Doc.: IEEE 802.15 - 03/123r6 PHY proposal July-2003 Michael Mc Laughlin, ParthusCevaSlide 1 of 47...

July-2003

Michael Mc Laughlin, ParthusCevaSlide 1 of 47

doc.: IEEE 802.15 - 03/123r6

PHY proposal

Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs)Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs)

Submission Title: [The ParthusCeva Ultra Wideband PHY proposal]Date Submitted: [05 May, 2003]Source: [Michael Mc Laughlin, Vincent Ashe] Company [ParthusCeva Inc.]Address [32-34 Harcourt Street, Dublin 2, Ireland.]Voice:[+353-1-402-5809], FAX: [-], E-Mail:[[email protected]]

Re: [IEEE P802.15 Alternate PHY Call For Proposals. 17 Jan 2003]

Abstract: [Proposal for a 802.15.3a PHY]

Purpose: [To allow the Task Group to evaluate the PHY proposed]

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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doc.: IEEE 802.15 - 03/123r6

PHY proposal

The ParthusCeva PHYProposal

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PHY proposal

Overview of Presentation

• Coding– DSSS Coding scheme - biorthogonal coding– Ternary spreading codes– Reed Solomon FEC code– Optionally concatenated with convolutional code

• Preamble• Implementation Overview

• Performance– Link margin– Test results– Throughput, Multiple piconet performance

• Complexity

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PHY proposal

Symbol coding

• 64 biorthogonal signals [Proakis1]

• 64 signals from 32 orthogonal sequences

• Ternary sequences chosen for their auto-correlation properties

• Code constructed from binary Golay-Hadamard sequences

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Spreading code comparison

Code Length mean aamf min aamf

Best Ternary Golay Hadamard 40 5.90 4.54


Best Binary Golay Hadamard 32 4.43 2.21


Orthogonal Gold 32 2.22 1.19


• Length 32 code chosen for aamf and best matching with bit rates.

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PHY proposal

Sample rate and pulse repetition frequency

• Signal bandwidth chosen is 3.85GHz to 7.7GHz

• Sampling rate chosen is 7.7Ghz

• 32 chips per codeword, 6 channel bits / symbol

55Mbps 110Mbps 220Mbps 490Mbps 980Mbps/880Mbps

PRF 0.48 Gpps 0.96 Gpps 1.92 Gpps 3.86Gpps 7.7Gpps

Symbol rate 15Msym/sec

30Msym/sec

60Msym/sec

120Msym/sec

240Msym/sec

Samples/pulse

16 8 4 2 1

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PHY proposal

FEC Scheme

• Concatenated code for 110 , 220Mbps, 880Mbps

– Reed Solomon outer code (235,255)

– Convolutional rate 4/6 inner code

• Reed Solomon code (43,63) for 490Mbps, 980Mbps

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PHY proposal

FEC scheme - inner code

• A 0.667 rate (rate 4/6) convolutional code was chosen for the inner code at 110 and 200 Mbps. [Proakis2]

• Very low complexity 16 state code, constraint length 2, Octal generators 27, 75, 72.

• Each of 16 states can transition to any other state, outputting 16 of 64 possible codewords.

• Provides 3dB of gain over uncoded errors at a cost of 50% higher bit rate

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PHY proposal

Preamble Sequence

PACn PACn …….. PACn PACn …….. PACn

The preamble consists of 50-200 repetitions of PACn followed by 16 repetitions of itsnegative, PACn. The 180o transition to the negative provides a precise time marker for thereceiver.

PACn is a ternary sequence with perfect periodic autocorrelation i.e. its periodicautocorrelation is a Kronecker delta function. It is one of a family of ternary sequenceswith perfect periodic autocorrelation discovered by Valery Ipatov [Ipatov] and extended byHøholdt and Justesen [Høholdt et al]. There are many sequences in this family, e.g.lengths 381, 553, 651, 757, 781, 871, 993. Each piconet uses a different length sequence.This makes the cross correlation between preambles of different sequences very low. Thepreamble also serves as a marker for the packet.

A receiver searches for a packet or a beacon by correlating with a copy of the particularPACn associated with that piconet. We propose using lengths 381,553,651,757,781 and871.

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PHY proposal

PAC properties

• Because of the perfect autocorrelation property, the channel impulse response can be obtained in the receiver by correlating with the sequence and averaging the results.

• Because the sequence consists of mostly 1, -1 with a small number of zeros, correlation can be economically implemented. (a length 553 PAC has 24 0’s)

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PHY proposal

Preamble properties

• Very good detect rate and false alarm probability. Pfa and Pmd < 10-4 for CM1 to CM4 test suite at 10 metres. Detected in 2s using matched filter architecture.

• Matched filter is equivalent of 553 parallel correlators

• Different length sequences means other piconets won’t trigger detection i.e. Pfa still < 10-3 for a different piconets PACn, even at 0.3m separation.

• Preamble length varies from ~5s to ~15s depending on the bit rate. Lower bit rates use longer preambles (Longer distances need more training time)

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PHY proposal

PHY Header

• The PHY header is sent at an uncoded 45Mbps rate, but with no convolutional coding. It is repeated 3 times.

• The PHY header contents are the same as 802.15.3 i.e. Two octets with the Data rate, number of payload bits and scrambler seed.

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PHY proposal

Scrambler/Descrambler

• It is proposed that the PHY uses the same scrambler and descrambler as used by IEEE 802.15.3

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PHY proposal

Typical Tx/Rx configuration

Channel Matched filter (Rake Receiver)

A/D 7.7GHz, 1 bit

Correlator Bank

Viterbi Decoder

Output data at 55 - 960 Mbps

Antenna

Convolutional encoder

8-240M symbols/sec

Code GeneratorChip to Pulse Generator

Input data at 55- 960 Mbps

256 - 3800 Mchips/sec

Descramble

Scramble

Fine/Band Reject Filter

LN

ASwitch / Hybrid

Band Pass Filter*

Band Pass Filter

Band Reject Filter

* Can be avoided with good LNA dynamic range

Single Chip Possible

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PHY proposal

Band reject Filter **

Possible RF front end configuration

• Total Noise Figure = 6.6dB

Tx/Rx switch / hybrid

BP Filter*

From Tx

Fine Filter**

Filter

NF= 2.0dB

NF= 0.8dB

NF= 3.5dB

NF= 0.3dB(input referred)

To Rx

* Can be avoided with good LNA dynamic range

LN

A

** Depending on Local National or User requirements

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PHY proposal

Matched Filter configuration

Cn Di Cn+N Di-N

4 1

4x 4x

4x

44

+

+

Cn+1 Di-1 Cn+N+1 Di-N-1

4 1

4x 4x

4x

4 4

4 bit adder

5 bit adder

…..

…..

…..

…..

…..

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PHY proposal

Matched Filter configuration

• Structure repeated 16 times e.g. a 500 tap filter with 4 bit coefficients would have 500 x 16 x 4 AND gates in first stage

• Calculates 16 outputs in parallel, each runs at (480/mps) MHz.– e.g. 120MHz for 220Mbps

• Multiplier is 4 AND gates.

• First adder stage is 4 OR gates. Very little performance loss. (0dB for CM1-3, 0.23dB for CM4).

• Coefficients are pre-processed to remove smallest if two clash.

• mps is max pulses/sample. = 1440/(channel bit rate (Mbps))

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PHY proposal

Matched filter

• 560 tap filter takes 135k gates or 0.82 sq mm in 0.13 standard cell CMOS

• Worst case power consumption = 120mW ( at 490Mbps ), proportional to data rate. Much lower for CM1 because of fewer taps.

• Matched filter re-used for correlation with training sequence during training phase

• All simulations were carried out with this filter/correlator structure

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Link Budget

Parameter Value Value Value Value

Throughput (Rb) 110 Mb/s 220 Mb/s 490 Mb/s 880 Mb/s

Tx power ( TP ) -5.9dBm -5.9dBm -5.9dBm -5.9dBm

Tx antenna gain ( TG ) 0 dBi 0 dBi 0 dBi 0 dBi

Centre frequency 5.48GHz 5.48GHz 5.48GHz 5.48GHz

Loss at 1 metre 47.1dB 47.1dB 47.1dB 47.1dB

Loss at d metres 20 dB (10m) 12 dB (4m) 12 dB (4m) 6 dB (2m)

Rx antenna gain 0 dBi 0 dBi 0 dBi 0 dBi

Rx power -73dBm -65dBm -65dBm -62.5dBm

Noise power/bit -93.6dBm -90.6dBm -87.2dBm -84.6dBm

Rx Noise Figure 6.6dB 6.6dB 6.6dB 6.6dB

Noise power/bit -86.6dBm -83.6dBm -80.6dBm -77.6dBm

Min Eb/N01 (S) 2.3dB 2.3dB 3.0dB 2.3dB

Imp. Loss2 (I) 4.0dB 4.0dB 4.0dB 4.0dB

Link Margin 7.7dB 12.7dB 8.6dB 9.1dB

Rx Sens. Level -80.7dBm -77.7dBm -73.6dBm -71.7dBm

Notes:1 - Minimum Eb/No for <8% PER for AWGN channel.2 - 2 dB for 1 bit ADC and 2dB for timing jitter. Channel capture of <100% adds 0.5dB(CM1) to 2.5dB(CM4)

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PHY proposal

Distance achieved for mean packet error rate of best 90% = 8%

Mean PER = 8% AWGN CM1 CM2 CM3 CM4

110Mbps 23.4 m 16.7 m 15.0 m 15.0 m 15.0 m

220Mbps 16.6 m 11.5 m 10.3 m 10.7 m 10.6 m

490Mbps 10.1 m 6.5 m 5.6 m 5.5 m 5.0 m

AWGN figures are for a fully impaired simulation except using a single ideal channel instead of CM1-4.

0

510

1520

25

AWGN CM1 CM2 CM3 CM4

110M

220M

490M

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Distance achieved for at worst packet error rate of best 90% = 8%

Worst PER = 8% AWGN* CM1 CM2 CM3 CM4

110Mbps 23.4 m 14.2 m 12.5 m 14.1 m 13.5 m

220Mbps 16.6 m 9.7 m 8.8 m 9.6 m 9.6 m

490Mbps 10.1 m 5.4 m 4.8 m 4.9 m 3.9

AWGN figures are for a fully impaired simulation except using a single ideal channel instead of CM1-4.

0

510

1520

25

AWGN CM1 CM2 CM3 CM4

110M

220M

490M

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200 Mbps Performance comparison

Worst PER = 8% AWGN CM1 CM2 CM3 CM4

PCVA - 220Mbps 16.6 m 9.7 m 8.8 m 9.6 m 9.6 m

STM – 250Mbps 11.1 m 7.7 m 6.9 m - -

OFDM – 200Mbps 14.1 m 6.9 m 6.3 m 6.8 m 5.0 m

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PHY proposal

110 Mbps average PER

10 11 12 13 14 15 16 17 18 19 20-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0Average PER vs Distance at 110Mbps

distance (m)

log 10

PE

R

channel model 1channel model 2channel model 3channel model 4

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8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5


distance (m)

log 10

PE

R

channel model 1channel model 2channel model 3channel model 4

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PHY proposal


2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5


distance (m)

log 10

PE

R channel model 1channel model 2channel model 3channel model 4

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PHY proposal

Multiple Piconet Interferers

• Tests were done according to the Multiple Piconet interference procedure outlined in the latest revision of the selection criteria (03031r11).

• The distance to the receiver under test was set at 0.707 of the 90% link success probability distance.

• Tests results were obtained for 1,2 and 3 interfering piconets

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Single adjacent piconet

dint/dref

1 interfererCM1 CM2 CM3 CM4

110Mbps 0.40 0.39 0.38 0.38

220Mbps 0.55 0.54 0.56 0.55

490Mbps 1.33 1.34 1.33 1.31

Relative distance to a single adjacent piconet interferer

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Two adjacent piconets

dint/dref

2 interferersCM1 CM2 CM3 CM4

110Mbps 0.53 0.52 0.56 0.53

220Mbps 0.85 0.86 0.88 0.86

490Mbps 1.90 1.92 2.06 2.02

Relative distance to two adjacent piconet interferers

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Three adjacent piconets

dint/dref

3 interferersCM1 CM2 CM3 CM4

110Mbps 0.65 0.65 0.65 0.64

220Mbps 0.96 0.96 0.96 0.99

490Mbps 2.25 2.30 2.55 2.45

Relative distance to three adjacent piconet interferers

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Co-channel interference

• Different piconets use exactly the same data mode codes as each other.

• Separation is achieved because – a) a different piconet will have a different impulse response and thus will not

correlate with the matched filter which has been trained for the piconet of interest.

– b) Codes won’t be synchronised

• Co-channel data mode interference is exactly the same as adjacent channel interference.

• Training to the preamble will be affected more markedly by co-channel interference. Difficult to simulate.

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Co existence

• Out of band signals, e.g. 802.11b, (< 3.1GHz and >10.6GHz) are always filtered out.

• Any desired in band energy can be filtered out, with minimal effect on performance because the whole band is used to transfer data.

• Only adverse effect is the transmit power reduction (e.g. Dropping 400MHz for 802.11a loses <0.5dB)

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Co-existence with 802.11a

• Filtering out the UNII band spectrum from the transmitter has very little effect on the performance

• The receive matched filter will cope with it automatically

• Only 1.25dB of power is lost by filtering out the Tx signal from 5GHz to6GHz

• This is the equivalent of a 15% loss in distance

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Interference and susceptibility

• As for co existence, out of band signal, e.g. 802.11b, are always filtered out.

• Again, any desired in band energy can be filtered out, with minimal effect on performance because the whole band is used to transfer data.

• Only adverse effect is the receive power reduction (e.g. Dropping 400MHz for 802.11a loses <0.5dB), its just a part of the channel.

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Narrowband interference

• Immunity to narrowband interference

• With no filtering– Processing a gain of e.g. ~24dBs at 110Mbps. Any interfering tone

is reduced by this amount.

• With digital notch filter– Tones can be detected at the A/D output.

– A simple notch filter either at the input or output of the matched filter can then remove this completely with no loss in performance (if notch is narrow enough)

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PHY proposal

PayloadBitrate

Preamble lengthT_PA_INIT,T_PA_CONT

Throughput :1 frame /Preamble

Throughput :4 frames /Preamble

110Mbps 15.5μs 88Mbps 104Mbps



PHY-SAP Data Throughput

• At higher bit rates, a 1024 byte frame is very short.

• The channel will be stationery for more than one frame so it is possible to send multiple frames for each preamble.

• T_MIFS=1μs, T_SIFS=5μs, T_PHYHDR=1.1μs,T_HCS=0.29μs, T_MACHDR=1.45μs

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Scalable solution

• 55 - 980 Mbps. Gate count depends on maximum bit rate and power consumption of baseband PHY is proportional to bit rate.

• 880Mbps has 90% link success on CM1-CM3 at over 3.4m, 2.8m and 2.6m with exactly same RF and sample rate as the other rates

• Receiver here uses 3.85 - 7.7GHz. – 2.5dB extra performance gain if full band used.

– 1.0dB lower performance if 3.2-4.8 GHz band used with ~50% power reduction

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Complexity - Area/Gate count, Power consumption

• These figure are for a standard cell library implementation in 0.13µm CMOS

Gateequiv

Area(mm2)

Power mWRx Data @120Mbps

Power mWRx Data @480Mbps

Power mWPreambleRx

RF section (Up to and incl.A/D - D/A)

- 2.8 80 80 80

RAM - 24kbits 22k 0.13 10 10 10

Matched filter 135k 0.41 25 100 -

Channel estimation(length 871 PAC)

24kextra

0.15 - - 45

Viterbi Decoder, RSdecoders

60k 0.36 5 20 -

Rest of Baseband Section 65k 0.40 25 60 25

Total 306k 4.25mm2 145mW 270mW 160mW

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How can it be so good?

• Where does this large Performance/Cost/Power advantage come from

• Compare with two proposals other proposals - TFI OFDM and Multiband

• These two were chosen because of their prominence and fairly comprehensive results available

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Performance- How much better?

• All similar under AWGN, i.e. 20 odd metres at 110Mbps.

• 200/220/240 Mbps– ~50% farther than either TFI-OFDM or Multiband over CM1

– 92% farther than TI-OFDM and 230% farther than Multiband over CM4

• 110/120 Mbps– 22/25% farther over CM1– 22% farther than TFI-OFDM and 75% farther than Multiband over CM4

• 480 Mbps - 86% farther than TFI-OFDM over CM1, no CM4 or Multiband figures available.

• NB: The distances quoted for TFI-OFDM and Multiband do not take into account the 4.7dB loss required for FCC compliance i.e. a further 1.72 gain factor.

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Performance - Why is it better?

• Gap is small with no multipath at low rates, larger as the multipath increases and speed increases.

• Multiband approach only gathers a small amount of multipath energy. 16ns at 120Mbps and 8ns at 240Mbps. CM4 channels have significant energy spread over 100ns

• ParthusCeva PHY - has equivalent of a 230 finger rake.

• Ternary codes were chosen for their multipath immunity

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Power

• 110/120Mbps Rx @ 0.13– This approach up to 145mW

– Multiband approach 170-200mW

– TFI - OFDM 205mW

• Why so good?– Simple analog Rx section

• Single bit ADC• No AGC• No mixer

– No FFT in the receiver. Matched filter with 1 bit inputs. Low complexity decoders

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Cost

• Comparison at 0.13µ

– This approach 4.25mm2

– Multiband approach 7.3mm2

– TFI - OFDM approach 6.9mm2

• Why the difference ?

– Same reasons as power, low complexity digital and analog requirements

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Summary of advantages

• Ternary spreading codes– Better auto-correlation properties

• Perfect PAC training sequence• Simple RF section

– 1 bit A/D converter– No AGC required– No Rx mixers required

• Long rake possible - near multipath immunity– 4 bit coefficients– 1 bit data– no multipliers

• Cost and Power very similar to Bluetooth

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The ParthusCeva PHY

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PHY proposal

Backup Slides

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CRITERIA REF.IMPORTANCE

LEVELPROPOSER RESPONSE

Unit ManufacturingComplexity (UMC)

3.1 B+ Single chip possible, smallsilicon area

Signal RobustnessInterference AndSusceptibility

3.2.2 A+ Interferers filtered out

Coexistence 3.2.3 A+ Tx filtering.

Technical Feasibility

Manufacturability 3.3.1 A+ Single chip possible

Time To Market 3.3.2 A+ Technology proven

Regulatory Impact 3.3.3 A+ Within FCC limits

Scalability (i.e. Payload BitRate/Data Throughput,Channelization – physical or coded,Complexity, Range, Frequencies ofOperation, Bandwidth of Operation,Power Consumption)

3.4 A + 30 - 960Mbps possible. Very lowcomplexity solution possible

Location Awareness 3.5 C + Within 40cm with no extra effort

Self evaluation : General Criteria

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Self evaluation : PHY protocol


LEVELPROPOSER RESPONSE

Size And Form Factor 5.1 B+ Single chip solution possible

PHY-SAP Payload Bit Rate & Data ThroughputPayload Bit Rate 5.2.1 A + 480Mbps evaluated, 960Mbps

possiblePHY-SAP Data Throughput 5.2.2 A + Very close to Payload rate

480Mbps gives 415MbpsSimultaneously OperatingPiconets

5.3 A + Different length trainingsequences

Signal Acquisition 5.4 A + Pfa and Pmd <10-4 after 2s

Link Budget 5.5 A + Overhead available

Sensitivity 5.6 A + As for link budget

Multi-Path Immunity 5.7 A + Matched filter means multipathhas very little effect

Power Management Modes 5.8 B + Most power used while receivingpackets

Power Consumption 5.9 A + Simple RF section, simple codingreduces power consumption

Antenna Practicality 5.10 B + Easier because Highest frequencyno more than twice the lowest.

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Self evaluation : MAC enhancements


LEVEL PROPOSER RESPONSE

MAC EnhancementsAnd Modifications

4.1. C + Externally similar to802.15.3 PHY

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Ternary orthogonal sequences

• From any base set of 32 orthogonal binary signals, can generate 32C16 sets of 32 orthogonal ternary sequences.

• Generate by adding and subtracting any 16 pairs.

• Generally, if the base set has good correlation properties, so will a generated set.

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Good base binary set

• Base set is a set of binary Golay-Hadamard sequences• Take a binary Golay complementary pair.

• s116=[1 1 1 1 1 1 -1 -1 -1 1 1 -1 -1 1 -1 1];

• s216=[1 1 1 1 -1 -1 1 1 -1 1 1 -1 1 -1 1 -1];

• if A=circulant(s116) and B=circulant(s216)

• and G32= A B

BT -AT • then G32 is a Hadamard matrix. [Seberry]

• This type has particularly good correlation properties[Seberry]

• Detector can use the Fast Hadamard Transform

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Creating Orthogonal Ternary Sequences

• Take a matrix of binary orthogonal sequences

• Add any two rows to get a ternary sequence

• Sum of any other two rows is orthogonal to this

• Continue till all the rows are used

• Repeat but subtracting instead of adding

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Orthogonal Ternary Example

• E.g. 1 1 1 1• 1 -1 1 -1• 1 -1 -1 1• 1 1 -1 -1

• pairing 1 with 3 and 2 with 4 gives this orthogonal matrix

• 2 0 0 2• 2 0 0 -2• 0 2 2 0• 0 -2 2 0

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Finding good Ternary Golay Hadarmard codes

• Large superset of orthogonal sequence sets to test

• Define aperiodic autocorrelation merit factor (aamf) as the ratio of the peak power of the autocorrelation function to the mean power of the offpeak values divided by the length of the code.

• Random walk used to find set with best aamf

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Code comparison

Code Length mean aamf min aamf







• Length 32 code chosen for aamf and best matching with bit rates.

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Rate 4/6 Convolutional coder

Map every 6 bits to one of 64

biorthogonal codewords

+

+

2 bits in

+

3 bits out

1 of 64

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PHY proposal

Ternary Orthogonal Length 32 Code Set

• + 0 - 0 - 0 - 0 + 0 + 0 - 0 + 0 + 0 - 0 - 0 - 0 - 0 - 0 + 0 - 0• - 0 + - 0 - 0 - + + + 0 0 0 0 0 0 0 0 0 - 0 + 0 0 - 0 - - + - -• 0 0 0 0 - - 0 0 0 0 0 0 + + 0 0 - + 0 0 - - - + - + 0 0 - - + -• 0 0 0 + + - - 0 0 - 0 0 + 0 + - 0 0 0 0 + - - 0 0 - 0 - - 0 - +• - + + 0 0 0 0 - - 0 - + 0 + 0 0 + - - + 0 0 0 - - 0 - 0 0 - 0 0• 0 0 0 + - 0 0 0 0 0 0 - + 0 0 0 - 0 0 - + + + - - 0 0 - + - - -• 0 + - 0 0 0 + + - - 0 0 - 0 0 + 0 - + 0 0 0 0 + - - 0 0 - 0 - -• 0 0 0 0 + + - 0 + - - - 0 0 0 + 0 0 0 0 - 0 0 0 + - - - 0 - + -• 0 0 0 0 0 0 + - 0 0 0 0 0 0 - + - - - - 0 0 - + + + - - 0 0 - +• 0 0 0 + 0 0 0 0 - + + 0 - - + - 0 - - - 0 0 0 0 + 0 0 0 - - + -• 0 0 0 0 + + 0 0 0 0 0 0 - - 0 0 - + 0 0 - - + - - + 0 0 - - - +• + - 0 0 0 + 0 0 0 0 - + + 0 - - + - 0 - - - 0 0 0 0 + 0 0 0 - -• 0 0 0 0 0 0 + + 0 0 0 0 0 0 - - - + - + 0 0 - - + - - + 0 0 - -• - - + - 0 0 0 + 0 0 0 0 - + + 0 - - + - 0 - - - 0 0 0 0 + 0 0 0• 0 0 0 0 - + 0 0 0 0 0 0 + - 0 0 - - 0 0 - + - - - - 0 0 - + + +• + 0 - - + - 0 0 0 + 0 0 0 0 - + 0 0 - - + - 0 - - - 0 0 0 0 + 0• 0 + 0 - 0 + 0 + 0 + 0 + 0 + 0 - 0 + 0 - 0 + 0 + 0 - 0 - 0 - 0 +• 0 + 0 0 - 0 + 0 0 0 0 + + - + + + + + - 0 - 0 - + 0 - 0 0 0 0 0• + - + + 0 0 - + - + + + 0 0 - + 0 0 + + 0 0 0 0 0 0 - - 0 0 0 0• + + - 0 0 0 0 - + 0 + + 0 + 0 0 - - + + 0 0 0 - + 0 + 0 0 - 0 0• 0 0 0 - + + - 0 0 + 0 0 + 0 + + 0 0 0 0 + + - 0 0 + 0 + - 0 - -• + - + 0 0 + + - - - + 0 0 + + + 0 + - 0 0 0 0 0 0 - + 0 0 0 0 0• + 0 0 + + - 0 0 0 0 - + 0 + + 0 - 0 0 - - + + 0 0 0 - + 0 + 0 0• + + + - 0 0 0 + 0 0 0 0 + - + 0 - - - + 0 - + + 0 0 0 0 + 0 0 0• + + + + - + 0 0 + + - - - + 0 0 0 0 0 0 + - 0 0 0 0 0 0 - + 0 0• + + + 0 + - + + 0 0 0 - 0 0 0 0 + 0 0 0 - + - - 0 + + - 0 0 0 0• - + + + 0 0 - + + - + + 0 0 - + 0 0 - - 0 0 0 0 0 0 + + 0 0 0 0• 0 0 + + + 0 + - + + 0 0 0 - 0 0 0 0 + 0 0 0 - + - - 0 + + - 0 0• - + - + + + 0 0 - + + - + + 0 0 0 0 0 0 - - 0 0 0 0 0 0 + + 0 0• 0 0 0 0 + + + 0 + - + + 0 0 0 - 0 0 0 0 + 0 0 0 - + - - 0 + + -• - - - + 0 0 + + + + - + 0 0 + + 0 0 - + 0 0 0 0 0 0 + - 0 0 0 0• 0 - 0 0 0 0 + + + 0 + - + + 0 0 + - 0 0 0 0 + 0 0 0 - + - - 0 +

July-2003


doc.: IEEE 802.15 - 03/123r6

PHY proposal

Matlab Code to generate PAC sequences• % function phi=ipatov(nu,multiplier,mul2);• %• % Generate a length nu, ternary perfect periodic autocorrelation sequence• % using Singer Cyclic Difference Sets e.g. (553, 24, 1)• %• function phi=ipatov(nu,multiplier,mul2);

• if nargin==1 multiplier=1; mul2=-1; end % multipliers 1,-1 are most commonly good

• if nargin==2 mul2=-1; end % multipliers 1,-1 are most commonly good

• phi=0;

• if gcd(nu,multiplier)>1; % must not be a common divisor of nu• return;• end

• if gcd(nu,mul2)>1; % must not be a common divisor of nu• return;• end

• switch nu

• case 7 %• nu=7;k=3;lamda=1;• D=[1 2 4 ];

• case 13• nu=13;k=4;lamda=1;• D=1+[ 0 1 3 9 ];

• case 21• nu=21;k=5;lamda=1;• D=[3,6,7,12,14];

• case 31• nu=31;k=6;lamda=1;• D=[1 5 11 24 25 27 ];

• case 57• nu=57;k=8;lamda=1;• D=[0 1 6 15 22 26 45 55 ];

• case 63 % multipliers 1,5 gives perfect ternary• nu=63;k=31;lamda=15;• D=1+[0 1 2 3 4 6 7 8 9 12 13 14 ...• 16 18 19 24 26 27 28 32 33 35 36 38 ...• 41 45 48 49 52 54 56 ];

• case 73• nu=73;k=9;lamda=1;• D=[1, 2, 4, 8, 16, 32, 37, 55, 64]; % P73

• case 91• nu=91;k=10;lamda=1;• D= [1 2 4 10 28 50 57 62 78 82]; %

• case 133• nu=133;k=12;lamda=1;• D=[ 1 10 11 13 27 31 68 75 83 110 115 121];

• case 183• nu=183;k=14;lamda=1;

• D=[ 1 13 20 21 23 44 61 72 77 86 90 116 ...• 122 169 ];

• case 273• nu=272;k=17;lamda=1;• D=[0 1 22 33 83 122 135 141 145 159 175 200 ...• 226 229 231 238 246];

• case 307• nu=307;k=18;lamda=1;

• D=[ 0 1 3 30 37 50 55 76 98 117 129 133 ...• 157 189 199 222 293 299 ];

• case 341• nu=341;k=85;lamda=21; % 1,5 gives a perfect ternary sequence

• D= [ 0 1 2 3 5 7 8 11 15 17 20 23 ...• 24 31 32 35 40 41 42 47 49 58 63 65 ...• 68 71 76 80 81 83 85 95 99 117 120 127 ...• 128 130 131 132 137 142 143 153 161 163 167 170 ...• 171 174 180 182 186 190 191 199 204 208 210 230 ...• 234 235 236 241 255 257 260 261 263 265 272 274 ...• 275 285 287 288 300 306 307 314 320 323 327 330 ...• 335 ];

• case 364• nu=364;k=121;lamda=40; % 1,5 gives a perfect ternary sequence• D=[0 1 2 3 4 6 8 9 11 16 17 19 ...• 22 24 32 35 36 41 42 46 48 50 56 73 ...• 76 78 79 80 88 89 92 99 105 106 107 109 ...• 110 111 114 122 123 127 128 132 133 134 142 151 ...• 152 153 156 162 163 169 171 174 177 181 183 187 ...• 189 190 198 201 203 207 210 212 214 218 221 222 ...• 223 224 229 234 237 241 246 248 249 250 251 256 ...• 260 262 264 274 281 283 285 286 289 292 299 300 ...• 302 305 306 307 309 311 314 315 317 318 322 326 ...• 327 330 331 336 343 348 350 351 353 354 357 358 ...• 360 ];

• case 381• nu=381;k=20;lamda=1;• D=1+[0 1 19 28 96 118 151 153 176 202 240 254 ...• 290 296 300 307 337 361 366 369 ];

• case 511 % 1,3 gives a perfect ternary sequence• nu=511;k=255;lamda=127;

• D=[ 1 2 4 7 8 13 14 16 17 21 23 26 ...• 28 31 32 33 34 35 37 39 42 46 49 51 ...• 52 53 55 56 59 61 62 64 66 68 70 74 ...• 75 77 78 79 81 83 84 85 89 91 92 95 ...• 98 99 101 102 103 104 105 106 109 110 112 113 ...• 115 118 121 122 123 124 128 131 132 133 136 137 ...• 140 141 143 147 148 149 150 153 154 155 156 158 ...• 161 162 163 165 166 168 169 170 178 182 183 184 ...• 187 190 196 198 199 201 202 203 204 206 207 208 ...• 210 211 212 215 217 218 219 220 221 223 224 225 ...• 226 227 230 235 236 237 242 244 246 248 249 251 ...• 256 259 262 264 266 267 271 272 273 274 275 280 ...• 281 282 283 285 286 293 294 295 296 297 298 300 ...• 301 303 305 306 307 308 310 312 313 316 317 321 ...• 322 324 326 327 329 330 332 333 336 337 338 340 ...• 347 349 355 356 357 359 361 363 364 365 366 367 ...• 368 369 373 374 380 381 385 389 391 392 393 396 ...• 397 398 402 403 404 406 407 408 409 412 414 416 ...• 419 420 422 424 429 430 433 434 435 436 437 438 ...• 439 440 442 446 448 450 451 452 454 457 459 460 ...• 465 470 472 473 474 475 481 484 485 488 492 493 ...• 496 498 502];

• case 553• nu=553;k=24;lamda=1;• D=[ 1 23 52 90 108 120 152 163 173 178 186 223 ...• 232 272 359 407 411 431 438 512 513 515 529 548];

• case 651• nu=651;k=26;lamda=1;• D=[ 0 1 3 43 64 73 92 161 169 175 214 251 ...• 268 309 396 421 453 471 500 505 515 527 531 538 ...• 551 586 ];

• case 757• nu=757;k=28;lamda=1;• D=[ 1 2 63 103 112 114 119 158 171 199 242 264 ...• 333 345 363 371 405 408 437 556 591 644 661 680 ...• 711 734 738 744];

• case 781• nu=781;k=156;lamda=31; % 1,2 gives a perfect ternary sequence

• D=1+[0 1 2 3 5 6 7 10 11 15 25 26 ...• 27 30 31 35 38 41 48 50 51 55 57 64 ...• 67 75 83 86 94 96 112 113 117 125 126 127 ...• 130 131 135 137 143 150 151 153 155 169 175 190 ...• 197 198 202 204 205 209 222 229 237 239 240 244 ...• 250 251 255 258 264 266 272 275 285 301 303 313 ...• 320 322 329 335 341 343 352 364 373 375 381 387 ...• 402 404 414 415 417 419 430 439 448 451 457 458 ...• 462 469 470 474 480 482 491 492 494 496 508 509 ...• 513 516 523 533 539 546 549 552 560 561 565 567 ...• 579 582 585 588 594 597 616 625 626 627 630 631 ...• 633 635 642 644 650 651 655 675 678 685 693 701 ...• 715 723 724 728 734 737 748 750 751 755 765 775];

• case 871• nu=871;k=30;lamda=1;• D=[ 1 24 29 69 151 167 216 234 259 263 295 321 ...• 329 414 488 543 582 599 645 659 683 689 696 716 ...• 731 819 820 822 831 841 ];

• case 993• nu=993;k=32;lamda=1;• D=1+[ 0 1 3 13 101 127 154 169 204 210 226 235 ...• 259 289 297 317 356 434 474 478 495 538 570 584 ...• 589 607 618 654 749 756 801 920 ];

• case 1057• nu=1057;k=33;lamda=1;

• D=[ 1 2 32 36 41 150 156 172 192 370 397 426 ...• 451 509 522 559 614 628 652 675 701 716 718 775 ...• 778 786 796 885 913 961 1007 1014 1026];

• case 1407• nu=1407;k=38;lamda=1;• D=1+[ 0 1 37 63 205 274 289 302 314 316 321 362 ...• 414 420 436 465 469 486 550 621 644 652 655 711 ...• 731 844 854 924 981 1098 1122 1152 1187 1230 1248 1316 ...• 1325 1369 ];

• case 1723• nu=1723;k=42;lamda=1;

• D=[ 0 1 3 107 125 216 224 239 245 291 295 422 ...• 435 444 471 499 770 807 840 909 935 952 982 992 ...• 1050 1103 1138 1183 1222 1264 1296 1312 1372 1459 1545 1564 ...• 1569 1589 1623 1630 1661 1712];

• otherwise• return

• end % end switch

• D=sort(mod(D*multiplier,nu)); % transform to new difference set.• while any(D==0)• D=mod(D+1,nu);• end

• Dhat=sort(mod(D*mul2,nu)); % transform to another new difference set• while any(Dhat==0)• Dhat=mod(Dhat+1,nu);• end• ;• Xd=zeros(1,nu);• Xdhat=Xd;• Xd(D)=1;• Xdhat(Dhat)=1;• phi=xcorr([Xd Xd],[Xdhat])-lamda;• phi=round(phi(2*nu+1:2*nu+nu)); % phi is the ternary sequence• if nargout==0• plot(xcorr(phi,[phi phi phi]))• end

July-2003


doc.: IEEE 802.15 - 03/123r6

PHY proposal

References

• [Proakis1] John G. Proakis, Digital Communications 2nd edition. McGraw Hill. pp 224-225.

• [Proakis2] John G. Proakis, Digital Communications 2nd edition. McGraw Hill. pp 466-470.

• [Seberry et al] J. Seberry, B.J. Wysocki and T.A. Wysocki, Golay Sequences for DS CDMA Applications, University of Wollongong

• [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.

Doc.: IEEE 802.15 - 03/123r6 PHY proposal July-2003 Michael Mc Laughlin, ParthusCevaSlide 1 of 47...

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