting the time domain samples. The channel simulation will allow examination of the effects of noise, multipath, and clipping. By adding random data to the transmitted signal, simple noise can be simulated. Multipath simulation involves adding attenuated and delayed copies of the transmitted signal to the original.

The receiver performs the inverse of the transmitter. First, the OFDM data are split from a serial stream into parallel sets. The Fast Fourier Transform (FFT) converts the time domain samples back into a frequency domain representation. The magnitudes of the frequency components correspond to the original data. Finally, the parallel to serial block converts this parallel data into a serial stream to recover the original input data. [12]

## 3.3 OFDM Advantages and Disadvantages

## 3.3.1 OFDM Advantages

OFDMA which is the newest multi carrier technique has been recognized as the most feasible multiple access technique for broadband data services. OFDMA provide number of advantages which are described below and have some shortcomings too. [13]

High Spectral Efficiency: OFDM achieves high spectral efficiency by using orthogonal sub-carriers. Orthogonality allows sub-carriers' spectra to overlap which in turn enables transmission of more data than FDM over the same fixed bandwidth.

Resistance against fading and interference: OFDM is relatively robust against interference since it usually affects only a fraction of the sub-carriers. Frequency-selective fading on the other hand can affect each subcarrier's performance.

However, since the bandwidth of each subcarrier is small, the performance loss of these sub-carriers can be accommodated with efficient coding. OFDM facilitates coding and interleaving across sub-carriers in the frequency domain that can provide robustness against burst errors.

Reduced Computational Complexity: The FIT and IFFT reduce the modem complexity and the processing requirements grow only slightly higher than linearly with data rate or bandwidth. With the FFT the number of operations in each OFDM symbol is in the order of N log: N. The implementation complexity of single carrier systems u ill) an equalizer is at least Nix1, where lxÂ» is the number of taps in the equalizer.

Modulation and Coding: OFDM allows different modulation and coding schemes for each subcarrier. This capability improves the end-user performance in comparison to when only one modulation and one or few code rates are used. OFDM is well suited for adaptive modulation and coding, which allows the system to make the best of the available channel conditions.

## 4.3.2 OFDM Disadvantages [14]

Frequency offset: In systems a local oscillator (LO) and a mixer are used at the transmitter to convert lower frequencies onto a higher frequency carrier. The receiver reverses the operation to extract the lower frequency content. If the LOs at both ends do not use the exact same frequency, the result will be an offset in the frequency. A frequency offset at the OFDM receiver can cause losses in subcarrier Orthogonality, and thus introduce inter-channel interference (ICI).

Phase offset: The changes in the phase also cause offsets and loss of Orthogonality at the receiver. Phase changes mainly occur due to multipath fading over the radio interface. The minor phase shifts can be corrected by an equalizer while larger ones can cause ambiguity in bit interpretations.

High peak to mean envelope power ratio (PMEPR): A process OFDM signal can have large peaks resulting in a large dynamic range and a high PMEPR. If the received signal level is very high it can saturate receiver amplifiers or D/A converters; the result will be a distorted signal. The distortion will increase the SNR needed to maintain adequate performance. Linearity requirements in both the receiver and transmitter must be adjusted to account for PMEPR.

I/Q imbalance: OFDM signals are combined with high order modulation to maximize spectral efficiency and achieve broadband data rates. The analogue in-phase and quadrature (I/Q) modulators and demodulators are often used in OFDM communications. These I/Q modulators and demodulators have imperfections that result in an imperfect match between the two baseband signals, I and Q, which represent the complex carrier. For example, gain mismatch might cause the "I" signal to be slightly smaller than the "Q."

## .

## Chapter 4

## Techniques to tackle high PMEPR

Techniques to Tackle High PMEPR

## 4.1 Introduction

To minimise the OFDM system performance degradation due to PMEPR, several techniques has been explored each with varying degrees of complexity and performance enhancements. These schemes can be divided into three general categories.

Signal distortion techniques

Signal clipping

Peak windowing

Peak cancellation

Coding techniques

Symbol scrambling techniques

The clipping technique employs clipping or nonlinear saturation around the peaks to reduce the PAPR. It is simple to implement, but it may cause in-band and out-of-band interferences while destroying the Orthogonality among the subcarriers. This particular approach includes block-scaling technique, clipping and filtering technique, peak windowing technique, peak cancellation technique, Fourier projection technique, and decision-aided reconstruction technique. [15]

The coding technique is to select such code words that minimize or reduce the PAPR. It causes no distortion and creates no out-of-band radiation, but it suffers from bandwidth efficiency as the code rate is reduced. It also suffers from complexity to find the best codes and to store large lookup tables for encoding and decoding, especially for a large number of subcarriers. Golay- complementary sequence. Reed-Mullercodc, M-scquencc. or Hadamard code can be used in this approach.

The probabilistic (scrambling) technique is to scramble an input data block of the OFDM symbols and transmit one of them with the minimum PAPR so that the probability of incurring high PAPR can be reduced. While it does not suffer from the out-of-band radiation power. The spectral efficiency decreases and the complexity increases as the number of subcarriers increases. Furthermore, it cannot guarantee the PMEPR below a specified level. This approach includes SLM (Selective Mapping), PTS (Partial Transmit Sequence), TR (Tone Reservation) and TI (Tone Injection) techniques. [15]

The adaptive pre-distortion technique can compensate the nonlinear effect of a high power amplifier (HPA) in OFDM systems. It can cope with time variations of nonlinear HPA by automatically modifying the input constellation with the least hardware requirement (RAM and memory lookup encoder). The convergence time and MSE of the adaptive pre-distorter can be reduced by using a broadcasting technique and by designing appropriate training signals.

The DFT-spreading technique is to spread the input signal with DFT. which can be subsequently taken into I FFT. This can reduce the PAPR of OFDM signal to the level of single-carrier transmission. This technique is particularly useful for mobile terminals in uplink transmission. It is known as the Single Carrier-FDMA (SC-FDMA), which is adopted for uplink transmission in the 3GPP ITE standard. [15]

## 4.2 Comparison of methods

Several methods for PMEPR reduction have been since, for most of the approaches, there is currently no theoretical method predicting their PMEPR reduction capability; one should gain intuition from particular simulation results. The main characteristics of reduction methods are the capability of PMEPR reduction, distortion in the signal the method yields, the rate hit. Whether the method requires transmission of side information, and the complexity of implementation of the method. In Table 1, the mentioned characteristics are summarized for the described methods.

Method

PMEPR reduction

Distortion

Rate Hit

Side Information

Complexity

Coding

H

N

H

N

H

Clipping

H

Y

L

N

L

SLM

M

N

L-H

Y

L-H

Balancing

M

N

H

N

L

Codes of strength

M

N

L

Y

H

Trellis shaping

M

N

L-H

N

H

Tone injection

M

N

H

N

L-H

ACE

L

N

L

N

H

Constellation shaping

H

N

H

N

H

PTS

L

N

L-H

Y

L-H

Reduction carriers

M

N

L-H

N

H

Table 1 - Comparison between various PMEPR reduction techniques [16]

## 4.3 Evaluation of PMEPR reduction techniques

There are different approaches have been used to reduce the high peaks in OFDM wave form. And these have different strengths and drawbacks when it comes to reducing high PMEPR and they can be described using following categories. [17]

Distortion: Clipping introduces in-band and out-of-band distortion, thus increasing the error probability. Filtering removes the out-of-band radiation, but at the same time yields peak regrowth.

Rate hit: The price to be paid for PMEPR reduction is a loss in the number of possible transmits sequences. This loss is essential when coding is used and none when clipping or ACE is employed. The rate hit is low when either SLM. PTS, CS. Or TS is used for PMEPR reduction to the typical values, while it is high if we want to further decrease it. In TI and constellation shaping, the rate hit is high, since the total number of sequences chosen from the extended constellation is large. The rate loss in using reduction carriers depends on the choice of the number of such carriers. However, according to simulations, the method becomes efficient if the percentage of the reserved tones is high.

Side information: Transmission of side information may be problematic, and reÂquires special attention. Such methods as SLM, PTS, and CS require transmission of side information, although for each of them there exist modifications allowing this to be avoided.

Complexity: Such methods as SLM. PTS and CS require a comparison of the PMEPR of several sequences, which in turn yields a necessity of several DFTs. This may essentially increase the complexity of the transmitter. On the other hand, TI, ACE, and RC use iterative algorithm implementation, which could be challenging. As well as this, some of the methods, for instance TI and ACE. may lead to power increase in the transmit signal.

## Chapter 5

## Implementation and Results

Implementation and Results

## 5.1 Introduction

In this project amplitude clipping and selective mapping techniques have been simulated which are most effective and efficient techniques that use to reduce the peak to mean envelope power ratio. This is a crude method of combating the peak signals.

The effect of clipping in OFDM signals is that when transmitted signals have high PMPER, amplifiers may produce "clipping". In some way, clipping can be regarded as peaks of the input signal being simply cut-off by amplifiers. In selective mapping, different phase rotations are given to the symbols and symbol sequences which have minimum PMEPR is selected and transmit.

Finally, for implementation and simulation purposes Mat lab Software was used which is a technical computing language for high-performance numeric computation and data visualisation. Besides common matrix algebra operations, Matlab offers array operations that allow one to quickly manipulate sets of data in wide variety of ways.

## 5.1 Amplitude Clipping

The simplest technique for PAPR reduction might be amplitude clipping. Amplitude clipping limits the peak envelope of the input signal to a predetermined value or otherwise passes the input signal through unperturbed, that is, transmitted signal is clipped at amplitude A as follows:[18]

{ -A (If x < -A )

Y = X (If -A < x < A)

A (If x > A )

where 'X' denotes the signal before clipping and 'y' denotes the signal after clipping. Since the probability of the occurrence of the high peak power is low, clipping is effective for reducing the PMEPR. Block diagram on Figure 7 illustrates the OFDM transmitter where the amplitude clipping technique has applied in this stimulation, to reduce PMEPR

Figure 7 - OFDM transmitter with amplitude clipping

Figure 8 illustrates the output of the parallel to serial conversion on time domain, at the OFDM output wave form before applying amplitude clipping.

Figure 5 - OFDM output wave without clipping

Figure 8 - OFDM waveform without amplitude clipping

It can be recognized the high amplitudes occur at OFDM output wave form. And the next step was applying amplitude clipping to reduce or limit the high amplitudes at pre defined threshold value. Here, 0.4 is configured as threshold value and Figure 9 illustrates the OFDM output where the amplitudes were limited to 0.4.

Figure 6 - OFDM transmitter with amplitude clipping

In general, The performance of PAPR reduction schemes can be evaluated by using BER performance. According to Figure 10, it is observed that BER performance degradation once amplitude clipping technique is applied to the OFDM output waveform.

Figure 10 - BER Vs SNR for amplitude clipping

## 5.1.1 Analysis on Amplitude clipping

The transmitted OFDM signal could be heavily clipped with little effect on the received BER. The signal could the clipped without a significant increase in the BER. This means that the signal is highly resistant to clipping distortions caused by the power amplifier used in transmitting the signal.

The distortion caused by amplitude clipping can be viewed as another source of noise. The noise caused by amplitude clipping falls both in-band and out-of-band. In-band distortion cannot be reduced by filtering and results in error performance degradation, while out-of-band radiation reduces spectral efficiency [19] .

Filtering after clipping can reduce out-of-band radiation, but may also cause some peak regrowth so that the signal after clipping and filtering will exceed the clipping level at some points. To reduce overall peak regrowth, a repeated clipping-and-filtering operation can be used. Generally, repeated clipping-and-filtering takes many iterations to reach a desired amplitude level.

## 5.2 Selective Mapping

Selected mapping is considered as one of the efficient and effective which is being used for minimization of peak to mean envelope power of multicarrier transmission systems. A complete set of candidate signal is generated signifying the same information in selected mapping, and then concerning the most favourable signal is selected as consider to PAPR and transmitted. Figure 11 illustrate the block diagram of selective mapping method.

Figure 11 - OFDM transmitter with SLM technique

Simulation results shows, high PMEPR available at OFDM output wave form before applying any phase rotations and recorded as Figure 12.

Figure 12 - OFDM waveform without SLM

As the next step possible phase rotations 0 to 90 degrees, were applied and PMEPR was calculated and recorded in Figure 13.

Figure 13 - PMEPR Vs Phase rotations

It is noticed that the calculated PMEPR value before applying any phase rotations was 30. And after applying possible phase rotations, the minimum PMEPR can be observed when applying 11 degrees phase rotations and it was 4.59. OFDM output waveform was recorded in Figure 14.

Figure 14 - OFDM waveform with phase rotation

BER can be significantly higher at output wave form when using amplitude clipping as peak power reduction technique though it reduce high peaks significantly. Instead Selective mapping technique doe not cut off or remove the amplitudes in output waveform. Hence the degradation in BER is not significant as amplitude clipping. Observed BER performance curve is shown in Figure 15.

Figure 15 - BER Vs SNR for Selective mapping

## 5.2.1 Analysis on Selective Mapping

In the process of selective mapping it is necessary to transmit the side information indicating of selected signal to receiver. And erroneous decision of side information will seriously degrade the error performance. Also, it is requires a bank of IFFT to generate signals in the original SLM which usually increases the computational complexity significantly. 16 - Orthogonal subcarriers have been used for this simulation and it is said that if the number of subcarriers increases that leads to increasing of PMEPR and then the minimum PMEPR may give a different rotation of Phases.

## Chapter 6

## Conclusion

Conclusion

## 5.1 Conclusion

It has to be remembering that PMEPR is one of the significant issues that multi carrier systems are suffering from. Several methods have been deployed to reduce high peak to mean envelope power to make an efficient multicarrier transmission. Different methods have different abilities in degration of PMEPR with shortcomings.

During this project, the two most effective techniques, Amplitude clipping and Selective mapping have been simulated for observe their ability of high peak reduction. By observing the results it is noticed that amplitude clipping is an very effective solution for PMEPR and it reduce the complicity of the system. The main drawback of this technique is it leads to degration in BER due to amplitude cut-off.

To keep the BER in low as possible the system gives better performance, hence selective mapping is a better selection for reduce high peaks in OFDM wave form. Without applying clipping to the output waveform it dose apply different phase rotations to the output wave form and signal that have minimum PMEPR is selected and transmitted and gives significant reduction in PMEPR.

Finally, it can be recommended that between two methods which simulated selective mapping is a superior technique than amplitude clipping.

## 5.2 Future developments

Than staying on basics it is necessary to make the basics to improved version and efficiently overcome high peak to mean envelop power ratio. Therefore different improvements have been applied to the basic technologies which are already being used to mitigate shortcoming.

The distortion caused by amplitude clipping can be viewed as another source of noise. The noise caused by amplitude clipping falls both in-band and out-of-band. In-band distortion cannot be reduced by filtering and results in error performance degradation, while out-of-band radiation reduces spectral efficiency. Filtering after clipping can reduce out-of-band radiation, but may also cause some peak regrowth so that the signal after clipping and filtering will exceed the clipping level at some points. To reduce overall peak regrowth, a repeated clipping-and-filtering operation can be used. Hence applying clipping and filtering repeatedly can be used in amplitude clipping than using it once during process as future development.

The partial transmit sequence (PTS) scheme is another efficient approach for reducing PMEPR. One of the most important advantages of the PTS scheme as compared with other PMEPR reduction schemes is that we can apply it to a multi-carrier system with an arbitrary number of sub-carriers, and any order of modulation scheme. Implementing PTS scheme can be construct as future development and compare the performance of it with the other techniques which were simulated using matlab.

Considering Selective mapping (SLM) it is necessary to transmit the side information indicating of selected signal to receiver. And erroneous decision of side information will seriously degrade the error performance. Also, it is requires a bank of IFFT to generate signals in the original SLM which usually increases the computational complexity significantly. Hence, selective mapping with turbo codings or any other improved version of selective mapping can be simulated as a future development in this project.