OFDM Report

Implementation of OFDM ________________________________________________________________________

_____________________________________________________________________ MKSSS’s Cummins College of Engineering, Pune

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REPORT ON THE SEMINAR TOPIC

Analysis of Companding and Windowing Techniques to reduce Peak-to-Average

Power Ratio(PAPR) in Orthogonal Frequency Division Division

Multiplexing(OFDM)

delivered by Student name (s) Exam Seat no.(s)

ASHWINI S. DESAI B3203028

MADHURI R. MOHOD B3203080

in partial fulfillment for the award of the degree of

Bachelor Of Engineering In ELECTRONICS AND TELECOMMUNICATION of

UNIVERSITY OF PUNE ,

in

CUMMINS COLLEGE OF ENGINEERING FOR WOMEN , KARVENAGAR , PUNE -411052 , in the Department of Electronics and

Telecommunication

under the guidance of

Name of Internal guide ( Prof.Mr. A.R. Khedkar )

in the Academic year

2008 - 09



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This is to certify that

Student names

MOHOD MADHURI RAMESH

DESAI ASHWINI SRINIVAS

have successfully delivered a SEMINAR on their PROJECT TOPIC ANALYSIS OF COMPANDING AND WINDOWING TECHNIQUES FOR REDUCTION

OF PEAK-TO-AVERAGE POWER RATIO (PAPR) IN ORTHOGONAL FREQUENCY

DIVISION MULTIPLEXING (OFDM)

in partial fulfillment for the award of the degree of

Bachelor of Engineering in ELECTRONICS AND TELECOMMUNICATION of UNIVERSITY OF

PUNE ,

in

CUMMINS COLLEGE OF ENGINEERING FOR WOMEN , KARVENAGAR ,

PUNE-52 .

Sign. of Internal guide Sign. of H.O.D. Sign. &

Seal of Principal (Name : - Prof. Mr. A.R. KHEDKAR)



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Acknowledgement

We would like to thank Prof. Mr. A.R. Khedkar for his continuous valuable

guidance, support, valuable suggestions and his precious time in every possible way inspite of his

busy schedule throughout our project activity.

We would also like to express our gratitude towards our Project Co-ordinator Prof.

Mr. M.S. Patankar for his constant guidance during our project. We would also like to thank our

H.O.D. Prof. Mr. S.V. Kulkarni for his continuous encouragement.

We take this opportunity to express our sincere thanks to all the staff members of

Electronic and Telecommunication Department for their help whenever required. Finally we express

our sincere thanks to all those who helped us indirectly or directly in this project.

Student Names:-

1. Ashwini S. Desai Exam no:-B3203028

2. Madhuri R. Mohod Exam no:-B3203080



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ABSTRACTABSTRACTABSTRACTABSTRACT

Digital multimedia applications create an ever increasing demand for broad band

communication systems. The technical requirements for related products are very high but

it is desired that the solutions must be cheap to implement, feasible or lead to sub optimal

results. Orthogonal Frequency Division Multiplexing (OFDM) is a method that allows to

transmit high data rates over extremely hostile channels at a comparatively low

complexity than the traditional single carrier techniques.

This project aims at implementing OFDM system in Matlab and at observing its

performance in the presence of noise. By utilizing two techniques, namely-Companding

and Windowing we intend to obtain transmitted data with reduced Peak-to-Average Power

Ratio. In OFDM system, a large number of closely-spaced orthogonal sub-carriers are

used to carry data. The data are divided into several parallel data streams or channels, one

for each sub-carrier. Each sub-carrier is modulated with a conventional modulation

scheme such as quadrature amplitude modulation or phase shift keying at a low symbol

rate, maintaining total data rates similar to conventional single-carrier modulation schemes

in the same bandwidth. OFDM is especially suitable for high-speed communication due to

its resistance to intersymbol interference (ISI).

Matlab programming is used to implement OFDM transmitter and receiver.

Matlab simulation accepts inputs of text or audio files as well as binary, sinusoidal, or

random data. It then generates the corresponding OFDM transmission, simulates a

channel, attempts to recover the input data, and performs an analysis to determine the

PAPR of the system. Companding and Windowing techniques are then applied to obtain

the same data with reduced PAPR.



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Index

1. Abbreviations and symbols…………………………………….…..6

2. Study of basic communication systems……………………………8

2.1 3rd

Generation Wireless System………………………….……8

2.2 4th

Generation Wireless System……………………………......9

3. Orthogonal Frequency Division Multiplexing……………………...10

3.1 How is OFDM system different from

other communication system……………………………………11

3.2 Need for multiple carrier system………………………………..11

3.3 Orthogonality…………………………………………………...12

3.3.1 Advantages of Orthogonality…………………………………12

4. OFDM Transceiver……………………………………………...…..16

4.1 OFDM Transmitter………………………………………..…....17

4.2 OFDM Receiver……………………………………………..…18

4.2.1 Serial to parallel conversion……………………………….....19

4.2.2 Subcarrier modulation……………………………………..…19

4.2.3 Frequency to time domain conversion…………………….....19

4.2.4 Guard Period……………………………………………..…..19

4.2.5 Cyclic Prefix………………………………………….….…..20

4.3 Effect of White Gaussian Noise……………………………….21

4.4 Channel Coding……………………………………………..…21

4.4.1 Frequency Selective Fading………………………………….22

4.4.2 Interleaving………………………………………………..…23

5. Peak-to-Average Power Ratio(PAPR)……………………………...23

6. Techniques to overcome high PAPR…………………………….....25

5.1 Companding………………………………………………...….25

5.2 Windowing…………………………………………………......26



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Abbreviations and Symbols

2G: Second Generation mobile phone system (GSM, IS-95)

3G: Third Generation mobile phone system (systems using WCDMA)

4G: Fourth Generation mobile phone system

AM: Amplitude Modulation

AWGN : Additive White Gaussian Noise

B/s/Hz: Bits per second per hertz (unit of spectral efficiency)

BER: Bit Error Rate

Bps: Bits per second

BPSK: Binary Phase Shift Keying

BS: Base Station

CDMA: Code Division Multiple Access

CF: Crest Factor (peak to average power ratio of the RF envelope)

DAB: Digital Audio Broadcasting

dB: Decibel (ratio in log scale)

DC: Direct Current (0 Hz)

DFT: Discrete Fourier Transform

DSSS: Direct Sequence Spread Spectrum

FDM: Frequency Division Multiplexing

FFT: Fast Fourier Transform

FIR: Finite Impulse Response (digital filter)

FM: Frequency Modulation

Fs: Sample Frequency

FSK: Frequency Shift Keying

GHz: Gigahertz - 109 Hz

GMSK: Gaussian Minimum Shift Keying

GSM: Global System for Mobile communications

HDTV: High Definition Television

IFFT: Inverse Fast Fourier Transform

ISI: Inter-Symbol Interference

kbps Kilo bits per second (103 bps)

kHz: Kilohertz - 103 Hz

km : Kilometer (103 m)

mv: Metre

Mbps: Mega bits per second (106 bps)

MHz: Megahertz - 106Hz

MPEG Moving Picture Experts Group (Video compression standard)

OFDM: Orthogonal Frequency Division Multiplexing

PAPR Peak to Average Power Ratio

QAM Quadrature Amplitude Modulation

QOS Quality Of Service

QPSK Quadrature Phase Shift Keying



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Introduction important chapters Introduction important chapters

RF Radio Frequency

RMS Root Mean Squared

SNR Signal to Noise Ratio

SSB Single Side Band

TDM: Time Division Multiplexing

TDMA: Time Division Multiple Access

UMTS: Universal Mobile Telecommunications System

Ms: Microsecond (10-6 s)

W-CDMA: Wide-band Code Division Multiple Access

WLAN: Wireless Local Area Network

WLL: Wireless Local Loop



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1. Study of basic techniques of communication:

1.1 3rd

Generation Wireless System:

� Third generation mobile systems such as the Universal Mobile

Telecommunications System (UMTS) and CDMA2000 are striving to provide

higher data rates than current 2G systems.

� These systems shift to more data oriented services such as Internet access.

� Third generation systems use Wide-band Code Division Multiple Access

(WCDMA) as the carrier modulation scheme. This modulation scheme has a high

multipath tolerance, flexible data rate, and allows a greater cellular spectral

efficiency than 2G systems.

� Third generation systems provide a significantly higher data rate (64 kbps – 2

Mbps) than second-generation systems (9.6 – 14.4kbps). The higher data rate of

3G systems will be able to support a wide range of applications including Internet

access, voice communications and mobile videophones.

� In addition to this, they offer permanent network connectivity, such as wireless

appliances, notebooks with built in mobile phones, remote logging, wireless web

cameras, car navigation systems, and so forth.

� 3G technologies enable network operators to offer users a wider range of more

advanced services while achieving greater network capacity through improved

spectral efficiency. Services include wide-area wireless voice telephony, video calls,

and broadband wireless data, all in a mobile environment.

� 3G technologies enable network operators to offer users a wider range of more

advanced services while achieving greater network capacity through improved

spectral efficiency.



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1.2 4th

Generation Wireless System:

� The commercial rollout of these systems is likely to begin

around 2008 - 2012, and will replace 3rd generation technology

� It is likely that they will be able to extendthe capabilities of 3G networks,

allowing a greater range of applications, and improved universal access.

� Thus, 4G networks should encompass broadband wireless services, such as

High Definition Television (HDTV) (4 - 20 Mbps) and computer network

applications (1 - 100 Mbps). This will allow 4G networks to replace many of the

functions of WLAN systems.

� The spectral efficiency of 3G networks is too low to support high data rate

services at low cost.As a consequence one of the main focuses of 4G systems will

be to significantly improve the spectral efficiency.

� In addition to high data rates, future systems must support a higher Quality Of

Service (QOS) than current cellular systems, which are designed to achieve 90 -

95% coverage i.e. network connection can be obtained over 90 - 95% of the area of

the cell.

� This will become inadequate as more systems become dependent on wireless

networking. As a result 4G systems are likely to require a QOS closer to 98-99.5%.



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2. OFDM System:

Orthogonal frequency division multiplexing (OFDM) is becoming the chosen

modulation technique for wireless communications. Orthogonal Frequency Division

Multiplexing (OFDM) can be termed as an alternative wireless modulation technology to

CDMA. OFDM has the potential to surpass the capacity of CDMA systems and provide the

wireless access method for 4G systems. Many research centers in the world have specialized

teams working in the optimization of OFDM for countless applications.

History:

The origins of OFDM development started in the late 1950’s with the

introduction of Frequency Division Multiplexing (FDM) for data communications. In

1966 Chang patented the structure of OFDM and published the concept of

using orthogonal overlapping multi-tone signals for data communications. In 1971

Weinstein introduced the idea of using a Discrete Fourier Transform (DFT) for

implementation of the generation and reception of OFDM signals, eliminating the

requirement for banks of analog subcarrier oscillators. This presented an opportunity

for an easy implementation of OFDM, especially with the use of Fast Fourier

Transforms (FFT), which are an efficient implementation of the DFT. This suggested

that the easiest implementation of OFDM is with the use of Digital Signal Processing

(DSP), which can implement FFT algorithms. It is only recently that the advances in

integrated circuit technology have made the implementation of OFDM cost effective.

The reliance on DSP prevented the wide spread use of OFDM during the early

development of OFDM. It wasn’t until the late 1980’s that work began on the

development of OFDM for commercial use, with the introduction of the Digital

Audio Broadcasting (DAB) system.



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2.1 How is OFDM different from other communication

systems??

A common problem found in high-speed communication is inter-symbol interference

(ISI). ISI occurs when a transmission interferes with itself and the receiver cannot decode

the transmission correctly. For example, in a wireless communication system such as that

shown in the following figure, the same transmission is sent in all directions.

Because the signal reflects from large objects such as mountains or buildings, the receiver

sees more than one copy of the signal. In communication terminology, this is called

multipath. Since the indirect paths take more time to travel to the receiver, the delayed

copies of the signal interfere with the direct signal, causing ISI.



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2.2 Need For Multiple-Carrier System:

OFDM is especially suitable for high-speed communication due to its resistance to ISI.

OFDM overcomes the effects of multipath by breaking the signal into many narrow

bandwidth carriers. This results in a low symbol rate reducing the amount of ISI. In

addition to this, a guard period is added to the start of each symbol, removing the effects of

ISI for multipath signals delayed less than the guard period.

As communication systems increase their information transfer speed, the time for each

transmission necessarily becomes shorter. Since the delay time caused by multipath remains

constant, ISI becomes a limitation in high-data-rate communication. OFDM avoids this

problem by sending many low speed transmissions simultaneously. For example, the figure

below shows two ways to transmit the same four pieces of binary data.

Traditional vs. OFDM Communication

Suppose that this transmission takes four seconds. Then, each piece of data in the left picture

has a duration of one second. On the other hand, OFDM would send the four pieces

simultaneously as shown on the right. In this case, each piece of data has a duration of four

seconds. This longer duration leads to fewer problems with ISI. Another reason to consider

OFDM is low-complexity implementation for high-speed systems compared to traditional

single carrier techniques.



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In an OFDM scheme, a large number of orthogonal, overlapping, narrow band

Sub-channels or sub carriers, transmitted in parallel, divide the available transmission

bandwidth. The separation of the sub carriers is theoretically minimal such that

there is a very compact spectral utilization.

But the question arises…why we use a multi-carrier system. There are 2 main reasons:

� During transmission, data may be lost in one or two sub-carriers, but in a multi-carrier

system, we do not lose the whole stream

� It helps combat frequency-selective channel fading.



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Orthogonality:

2.3 Orthogonality:

� Signals are orthogonal if they are mutually independent of each other.

� Two signals are said to be orthogonal when their dot product is equal to zero.

� Let’s take a sine wave of frequency m and multiply it by sinusoid of a frequency n,

where both m and n are integers. The integral or the area under the product is given

by:

f(t) = sin mwt x sin nwt

By simple trigonometric relationship,yhis is equal to a sum of two sinusoids of

frequency (n-m) and (n+m)

= 0.5(n-m) + 0.5(n+m)

These two components are each a sinusoid,so the integral is equal to zero over one

period.

� Orthogonality is a property that allows multiple information signals to be transmitted

perfectly over a common channel and detected, without interference. Loss of

orthogonality results in blurring between these information signals and degradation in

communications.



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� The subcarriers in an OFDM signal are spaced as close as is theoretically possible

while maintain orthogonality between them. OFDM achieves orthogonality in the

frequency domain by allocating each of the separate information signals onto different

subcarriers.

� OFDM signals are made up from a sum of sinusoids, with each corresponding to a

subcarrier.

The baseband frequency of each subcarrier is chosen to be an integer multiple of the inverse

of the symbol time, resulting in all subcarriers having an integer number of cycles per

symbol. As a consequence the subcarriers are orthogonal to each other

The orthogonal nature of the transmission is a result of the peak of each subcarrier

corresponding to the nulls of all other subcarriers. When this signal is detected using a

Discrete Fourier Transform (DFT) the spectrum is not continuous , but has discrete

samples.This will be elaborated in the transceiver section of OFDM.

2.3.1 Advantages of Orthogonality:

• There is no need of introducing guard bands

• Orthogonality offers high spectral efficiency

• It simplifies design of transmitter and receiver

• Cross-talk is eliminated



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OFDM Transceiver

3. OFDM Transceiver

3. OFDM Transceiver



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3.1 OFDM TRANSMITTER

OFDM transmitters generate both the carrier and the data signal simultaneously with purely

digital circuits residing in the specialized DSP(Digital Signal Processor) microchips. The specific

process of digital signal generation used in OFDM is based on the series of mathematical

computations known as an Inverse Fourier Transform, and the process results in the formation of

a complex modulated waveform at the output of the transmitter.The incoming serial data is first

converted from serial to parallel and grouped into x bits each to form a complex number. The

complex numbers are modulated in a base band fashion by the IFFT and converted back to serial

data for transmission. A guard interval is inserted between symbols to avoid intersymbol

interference (ISI) caused by multipath distortion. The discrete symbols are converted to analog

and lowpass filtered for RF up-conversion.



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3.2 OFDM RECEIVER

The receiver performs the reverse operation of the transmitter, mixing the RF signal to base

band for processing, then using a Fast Fourier Transform (FFT) to analyse the signal in the

frequency domain. The amplitude and phase of the subcarriers is then picked out and converted

back to digital data.

The IFFT and the FFT are complementary function and the most appropriate

term depends on whether the signal is being received or generated. In cases where the signal is

independent of this distinction then the term FFT and IFFT is used.



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3.2.1 SERIAL TO PARALLEL CONVERSION

Data to be transmitted is typically in the form of a serial data stream. In OFDM, each symbol

typically transmits 40 - 4000 bits, and so a serial to parallel conversion stage is needed to

convert the input serial bit stream to the data to be transmitted in each OFDM symbol. The data

allocated to each symbol depends on the modulation scheme used and the number of sub

carriers. For example, for a sub carrier modulationof 16-QAM each sub carrier carries 4 bits of

data, and so for a transmission using 100 sub carriers the number of bits per symbol would be

400.

3.2.2 SUB CARRIER MODULATION

Once each subcarrier has been allocated bits for transmission, they are mapped using a

modulation scheme to a subcarrier amplitude and phase, which is represented by a complex In-

phase and Quadrature-phase (IQ) vector.

In the receiver, mapping the received IQ vector back to the data

word performs subcarrier demodulation.

3.2.3 FREQUENCY TO TIME DOMAIN CONVERSION

After the subcarrier modulation stage each of the data subcarriers is set to an amplitude and

phase based on the data being sent and the modulation scheme; all unused subcarriers are set to

zero. This sets up the OFDM signal in the frequency domain. An IFFT is then used to convert

this signal to the time domain, allowing it to be transmitted.

3.2.4 GUARD PERIOD

For a given system bandwidth the symbol rate for an OFDM signal is much lower than a single

carrier transmission scheme. For example for a single carrier BPSK modulation, the symbol rate

corresponds to the bit rate of the transmission. However for OFDM the system bandwidth is

broken up into Nc subcarriers, resulting in a symbol rate that is Nc times lower than the single

carrier transmission. This low symbol rate makes OFDM naturally resistant to effects of Inter-

Symbol Interference (ISI) caused by multipath propagation.



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3.2.5 Cyclic Prefix:

� In an OFDM symbol the cyclic prefix is a repeat of the end of the symbol at the

beginning

� The purpose is to allow multipath to settle before the main data arrives at the receiver

� The length of the cyclic prefix is often equal to the guard interval



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3.3 EFFECT OF ADDITIVE WHITE GAUSSIAN NOISE

ON OFDM: Noise exists in all communications systems operating over an analog physical channel, such as

radio. The main sources are thermal background noise, electrical noise in the receiver amplifiers,

and inter-cellular interference. In addition to this noise can also be generated internally to the

communications system as a result of Inter-Symbol Interference (ISI), Inter-Carrier Interference

(ICI), and Inter-Modulation Distortion (IMD). These sources of noise decrease the Signal to

Noise

Ratio (SNR), ultimately limiting the spectral efficiency of the system.

Most types of noise present in radio communication systems can be modelled

accurately using Additive White Gaussian Noise (AWGN). This noise has a uniform spectral

density making it white and a Gaussian distribution in amplitude also referred to as a normal

distribution or bell curve.

OFDM signals have a flat spectral density and a Gaussian amplitude

distribution provided that the number of carriers is large. Because of this the inter-cellular

interference from other OFDM systems have AWGN properties. For the same reason

ICI, ISI, and IMD also have AWGN properties for OFDM signals.

3.4 CHANNEL CODING

The goal of channel coding, or error control coding, is to improve bit error ratio (BER)

performance by adding structured redundancy to the transmitted data. Channel coding means that

additional redundant bits are added to the signal to enable error detection and error correction.

Channel impairments can cause errors to the signal; these impairments can be e.g. noise, fading,

interference or jamming. Basic channel coding methods are block coding and convolution

coding.

In OFDM channel coding is done with convolution coding, because

convolution coding offer good performance with low implementation cost. Coding is performed

on serial data before symbol mapping. Convolution coding operates with bit streams



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and has memory that utilizes previous bits to encode or decode following bits. Convolution

encoder is defined with three variables: number of output bits n, number of input bits k and

memory depth L. Encoder maps k input bits into n output bits. From memory length can be

derived constraint length using the equation given below.

Constraint length tells how many output bits are influenced with single input bit. The error

correction capacity is related with this value.

C=n (L+1)

3.4.1 FREQUENCY SELECTIVE FADING

Multipath causes fading changes with frequency. This is due to the phase response of the multipath

components varying with frequency. The received phase, relative to the transmitter, of a multipath

component corresponds to the number of wavelengths the signal has travelled from the

transmitter. The wavelength is inversely proportional to frequency and so for a fixed

transmission path the phase will change with frequency. The path distances of each of the

multipath component is different and so results in a different phase change. Below is an

example of a two-path transmission.



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Path 1 is a direct signal and has a transmission distance of 10m, while the second path is a

reflection with a longer transmission distance of 25 m. This makes the two paths out of phase,

which results in a reduction in the signal amplitude at this frequency.

3.4.2 INTERLEAVING

Because of frequency selective fading, in OFDM certain sub channels can be located in a

deep fades in channel and information carried by these sub carriers are lost. This effect

causes errors to occur in bursts rather than being randomly scattered. To make errors appear

more randomly, interleaving is performed on the coded bit stream. Interleaving is a way to

permute bits in a certain way and at the receiver reverse permutation is performed. A

commonly used interleaving method is block interleaving. In block interleaving data is

written in to a matrix row-by-row and read out column-by-column.

4. PEAK TO AVERAGE POWER RATIO

The main disadvantage of OFDM is high peak to average power ratio(PAPR).A high peak to

average power ratio causes saturation in power amplifiers, leading to intermodulation

products among the sub carriers and disturbing out of band energy. Therefore, it is desirable

to reduce the PAPR.

By definition we have,

PAPR= Peak Amplitude of the Signal

Average value of the Signal



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An OFDM signal consists of a number of independent sub carriers, which can give a large

peak-to-average power ratio (PAPR) when added coherently. When N signals are

added with the same phase, they produce a peak power that is N times the average power.

As a result, linear behavior of the system over a large dynamic range is needed and the

efficiency of the output amplifier is reduced. The average power must be kept low in order

to prevent the transmitter amplifier saturation. Minimizing the PAPR allows higher.

By definition we have,

PAPR= Peak Amplitude of the Signal

Average value of the Signal

PAPR = ((xk)^2)max / E{(xk)^2 1<=k<=N

Where E{(xk)^2} stands for the expected value or average value of the time domain signal.



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5. TECHNIQUES TO OVERCOME HIGH PAPR:

A) Companding

B) Windowing

5.1 Companding

In companding method, compression is used in the transmitter and expansion in the receiver. By

considering the approximate Rayleigh distribution of the OFDM amplitudes, we compress the

dynamic range with a memory-less transformation at the transmitter and expand the amplitude

level at the receiver. This transformation essentially changes the probability distribution of the

amplitude of OFDM signal and achieves the PAPR reduction by both enlarging the small

amplitudes and compressing large signals. The power is adaptively allocated for each sub-

carrier according to the distribution in each block.

Companding Transform Our strategy in this work involves applying u-law companding at the transmitter to

reduce the PAPR of the transmitted waveform so as to reduce distortion through the

transmit amplifier and allow operation closer to amplifier saturation. Values of u ranging

between 0.125 and 64 were used in the study since the optimal performance was found to

reside within this range of operation.

Let sdat(n) be the baseband OFDM signal associated with the data symbol. In the case of u-law

companding for a selected u, the compressed OFDM signal, sc(n), is formed as:

Sc(n)= K(u) Smax{ ln[1+ u |Sdat (n)|]}

{ln[1+u]} * sign[Sdat (n)]

Where Smax = max (Sdat (n))

and where K(u) is a normalization constant such that the average power of the

companded signal is equal to the average power of the uncompanded signal. A proposed

approximation for K(u) is

K(u) = ln(1 + u)

u



26

However, this approximation is not highly accurate, and in practice, would lead to

unnecessary degradation in the demodulation performance. To mitigate errors

introduced by normalization inaccuracies, numerically-determined values of K(u) were

computed and employed instead, where long-term power averages of both uncompanded

and companded OFDM symbols were numerically estimated to find K(u). The resulting

values are plotted in the figure along side the approximation.

Normalization Constant for Different Values of the Companding

Parameter, with No=64 and 4x Oversampling



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An example of a time-domain signal associated with a data symbol before and after

companding (with u = 16) is shown in the figure below, where the companded signal is scaled

to yield an average power equal to the uncompanded signal. The net result is that companding

increases the low-level signal components and reduces the high-level signal components. In

the figure, the solid line corresponds to the uncompanded signal, and the dashed line

corresponds to the companded signal.

Uncompanded and Companded Signals with Equal Average Power



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5.2 Windowing

A different approach to reduce the PAPR is to multiply large signal peak with a Gaussian shaped

window or any other window with good spectral properties. Since the OFDM signal is multiplied

with several of these windows the resulting spectrum is a convolution of the original OFDM

spectrum with the spectrum of the applied window. So, ideally the window should be as narrow

band as possible. On the other hand, the window should not be too long in the time domain,

because that implies that many signal samples are affected, which increases the bit error ratio.

Examples of suitable window functions are the Cosine, Kaiser and Hamming window. Peak

windowing technique offers reasonably good reduction in PAPR achieved independent from

number of sub-carriers, at the cost of a slight increase in BER and out of band radiation.

Windowing parameters, window width and attenuation factor, should be selected such a way that it

will reduce the PAPR. However, it is difficult to find a relationship between windowing

parameters and PAPR since the PAPR is random. Generally, the window width should be small in

order to avoid distorting many sample values and the attenuation factor should be selected by

considering PAPR reduction and signal distortion. Further, it is necessary to relate OFDM

parameters with peak windowing.

Peak windowing method is implemented by first considering the

clipping ratio. Here, OFDM signal is clipped whenever it exceeds a clip level say S. The

normalized clipping level, called the clipping ratio, is defined as

Clipping ratio= S/σ

Where σ is the rms power of the OFDM signal and it can be shown that, for an OFDM signal

with N subchannels, s = N for a baseband signal and s = N / 2 for a bandpass signal.

OFDM signal is multiplied by the window function when the signal peak exceeds the

clipping level. Unlike the clipping, the OFDM signal within the windowing width is

modified. This results in a smoothed OFDM signal.



29

The PAPR reduction is achieved at the expense of bit error rate (BER)

performance degradation and the out of band radiation. On the other hand PAPR can not be

reduced beyond a certain limit by removing peaks, as the average value of the OFDM signal, also

decreases, which in turn increases the PAPR. Peak windowing method concerns only removing

the peak values, which have low probability of occurrence. OFDM signal exhibits some low

values, we will call it "bottoms", with low probability of occurrence, like peaks. By increasing

these bottoms above certain level, the average value of OFDM signal can be shifted up. These

results in PAPR reduction. Basically, this is like inverted windowing.

Peak Windowing distorts the OFDM signal causing inband distortion and out of band

radiation. Inband distortion causes to BER performance degradation. Figure 4.6 shows

the BER performance of an OFDM signal after windowing for different value of clipping

ratio. When clipping ratio is increased the BER performance is better, but, the reduction

in PAPR is not much. When clipping ratio is low, the amount of peaks removed is high.

Thus, signal has been distorted very much and BER performance degrades. When

clipping ratio is 1.8, there is about 0.5dB loss in SNR at 10-4 BER and PAPR is reduced

by 5dB.

Power Spectral Density of an OFDM Signal



30

Conclusion:

We have investigated the performance of OFDM system with companding and windowing as a

PAPR reduction strategy. Impairments from AWGN noise from the channel, and noise

amplification due to the expansion transform at the receiver were considered. MATLAB

Simulation was employed to investigate performance trends. We have seen that with an

appropriate choice of u and amplifier backoff, the companding system can outperform a

system without companding. Thus, Orthogonal Frequency Division Multiplexing is a form of

multi-carrier modulation technique with high spectral efficiency, robustness to channel fading,

immunity to impulse interference, uniform average spectral density capability of handling very

strong echoes and less non linear distortion. We have also inferred that by implementing

Windowing and Companding, the high PAPR of the OFDM system reduces and we obtain a

better quality signal at the receiver.



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References: 1. www.skydsp.com

2. www.complex2real.com 3. OFDM Link Performance with Companding for PAPR Reduction in the Presence

of Non-Linear Amplification Thomas G. Pratt, Nathan Jones, Leslie Smee, and

Michael Torrey

4. Adaptive Techniques for Multiuser OFDM Eric Phillip LAWREY BE (Hons)



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Documents

OFDM Report