Spreading codes

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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 Voice353-1-2954937 , FAX Whats a
FAX?, E-Mail michael_at_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.
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Spreading sequencesDesirable properties
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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

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Periodic Autocorrelation (1)

• For channel sounding, a repeated sequence is
  appropriate.
• gt 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.

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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.

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Example Correlator Outputs
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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)

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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

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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.

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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.

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Example sequences

• One of the Ipatov length 57 sequences
• -00--0--------0-0-----0--0
  0--
• 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 7,13,21,31,57,73,91,133,183,273,307,381,5
  53,651,757,871,993,1057,1407,1723

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Sequence length and PRF

• If sequence is repeated, spectral lines spaced at
  the 1/sequence length apart.
• Want these to be lt 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.

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TG4a CM8 Magnitudes