2. CONTENTS :
Introduction
OFDM Overview
Orthogonality Principle
OFDM Transceiver
Introduction to PAPR
PAPR reduction techniques
SLM technique for PAPR reduction
PTS technique for PAPR reduction
Hybrid techniques for PAPR reduction
Results and conclusion
References
3. INTRODUCTION :
Single Carrier System
Transmitted using only one carrier at a time
o Frequency Division Multiplexing
involves assigning non – overlapping
frequency ranges or channels to different signals or to
each user of a medium.
5. ORTHOGONALITY PRINCIPLE
𝑎
𝑏
𝜓𝑚 𝑡 𝜓𝑚
∗ 𝑡 𝑑𝑡 = 0, 𝑤ℎ𝑒𝑟𝑒 𝑛 ≠ 𝑚
related to dot product of signals
Mathematically represented as
Time
T
Base frequency = 1/T , T= symbol period
6. OFDM Subcarrier Spectra
Carriers allows their overlapping while disabling the occurrence
of crosstalk.
Fig. 1
Fig. 2
7. ORTHOGONALITY TEST
Fig.: Different Sinusoidal signals
Fig 1.5: Orthogonality test result.
Fig 1.5: Orthogonality test result.
Fig.: Orthogonality test result.
8. OVERVIEW ABOUT OFDM
OFDM was invented more than 40 years ago.
OFDM has been adopted for several technologies:
1. Asymmetric Digital Subscriber Line (ADSL)
services.
2. IEEE 802.11a/g, IEEE 802.16a.
3. Digital Audio Broadcast (DAB).
4. Digital Terrestrial Television Broadcast: DVD in
Europe, ISDB in Japan
5. 4G, IEEE 802.16, and IEEE 802.20.
9. OFDM can be viewed modulation cum multiplex
technique.
Modulation technique
Viewed by the relation between input and output
signals
Multiplex technique
Viewed by the output signal which is the linear sum of
the modulated signals
How Signals are transmitted without interference???
10. a) Spectrum of normal time domain
sequence
b) Spectrum of classical frequency division
multiplexing (FDM)
c) Spectrum of OFDM
Fig :OFDM can be thought as
12. Mathematical Equation
The baseband OFDM signals can be written as
Where is the central frequency of the mth sub
channel and is the corresponding transmitted
symbol.
1
0
0
,
2
exp
)
(
N
m
m T
t
t
T
m
j
X
t
x
T
m
fm
m
X
13. Sub – Carriers
subcarriers are sinusoids
the sum of the sub – carriers is then the baseband OFDM
Fig : Subcarriers
15. Cyclic prefix helps in proper recovery of signal
Disadvantage - some loss in efficiency results as cyclic
prefix has no new information
Cyclic Prefix
Fig : Cyclic Prefix
16. Advantages and Drawbacks of OFDM
1. Advantages :
OFDM converts frequency selective fading channels to non-
selective fading subchannels (flat fading).
Bandwidth efficient
flexible to the channel conditions.
Robust to ISI and ICI
17. Ch.1
Ch.2 Ch.3 Ch.4 Ch.5 Ch.6 Ch.7 Ch.8 Ch.9 Ch.10
Saving of bandwidth
Ch.3 Ch.5 Ch.7 Ch.9
Ch.2 Ch.4 Ch.6 Ch.8 Ch.10
Ch.1
50% bandwidth saving
frequency
frequency
Fig: Bandwidth saving using OFDM
18. 2. Drawbacks :
sensitive to the carrier frequency offset and Doppler shift.
more complicated than single-carrier modulation.
High peak to average power ratio problem
20. WHY PAPR IS LARGE?
OFDM uses N-point IFFT.
IFFT uses the principle of linear combination.
The central limit theorem states that a linear combination
of a large number of independent random signals is
approximated by Gaussian.
(* N is usually large in OFDM.)
This implies that some samples have a high probability
of high peaks.
21. The major disadvantages of a high PAPR are-
1. Increased complexity in the analog to digital and digital to
analog converter.
2. Reduction in efficiency of RF amplifiers.
High PAPR=16 Low PAPR=2.25
PAPR example
22. THE CCDF OF THE PAPR
F(z) = 1 – exp(z)
PAPR is random Variable
Level crossing rate theorem is used for measurement
PAPR is calculated by using CCDF as
CCDF(PAPRo) = Pr(PAPR > PAPRo)
Complementary Commulative Distributive Function
𝑃 𝑃𝐴𝑃𝑅 > 𝑍 = 1 − 𝑃 𝑃𝐴𝑃𝑅 ≤ 𝑍
= 1 − 𝐹(𝑍)𝑁
= 1 − (1 − exp(−𝑍))𝑁
23. CRITERIA FOR SELECTION OF PAPR
REDUCTION TECHNIQUE
PAPR reduction capability
Power increase in transmit signal
BER increase at the receiver
Loss in data rate
Computational complexity
24. Signal Scrambling Techniques
• Selected Mapping (SLM)
• Partial Transmit Sequence (PTS)
• Tone Reservation (TR)
• Tone Injection (TI)
b) Signal Distortion Techniques
• Peak Windowing
• Peak Reduction Carrier
• Clipping and Filtering
PAPR Reduction Techniques
25. Simple approach requiring multiple sequential FFTs.
𝐵 𝑥 =
𝑥 𝑥 ≤ 𝐴
𝐴𝑒𝑗𝜙(𝑥)
, 𝑥 > 𝐴
Live with in-band clipping noise and effect on
performance.
Clipping and Filtering method
Fig :-Clipping and filtering
26. Tone Reservation
• This method describes an additive method for reducing PAPR
• some subcarriers are reserved
• This methods may reduce the system bit rate if many tones are reserved for
PAPR reduction purposes
Drawbacks:
– Increase in the average energy per bit which might reduce the BER
performance improvement.
– Loss of spectral efficiency due to tone reservation
27. Selective Level Mapping (SLM)
Basic scrambling technique.
Symbols are divided and multiplied with phase sequences.
It requires transmitting bits of side information per OFDM symbol
Fig :- Block diagram of SLM technique
29. Fig : CCDF of PAPR with Different set of phase vectors( Elapsed time is 0.865826 seconds.)
Results :
30. Fig : CCDF of PAPR with Different set of phase vectors( Elapsed time is 0.576960 seconds.)
Fig : CCDF of PAPR with Different set of phase vectors( Elapsed time is 1.268421 seconds.)
31. Fig:- CCDF of PAPR of SLM technique using QAM modulation
32. Input OFDM signal is divided into sub-blocks.
Phase optimization method is used.
6) Partial Transmit Sequence (PTS)
Fig:- PTS block diagram
34. Conclusions :
By using SLM Method PAPR is reduced but
computational complexity and side information is
increased.
PTS method gives better performance as compared
to SLM, but has more computational complexity.
35. REFERENCES
[1] R. van Nee and R. Prasad, OFDM for Wireless Multimedia Communications,
Boston: Artech House, 2000.
[2] Hong-Jie Chou, Ping-You Lin and Jung-Shan Lin, “PAPR Reduction Techniques
with Hybrid SLM-PTS Schemes for OFDM Systems.”IEEE Transactions, 2012.
[3] Hermann Rohling, “OFDM Concepts for Future Communication Systems”.
Springer,ISSN: 1860-4862, ISBN: 978-3-642-17495-7, e-ISBN: 978-3-642-17496-4,
DOI: 10.1007/978-3-642-17496-4
[4] John G. Proakis, “Digital Communications”, 4th edition. McGraw Hill.
[5] E. Alsusa and L. Yang, “A Low-Complexity Time-Domain Linear Symbol
Combining Technique for PAPR Reduction in OFDM Systems,” IEEE Transactions
on Signal Processing, Vol. 56, No. 10, Oct. 2008.
36. REFERENCES
[6] S. H. M¨uller and J. B. Huber, “A Novel Peak Power Reduction Scheme for OFDM,”
Proceedings of International Symposium on Personal, Indoor and Mobile Radio
Communications (PIMRC’97), Vol. 3, Helsinki, Finland, pp. 1090-1094, Sep. 1997.
[7] S. H. M¨uller and J. B. Huber, “OFDM with Reduced Peak-to-Average Power Ratio
by Optimum Combination of Partial Transmit Sequences,” IEE Electronics Letters, Vol.
33, No. 5, pp. 368-369, Feb. 1997.
[8] P. A. Pushkarev, K.-W. Ryu, K.-Y. Yoo and Y.-W. Park, “A Stud yon the PAR
Reduction by Hybrid Algorithm Based on the PTS and SLM Techniques,” Proceedings
of the 57th IEEE Vehicular Technology Conference, Vol. 2, pp. 1263-1267, 2003.
[9] R. B¨auml, R. F. H. Fischer and J. B. Huber, “Reducing the Peak-to-Average Power
Ratio of Multicarrier Modulation by Selected Mapping,”IEE Electronics Letters, Vol. 32,
No. 22, pp. 2056-2057, Oct. 1996.
[10] Zakee Ahmed, Shete A.K,”A Comparative Study of PAPR Reduction Techniques
in OFDM”, International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 1, July 2012
