This document summarizes research on reducing peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. It discusses using a companding technique with Gaussian distribution to compress the signal before transmission and decompress it upon reception. The key aspects covered are: applying a compander and decompander with Gaussian distribution parameters at the transmitter and receiver; how the central limit theorem allows the sum of subcarriers to approximate a Gaussian distribution for large numbers; and how this technique reduces PAPR by increasing average power while keeping peak power the same. Performance is analyzed by simulating PAPR and bit error rate with and without companding under different parameters.

1. DEPARTMENT OF ELECTRONICS AND COMMUNICATION
ENGINEERING
PRESENTED BY :-
HEMANT CHOUBEY
SISTEC-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

2. 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.

3.  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

4. 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

5. Serial-to-
Parallel
Converter
Signal
Mapper
IFFT
Parallel-
to-Serial
Converter
Guard
Interval
Insertion
Serial
Data
Input
x bits
0d
1d
1nd
0s
1s
1ns
D/A &
Low pass
Filter
Up-
Converter
Down-
Converter
A/D
Guard
Interval
Removal
Serial-to-
Parallel
Converter
FFT
One-tap
Equalizer
Signal
Demapper
Parallel-
to-Serial
Converter
Serial
Data
Output
0
ˆdx bits
1
ˆd
1
ˆ
nd
0
ˆs
1
ˆs
1
ˆns
Channel
)(ts
Time
Frequency
Subchannels
Fast Fourier
Transform
Guard
Intervals
Symbols

6. Signal
Mapper
(QPSK)
IFFT
Parallel-
to-Serial
Converter
Guard
Interval
Insertion
Serial-to-
Parallel
Converter
2d
1nd
Serial
Data
Input
  
1s
2s
1ns
x bits
D/A
&
Lowpass
Filter
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
…..

7. DATA CP
CP
CP
CP
CP
1
1
1
i
i
d
é ù
ê ú
ê ú
ê ú
ê ú= ê ú
ê ú
ê ú
ê 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)
IFFT
Parallel-
to-Serial
Converter
Guard
Interval
Insertion
Serial-to-
Parallel
Converter
2d
1nd
Serial
Data
Input
  
1s
2s
1ns
x bits
D/A
&
Lowpass
Filter
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

8. In OFDM system design, the series and
parallel converter is considered to realize the
concept of parallel data transmission.
Serial-to-
Parallel
Converter

Serial
data
Parallel
data
s bT NTbT 2 bT 00 t t

9.  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.

10.  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

11.  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.

12.  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
2 12
cos 2 0 , 1,2,...,s
i c s
s
iE
s t f t t T i M
T M
2 1i i M
1,2,...,i M
sE sT
cf

13. An example of signal-space diagram for 8-PSK .
sE
2m
3m
4m
5m
6m
7m
8m
Decision
boundary
2
message
point
sE
sE
d
d
M
M 1m
Decision
region
1
sE

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

15. Time domain Frequency domain
Example of four subcarriers within one OFDM symbol Spectra of individual subcarriers

16. 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.

17. Delay spread
Environment Delay Spread
Home < 50 ns
Office ~ 100 ns
Manufactures 200 ~ 300 ns
Suburban < 10 us

18. If Tg < Tdely-spread
Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 4
Tdely-spread
If Tg > Tdely-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
﹒ ﹒ ﹒ ﹒
﹒ ﹒ ﹒ ﹒
﹒ ﹒ ﹒ ﹒
﹒ ﹒ ﹒ ﹒

19. 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
(Cyclic Extension)

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

21. Time and frequency representation of OFDM with guard
intervals.
Time
Frequency
T
Tg
1/T Subchannels
Fast Fourier Transform
Guard Intervals
Symbols

22. ◦ Immunity to delay spread
◦ Resistance to frequency selective
fading
◦ Simple equalization
◦ Efficient bandwidth usage

23. ◦ The problem of synchronization
 Symbol synchronization
 Frequency synchronization
◦ Need FFT units at transmitter,
receiver

24. ◦ 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

25. Various reduction techniques of peak to average
power reduction (PAPR) of ofdm.
o Selective mapping
o Partial transmit sequence
o Companding

29. Research Methodology

31. 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 .

32. 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

33. PAPR =

34. 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.

35. 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

36. 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.

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

38. N
Orthogonal
carrier
SNR(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 Analysis
Table1:Comparison of various parameter used in OFDM

39. 1 2
0
0.5
1
1.5
2
2.5
Simple OFDM,OFDM compander
PAPR
Simulated PAPR for OFDM with and without Compander
RESULTS
PAPR with and without companding

40. 0 1 2 3 4 5 6 7 8 9 10
10
-5
10
-4
10
-3
10
-2
10
-1
Eb/No, dB
BitErrorRate
Simulated BER for OFDM with different Codes under AWGN Channel
Simple OFDM
OFDM compander
BER with and without companding

41. [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

42. THANKS