Advances in OFDM Peak Power Control

1. Advances in OFDM Peak Power Control Scott CH Huang National TsingHua University

2. Outline • Background • OFDM, PAPR/PMEPR • Main Topics of this talk • Golay-based sequences construction • General sequence manipulation techniques

3. 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.

4. 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

5. 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

6. Definitions of PMEPR & PAPR • Consider a Multicarrier signal

7. Some Relations regarding PAPR & PMEPR [Sharif, Gharavi-Alkhansari, Khalaj, IEEE Trans on Comm, 2003]

8. The PMEPR Problem • OFDM usually exhibits a high PMEPR. • High PMEPR • increases the complexity of A/D & D/A converters • reduces the efficiency of RF power amplifier • PMEPR puts a stringent requirement on the power amplifier design

9. Existing Solutions to the PMEPR Problem • Signal distortion techniques • clipping, peak window, peak cancellation • Redundancy-based techniques • Adaptive subcarrier selection (ASUS) • Selected Mapping (SLM) • Partial Transmit Sequences (PTS) • Coding techniques • Golay sequences • Combination of Golay sequences • Combination of shorter sequences

10. 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.

11. 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]

12. Coding Techniques • Golay Sequences/ Golay Complementary Pairs • Golay-based sequences • General sequence manipulation techniques

13. 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.

14. 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 • Davis & Jedwab, IEEE Trans on IT 1999 • referred to as the GDJS/GDJCP • Whether we can construct all GSs/GCPs of length 2m is still unknown.

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

16. 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

17. 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

18. QPSK GCPs (cont) • are a GCP iff

19. 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 16-QAM sequences.

20. QPSK & 16-QAM Symbols

21. Mappings between QPSK & 16-QAM Symbols/Sequences • Mapping between symbols • Induced mapping between sequences

22. 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]

23. 64-QAM Constellation

24. 64-QAM Constellation & Mappings

25. 64-QAM Golay-based Sequences PMEPR=2.85 [Scott CH Huang, HC Wu, IEEE Trans on Comm 2010]

26. 22h-QAM Constellations

27. 22h-QAM Mappings

28. 256-QAM Golay-based Sequences Basic Types P,R Miscellaneous Types M1~M5 [Scott CH Huang, HC Wu, John Cioffi, Globecom 2010]

29. Comparisons

30. 22h-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]

31. General Sequence Manipulation Techniques • Golay-based sequences: • Smaller constellation  Larger Constellation • Same Length • Cartesian Product • Shorter sequences  Longer sequences • Same-size constellation • Not necessarily Golay

32. Cartesian Product of OFDM Sequences • Cartesian product of two sequences is simply concatenation. • Given two constellations [Scott CH Huang, HC Wu, Globecom 2012]

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

34. Cartesian Product & PMEPR

35. Multiple Product & PMEPR

36. Cartesian Product & Code Rate

37. Conclusions • Peak Power Control Introduction • Signal distortion-based, redundancy-based, coding • SLM Techniques • SLM Turbo-coded OFDM architecture (Mao-Chao Lin) • Golay Sequences • GDJCP≠GCP (Ying Li) • Golay complementary set (Chi-Chao Chao) • Sequence Manipulation • Combination of Golay sequences (Scott CH Huang) • Combination of shorter sequences (Scott CH Huang)

38. Thank you!