DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

PRESENTED BY :-HEMANT CHOUBEYSISTEC-E RATIBAD

DEPARTMENT OF ELECTRONICS AND COMMUNICATION

www.sistec.ac.in

EFFICIENT PAPR REDUCTION IN OFDM SYSTEM BASED ON A COMPANDING

TECHNIQUE WITH GAUSSIAN DISTRIBUTION

Literature survey

1 .S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun., vol. 12, pp. 56–65, Apr. 2005.

2. T. Jiang and Y.Wu, “An overview: Peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast., vol. 54, no. 2, pp. 257–268, Jun. 2008.

3. C. P. Li, S. H. Wang, and C. L. Wang, “Novel low-complexity SLM schemes for PAPR reduction in OFDM systems,” IEEE Trans. Signal Process., vol. 58, no. 5, pp. 2916–2921, May 2010.

The Basic Principles of OFDM◦ FFT-based OFDM System◦ Serial and Parallel Concepts◦ Modulation/Mapping

M-ary Phase Shift Keying M-ary Quadrature Amplitude Modulation

◦ IFFT and FFT Signal Representation of OFDM using IDFT/DFT

◦ Orthogonality◦ Guard Interval and Cyclic Extension◦ Advantages and Disadvantages◦ Background theory◦ Selective mapping◦ Partial transmit sequence◦ Companding◦ Companding with gaussian distribution◦ Central limit theorem◦ Reference

Outlines Of Presentation

OFDM is the most popular one. The first OFDM scheme was proposed by Chang in 1966. Even though the concept of OFDM has been around for several years, but it has not been recognized as a great method for high speed bi-directional wireless data communication until recent years. The first applications of OFDM were in the military HF radio links. Today, the OFDM technique is in many wirelesses and wired applications, such as broadband radio access networks (BRAN), Digital Audio Broadcasting (DAB), Digital Video Broadcasting-Terrestrial (DVB-T) and Asymmetric Digital Subscriber Line (ADSL)

Basic Principles of OFDM

FFT-based OFDM System

Serial-to-Parallel

Converter

SignalMapper

IFFTParallel-to-Serial

Converter

GuardIntervalInsertion

Serial Data Input

x bits0d

1d

1nd

0s

1s

1ns

D/A &Low pass

Filter

Up-Converter

Down-Converter

A/D Guard

IntervalRemoval

Serial-to-Parallel

ConverterFFT

One-tapEqualizer

SignalDemapper

Parallel-to-Serial

Converter

Serial Data

Output

0dx bits

1d

1ˆ

nd

0s1s

1ˆ ns

Channel

)(ts

Time

Frequency

Subchannels

Fast Fourier Transform

Guard Intervals

Symbols

FFT-based OFDM System OFDM Transmitter

Signal Mapper(QPSK)

IFFTParallel-to-Serial Converter

Guard IntervalInsertion

Serial-to-Parallel

Converter

2d

1nd

Serial

Data

Input

1s

2s

1ns

x bits

D/A&

LowpassFilter

1x 1d

2x

1nx

x=[0,0,0,1,1,0,1,1,….]

x1=[0,0]

x2=[0,1]

x3=[1,0]

x4=[1,1]

Q

.I

.

.

. 00

01

11

10

.I

.

.

. 00

01

11

10

Q

.

.

.

. 00

01

11

10

I.

.

.

. 00

01

11

10

d1=1

d2=i

d3=-1

d4=-i

…..

FFT-based OFDM System OFDM Transmitter

DATA CP

CP

CP

CP

CP

1

1

1

i

i

d

é ùê úê úê úê ú= ê úê úê úê ú-ê úë û

M

0 10 20 30 40 50 60 70-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

[ ]-0.09, -0.003-0.096i, , 0.01+ 0.247i, -0.035-0.0472is = L

0 10 20 30 40 50 60 70 80-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Signal Mapper(QPSK)

IFFTParallel-to-Serial Converter

Guard IntervalInsertion

Serial-to-Parallel

Converter

2d

1nd

Serial

Data

Input

1s

2s

1ns

x bits

D/A&

LowpassFilter

1x 1d

2x

1nx

0 10 20 30 40 50 60 70 80-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

In OFDM system design, the series and parallel converter is considered to realize the concept of parallel data transmission.

Series and Parallel Concepts

Serial-to-Parallel

Converter

Serial data

Parallel data

s bT NTbT 2 bT 00 t t

Series ◦In a conventional serial data system, the

symbols are transmitted sequentially, with the frequency spectrum of each data symbol allowed to occupy the entire available bandwidth.

◦When the data rate is sufficient high, several adjacent symbols may be completely distorted over frequency selective fading or multipath delay spread channel.

Parallel

◦The spectrum of an individual data element normally occupies only a small part of available bandwidth.

◦Because of dividing an entire channel bandwidth into many narrow subbands, the frequency response over each individual subchannel is relatively flat.

◦A parallel data transmission system offers possibilities for alleviating this problem encountered with serial systems. Resistance to frequency selective

fading

The process of mapping the information bits onto the signal constellation plays a fundamental role in determining the properties of the modulation.

An OFDM signal consists of a sum of sub-

carriers, each of which contains 1. M-ary Phase Shift Keying (PSK) or 2. Quadrature Amplitude Modulated (QAM)

signals.

Modulation/Mapping

M-ary phase shift keying ◦Consider M-ary phase-shift keying (M-PSK) for

which the signal set is

where is the signal energy per symbol, is the symbol duration, and is the carrier frequency.

◦This phase of the carrier takes on one of the M possible values, namely , where

Mapping - Phase Shift Keying

2 12cos 2 0 , 1, 2,...,s

i c ss

iEs t f t t T i M

T M

2 1i i M

1,2,...,i M

sEsT

cf

An example of signal-space diagram for 8-PSK .

Mapping - Phase Shift Keying

sE

2m

3m

4m

5m

6m

7m

8m

Decisionboundary

2

messagepoint

sE

sE

d

d

MM 1m

Decisionregion

1sE

An example of signal-space diagram for 16-square QAM.

Mapping – QAM

Time domain Frequency domain

Orthogonality

Example of four subcarriers within one OFDM symbol

Spectra of individual subcarriers

Two different sources of interference can be identified in the OFDM system.

◦ Inter Symbol Interference (ISI) - crosstalk between signals within the same sub-channel of consecutive FFT frames, which are separated in time by the signaling interval T.

◦ Inter Carrier Interference (ICI) - crosstalk between adjacent sub channels or frequency bands of the same FFT frame.

Guard Interval and Cyclic Extension

Delay spread

Guard Interval and Cyclic Extension

Environment Delay Spread

Home < 50 ns

Office ~ 100 ns

Manufactures 200 ~ 300 ns

Suburban < 10 us

Guard Interval and Cyclic ExtensionIf T g < T dely-spread

Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 4

Tdely-spread

If Tg > T dely-spread

Tg Symbol 1 Tg Symbol 2 Tg Symbol 3

Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 4

Tg Symbol 1 Tg Symbol 2 Tg Symbol 3

Tdely-spread

﹒﹒﹒﹒

﹒﹒﹒﹒

﹒﹒﹒﹒

﹒﹒﹒﹒

o To eliminate ICI, the OFDM symbol is cyclically extended in the guard interval.

o This ensures that delayed replicas of the OFDM symbol always have an integer number of cycles within the FFT interval, as long as the delay is smaller than the guard interval.

Guard Interval and Cyclic Extension

Guard Interval(Cyclic Extension)

Effect of multipath with zero signals in the guard interval, the delayed subcarrier 2 causes ICI on subcarrier 1 and vice versa.

Guard Interval and Cyclic Extension

Part of subcarrier #2 causing ICI on subcarrier #1

Guard time FFT integration time=1/carrier spacing Guard time FFT integration time=1/carrier spacing

OFDM symbol time OFDM symbol time

Subcarrier #1

Delayed subcarrier #2

Guard Interval and Cyclic Extension

Time and frequency representation of OFDM with guard intervals.

Time

Frequency

T

Tg

1/T Subchannels

Fast Fourier Transform

Guard Intervals

Symbols

◦Immunity to delay spread

◦Resistance to frequency selective fading

◦Simple equalization

◦Efficient bandwidth usage

Advantages

◦The problem of synchronization Symbol synchronization Frequency synchronization

◦Need FFT units at transmitter, receiver

Disadvantages

◦Sensitive to carrier frequency offset ◦Problem of high peak to average power ratio

(PAPR)Problem 1. Increased complexity of ADC and DAC.Problem 2. Reduced efficiency of the RF power amplifier.

Solutions Signal distortion techniques Special forward-error-correction code Scrambling

Various reduction techniques of peak to average power reduction (PAPR) of ofdm.

o Selective mappingo Partial transmit sequenceo Companding

Background Theory

Selective Mapping

Partial Transmit Sequence

Basics Of Companding

Research Methodology

o Companding is another popular PAPR reduction scheme. Companding is a composite word formed by combining compressing and expanding. In this scheme, at the transmitter a signal with high dynamic range is applied to a compander and at the receiver a decompanding function (the inverse of companding function) is used to recover the original signal

o It increases the average power while peak remains the same therefore PAPR reduced .

Companding

function [y] = compressor(x,mu,sigma) y = (1/(sigma*sqrt(2*pi)))*exp(-((x-mu).^2)./(2*sigma^2));end function [y] = decompressor(x,mu,sigma) y = sqrt(-1*(2*sigma^2)*(log(sigma*sqrt(2*pi).*x))) + mu; end

Compression and decompression

PAPR =

Gaussian probability distribution is perhaps the most used distribution in all of science. It is also called “bell shaped curve” or normal distribution. Unlike the binomial and Poisson distribution, the Gaussian is a continuous distribution.

Companding with Gaussian distribution

The important thing to note about a normal distribution is the curve is concentrated in the center and decreases on either side

A bell curve graph depends on two factors, the mean and the standard deviation

Central Limit Theorem

C.L.T. tells us that under a wide range of circumstances the probability distribution that describes the sum of random variables tends towards a Gaussian distribution as the number of terms in the sum tends to infinite.

Sum of 12 uniform random numbers minus 6 is distributed as if it came from a Gaussian pdf with m = 0 and s = 1

NOrthogonal

carrierSNR(dB) Sigma (σ) Mu(µ) PAPR

Average

power

1000 4 0-10 1 0 2.09 0.4955

10000 4 0-10 1 0 2.05 0.50246

100000 4 0-10 1 0 2.1095 0.49941

1000 8 0-10 1 0 2.02 0.49425

Performance AnalysisTable1:Comparison of various parameter used in OFDM

1 20

0.5

1

1.5

2

2.5

Simple OFDM,OFDM compander

PA

PR

Simulated PAPR for OFDM with and without Compander

RESULTS

PAPR with and without companding

0 1 2 3 4 5 6 7 8 9 1010

-5

10-4

10-3

10-2

10-1

Eb/No, dB

Bit E

rror

Rate

Simulated BER for OFDM with different Codes under AWGN Channel

Simple OFDM

OFDM compander

BER with and without companding

[1] Richard van Nee, Ramjee Prasad, OFDM wireless multimedia communication, Artech House Boston London, 2012.

[2] Ahmad R. S. Bahai and Burton R. Saltzberg, Multi-carrier digital communications - Theory and applications of OFDM, Kluwer Academic / Plenum Publishers New York, Boston, Dordrecht, London, Moscow, 2011.

[3] Ramjee Prasad, “OFDM based wireless broadband multimedia communication,” Letter Notes on ISCOM’99, Kaohsiung, Taiwan, Nov. 7-10, 2010.

[4] L. Hanzo, W. Webb and T. Keller, Single- and multi-carrier quadrature amplitude modulation – Principles and applications for personal communications, WLANs and broadcasting, John Wiley & Sons, Ltd, 2013.

[5] Mark Engels, Wireless Ofdm Systems: How to Make Them Work? Kluwer Academic Publishers.

[6] Lajos Hanzo, William Webb, Thomas Keller, Single and Multicarrier Modulation: Principles and Applications, 2nd edition, IEEE Computer Society.

[7] Zou, W.Y.; Yiyan Wu, “ COFDM: An overview ” Broadcasting, IEEE Transactions on, Vol. 41, Issue 1, pp. 1 –8, Mar. 2011.

[8] Emmanuel C. Ifeachor & Barrie W. Jervis, Digital signal processing – A practical approach, Addision-Wesley, 2012.

[9] Blahut, R. E., Fast Algorithms for digital processing. Reading, Ma: Addison-Wesley, 2011.

[10] Simon Haykin, Communication Systems, John Wiley & Sons, Inc., 3rd edition, 2012.

[11] Roger L. Peterson, Rodger E. Ziemer, David E. Borth, Introduction to spread spectrum communications, Prentice Hall International Editions, 2010

References

THANKS