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**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

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**Spreading sequences: Desirable properties**

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

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**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

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**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

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**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

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**Example Correlator Outputs**

July, 2005 Example Correlator Outputs Mc Laughlin, Decawave

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**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

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**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

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**Autocorrelation: High GMF**

July, 2005 Autocorrelation: High GMF Mc Laughlin, Decawave

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**Autocorrelation: Low GMF**

July, 2005 Autocorrelation: Low GMF Mc Laughlin, Decawave

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**Matched Filter Output – High GMF**

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

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**Matched Filter Output – Low GMF**

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

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**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

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**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

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**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

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**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

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July, 2005 TG4a CM1 Magnitudes Mc Laughlin, Decawave

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July, 2005 TG4a CM8 Magnitudes Mc Laughlin, Decawave

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July, 2005 TG4a CM6 Magnitudes Mc Laughlin, Decawave

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**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

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**Auto correlation. Fewest zeros ipatov sequence**

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

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**Auto correlation. Balanced zero ipatov sequence**

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

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**Autocorrelation of magnitude. Balanced zero codes**

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

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**Autocorrelation of magnitude. Fewest zero codes**

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

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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

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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

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**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

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**Best 20 of Length 31 Fewest zero codes**

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

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**SPAR, L=31 balanced codes Lower is better July, 2005**

Mc Laughlin, Decawave

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**Autocorrelation: Golay Merit Factor L=31 balanced codes**

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

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**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

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**Preamble PSD for BITS at 30.875MHz PRF**

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

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**Preamble Spectrum Analyzer Output BITS: 30.875MHz PRF**

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

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**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

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**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

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**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

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**Aperiodic PSD – 15.4MHz PRF Codeword No. 10 : SPAR = 3.26dB July, 2005**

Mc Laughlin, Decawave

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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

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**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

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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

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