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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]

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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

five key properties
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

Mc Laughlin, Decawave

periodic autocorrelation 1
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.

Mc Laughlin, Decawave

periodic autocorrelation 2
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.

Mc Laughlin, Decawave

example correlator outputs
Example Correlator Outputs

Mc Laughlin, Decawave

aperiodic autocorrelation
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

golay merit factor
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

Mc Laughlin, Decawave

autocorrelation high gmf
Autocorrelation: High GMF

Mc Laughlin, Decawave

autocorrelation low gmf
Autocorrelation: Low GMF

Mc Laughlin, Decawave

spectral peak to average ratio spar
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.

Mc Laughlin, Decawave

temporal peak to average ratio
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.

Mc Laughlin, Decawave

example sequences
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

sequence length and prf
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

tg4a cm8 magnitudes
TG4a CM8 Magnitudes

Mc Laughlin, Decawave

tg4a cm6 magnitudes
TG4a CM6 Magnitudes

Mc Laughlin, Decawave

basic difference sets for length 31 codes
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 ];

Mc Laughlin, Decawave

cross correlation of fewest zeros ipatov with modified magnitude sequence
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

cross correlation of balanced zeros ipatov with modified magnitude sequence
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

12 length 31 codes balanced ipatov sequences bits
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

spar l 31 balanced codes
SPAR, L=31 balanced codes

Lower is better

Mc Laughlin, Decawave

autocorrelation golay merit factor l 31 balanced codes
Autocorrelation: Golay Merit FactorL=31 balanced codes

Higher is better

Mc Laughlin, Decawave

cross correlation
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

spar vs data mode psd bits codeword no 10
SPAR vs Data mode PSDBITS:- Codeword No. 10

Codeword No. 10 : SPAR = 3.26dB

Mc Laughlin, Decawave

spar vs data mode spectrum bits codeword no 10
SPAR vs Data mode SpectrumBITS:- Codeword No. 10

Codeword No. 10 : SPAR = 3.26dB

Mc Laughlin, Decawave

aperiodic psd 30 85mhz prf
Aperiodic PSD – 30.85MHz PRF

Codeword No. 10 : SPAR = 3.26dB

Mc Laughlin, Decawave

aperiodic psd 15 4mhz prf
Aperiodic PSD – 15.4MHz PRF

Codeword No. 10 : SPAR = 3.26dB

Mc Laughlin, Decawave

using one of these codes for data
Using one of these codes for data

bi-1 = 0, bi = 0

bi-1 = 0, bi = 1

bi-1 = 1, bi = 0

bi-1 = 1, bi = 1

Mc Laughlin, Decawave

conclusion
Conclusion
  • 2 Recommendations
    • Use periodic BITS codes at 30.875 MHz PRF for Preamble
    • Use BPSK BITS codes at variable PRF for Data Transmission

Mc Laughlin, Decawave

references
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