Advances in Advances in OFDM Peak OFDM Peak

Power ControlPower ControlScott CH Huang

National Tsing Hua University

OutlineOutline• Background

o OFDM, PAPR/PMEPR• Main Topics of this talk

o Golay-based sequences constructiono General sequence manipulation techniques

OFDMOFDM• 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)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 OFDMAdvantages 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 Definitions of PMEPR & PAPRPMEPR & PAPR

• Consider a Multicarrier signal

Some Relations Some Relations regarding PAPR & regarding PAPR &

PMEPRPMEPR

[Sharif, Gharavi-Alkhansari, Khalaj, IEEE Trans on Comm, 2003]

The PMEPR ProblemThe PMEPR Problem• OFDM usually exhibits a high PMEPR.• High PMEPR

o increases the complexity of A/D & D/A converterso reduces the efficiency of RF power amplifier

• PMEPR puts a stringent requirement on the power amplifier design

Existing Solutions to Existing Solutions to the PMEPR Problemthe PMEPR Problem

• Signal distortion techniqueso clipping, peak window, peak cancellation

• Redundancy-based techniqueso Adaptive subcarrier selection (ASUS)o Selected Mapping (SLM)o Partial Transmit Sequences (PTS)

• Coding techniqueso Golay sequenceso Combination of Golay sequenceso Combination of shorter sequences

Select-ed/-ive MappingSelect-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 SLM for Turbo-coded OFDMOFDM

• 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 TechniquesCoding Techniques• Golay Sequences/ Golay Complementary Pairs• Golay-based sequences• General sequence manipulation techniques

Golay Complementary Golay Complementary Pairs (GCPs)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 GCPsBinary 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 constructedo Davis & Jedwab, IEEE Trans on IT 1999o referred to as the GDJS/GDJCP

• Whether we can construct all GSs/GCPs of length 2m is still unknown.

GDJCP =? GCPGDJCP =? GCP• No!• [Ying Li, Wen-Bin Chu, IEEE Trans on IT, 2005]• Therefore,

Golay Complementary Golay Complementary Sets?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 GCPsQPSK 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)QPSK GCPs (cont)• are a GCP iff

Construct 16-QAM Construct 16-QAM GCPs using QPSK GCPs using QPSK

GCPsGCPs• 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 16-QAM sequences.

QPSK & 16-QAM QPSK & 16-QAM SymbolsSymbols

Mappings between QPSK Mappings between QPSK & 16-QAM & 16-QAM

Symbols/SequencesSymbols/Sequences• Mapping between symbols

• Induced mapping between sequences

16-QAM Golay-based 16-QAM Golay-based SequencesSequences

PMEPR=3.6[Rößing and Tarokh, IEEE Trans on IT 2001 ]

PMEPR=2[Chong, Venkataramani, Tarokh, IEEE Trans on IT 2004]

64-QAM Constellation64-QAM Constellation

b04b2

2b1 c

64-QAM Constellation 64-QAM Constellation & Mappings& Mappings

64-QAM Golay-based 64-QAM Golay-based SequencesSequences

PMEPR=2.85[Scott CH Huang, HC Wu, IEEE Trans on Comm 2010]

222h2h-QAM -QAM ConstellationsConstellations

222h2h-QAM Mappings-QAM Mappings

256-QAM Golay-based 256-QAM Golay-based SequencesSequences

Basic Types P,R

Miscellaneous Types M1~M5

[Scott CH Huang, HC Wu, John Cioffi, Globecom 2010]

ComparisonsComparisonsConstellation Sequence PMEPR

256-QAM

2.945.883.603.703.454.664.87

PG8RG8

18MG

28MG

38MG

48MG

58MG

222h2h-QAM Mappings-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 General Sequence Manipulation Manipulation TechniquesTechniques

• Golay-based sequences: o Smaller constellation Larger Constellationo Same Length

• Cartesian Producto Shorter sequences Longer sequenceso Same-size constellationo Not necessarily Golay

Cartesian Product of Cartesian Product of OFDM SequencesOFDM Sequences

• Cartesian product of two sequences is simply concatenation.

• Given two constellations

[Scott CH Huang, HC Wu, Globecom 2012]

Multiple Cartesian Multiple Cartesian ProductProduct

• The Cartesian product of two sets of sequences can be generalized to multiple sets of sequences.

Cartesian Product & Cartesian Product & PMEPRPMEPR

Multiple Product & Multiple Product & PMEPRPMEPR

Cartesian Product & Cartesian Product & Code RateCode Rate

ConclusionsConclusions• 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 Manipulationo Combination of Golay sequences (Scott CH Huang)o Combination of shorter sequences (Scott CH Huang)

Thank you!Thank you!