Properties of Spreading Sequences

1. Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs) Submission Title: [Spreading sequences properties] 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 • 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. the periodic autocorrelation function is a single pulse at one sample period and zero everywhere else. • 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

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. 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. • GMF greater than 6 is rare Mc Laughlin, Decawave

9. 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

10. Temporal Peak to Average Ratio • Need low TPAR, otherwise need high voltage power supply. • Best GMF (Infinite) is a single impulse. • Implulse 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

11. 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 completely flat spectrum • Can be used for data because good periodic ACF means GMF is also quite good. • Still, it could be better. • Ipatov sequences are available at the following lengths: 7,13,21,31,57,73,91,133,183,273,307,381,553,651,757,871,993,1057,1407,1723 Mc Laughlin, Decawave

12. Sequence length and PRF • If sequence is repeated, spectral lines spaced at the 1/sequence length apart. • Want these to be < 1MHz 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 Ipatov requires ~10 times lower TPAR than length 57, but ~10 times larger PRF. Mc Laughlin, Decawave

13. TG4a CM8 Magnitudes Mc Laughlin, Decawave