1. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 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.

2. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 2 Spreading sequences: Desirable properties

3. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 3 Five KEY properties 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

4. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 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 m−sequences have “ideal” periodic autocorrelation, i.e. their autocorrelation function is N (the sequence length) at one sample period and −1 everywhere else.

5. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 5 Periodic Autocorrelation (2) This means that the output of a correlator operating on repeated Ipatov Transmitted sequences is EXACTLY, the channel impulse repeated, plus noise. The output of a correlator operating on a repeated m−sequence is CLOSE TO the channel impulse response + noise.

6. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 6 Example Correlator Outputs

7. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 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)

8. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 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- Hadamard matrix is 0.194. GMF greater than 6 is rare

9. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 9 Autocorrelation: High GMF

10. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 10 Autocorrelation: Low GMF

11. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 11 Matched Filter Output – High GMF

12. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 12 Matched Filter Output – Low GMF

13. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 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.

14. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 14 Temporal Peak to Average Ratio Need low TPAR, otherwise need high voltage power supply. Best GMF (Infinite) is a single impulse. Impulse has 0dB SPAR TPAR of Impulse is worst Need to balance sequence length and PRF to get a good SPAR and a good TPAR.

15. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 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: 7,13,21,31,57,73,91,127,133,183,273,307,381,512,553,651,75 7,871,993,1057,1407,1723

16. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 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.

17. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 17 TG4a CM8 Magnitudes

18. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 18 TG4a CM6 Magnitudes

19. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 19 Basic Difference sets for length 31 codes Few 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 ];

20. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 20 Auto correlation. Fewest zeros ipatov sequence

21. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 21 Auto correlation. Balanced zero ipatov sequence

22. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 22 Autocorrelation of magnitude. Balanced zero codes

23. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 23 Autocorrelation of magnitude. Fewest zero codes

24. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 24 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

25. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 25 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

26. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 26 12 Length 31 codes Balanced Ipatov Sequences (BITS) *6 Combination of 6 codes with best cross correlation **3 Combination of 3 codes with best cross correlation

27. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 27 Best 20 of Length 31 Fewest zero codes

28. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 28 SPAR, L=31 balanced codes Lower is better

29. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 29 Autocorrelation: Golay Merit Factor L=31 balanced codes Higher is better

30. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 30 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

31. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 31 Preamble PSD for BITS at 30.875MHz PRF

32. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 32 Preamble Spectrum Analyzer Output BITS: 30.875MHz PRF

33. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 33 SPAR vs Data mode PSD BITS:- Codeword No. 10 Codeword No. 10 : SPAR = 3.26dB

34. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 34 SPAR vs Data mode Spectrum BITS:- Codeword No. 10 Codeword No. 10 : SPAR = 3.26dB

35. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 35 Aperiodic PSD – 30.85MHz PRF Codeword No. 10 : SPAR = 3.26dB

36. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 36 Aperiodic PSD – 15.4MHz PRF Codeword No. 10 : SPAR = 3.26dB

37. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 37 Using one of these codes for data b i-1 = 0, b i = 0 b i-1 = 0, b i = 1 b i-1 = 1, b i = 1 b i-1 = 1, b i = 0

38. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 38 Conclusion 2 Recommendations –Use periodic BITS codes at 30.875 MHz PRF for Preamble –Use BPSK BITS codes at variable PRF for Data Transmission

39. doc.: IEEE 802.15−05−0393−00−004a Submission July, 2005 Mc Laughlin, DecawaveSlide 39 References [Ipatov] V. P. Ipatov, “Ternary sequences with ideal autocorrelation properties” Radio Eng. Electron. Phys., vol. 24, pp. 75−79, Oct. 1979. [ H ø holdt et al] Tom Høholdt and Jørn Justesen, “Ternary sequences with Perfect Periodic Autocorrelation”, IEEE Transactions on information theory.