Advances in OFDM
Peak Power Control
Scott CH Huang
National Tsing Hua University
Outline
• Background
o OFDM, PAPR/PMEPR
• Main Topics of this talk
o Golay-based sequences construction
o General sequence manipulation techniques
OFDM
• OFDM is widely used in wireless communication
nowadays.
• Basic principle is slitting a high-rate data stream into
a number of lower rate stream and transmit them
simultaneously over many carriers.
• It essentially transforms a signal from frequency
domain to time domain
• It can be regarded as both a modulation scheme
and a multiplex technique.
OFDM (cont)
•
•
•
•
•
A multi-carrier modulation scheme
Data transmitted over many low-rate subcarriers
Subcarriers mutually orthogonal
Frequency band divided into many subchannels
Subchannels modulated separately
Advantages of OFDM
• Ability to cope with severe channel condition (e.g.
attenuation in high freq)
• Immunity to delay spread and multipath
• Resistance to frequency selective fading
• Simple equalization
• Efficient bandwidth usage
Definitions of
PMEPR & PAPR
• Consider a Multicarrier signal
Some Relations regarding
PAPR & PMEPR
[Sharif, Gharavi-Alkhansari, Khalaj, IEEE Trans on Comm, 2003]
The PMEPR Problem
• OFDM usually exhibits a high PMEPR.
• High PMEPR
o increases the complexity of A/D & D/A converters
o reduces the efficiency of RF power amplifier
• PMEPR puts a stringent requirement on the power
amplifier design
Existing Solutions to the
PMEPR Problem
• Signal distortion techniques
o clipping, peak window, peak cancellation
• Redundancy-based techniques
o Adaptive subcarrier selection (ASUS)
o Selected Mapping (SLM)
o Partial Transmit Sequences (PTS)
• Coding techniques
o Golay sequences
o Combination of Golay sequences
o Combination of shorter sequences
Select-ed/-ive Mapping
• Generate several OFDM symbols in a special
manner and select the lowest PAPR for actual
transmission.
• SLM creates several independent time domain
signals
• How many signals should we generate to select
from? It is important to know PMEPR/PAPR statistical
distributions.
SLM for Turbo-coded
OFDM
• Turbo-coded OFDM with m-sequences (SLM w/
Reed-Muller-coded side info)
• Distinct interleaver (SLM w/o side info)
[MC Lin et al, IWCMC 2005]
Coding Techniques
• Golay Sequences/ Golay Complementary Pairs
• Golay-based sequences
• General sequence manipulation techniques
Golay Complementary
Pairs (GCPs)
• It is originally used in multislit dispersion optical
spectroscopy.
• It has many mathematical properties that can be
used to reduce PMEPR.
• Originally it’s binary, but it can be generalized to
tertiary, quaternary (complex-valued),… etc.
• We focus on Golay sequences over an arbitrary
constellation with QAM modulation.
Binary GCPs
• Originally used in Multislit spectroscopy without
direct construction method
• A sequence is a GS if it is a member of some GCP.
• The existence of GSs/GCPs of an arbitrary length n is
unknown.
• GSs/GCPs of length 2m can be constructed
o Davis & Jedwab, IEEE Trans on IT 1999
o referred to as the GDJS/GDJCP
• Whether we can construct all GSs/GCPs of length 2m
is still unknown.
GDJCP =? GCP
• No!
• [Ying Li, Wen-Bin Chu, IEEE Trans on IT, 2005]
• Therefore,
Golay Complementary
Sets?
• C.-Y. Chen, C.-H. Wang, and C.-C. Chao, IEEE
Comm Letters 2008.
• C.-Y. Chen, C.-H. Wang, and C.-C. Chao, AAECC
2006
• C.-Y. Chen, Y.-J. Min, K.-Y. Lu, and C.-C. Chao, IEEE
ICC 2008
QPSK GCPs
• Defined over a constellation
• Easy to define.
• Can be used as a building block to construct more
general GCPs
• Given sequence
, the aperiodic
autocorrelation is defined as
QPSK GCPs (cont)
•
are a GCP iff
Construct 16-QAM GCPs
using QPSK GCPs
• There is a one-to-one mapping (bijection) from two
QPSK symbols to one 16-QAM symbol.
• Consequently there is a one-to-one mapping
(bijection) from two QPSK sequences to one 16QAM sequences.
QPSK & 16-QAM
Symbols
Mappings between QPSK &
16-QAM Symbols/Sequences
• Mapping between symbols
• Induced mapping between sequences
16-QAM Golay-based
Sequences
PMEPR=3.6
[Rößing and Tarokh, IEEE Trans on IT 2001 ]
PMEPR=2
[Chong, Venkataramani, Tarokh, IEEE Trans on IT 2004]
64-QAM Constellation
2b1
4b2
c
b0
64-QAM Constellation &
Mappings
64-QAM Golay-based
Sequences
PMEPR=2.85
[Scott CH Huang, HC Wu, IEEE Trans on Comm 2010]
2h
2 -QAM
Constellations
2h
2 -QAM
Mappings
256-QAM Golay-based
Sequences
Basic Types P,R
Miscellaneous Types M1~M5
[Scott CH Huang, HC Wu, John Cioffi, Globecom 2010]
Comparisons
Constellation
256-QAM
Sequence
PMEPR
G
2.94
G
5.88
G
3.60
G
3.70
G
3.45
G
4.66
G
4.87
P
8
R
8
M1
8
M2
8
M3
8
M4
8
M5
8
2h
2 -QAM
Mappings
• 22h-QAM sequences have more miscellaneous
types and are hard to analyze & categorize
• The problem of which building block coupled with
which and how does that affect the PMEPR well as
code rate can be rephrased as an optimization
problem. [Scott CH Huang, HC Wu, Globecom 2011]
General Sequence
Manipulation Techniques
• Golay-based sequences:
o Smaller constellation  Larger Constellation
o Same Length
• Cartesian Product
o Shorter sequences  Longer sequences
o Same-size constellation
o Not necessarily Golay
Cartesian Product of
OFDM Sequences
• Cartesian product of two sequences is simply
concatenation.
• Given two constellations
[Scott CH Huang, HC Wu, Globecom 2012]
Multiple Cartesian
Product
• The Cartesian product of two sets of sequences can
be generalized to multiple sets of sequences.
Cartesian Product &
PMEPR
Multiple Product &
PMEPR
Cartesian Product & Code
Rate
Conclusions
• Peak Power Control Introduction
o Signal distortion-based, redundancy-based, coding
• SLM Techniques
o SLM Turbo-coded OFDM architecture (Mao-Chao Lin)
• Golay Sequences
o GDJCP≠GCP (Ying Li)
o Golay complementary set (Chi-Chao Chao)
• Sequence Manipulation
o Combination of Golay sequences (Scott CH Huang)
o Combination of shorter sequences (Scott CH Huang)
Thank you!