Excerpt

## Table of Contents

I Introduction

1.1 Introduction to LTE

1.2 Technologies Involved

1.2.1 OFDM (Orthogonal Frequency Division Multiplexing)

1.2.2 OFDMA (Orthogonal Frequency Division Multiplexing Access)

1.2.3 MIMO (Multiple Input Multiple Output)

1.2.4 SC-FDMA (Single Carrier Frequency Division Multiple Access)

1.3 Brief History of OFDM

1.3.1 Multipath Channels

1.4 Basic Concepts

1.4.1 Frequency Division Multiplexing (FDM)

1.4.2 Time Division Multiplexing (TDM)

1.4.3 Orthogonal Frequency Division Multiplexing (OFDM)

1.5 Introduction to OFDM

1.5.1 Orthogonal Frequency Division Multiplexing (OFDM)

1.5.2 OFDM is a special case of FDM

1.6 SC-FDMA and OFDMA Tx-Rx Structure

1.7 Inter-Symbol Interference

1.8 Inter Carrier Interference

1.9 Understanding concept of Cyclic Prefix

1.10 OFDM using Inverse DFT

1.11 Advantages of OFDM

1.12 Disadvantages of OFDM

1.13 Peak to Average Power Ratio

1.14 PAPR Reduction Techniques

II Literature Review

2.1 Different methods for Peak-to-Average Power (PAPR) Reduction in Orthogonal Frequency Division Multiplexing (OFDM)

III Problem Identification

3.1 Clipping & Filtering

3.2 Coding

3.3 Interleaving

3.4 Companding

3.5 Peak Windowing

3.6 Addictive Corrective Function

3.7 Selected Mapping (SLM)

3.8 Tone Reservation

3.9 Tone Injection

3.10 Selective Scrambling (Interleaving)

IV Methodology

4.1 Objectives

4.2 Hardware& Software Required

4.2.1 Hardware Required

4.2.2 Software Required

4.3 Simulation model of OFDM System

4.3.1 Random Data Generator

4.3.2 Serial to Parallel Conversion

4.3.3 Modulation of Data

4.3.4 Inverse Fourier Transform

4.3.5 Guard Period

4.3.6 Parallel to Serial Converter

4.3.7 Channel

4.3.8 Receiver

4.4 Calculation of PAPR & CCDF of Original OFDM Signal

4.5 Complimentary Cumulative Distribution Function (CCDF)

4.6 Calculation of SNR & BNR of Original OFDM Signal

4.6.1 Additive White Gaussian Noise (AWGN) Channel

4.6.2 Signal to Noise Ratio (SNR)

4.6.3 Bit Error Rate (BER)

4.7 Criteria for Selection of PAPR Reduction Techniques

4.8 Definition of Efficient PAPR

V PAPR Reduction Techniques

5.1 Selective Mapping

5.2 Clipping - Based Active Constellation Extension Algorithm

5.2.1 Limitations of CB-ACE Algorithm

5.3 Exponential Companding Transform

5.3.1 Companding of original OFDM Signal by using Exponential Companding Transform

5.3.2 Advantages of Exponential Companding Transform

5.3.3 Limitation of Exponential Companding Transform

5.4 Adaptive Active Constellation extension Algorithm

VI Proposed Method

6.1 Selected Mapping with Riemann Matrix

6.2 Concept of Riemann matrices

VII Results and Discussion

7.1 PAPR vs CCDF of Original OFDM Signal

7.2 BER of Original OFDM Signal

7.3 PAPR vs CCDF of Original OFDM signal using Selective Mapping (SLM) Technique

7.4 CCDF plot for Clipping-based Active Constellation Extension (CB-ACE) Technique

7.5 BER plot for Clipping-based Active Constellation Extension (CB-ACE) Technique

7.6 CCDF plot for Adaptive Active Constellation Extension (Adaptive-ACE) Technique

7.7 BER plot for Adaptive Active Constellation Extension (Adaptive-ACE) Technique

7.8 CCDF plot for Exponential Companding Technique

7.9 BER plot for Exponential Companding Technique

7.10 CCDF plot for proposed technique- SLM with Riemann Matrix

7.11 BER plot for proposed technique- SLM with Riemann Matrix

VII Conclusion and Future Scope

Research Paper Published

References

## ABSTRACT

As a promising technique, OFDM has been widely used in emerging broadband communication systems, such as digital audio broadcasting (DAB), high-definition television (HDTV), wireless local area network (IEEE 802.11a and HIPERLAN/2).

However, as the OFDM signals are the sum of signals with random amplitude and phase, they are likely to have large PAPR that requires a linear high-power- amplifier (HPA) with an extremely high dynamic range, which is expensive and inefficient. Furthermore, any amplifier nonlinearity causes intermodulation products resulting in unwanted out-of-band power. A number of approaches have been proposed to deal with the PAPR problem, including clipping, clipping-and-filtering (CF), coding, companding transform, active constellation extension (ACE), selected mapping (SLM), partial transmit sequence (PTS), and so on.

This thesis proposes an improvement in Selected Mapping technique and Simulation results are compared to existing techniques namely Exponential Companding Transform, Repeated Clipping and Filtering and Adaptive Active Constellation Extension. The improvements which are proposed in classical Selective Mapping technique satisfies the PAPR Reduction criteria with reducing the computational complexity. Also this new scheme has an important advantage of avoiding the extra bits along with the transmitted OFDM signal .This scheme can also be applied to the multiple transmitting antenna cases.

## LIST OF ABBREVIATIONS

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## LIST OF TABLES

3.2 PAPR values of all possible data blocks for an OFDM signal with four subcarriers and BPSK modulation

8.1 Comparison of various PAPR reduction techniques in terms of CCDF

1.4.1 Comparison of various PAPR reduction techniques in terms of SNR and BER

## LIST OF FIGURES

1.1 Multiple Access Schemes

1.3.1 Multipath Propagation

1.4.1 Frequency Division Multiplexing

1.4.2 Time Division Multiplexing

1.5.1(a) Multi-carrier FDM and Multi-Code Division Multiplex

1.5.1(b) Minimum frequency difference required for carriers to be orthogonal

1.5.1(c) Example of OFDM spectrum for 5 orthogonal carriers

1.5.1(d) The area under a sine and a cosine wave over one period is always zero

1.5.2(a) Bandwidth utilization in Frequency Division

1.5.2(b) Bandwidth utilization of OFDM

1.6 SC-FDMA and OFDMA Tx-Rx Structure

1.9(a) Example of delay spread

1.9(b) Delayed version of Copied signal

1.9(c) Arrived delayed signal

1.9(d) Extended symbol using Cyclic prefix

1.9(e) Continuous signal after addition of cyclic prefix

1.9(f) Cyclic prefix of the signal

3.1 Power Amplifier Characteristics

3.2 Amplifier response of OFDM signal

3.3 Distortion in the Spectrum of OFDM signal after passing through HPA

3.4 Distortion in the Signal Constellation of OFDM signal after passing through HPA

3.3 Principle Schematic of PAPR Reduction by Interleaving

4.2.1 Block Diagram of OFDM System

5.1.1 Block Diagram of Selective Mapping Technique

6.2.1 Flow chart of proposed method

6.2.2 Block Diagram of proposed SLM Technique

7.1 PAPR Vs CCDF of OFDM signal

7.2 SNR vs BER of Original OFDM Signal

7.3.1 Independent signals generated with various phase rotations

7.3.2 Calculation of PAPR of independent carriers in SLM technique in Matlab Command Window

7.3.3 PAPR vs CCDF plot for SLM Technique for various N

7.3.4 Comparison of PAPR vs CCDF plot for original OFDM signal and then with SLM technique for N=

7.4.1 PAPR vs CCDF plot for combination of Clipping and Active Constellation Extension for various target ratios

7.5.1 SNR vs BER plot for combination of Clipping and Active Constellation Extension for various order of modulation techniques

7.6.1 PAPR vs CCDF plot for Adaptive ACE technique for different target clipping ratios

7.7.1 SNR vs BER plot for combination of Clipping and Active Constellation Extension for various modulation techniques

7.8.1 CCDF plot for Exponential Companding Technique

7.9.1 SNR vs BER by using Exponential Companding Transform

7.10.1 CCDF plot using SLM with Riemann Matrix

7.11.1 BER plot using SLM with Riemann Matrix

## INTRODUCTION

### 1.1 Introduction to Long term evolution (LTE)

The ever increasing demand for high data rates in wireless communications systems has arisen in order to support broadband services. Long term evolution (LTE) is standardized by the third generation partnership project (3GPP) and is an evolution of existing 3G technologies in order to meet projected customer needs over the next decades. Current working assumptions in 3GPP LTE are to use orthogonal frequency division multiplexing access (OFDMA) for downlink and single carrier-frequency division multiple access (SC- FDMA) for uplink. SC-FDMA is a promising technique for high data rate transmission that utilizes single carrier modulation and frequency domain equalization. Single carrier transmitter structure leads to keep the peak-to-average power ratio (PAPR) as low as possible that will reduce the energy consumption. SC-FDMA has similar throughput performance and essentially the same overall complexity as OFDMA.^{29}

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*Figure 1.1: Multiple access schemes ^{28} *

Recently, OFDMA has received much attention due to its applicability to high speed wireless multiple access communication systems. The problems associated with OFDM, however, are also inherited by OFDMA. Hence, OFDMA also suffers from high PAPR. In OFDMA process the whole data block is treated as one unit. OFDMA systems are more difficult since only part of the subcarriers in one OFDMA data block are of demodulated by each user’s receiver. If downlink PAPR reduction is achieved by schemes designed for OFDM, each user has to process the whole data block,then each user demodulates the assigned sub-carriers meant for them and extract their own information. This introduces additional processing for each user’s receiver. Various statistical PAPR characteristics and PAPR reduction in OFDM signals are analyzed in different research papers and various approaches have been proposed to reduce the PAPR including amplitude clipping, selected mapping technique, coding schemes, tone reservation technique etc.^{29}

3GPP is a standardization committee that has produced several specification documents for LTE. The different targets of LTE are^{30}:

- Peak Data Rates: Evolved Universal Terrestrial Radio Access (E-UTRA) is expected to support significantly increased instantaneous peak data rates. The peak data rates may depend on the number of transmit and receive antennas at the User Equipment (UE). For this baseline configuration, the system should support an instantaneous downlink peak data rate of 100 Mb/s within a 20 MHz downlink spectrum allocation and an instantaneous uplink peak data rate of 50 Mb/s within a 20 MHz uplink spectrum allocation.

- Latency: It is expected that at each user plane, latency should be less than 5 ms oneway and a control plane transition time of less than 50 ms from dormant to active mode and less than 100 ms from idle to active mode.

- User throughput: It is expected that 2-3 times higher downlink throughput than HSDPA.

- Spectrum efficiency: 3-4 times higher spectrum efficiency (in bits/s/Hz/site) in downlink and 2-3 times higher in uplink, compared to Release 6 High-Speed Downlink Packet Access (HSDPA).

- Mobility: LTE should support mobility across the cellular network and should be optimized for 0 to 15 km/h. Furthermore, should also support higher performance at 15 and 120 km/h. Connection shall be maintained at speeds from 120 km/h to 350 km/h (or even up to 500 km/h depending on the frequency band). Coverage: Cell ranges up to 5 km support the above targets; up to 30 km will suffer some degradation in throughput and spectrum efficiency and up to 100 km will have overall performance degradation.

- Spectrum flexibility: LTE should support several different spectrum allocation sizes

as: 1.25 MHz, 1.6 MHz, 2.5 MHz, 5 MHz, 10 MHz, 15 MHz and 20 MHz with both TDD and FDD modes. Shall also enable the flexibility to modify the radio resource allocation for broadcast transmission according to specific demand or operator’s policy.^{30}

### 1.2 Technologies involved

LTE employs different technologies such as OFDM, OFDMA, MIMO and SCFDMA. These methods are briefly described in the following subsections^{32}.

#### 1.2.1 OFDM (Orthogonal Frequency Division Multiplexing)

OFDM is a digital multi-carrier modulation scheme that distributes the data over a large number of carriers closely spaced. The two main characteristics are that each subcarrier is modulated using varying levels of QAM modulation and each OFDM symbol is preceded by a cyclic prefix (CP) used to effectively eliminate intersymbol interference (ISI). OFDM has several advantages such as can easily adapt to severe channel conditions, is robust against ISI and fading caused by multipath and provide high spectral efficiency. But it also has disadvantages as it is sensitive to Doppler shift, defined as the change in frequency of a wave for an observer moving relative to the source of the waves. It is also sensitive to frequency synchronization problems and having high peak-to-average-power ratio (PAPR).

#### 1.2.2 OFDMA (Orthogonal Frequency Division Multiple Access)

Orthogonal Frequency Division Multiple Access (OFDMA) is a multi-user version of OFDM. Multiple access is achieved by assigning different OFDM sub-channels to different users.

Among the advantages of OFDMA, one important property is having its robustness to fading and interference. It also averages the interferences within the cells using allocation with cyclic permutation and offers frequency diversity by spreading the carriers all over the used spectrum. On the other hand, OFDMA is higher sensible to frequency offsets and phase noise .Moreover, the resistance to the frequency-selective fading may partly be lost if very few sub-carriers are assigned to each user and if the same carrier is used in every OFDM symbol. OFDMA is used as the multiplexing scheme in the LTE downlink.

### 1.2.3MIMO (Multiple Input Multiple Output)

MIMO technology offers significant increases in data throughput and link range without additional bandwidth or transmitted power. There are multiple transceivers at both the base station and UE in order to enhance link robustness and increase data rates for the LTE downlink.

#### 1.2.4 SC-FDMA (Single Carrier Frequency Division Multiple Access)

LTE requirements in uplink differ in several aspects from downlink. The main fact is the transmission scheme used. Power consumption is a key consideration for UE terminals and for this; the high PAPR and related loss of efficiency associated to OFDM signaling are major concerns. As a result, an alternative to OFDM was sought for use in the LTE uplink.

The solution is Single Carrier - Frequency Domain Multiple Access (SC-FDMA) that suits very well with the LTE uplink requirements. The basic transmitter and receiver architecture is very similar (nearly identical) to OFDMA as shown in Figure 2., and it offers the same degree of multipath protection^{32}.

### 1.3 Brief History of OFDM

The idea of Orthogonal Frequency Division Multiplexing (OFDM) was proposed in mid 1960’s which used parallel data transmission and Frequency Division Multiplexing. In the 1960’s the OFDM was used in several high frequency military systems .In 1971 Weinstein and Ebert applied the Discrete Fourier Transform to parallel data transmission systems as a part of modulation and Demodulation process. In 1980’s OFDM was studied for high speed modem digital mobile communication and high density recording in which pilot tone was used to stabilize carrier and Frequency control and Trellis code was implemented which gave rise to Coded-OFDM.In 1780, Hirosaki suggested an equalization algorithm in order to suppress both intersymbol and intercarrier interference caused by the channel impulse response or timing and frequency errors. In 1980 , Hirosaki introduced the DFT -based implementation of Saltzburg’s O-QAM OFDM system. In 1990s, OFDM has been used extensively for wideband data communication over mobile radio FM channels, high-bit-rate digital subscriber lines (HDSL, 1.6 Mb/s), asymmetric digital subscriber lines (ADSL, 1536 Mb/s), very high-speed digital subscriber lines (VHDSL, 100 Mb/s), digital audio broadcasting (DAB) and HDTV terrestrial broadcasting. OFDM is used in wireless digital radio, TV transmissions, particularly in Europe, also used in wireless Local Area Networks (LANs) as specified by the IEEE 802.11, IEEE 802.16, IEEE802.20 and the European Telecommunications Standards Institute (ETSI) HiperLAN/2 standards.^{27}

#### 1.3.1 Multipath Channels

The transmitted signal faces various obstacles and surfaces of reflection, as a result of which the received signals from the same source reach at different times. This gives rise to the formation of “echoes” which affect the other incoming signals. Dielectric constants, permeability, conductivity and thickness are the main factors affecting the system. Multipath channel propagation is devised in such a manner that there will be a minimized effect of the echoes in the system in an indoor environment. Measures are needed to be taken in order to minimize echo in order to avoid ISI.

illustration not visible in this excerpt

*Figure 1.3.1 Multipath Propagation*

### 1.4 Basic Concepts

#### 1.4.1 Frequency Division Multiplexing (FDM)

Frequency Division Multiplexing is being used for a long time to carry the data more than one carrier signal. It divides the total channel bandwidth into sub channels so that each sub channel carries the modulated data into a separate carrier frequency. There will be some guard bands between the adjacent channels so that there is no inter channel interference .FDM technique are quite popular technique used in telephones line.

illustration not visible in this excerpt

*Figure 1.4.1 Frequency Division Multiplexing*

#### 1.4.2 Time Division Multiplexing (TDM)

Time Division Multiplexing is another efficient technique which improves the capacity by splitting the frequencies in different time slots. It allows the user to access the entire frequency band at a particular instant of time. Other users share the same frequency channel at different time slot. TDMA system divide the radio spectrum into time slots, and in each slot only one user is allowed to transmit and receive

illustration not visible in this excerpt

*Figure 1.4.2 Time Division Multiplexing*

#### 1.4.3 Orthogonal Frequency Division Multiplexing (OFDM)

In order to solve the bandwidth efficiency problem, Orthogonal Frequency Division Multiplexing (OFDM) technique is used. OFDM is a multicarrier transmission technique, which divides the total available bandwidth into many subcarriers; each subcarrier is modulated by a low rate data stream. In term of multiple access technique OFDM is similar to FDMA such that the multiple users access is achieved by subdividing the available bandwidth into multiple channels. However, OFDM uses the spectrum much more efficiently by spacing the channels much closer together. This is achieved by making all the carriers orthogonal to one another, preventing interference between the closely spaced carriers. The orthogonality of the carriers means that each carrier has an integer number of cycles over a symbol period. Due to this, the spectrum of each carrier has a null at the center frequency of each of the other carriers in the system. This results in no interference between the carriers, allowing to be spaced as close as theoretically possible. This overcomes the problem of overhead carrier spacing required in FDMA.^{27}

### 1.5 Introduction to OFDM

#### 1.5.1 Orthogonal Frequency Division Multiplexing (OFDM)

Orthogonal Frequency Division Multiplexing (OFDM) is a method of Digital Modulation in which a signal is split into several narrowband channels at different frequencies. The OFDM technology was first conceived in the 1960s and 1970s during the research into minimizing interference among the channels near each other in frequency. The main idea behind the OFDM is that since low-rate modulations are less sensitive to multipath, the better way is to send a number of low rate streams in parallel than sending one high rate waveform. This can be exactly done in OFDM. The OFDM divides the frequency spectrum into sub-bands small enough so that the channel effects are constant (flat) over a given sub-band. Then a classical IQ modulation (BPSK, QPSK, M-QAM, etc.) is sent over the sub-band. If designed correctly, all the fast changing effects of the channel disappear as they are now occurring during the transmission of a single symbol and are thus treated as flat fading at the received.

A large number of closely spaced orthogonal subcarriers are used to carry data. The data is divided into several parallel data streams or channels, one for each subcarrier.Each subcarrier is modulated with a conventional modulation scheme such as Quadrature Amplitude Modulation (QAM) or Phase Shift Keying (PSK) at a low symbol rate. The total data rate is to be maintained similar to that of the conventional single carrier modulation scheme with the same bandwidth. Orthogonal Frequency Division Multiplexing (OFDM) is a promising technique for achieving high data rates and combating multipath fading in Wireless Communications.

The independent sub-channels can be multiplexed by frequency division multiplexing called as multi carrier transmission and if they are multiplexed by Code division multiplexing then it is called multi-code transmission.

There is a precise mathematical relationship between the frequencies of the carriers. It is possible to arrange the carriers in an OFDM signal so that the sidebands of the individual carriers overlap and the signals can still be received without adjacent carrier interference. In order to do this the carriers must be mathematically orthogonal. The carriers are linearly independent (i.e. orthogonal) if the carrier spacing is a multiple of [Abbildung in dieser Leseprobe nicht enthalten]where[Abbildung in dieser Leseprobe nicht enthalten]is the symbol duration. Figure 1.5.1(b) shows the minimum frequency difference required for carriers to be orthogonal .The OFDM system transmits a large number of narrowband carriers, which are closely spaced.^{47}

illustration not visible in this excerpt

*Figure 1.5.1(a) Multi-carrier FDM and Multi-Code Division Multiplex*

If a sine wave of frequency a multiplied by a sinusoid (sine or cosine) of a frequency b,

illustration not visible in this excerpt

here both a and b are integers, since these two components are each a sinusoid, the integral is equal to zero over one period. The integral or area under this product is given by

illustration not visible in this excerpt

Since the carriers are all sine/cosine wave, we know that area under one period of a sine or a cosine wave is zero.So when a sinusoid of frequency *n* multiplied by a sinusoid of frequency *m/n*, the area under the product is zero. In general for all integers *n* and *m*, sin *mx*, cos *mx*, cos *nx*, sin *nx* are all orthogonal to each other. These frequencies are called harmonics.

illustration not visible in this excerpt

*Figure 1.5.1(b) minimum frequency difference required for carriers to be orthogonal*

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*Figure 1.5.1(c) Example of OFDM spectrum for 5 orthogonal carriers*

. The orthogonality allows simultaneous transmission of many sub-carriers in a tight frequency space without interference from each other. This is similar to CDMA, where codes are used to make data sequences independent (also orthogonal) which allows many independent users to transmit in same space successfully.^{13}

illustration not visible in this excerpt

*Figure 1.5.1 (d) The area under a sine and a cosine wave over one period is always zero.*

#### 1.5.2 OFDM is a special case of FDM

Orthogonal Frequency Division Multiplexing (OFDM) is a special case ofFrequency Division Multiplexing(FDM). Suppose a bandwidth goes from frequency say *a* to *b*, then this can be subdivided into a frequency of equal spaces. In frequency space the modulated carriers would look like this.

illustration not visible in this excerpt

*Figure 1.5.2(a) Bandwidth utilization in Frequency Division Multiplexing*

The frequencies a and bcan be anything, integer or non-integer since no relationship is implied between *a* and *b* same is true of the carrier center frequencies which are based on frequencies that do not have any special relationship to each other. If frequency[Abbildung in dieser Leseprobe nicht enthalten]and[Abbildung in dieser Leseprobe nicht enthalten]were such that for any *n*, an integer, the following holds.

illustration not visible in this excerpt

All three of these frequencies are harmonic to[Abbildung in dieser Leseprobe nicht enthalten]

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*Figure 1.5.2(b) Bandwidth utilization of OFDM*

In this case, these carriers are orthogonal to each other. Hence when added together, they do not provide interference with each other. In FDM, frequenciesare not orthogonal to each other, so it suffers interference from neighbor carriers. To provide adjacent channel interference protection, signals are moved further apart. Each carrier is separated apart by a 10% guard band. It is the guard band that keeps interference under control.^{27}

### 1.6 SC-FDMA and OFDMA Tx-Rx Structure

The transmitter of an SC-FDMA system converts a binary input signal to a sequence of modulated subcarriers. To do so, it performs the signal processing operations as shown in Figure 1.6.Signal processing is repetitive in a few different time intervals. Resource assignment takes place in transmit time intervals (TTIs).The TTI is further divided into time intervals referred to as blocks. A block is the time used to transmit all of subcarriers once. At the input to the transmitter, a baseband modulator transforms the binary input to a multilevel sequence of complex numbers xn in one of several possible modulation formats including binary phase shift keying (BPSK), quaternary PSK (QPSK), 16 level quadrature amplitude modulation (16-QAM) and 64-QAM.

illustration not visible in this excerpt

*Figure 1.6: SC-FDMA and OFDMA Tx-Rx Structure ^{18} *

Next,the transmitter groups the modulation symbols,[Abbildung in dieser Leseprobe nicht enthalten] into blocks, each containing N symbols. The first step in modulating the SC-FDMA subcarriers is to perform an N-point Discrete Fourier Transform (DFT), to produce a frequency domain representation[Abbildung in dieser Leseprobe nicht enthalten]of the input symbols. Then mapping of each of the N DFT outputs to one of the M (> N) orthogonal subcarriers that can be transmitted. As in OFDMA, a typical value of M is 256 subcarriers and [Abbildung in dieser Leseprobe nicht enthalten]is an integer submultiple of[Abbildung in dieser Leseprobe nicht enthalten]is the bandwidth expansion factor of the symbol sequence.

The transmitter performs two other signal processing operations prior to transmission. It inserts a set of symbols referred to as a cyclic prefix (CP) in order to provide a guard time to prevent inter-block interference (IBI) due to multipath propagation. The transmitter also performs a linear filtering operation referred to as pulse shaping in order to reduce out-of- band signal energy.

Thus, transmitted data propagating through the channel can be modelled as a circular convolution between the channel impulse response and the transmitted data block, which in the frequency domain is a point wise multiplication of the DFT frequency samples. Then, to remove the channel distortion,the DFT of the received signal can simply be divided by the DFT of the channel impulse response.

### 1.7 Inter - Symbol Interference(ISI)

Inter-Symbol Interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable. It is usually caused by multipath propagation or the inherent non - linear frequency response of a channel causing successive symbols to blur together. The presence of ISI in the system introduces error in the decision device at the receiver output. Therefore, in the design of the transmitting and receiving filters, the objective is to minimize the effects of ISI and thereby deliver the digital data to its destination with the smallest possibleerror rate.

### 1.8 Inter - Carrier Interference

Presence of Doppler shifts and frequency and phase offsets in an OFDM system causes loss in orthogonality of the sub-carriers. As a result, interference is observed between sub-carriers. This phenomenon is known as inter - carrier interference (ICI).

### 1.9 Understanding Concept of Cyclic Prefix

Cyclic Prefix can be best understood with the following example.Suppose you are driving a car in rain, and the car in front of you splashes a bunch of water on you. What do you do? You move further back and put a little distance between you and the front car, far enough so that the splash won’t reach you. If we compare the reach of splash to delay spread of a splashed signal then we have a better picture of the phenomena and how to avoid it.^{33}

illustration not visible in this excerpt

*Figure 1.9(a) Example of Delay spread*

Increasing the distance avoid splashesfrom front car. The time elapsed to reach the splash is same as the delay spread of a signal. Figure 1.9(a)shows the symbol and its splash. In composite, these splashes are noise and affect the beginning of the next symbol.

illustration not visible in this excerpt

*Figure 1.9(b) Delayed version of the copied signal*

To mitigate this noise at the front of the symbol, symbol is further moved away from the region of delay spread as shown below. A little bit of blank space has been added between symbols to catch the delay spread

illustration not visible in this excerpt

*Figure 1.9(c) Arrived delayed signal*

But signalscannot have blank spaces. This will not work for the hardware which likes to crank out signals continuously. So there should be something here. Suppose the symbol run longer as the first choice.

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*Figure 1.9(d)Extended symbol using cyclic prefix*

Suppose the symbol is extended into the empty space, so that the actual symbol is more than one cycle. But now the start of the symbol falls into the danger zone, and this start is the most important thing about the symbol because the slicer needs it to take a decision about the bit. The start of the symbol is undesired to fall in this region, so the symbol is slided backwards, so that the start of the original symbol lands at the outside of this zone.

*Figure 1.9(e)Continuous signal after addition of cyclic prefix*

1. The start of the symbol should be out of the delay spread zone so that it will not corrupt.

2. The signal should be started at the new boundary so that the actual symbol falls outside this zone *.*

Therefore symbol is slided to start at the edge of the delay spread time and then the guard space is filled with a copy of tail end of the symbol. Then, the symbol is extended to 1.25 times long.To do this, copy the back of the symbol is taken and glued in the front. In reality, the symbol source is continuous, so the starting phase is adjusted ,making the symbol period longer.

illustration not visible in this excerpt

*Figure 1.9(f)Cyclic prefix of the signal*

This procedure is called adding a cyclic prefix. The prefix is 10% to 25% of the symbol time. We add the prefix just after doing the IFFT. When the signal arrives at the receiver, this cyclic prefix is removed, to get back the original periodic signal. After doing FFT the symbols are recovered on each carrier.^{13}

The Cyclic Prefix or Guard Interval is a periodic extension of the last part of an OFDM symbol that is added to the front of the symbol in the transmitter, and is removed at the receiver before demodulation.

The cyclic prefix has to two important benefits:

The cyclic prefix acts as a guard interval. It eliminates the inter-symbol interference from the previous symbol.

It acts as a repetition of the end of the symbol thus allowing the linear convolution of a frequency-selective multipath channel to be modeled as circular convolution which in turn maybe transformed to the frequency domain using a discrete fourier transform. This approach allows for simple frequency-domain processing such as channel estimation and equalization.

### 1.10 OFDM using Inverse DFT

Consider a data sequence[Abbildung in dieser Leseprobe nicht enthalten] where each[Abbildung in dieser Leseprobe nicht enthalten] is a complex symbol.(the data sequence could be the output of a complex digital modulator, such as QAM, PSK etc). Suppose we perform an IDFT on the sequence [Abbildung in dieser Leseprobe nicht enthalten](the factor 2 is used purely for scaling purposes), we get a result of [Abbildung in dieser Leseprobe nicht enthalten]complex numbers[Abbildung in dieser Leseprobe nicht enthalten]as:

[Abbildung in dieser Leseprobe nicht enthalten] represents the symbol interval of the original symbols. Passing the real part of the symbol sequence represented by equation (1.10.1) thorough a low-pass filter with each symbol separated by duration of[Abbildung in dieser Leseprobe nicht enthalten]second yields the signal,

illustration not visible in this excerpt

[Abbildung in dieser Leseprobe nicht enthalten]The signalrepresents the baseband version of the OFDM.

### 1.11 Advantages of OFDM

The Orthogonal Frequency Division Multiplexing (OFDM) transmission scheme has the following key advantages^{34}

- OFDM is computationally efficient by using FFT techniques to implement the modulation and demodulation functions.

- By dividing the channel into narrowband flat fading sub channels, OFDM is more resistant to frequency selective fading than single carrier systems. By using adequate channel coding and interleaving, the symbols lost can be recovered, due to the frequency selectivity of the channel.

- OFDM is a bandwidth efficient modulation scheme and has the advantage of mitigating ISI in frequency selective fading channels.

- Channel equalization becomes simpler as compared to adaptive equalization techniques with single carrier systems.

- In conjunction with differential modulation, there is no need to implement a channel estimator.

- OFDM provides good protection against co-channel interference and impulsive parasitic noise.

- OFDM can easily adapt to severe channel conditions without complex time- domain equalization.

- OFDM eliminates Inter Symbol Interference (ISI) through the use of a cyclic prefix.

- OFDM is less sensitive to sample timing offsets than the single carrier systems.

- OFDM provides greater immunity to multipath fading and impulse noise.

- OFDM makes efficient use of the spectrum by allowing overlapping.

1.12 Disadvantages of OFDM

The Orthogonal Frequency Division Multiplexing (OFDM) transmission scheme is an attractive technology but has the following disadvantages:

- OFDM is more sensitive to carrier frequency offset and drift than single carrier systems, due to leakage of the Discrete Fourier Transform (DFT).

- OFDM is sensitive to frequency synchronization problems.

- OFDM is sensitive to Doppler Shift.

- The OFDM signal has amplitude with a very large dynamic range; therefore it requires RF power amplifiers with a high Peak-to-Average Power Ratio (PAPR).

- The high PAPR increases the complexity of the Analog-to-Digital (A/D) and Digitalto-Analog (D/A) converters.

- The high PAPR also lowers the efficiency of power amplifiers.^{34}

### 1.13 Peak to Average Power Ratio

Presence of large number of independently modulated sub-carriers in an OFDM system the peak value of the system, can be very high as compared to the average of the whole system. This ratio of the peak to average power value is termed as Peak-to- Average Power Ratio. The coherent addition of N signals of same phase produces a peak which is N times the average signal.The major disadvantages of a high PAPR is increased complexity in the analog to digital and digital to analog converter.

The peak to average power ratio for a signal is defined as:

illustration not visible in this excerpt

(1.13.1)

illustration not visible in this excerpt

### 1.14 PAPR Reduction Techniques

The high Peak-to-Average Power Ratio (PAPR) or Peak-to-Average Ratio (PAR) or Crest Factor of the Orthogonal Frequency Division Multiplexing (OFDM) systems can be reduced by using various PAPR reduction techniques as follows^{20}:

- Tone Reservation (TR)

- Clipping

- Companding Transforms

- Constellation Shaping

- Phase Optimization

- Tone Injection (TI)

- Block Coding

- Partial Transmit Sequence (PTS)

- Selective Mapping (SLM)

- Interleaving

- Active Constellation Extension Methods

## CHAPTER 2 LITERATURE REVIEW

### 2.1 Different methods for Peak-to-Average Power (PAPR) Reduction in Orthogonal Frequency Division Multiplexing (OFDM)

Himanshu Bhushan Mishra et al.in 2012 proposed a new Selective-Mapping (SLM) technique in WIMAX without side information which is the major issue in theclassical SLM Technique. In this paper the PAPR performance is measured using complementary cumulative distribution function (CCDF) plot and the probability of SI detection error performance have been evaluated as the criteria for WiMAX standard IEEE 802.16e. WiMAX with its standard IEEE 802.16d/e is the advanced technology used for long range communication with high data rate. It is well known that the Orthogonal Frequency Division Multiplexing (OFDM) is a promising technique for getting high data rates in a multipath fading environment. Hence, the physical layer of WiMAX uses OFDM. But the main disadvantage of OFDM is the high peak to average power ratio (PAPR). In this paper PAPR reduction is achieved using selected mapping (SLM) technique and simultaneously without sending the side information (SI) along with the OFDM symbol.^{1}

E. Al-Dalakta et al. in 2012 proposed an efficient technique for reducing the biterror rate (BER) of Orthogonal FrequencyDivision Multiplexing (OFDM)signals transmitted over nonlinear solid-state power amplifiers (SSPAs).The proposed technique is based on predicting the distortion power thatan SSPA would generate due to the nonlinear characteristics of suchdevices. Similar to the Selective-Mapping (SLM) or Partial-Transmit-Sequence(PTS) schemes, the predicted distortion is used to select a set of phasesthat minimize the actual SSPA distortion. Simulation results confirmedthat the signal-to-noise ratio that is required to [Abbildung in dieser Leseprobe nicht enthalten]using the proposed technique is less by about 8 dB when it is obtain a BER of [Abbildung in dieser Leseprobe nicht enthalten]compared to the standard PTS utilizing 16 partitions. Moreover, complexity analysisdemonstrated that the proposed system offers a significant complexityreduction of about 60% compared to state-of-the-art methods.This work demonstrated that less direct PAPR indicators can provide better performance when combined with distortionless techniques such as PTS and SLM. Therefore, the proposed techniques are optimized to combat the consequences of high PAPR rather than reducing the PAPR itself. The proposed techniques are based on using the distortion level to select the optimal PTS and SLM system parameters.^{2}

Shiann-Shiun Jeng et al. in 2011 proposes a new method based on companding Peakto-Average Power Ratio (PAPR) Reduction of Orthogonal Frequency Division Multiplexing (OFDM) signals. This paper suggests that uniformly distributed companding scheme and piecewise companding scheme cannot deliver the performance that satisfies various requirements of the system. So, the distribution of the OFDM signal is transformed into the trapezium distributionand the general formulas for the proposed scheme are derived that enable the de- sired performance to be achieved by controlling the parameter.The simulation results reveal that the proposed scheme may offer the more efficient PAPR reduction or the lower BER than the uniformly-distributed and piecewise schemes under the condition of efficient PAPR reduction or efficient BER performance.^{3}

Suma M N et al. gives a survey on developments in OFDM so far. He suggested that apart from high Peak-to-Average Power Ratio (PAPR) there are many more techniques that are needed to increase the performance of OFDM systems like interference cancellation, phase noise mitigation, Synchronization among carriers and post equalization. In today's communication scenario, high data rate single-carrier transmission may not be feasible due to too much complexity of the equalizer in the receiver. To overcome the frequency selectivity of the wide band channel experienced by single-carrier transmission, multiple carriers can be used for high rate data transmission. Orthogonal Frequency Division Multiplexing (OFDM), is multicarrier system which has become a modulation in physical layer of next generation WiMAX, LTE system. In this work effort is made to present challenges in OFDM and work done so far in channel equalization and different transforms used in OFDM system like Discrete Fourier Transform (DFT) Based OFDM, Discrete Cosine Transform (DCT) Based OFDM, Wavelet based and Wavelet packet based OFDM, Discrete Hartley Transform (DHT) Based OFDM, and Coded OFDM which includes Turbo codes and Alamouti codes.^{4}

Jun Hou et al. proposed a nonlinear companding scheme toreduce the Peak-to- Average Power Ratio (PAPR) and improve Bit Error Rate (BER) for OFDMsystems. This proposed scheme mainly focuses on compressingthe large signals, while maintaining the average power constantby properly choosing transform parameters. Moreover, analysis shows that the proposed scheme without decompanding atthe receiver can also offer a good BER performance. Finally,simulation results show that the proposed scheme outperformsother companding scheme in terms of spectrum side-lobes, PAPRreduction and BER performance. ^{5}

Yuan Jiang in 2010 suggest a new companding algorithmthat offers improved performance in terms ofBER and OBI while reducing PAPR effectively.Orthogonal Frequency Division Multiplexing (OFDM) mitigates the effect of intersymbol interference (ISI) but it suffers from inter-block interference (IBI).A good remedy for the OBI is companding. This paper proposes and evaluates a new compandingalgorithm. This work uses the special airy function and isable to offer an improved bit error rate (BER) and minimizedOBI while reducing PAPR effectively.^{6}

Kitaek Bae et al. in 2010 proposed a new method for Peak-to-Average Power Ratio (PAPR) Reduction in Orthogonal Frequency Division Multiplexing (OFDM), a novelActive Constellation Extension (ACE) algorithm with adaptive clipping control namely Adaptive ACE which is an improvement in the technique based on the combination of two techniques namely clipping and Active Constellation Extension (ACE) known as Clipping-Based Active Constellation Extension (CB-ACE) technique. This work suggests that CB-ACE cannot achieve the minimum PAR when the target clippinglevel is set below an initially unknown optimum value. Toovercome this low clipping ratio problem, Adaptive ACE is proposed. Simulation resultsdemonstrate that proposed algorithm can reach the minimumPAR for severely low clipping ratios. In addition, thetradeoff between PAR and the loss in[Abbildung in dieser Leseprobe nicht enthalten]over an AWGNchannel in terms of the clipping ratio has also been described.^{7}

Ms. V. B. Malode et al. in 2010 proposed a new method to reduce Peak-to-Average Power Ratio (PAPR) Peak-to-Average Power Ratio (PAPR) by probabilistic method,modified selective mapping technique using the standard arrays of linear block codes. In this work lowest PAPR in each coset of a linear block codes is chosen as its coset leader from several transmitted signal , which further results in high performance ofwireless communication.^{8}

Stephane Y. Le Goff et al. in 2009 suggest an improvement in classical Selective Mapping (SLM) technique and proposed a new method in which SLM can be implemented without sending the side information which is a major issue in classical Selective Mapping (SLM) technique .SLM requiresthe transmission of several side information bits for each datablock, which results in some data rate loss. These bits mustgenerally be channel-encoded because they are particularlycritical to the error performance of the system. This increases thesystem complexity and transmission delay, and decreases the datarate even further. In this paper, we propose a novel SLM methodfor which no side information needs to be sent. This technique is particularly attractive for systemsusing a large number of subcarriers and the probabilityof SI detection error can be made very small by increasingthe extension factor and/or the number of subcarriers.^{9}

Sulaiman A. Aburakhia et al. in 2009 proposed a new linear companding transform (LCT)withmore design flexibility than linear nonsymmetricalcompanding transform (LNST) .Simulation results have been shown comparing both the above technique assuming AWGN channel .The results show that the proposed method has a higher PAPR reduction capability and better BER performance than LNST, with less spectral broadening. This work suggests that the proposed can be designed to meet system requirements, power amplifier characteristics, and achieve an excellent tradeoff betweenPAPR reduction and BER performance. Furthermore, the proposed transform is simple to implement and has no limitationson the system parameters such as number of subcarriers modulation order, or constellation type.^{10}

F.S. Al-kamaliet al. suggested the design of a newtransceiver scheme for the SCFDMA scheme using thewavelet transform. No redundancy is added to the newsystem because of the discrete wavelet transform. Thus, itscomplexity is slightly increased as compared to theconventional SC-FDMA scheme.This workdescribes that the proposed scheme has better PAPR performance and BER performance than theconventional SC-FDMA scheme.Theproposed HW-SC-FDMA scheme provides about 3 dBgain when compared to the conventional SC-FDMAscheme over the vehicular A channel.^{11}

**[...]**

^{1} Himanshu Bhusan Mishra, Madhusmita Mishra and Sarat Kumar Patra, “Selected Mapping Based PAPR Reduction in WiMAX Without Sending the Side Information” IEEE Conference Publication, March 2012

^{2} E. Al-Dalakta, A. Al-Dweik, A. Hazmi, C. Tsimenidis, B. Sharif, “Efficient BER Reduction Technique for Nonlinear OFDM Transmission Using Distortion Prediction” IEEE Transactions on Vehicular Technology, Vol. 61, No. 5, June 2011

^{3} Shiann-Shiun Jeng, and Jia-Ming Chen, “Efficient PAPR Reduction in OFDM Systems Based on a Companding Technique with Trapezium Distribution”, IEEE Transactions on Broadcasting, Vol. 57, No. 2, June 2011

^{4} Yasir Rahmatallah, Nidhal Bouaynaya and Seshadri Mohan, “On The Performance Of Linear And Nonlinear Companding Transforms In OFDM Systems” IEEE Conference on Wireless Telecommunications Symposium (WTS), pp 1-5, April 2011

^{5} Suma M N, Kanmani.B, “Developments in Orthogonal Frequency Division Mutiplexing (OFDM) system - A Survey”, IEEE Internet (AH-ICI), 2011 Second Asian Himalayas International Conference, pp 1-4, Nov 2011

^{6} Jun Hou, Jianhua Ge, Dewei Zhai, Jing Li, “Peak-to-Average Power Ratio Reduction of OFDM Signals With Nonlinear Companding Scheme” IEEE Transactions on Broadcasting, Vol. 56, No. 2, June 2010

^{7} Yuan Jiang, “New Companding Transform for PAPR Reduction in OFDM”, IEEE Communications Letters, Vol. 14, No. 4, April 2010

^{8} Kitaek Bae, Jeffrey G. Andrews and Edward J Powers, “Adaptive Active Constellation Extension Algorithm For Peak-to -Average Power Reduction in OFDM”, IEEE Communications letter , Vol. 14 , No. 1 , January 2010.

^{9} Ms. V. B. Malode, Dr. B. P. Patil, “PAPR Reduction Using Modified Selective Mapping Technique”Int. J. of Advanced Networking and Applications Vol.02, Issue: 02, pp: 626- 630, 2010

^{10} Stephane Y. Le Goff, Samer S. Al-Samahi, Boon Kein Khoo, Charalampos C. Tsimenidis, and Bayan S. Sharif, “Selected Mapping without Side Information for PAPR Reduction in OFDM,”IEEE Trans. Wireless Commun., vol. 8, no. 7, pp. 3320- 3325, Jul. 2009

^{11} Sulaiman A. Aburakhia, Ehab F. Badran, and Darwish A. E. Mohamed, “Linear

- Quote paper
- Neelam Dewangan (Author), 2012, Selective Mapping technique for PAPR reduction in LTE-OFDM Systems, Munich, GRIN Verlag, https://www.grin.com/document/204995

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