1. Submission Title: [Codes for preamble and data]
July, 2005
Project: IEEE P 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− ], FAX: [What’s a FAX?], E−Mail:
Re: [ a.]
Abstract: [Discusses the desirable properties of spreading sequences]
Purpose: [To promote discussion in a.]
Notice: This document has been prepared to assist the IEEE P 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 P
Mc Laughlin, Decawave

2. Spreading sequences: Desirable properties
July, 2005
Spreading sequences: Desirable properties
Mc Laughlin, Decawave

3. Five KEY properties of spreading sequences
July, 2005
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)
July, 2005
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)
July, 2005
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
July, 2005
Example Correlator Outputs
Mc Laughlin, Decawave

7. Aperiodic Autocorrelation
July, 2005
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
July, 2005
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 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
GMF greater than 6.0 is rare
Mc Laughlin, Decawave

9. Autocorrelation: High GMF
July, 2005
Autocorrelation: High GMF
Mc Laughlin, Decawave

10. Autocorrelation: Low GMF
July, 2005
Autocorrelation: Low GMF
Mc Laughlin, Decawave

11. Matched Filter Output – High GMF
July, 2005
Matched Filter Output – High GMF
Mc Laughlin, Decawave

12. Matched Filter Output – Low GMF
July, 2005
Matched Filter Output – Low GMF
Mc Laughlin, Decawave

13. Spectral Peak to Average ratio (SPAR)
July, 2005
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
July, 2005
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:
July, 2005
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
July, 2005
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. July, 2005
TG4a CM1 Magnitudes
Mc Laughlin, Decawave

18. July, 2005
TG4a CM8 Magnitudes
Mc Laughlin, Decawave

19. July, 2005
TG4a CM6 Magnitudes
Mc Laughlin, Decawave

20. Basic Difference sets used for length 31 Ipatov Ternary Sequences
July, 2005
Basic Difference sets used for length 31 Ipatov Ternary Sequences
Fewest zeros
Parameters L=31,k=6, λ=1
Difference set =[ ];
Balanced zeros
Parameters L=31,k=15, λ=7
Difference set =[ ];
Mc Laughlin, Decawave

21. Auto correlation. Fewest zeros ipatov sequence
July, 2005
Auto correlation. Fewest zeros ipatov sequence
Mc Laughlin, Decawave

22. Auto correlation. Balanced zero ipatov sequence
July, 2005
Auto correlation. Balanced zero ipatov sequence
Mc Laughlin, Decawave

23. Autocorrelation of magnitude. Balanced zero codes
July, 2005
Autocorrelation of magnitude. Balanced zero codes
Mc Laughlin, Decawave

24. Autocorrelation of magnitude. Fewest zero codes
July, 2005
Autocorrelation of magnitude. Fewest zero codes
Mc Laughlin, Decawave

25. July, 2005
Cross correlation of fewest zeros ipatov with modified magnitude sequence
Cross correlation of
with
i.e. 0 replaced by -4
Mc Laughlin, Decawave

26. July, 2005
Cross correlation of balanced zeros ipatov with modified magnitude sequence
Cross correlation of
with
i.e. 0 replaced by -1
Mc Laughlin, Decawave

27. 12 Length 31 codes Balanced Ipatov Sequences (BITS)
July, 2005
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
Mc Laughlin, Decawave

28. Best 20 of Length 31 Fewest zero codes
July, 2005
Best 20 of Length 31 Fewest zero codes
Mc Laughlin, Decawave

29. SPAR, L=31 balanced codes Lower is better July, 2005
Mc Laughlin, Decawave

30. Autocorrelation: Golay Merit Factor L=31 balanced codes
July, 2005
Autocorrelation: Golay Merit Factor L=31 balanced codes
Higher is better
Mc Laughlin, Decawave

31. Cross Correlation Coherent cross-correlation matrix 16 6 4 4 6 4
July, 2005
Cross Correlation
Coherent cross-correlation matrix
Non-coherent cross-correlation matrix
Mc Laughlin, Decawave

32. Preamble PSD for BITS at 30.875MHz PRF
July, 2005
Preamble PSD for BITS at MHz PRF
Mc Laughlin, Decawave

33. Preamble Spectrum Analyzer Output BITS: 30.875MHz PRF
July, 2005
Preamble Spectrum Analyzer Output BITS: MHz PRF
Mc Laughlin, Decawave

34. SPAR vs Data mode PSD BITS:- Codeword No. 10
July, 2005
SPAR vs Data mode PSD BITS:- Codeword No. 10
Codeword No. 10 : SPAR = 3.26dB
Mc Laughlin, Decawave

35. SPAR vs Data mode Spectrum BITS:- Codeword No. 10
July, 2005
SPAR vs Data mode Spectrum BITS:- Codeword No. 10
Codeword No. 10 : SPAR = 3.26dB
Mc Laughlin, Decawave

36. Aperiodic PSD – 30.85MHz PRF Codeword No. 10 : SPAR = 3.26dB
July, 2005
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 July, 2005
Mc Laughlin, Decawave

38. July, 2005
Using these codes for data BPSK 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 Data Transmission
July, 2005
Conclusion
Recommendations
Preamble
Use periodic BITS codes at MHz PRF for Preamble
Data Transmission
Use BITS codes
Use BPSK with PPM for non-coherent compatibility at variable PRF
Mc Laughlin, Decawave

40. July, 2005
References
[Ipatov] V. P. Ipatov, “Ternary sequences with ideal autocorrelation properties” Radio Eng. Electron. Phys., vol. 24, pp. 75−79, Oct
[Høholdt et al] Tom Høholdt and Jørn Justesen, “Ternary sequences with Perfect Periodic Autocorrelation”, IEEE Transactions on information theory.
Mc Laughlin, Decawave