Data Whitening in Base-band to Reduce PSD of UWB Signals

May 2003

Shaomin Mo, Panasonic -- PINTLSlide 2

IEEE 802.15-03/121r2

Submission

Data Whitening in Base-band to Reduce PSD of UWB Signals

Shaomin Mo

Panasonic Information and Networking Technologies Laboratories

May 2003


IEEE 802.15-03/121r2

Submission

Overview

• Power Spectra Density (PSD) issue in UWB• Analysis of PSD of UWB signals• Mechanisms to reduce PSD

– Phase reversion to reduce PSD– Architecture of using Linear Feedback Shift

Register– Phase reversion for SYNC

• Conclusion

May 2003


IEEE 802.15-03/121r2

Submission

PSD is an Important Issue in UWB Communication Systems

• FCC limited authorization of UWB technology, Feb 14, 2002

• Use in restrict spectrum at restrict power• Do not interfere with other wireless systems• Other agencies still have some reservations

about whether UWB will interfere with other wireless systems such as cellular, air navigation and landing systems

May 2003


IEEE 802.15-03/121r2

Submission

Emission Levels for GSM & TDMA in the Cellular Receiver Bands

Technology Frequency Range

(mobile RX) (MHz)

Emission Level (dBm),

Bandwidth (kHz)

Average Level

(dBm/MHz)

Part 15 Limit (dBm/MHz)

TDMA 869 – 894

1930 – 1990

-80 dBm, 30kHz

-80 dBm, 30kHz

-64.8

-64.8

-40.0

-53.3 indoor

-63.3 hand-held

GSM 869 – 894

1930 – 1990

-79 dBm, 100kHz

-71 dBm, 100kHz

-69.0

-61.0

-40.0

-53.3 indoor

-63.3 hand-held

Source: “Ultra-Wideband Radio – The New Part 15”, Microwave Journal, February 2003

May 2003


IEEE 802.15-03/121r2

Submission

Containing PSD is an Important Part in UWB System Design

• Repeat pulse trains may generate strong line spectra and high PSD

• Traditional scramblers are not sufficient to contain PSD

• PSD suppression leads to– Prevention of interference to existing systems– Potential increase in rate, Tx power (distance)

May 2003


IEEE 802.15-03/121r2

Submission

• Signal model

• Probability function of an

Model of Repeat Pulse Train

n

cn nTtwats )()(

1,1

1,}Pr{

n

nn ap

apa

Tc TcTc

t t+1 t+2 t+3

. . .

May 2003


IEEE 802.15-03/121r2

Submission

• Ps is determined by w(t) and Tc• Ps is not affected by Pr{an}

• Total PSD is determined by w(t) and Tc• Total PSD is not affected by Pr{an}

PSD of Repeat Pulse Train

pTk

kp

s cdffWdttwT

P222

)()(1

May 2003


IEEE 802.15-03/121r2

Submission

PSD of repeat pulse trains consists of • Sc(f) – continuous component• Sd(f) – discrete component


lD

d

c

Tc

lf

Tc

lW

Tc

pfS

pfWTc

fS

)(|)(|)12(

)(

)12(1|)(|1

)(

22

2

22

W(f)

Tcp

May 2003


IEEE 802.15-03/121r2

Submission

• W(f) – pulse shape & Tx power• Tc – clock period or pulse rate• p – probability in distribution function

– Does not affect total PSD– Changes distribution of PSD between continuous

and discrete components

Parameters that Determine PSD

May 2003


IEEE 802.15-03/121r2

Submission

Simplified Form of PSD

lD Tc

lf

Tc

lW

TcfB

fWTc

fA

)(|)(|1

)(

|)(|1

)(

2

2

2

2

)12(1)(

)12()(

ppD

ppC

)()(),(

)()(),(

pCfBpfS

pDfApfSd

c

May 2003


IEEE 802.15-03/121r2

Submission

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

p

C(p)D(p)

Relationship between Continuous and Discrete Components

)()(),(

)()(),(

pCfBpfS

pDfApfSd

c

May 2003


IEEE 802.15-03/121r2

Submission

• Because total PSD is constant

A(f) = B(f)

Max(Sc(f)) = Max(Sd(f))


May 2003


IEEE 802.15-03/121r2

Submission

• Total continuous PSD equals total discrete PSD

• The continuous distributes on all frequencies• The discrete distributes on those discrete

frequencies separated by 1/Tc.

• Continuous PSD is lower than that of discrete PSD on the same frequency components


May 2003


IEEE 802.15-03/121r2

Submission

PSD with Different p Has Same Envelop but Different Level

0 100 200 300 400-50

-40

-30

-20

-10

0(a): PSD of one pulse

0 100 200 300 400-40

-30

-20

-10

0

10(b): PSD of pulses for p=0.25

0 100 200 300 400-40

-30

-20

-10

0

10(c): PSD of pulses for p=0.5

0 100 200 300 400-30

-20

-10

0

10

20(d): PSD of pulses for p=1

PSD of single pulse P = 0.25

P = 0.5 P = 1.0Line spectra

peak = 15

peak = 9

peak = 3

May 2003


IEEE 802.15-03/121r2

Submission

• Contain PSD

• Reduce or eliminate discrete component of PSD reduce PSD across whole spectrum

• Make

Objective of Design

1,5.0

1,5.0}Pr{

n

nn a

aa

May 2003


IEEE 802.15-03/121r2

Submission

TDMA Systems

• Traditional communication systems require randomness inside a frame for timing recovery, equalization, etc.

frame N frame N+2frame N+1 . . .

Tc Tc

May 2003


IEEE 802.15-03/121r2

Submission

New Requirements to UWB Communication Systems

• Traditional: randomness in X direction• UWB: randomness in both X & Y directions

frame N

frame N+3

frame N+2

frame N+1

offset m

X

Y

blo

ck

s i

n T

DM

A

b its inside a block

Tc

Tc

Tc

May 2003


IEEE 802.15-03/121r2

Submission

PSD Analysis: if data is not evenly distributed in Y direction, line spectra appear

• Phase

0 10 20 30 40 50 60-1

-0.5

0

0.5

1(a): Waveform of single pulses

0 100 200 300 400-1

-0.5

0

0.5

1(b): Waveform of data

0 500 1000 1500-60

-50

-40

-30

-20

-10(c): PSD of single pulse

0 500 1000 1500-30

-20

-10

0

10

20(d): PSD of data

Waveform of single pulse Waveform of data

PS of single pulse PSD of data

Original stream: line spectra

& peak = 17

May 2003


IEEE 802.15-03/121r2

Submission

Propose 1: Phase Reversion to Reduce PSD

• A random sequence {bn} is generated with

• cn = an ^ bn. It can be proved that

• {cn} is used as the new data for transmission.

1,5.0

1,5.0}Pr{

n

nn b

bb

1,5.0

1,5.0}Pr{

n

nn c

cc

May 2003


IEEE 802.15-03/121r2

Submission

Using proposed scheme, line spectra is eliminated and PSD is reduced

0 10 20 30 40 50 60-1

-0.5

0

0.5

1(a): Waveform of single pulses

0 100 200 300 400-1

-0.5

0

0.5

1(b): Waveform of data

0 500 1000 1500-60

-50

-40

-30

-20

-10(c): PSD of single pulse

0 500 1000 1500-40

-30

-20

-10

0

10(d): PSD of data

Waveform of single pulse Waveform of data

PS of single pulse PSD of data

Proposed 1: PSD of cn, Line spectra gone

peak reduced to 8

May 2003


IEEE 802.15-03/121r2

Submission

• Signal model

Model of Repeat Pulse Train of Multi-band

Tc TcTc

t t+1 t+2 t+3 t+4

. . .

Tc Tc

Mmww

nTtwats

mn

ncnn

1:

,)()(

May 2003


IEEE 802.15-03/121r2

Submission

• {wm} is a set of waveforms on sub-bands

• Probability function of an, same on all sub-bands

Model of Repeat Pulse Train (cont.)

1,1

1,}Pr{

n

nn ap

apa

M

mm

mm

p

Mmpw

1

1

,...,1,}Pr{

May 2003


IEEE 802.15-03/121r2

Submission

PSD of repeat pulse trains consists of • Sc(f) – continuous component• Sd(f) – discrete component


Mm

Tc

lf

Tc

lWp

Tc

pfS

fWpTc

pfS

Dl

mmd

mmc

1

),()()12(

)(

)()12(1

)(

2

2

2

22

W(f)

Tcp

pn

May 2003


IEEE 802.15-03/121r2

Submission

• W(f) – pulse shape & Tx power• Tc – clock period or pulse rate

• pm – probability in distribution function of sub-bands

• p – probability in distribution function of waveforms– Does not affect total PSD– Changes distribution of PSD between continuous

and discrete components

Parameters that Determine PSD

May 2003


IEEE 802.15-03/121r2

Submission

• Contain PSD

• Reduce or eliminate discrete component of PSD

• Make

Objective of Design

1,5.0

1,5.0}Pr{

M

1 }Pr{

n

nn

m

a

aa

w

• Contain PSD

• Reduce or eliminate discrete component of PSD

• Make

May 2003


IEEE 802.15-03/121r2

Submission

To Make {wm} Evenly Distributed – Rotationally

w1

w4

w3

w2

w8

w7

w6

w5

Wm is waveform on sub-band m, 1 m M

May 2003


IEEE 802.15-03/121r2

Submission

To Make {wm} Evenly Distributed – Randomly

• Another way to make {wm} evenly distributed is to randomly and evenly choose wm so that

M

1 }Pr{ mw

May 2003


IEEE 802.15-03/121r2

Submission

To Make {an} Evenly Distributed

• A random sequence {bn} is generated with

• cn = an ^ bn. It can be proved that

• {cn} is used as the new data for transmission.

1,5.0

1,5.0}Pr{

n

nn b

bb

1,5.0

1,5.0}Pr{

n

nn c

cc

May 2003


IEEE 802.15-03/121r2

Submission

0 100 200 300 400 500-1

-0.5

0

0.5

1(a): Waveform of multi-band

0 2000 4000 6000 8000-40

-30

-20

-10(b): PS of multi-band waveforms

0 2000 4000 6000 8000-10

0

10

20

30(c): PSD of p=1

0 2000 4000 6000 8000-20

-10

0

10(d): PSD of whitened data

Waveforms in multi-band Original data, p = 1

PS of waveforms Result data

peak = 4

Line spectra peak = 21

PSD of BPSK Data with p=1 & rotationally

May 2003


IEEE 802.15-03/121r2

Submission

0 100 200 300 400 500-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-20

-10

0

10

20(c): PSD of p=0.25

0 2000 4000 6000 8000-20

-10

0


PSD of BPSK Data with p=0.25 & rotationally

Waveforms in multi-band Original data, p = 0.25


peak = 4


May 2003


IEEE 802.15-03/121r2

Submission

0 100 200 300 400 500-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-30

-20

-10

0

10(c): PSD of p=0.4

0 2000 4000 6000 8000-20

-10

0


PSD of BPSK Data with p=0.4 & rotationally



peak = 4


May 2003


IEEE 802.15-03/121r2

Submission

0 100 200 300 400 500-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-10

0

10

20

30(c): PSD of p=1

0 2000 4000 6000 8000-20

-10

0




peak = 5


PSD of BPSK Data with p=1 & randomly

May 2003


IEEE 802.15-03/121r2

Submission

0 100 200 300 400 500-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-20

-10

0

10

20(c): PSD of p=0.25

0 2000 4000 6000 8000-20

-10

0


PSD of BPSK Data with p=0.25 & randomly



peak = 5


May 2003


IEEE 802.15-03/121r2

Submission

0 100 200 300 400 500-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-30

-20

-10

0

10(c): PSD of p=0.4

0 2000 4000 6000 8000-20

-10

0


PSD of BPSK Data with p=0.4 & randomly



peak = 5


May 2003


IEEE 802.15-03/121r2

Submission

0 200 400 600 800 1000-1

-0.5

0

0.5

1(a): Waveform of multi-band QPSK

0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-20

-10

0

10

20(c): PSD of p=1

0 2000 4000 6000 8000-20

-10

0


PSD of QPSK Data with p=1 & rotationally



peak = 4


May 2003


IEEE 802.15-03/121r2

Submission

0 200 400 600 800 1000-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-20

-10

0

10

20(c): PSD of p=0.25

0 2000 4000 6000 8000-20

-10

0


PSD of QPSK Data with p=0.25 & rotationally



peak = 4


May 2003


IEEE 802.15-03/121r2

Submission

0 200 400 600 800 1000-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-30

-20

-10

0

10(c): PSD of p=0.4

0 2000 4000 6000 8000-20

-10

0


PSD of QPSK Data with p=0.4 & rotationally




peak = 4

May 2003


IEEE 802.15-03/121r2

Submission

0 200 400 600 800 1000-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-20

-10

0

10

20(c): PSD of p=1

0 2000 4000 6000 8000-20

-10

0


PSD of QPSK Data with p=1 & randomly



peak = 5


May 2003


IEEE 802.15-03/121r2

Submission

0 200 400 600 800 1000-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-20

-10

0

10

20(c): PSD of p=0.25

0 2000 4000 6000 8000-20

-10

0


PSD of QPSK Data with p=0.25 & randomly



peak = 4


May 2003


IEEE 802.15-03/121r2

Submission

0 200 400 600 800 1000-1

-0.5

0

0.5


0 2000 4000 6000 8000-40

-30

-20


0 2000 4000 6000 8000-30

-20

-10

0

10(c): PSD of p=0.4

0 2000 4000 6000 8000-20

-10

0


PSD of QPSK Data with p=0.4 & randomly




peak = 5

May 2003


IEEE 802.15-03/121r2

Submission

Major Challenge in Implementing Phase Reversion

• Simple way to generate random sequence

• Easy way to synchronize random number generators in both transmitters and receivers

May 2003


IEEE 802.15-03/121r2

Submission

Propose 2: Architecture of LFSR

• LFSR stands for Linear Feedback Shift Registers

• Easy implementation• Very suitable for semiconductor

implementation

May 2003


IEEE 802.15-03/121r2

Submission

LFSR is loaded with a RN per frame & updated per pulse

NX

OR

1 2 43 25 26 2827.

random num bers (RN)

May 2003


IEEE 802.15-03/121r2

Submission

Synchronization of LFSR

• Initial system channel access– Random vectors are generated in advance &

stored in an array– Transmitters & receivers keep same array– Index to a vector in the array is put in data to

transmit

• Initial traffic channel access– Sequence number can be used

May 2003


IEEE 802.15-03/121r2

Submission

15-bit LFSR vs. Idea Low Bound

• LFSR is too short• Strong line spectra exist

0 5 10

x 104

-10

0

10

20

30(1-a): PSD of proposed: 10

0 5 10

x 104

-20

-10

0

10

20(1-b): PSD of random: 10

0 5 10

x 104

-20

-10

0

10


0 5 10

x 104

-20

-10

0

10


0 5 10

x 104

-20

-10

0

10


0 5 10

x 104

-30

-20

-10

0

10(3-b): PSD of random:200

Phase controlled by RNs as

reference of low bound

Proposed LFSR implementation

May 2003


IEEE 802.15-03/121r2

Submission

0 5 10

x 104

-20

-10

0

10


0 5 10

x 104

-20

-10

0

10


0 5 10

x 104

-20

-10

0

10


0 5 10

x 104

-20

-10

0

10


0 5 10

x 104

-30

-20

-10

0


0 5 10

x 104

-30

-20

-10

0

10(3-b): PSD of random:200

28-bit LFSR vs. Idea Low Bound• LFSR is long enough• Line spectra is suppressed• Very close to reference

Phase controlled by RNs as

reference of low bound

Proposed LFSR implementation

May 2003


IEEE 802.15-03/121r2

Submission

Propose 3: Phase Reversion on SYNC

Three mechanisms can be used:• Phase reversion on the whole SYNC• SYNC is divided into symbols & phase

reversion on symbols• Phase reversion & scrambling on symbols

May 2003


IEEE 802.15-03/121r2

Submission

Phase Reversion on SYNC/symbols can eliminate line spectra but not ripples in PSD

0 100 200 300 400-1

-0.5

0

0.5

1(a): Waveform of one symbol

0 500 1000 1500-40

-30

-20

-10

0

10(b): PSD of one symbol

0 500 1000 1500-10

0

10

20

30

40(c): PSD of symbol: p=1

0 500 1000 1500-30

-20

-10

0

10

20(d): PSD of symbol: p=0.5

One cycle of symbols

PSD with phase reversionPSD without phase reversion

Waveform of symbols

Propose 3: line spectra goneOriginal: strong

line spectra

May 2003


IEEE 802.15-03/121r2

Submission

Scramble Symbols

Fram e N: 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , ...

Fram e N+7: 7, 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , ...

Fram e N+6: 6, 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , ...

Fram e N+5: 5, 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , ...

Fram e N+4: 4, 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , ...

Fram e N+3: 3, 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , ...

Fram e N+2: 2, 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , ...

Fram e N+1: 1, 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , ...

X

Y

Fram e N+9: 1, 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , ...

Fram e N+8: 0, 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 0 , ...

May 2003


IEEE 802.15-03/121r2

Submission

Phase Reversion & Scrambling on SYNC/symbols can smooth ripples & eliminate line: snap shot at 10,

50 200 runs

0 1000 2000 3000-30

-20

-10

0

10

20(1-a): PSD using 8 symbols: 1

0 1000 2000 3000-30

-20

-10

0

10

20(1-b): PSD of random pulses: 1

0 1000 2000 3000-40

-30

-20

-10

0


0 1000 2000 3000-40

-30

-20

-10

0


0 1000 2000 3000-40

-30

-20

-10

0


0 1000 2000 3000-40

-30

-20

-10

0


Proposed 3: PSD of symbol-based phase reversion & scrambling Very close to reference

Phase controlled by RNs as reference of low bound

May 2003


IEEE 802.15-03/121r2

Submission

Conclusion

• Phase reversion can effectively reduce PSD• Phase reversion can be applied to PAM,

PPM, Time-Hopping to reduce PSD• LFSR is an easy way to generate RNs with

good performance• Scrambling can enhance performance by

smoothing ripples in PSD with extra processing & can be extended beyond SYNC

May 2003


IEEE 802.15-03/121r2

Submission

Thank you

Documents

Data Whitening in Base-band to Reduce PSD of UWB Signals