Codes for Preamble and Data

1. Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs) Submission Title: [Codes for preamble and data] Date Submitted: [7 June, 2005] Source: [Michael Mc Laughlin] Company [Decawave Ltd.] Address [25 Meadowfield, Sandyford, Dublin 18, Ireland] Voice:[+353−1−2954937 ], FAX: [What’s a FAX?], E−Mail: [michael@decawave.com] Re: [802.15.4a.] Abstract: [Discusses the desirable properties of spreading sequences] Purpose: [To promote discussion in 802.15.4a.] Notice: This document has been prepared to assist the IEEE P802.15. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P802.15. Mc Laughlin, Decawave

2. Spreading sequences:Desirable properties Mc Laughlin, Decawave

3. Five KEY properties of spreading sequences • Sequence Length • Pulse Repetition Frequency • Autocorrelation properties • Periodic autocorrelation (Channel sounding) • Aperiodic autocorrelation (Data mode) • Spectral peak to average ratio (SPAR) • FCC requirements • Temporal peak to average ratio (TPAR) • Power supply requirements Mc Laughlin, Decawave

4. Periodic Autocorrelation (1) • For channel sounding, a repeated sequence is appropriate. • Periodic autocorrelation function is the important property for a channel sounding sequence • Ipatov ternary sequences have perfect periodic autocorrelation i.e. all side lobes are zero • PBTS codes (from WBA/I2R) also have perfect periodic autocorrelation Mc Laughlin, Decawave

5. Periodic Autocorrelation (2) • m−sequences have ideal periodic autocorrelation, i.e. their autocorrelation function is N (the sequence length) at one sample period and −1 everywhere else. • Correlator output operating on repeated, periodic sequences with perfect periodic autocorrelation is exactly, the channel impulse response, also repeated, plus noise. Mc Laughlin, Decawave

6. Example Correlator Outputs Mc Laughlin, Decawave

7. Aperiodic Autocorrelation • For transmitting data, aperiodic autocorrelation function (AACF) is appropriate • Previous and next sequences may not be the same • Good AACF means low ISI • Golay Merit Factor (GMF) is a common measure of goodness of AACF (Golay 1977) Mc Laughlin, Decawave

8. Golay Merit Factor • GMF is defined as where ac is the aperiodic auto correlation function of a length n sequence • The average GMF of binary sequences is 1.0 • Best known GMF for binary sequences is 14.08 for the Barker 13 sequence, next is 12.1 for the Barker 11 sequence. • The mean Golay merit factor of the length 32 Walsh codes is 0.194. • GMF greater than 6.0 is rare Mc Laughlin, Decawave

9. Autocorrelation: High GMF Mc Laughlin, Decawave

10. Autocorrelation: Low GMF Mc Laughlin, Decawave

11. Matched Filter Output – High GMF Mc Laughlin, Decawave

12. Matched Filter Output – Low GMF Mc Laughlin, Decawave

13. Spectral Peak to Average ratio (SPAR) • In absence of ITU recommendations, use the FCC requirements. • Spectrum measured in 1MHz frequency bins for 1ms intervals. • Need Low SPAR. • SPAR in dBs converts to power backoff required. • Best known** SPAR for ternary sequences known to author is 1.17 dB for the Barker 11 and next 1.32 for Barker 13. ** (aside, of course, from a single impulse) Mc Laughlin, Decawave

14. Temporal Peak to Average Ratio • Lower TPAR allows low voltage silicon • Best GMF (Infinite) is a single impulse. • Impulse also has 0dB SPAR • TPAR of an impulse is worst • Need to balance sequence length and PRF to get a good SPAR and a good TPAR. Mc Laughlin, Decawave

15. Example sequences • One of the Ipatov length 57 sequences: −0+0−−0−−−+−+−+++++−−+++−++0++−0++−+−++−+−−0−+++−00−−++++ • GMF is 3.75 • A Length 63 m sequence: −−−−−−+−+−+−−++−−+−−−+−−+−++−++−−−+++−+−−−−++−+−+++−−++++−+++++ • GMF is 3.52 • Both of these sequences, if transmitted repeatedly back to back, have a flat spectrum • Ipatov sequences are available at the following lengths: 7,13,21,31,57,73,91,127,133,183,273,307,381,512,553,651,757,871,993,1057,1407,1723 Mc Laughlin, Decawave

16. Sequence length and PRF • If sequence is repeated, spectral lines spaced at the 1/sequence length apart. • Want these to be < ~ 2MHz apart for FCC compliance and low SPAR • Needs to be longer than Channel Impulse Response • e.g. CM8 has significant energy to ~850ns. • For a 1000ns duration sequence, a length 553 sequence requires ~10 times lower TPAR than length 57, but ~10 times larger PRF. Mc Laughlin, Decawave

17. TG4a CM1 Magnitudes Mc Laughlin, Decawave

18. TG4a CM8 Magnitudes Mc Laughlin, Decawave

19. TG4a CM6 Magnitudes Mc Laughlin, Decawave

20. Basic Difference sets used for length 31 Ipatov Ternary Sequences • Fewest zeros • Parameters L=31,k=6, λ=1 • Difference set =[1 5 11 24 25 27 ]; • Balanced zeros • Parameters L=31,k=15, λ=7 • Difference set =[1 2 3 4 6 8 12 15 16 17 23 24 27 29 30 ]; Mc Laughlin, Decawave

21. Auto correlation. Fewest zeros ipatov sequence Mc Laughlin, Decawave

22. Auto correlation. Balanced zero ipatov sequence Mc Laughlin, Decawave

23. Autocorrelation of magnitude. Balanced zero codes Mc Laughlin, Decawave

24. Autocorrelation of magnitude. Fewest zero codes Mc Laughlin, Decawave

25. Cross correlation of fewest zeros ipatov with modified magnitude sequence Cross correlation of 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 with -4 1 1 -4 1 1 1 1 1 1 -4 -4 1 1 1 1 1 1 1 1 1 1 1 1 1 -4 1 1 1 -4 1 i.e. 0 replaced by -4 Mc Laughlin, Decawave

26. Cross correlation of balanced zeros ipatov with modified magnitude sequence Cross correlation of 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 with -1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 1 -1 -1 1 1 1 -1 -1 i.e. 0 replaced by -1 Mc Laughlin, Decawave

27. 12 Length 31 codesBalanced Ipatov Sequences (BITS) *6 Combination of 6 codes with best cross correlation **3 Combination of 3 codes with best cross correlation Mc Laughlin, Decawave

28. Best 20 of Length 31 Fewest zero codes Mc Laughlin, Decawave

29. SPAR, L=31 balanced codes Lower is better Mc Laughlin, Decawave

30. Autocorrelation: Golay Merit FactorL=31 balanced codes Higher is better Mc Laughlin, Decawave

31. Cross Correlation Coherent cross-correlation matrix 16 6 4 4 6 4 6 16 6 6 6 4 4 6 16 6 4 4 4 6 6 16 6 6 6 6 4 6 16 6 4 4 4 6 6 16 Non-coherent cross-correlation matrix 16 4 4 4 6 4 4 16 6 4 4 4 4 6 16 4 4 4 4 4 4 16 4 6 6 4 4 4 16 4 4 4 4 6 4 16 Mc Laughlin, Decawave

32. Preamble PSD for BITSat 30.875MHz PRF Mc Laughlin, Decawave

33. Preamble Spectrum Analyzer OutputBITS: 30.875MHz PRF Mc Laughlin, Decawave

34. SPAR vs Data mode PSDBITS:- Codeword No. 10 Codeword No. 10 : SPAR = 3.26dB Mc Laughlin, Decawave

35. SPAR vs Data mode SpectrumBITS:- Codeword No. 10 Codeword No. 10 : SPAR = 3.26dB Mc Laughlin, Decawave

36. Aperiodic PSD – 30.85MHz PRF Codeword No. 10 : SPAR = 3.26dB Mc Laughlin, Decawave

37. Aperiodic PSD – 15.4MHz PRF Codeword No. 10 : SPAR = 3.26dB Mc Laughlin, Decawave

38. Using these codes for dataBPSK with PPM for non-coherent compatibility bi-1 = 0, bi = 0 bi-1 = 0, bi = 1 bi-1 = 1, bi = 0 bi-1 = 1, bi = 1 Mc Laughlin, Decawave

39. Conclusion • Recommendations • Preamble • Use periodic BITS codes at 30.875 MHz PRF for Preamble • Data Transmission • Use BITS codes • Use BPSK with PPM for non-coherent compatibility at variable PRF Mc Laughlin, Decawave

40. References • [Ipatov] V. P. Ipatov,“Ternary sequences with ideal autocorrelation properties”Radio Eng. Electron. Phys., vol. 24, pp. 75−79, Oct. 1979. • [Høholdt et al] Tom Høholdt and Jørn Justesen, “Ternary sequences with Perfect Periodic Autocorrelation”, IEEE Transactions on information theory. Mc Laughlin, Decawave