a new uwb dual pulse transmission and detection...

A New UWB Dual Pulse Transmission andDetection Technique

Xiaodai Dong

University of Victoria, Victoria, BC, Canada

Alfred Lee

Lei Xiao

University of Notre Dame, Notre Dame, IN, USA

[email protected]

A New UWB Dual Pulse Transmission and Detection Technique – p.1/31

Overview

• Introduction• The UWB Channel Model• The Transmitted Reference (TR) System• The Novel Dual Pulse (DP) System• The Improved DP (iDP) System• Conclusion


Introduction

• Ultra-wideband (UWB) has been proposed as aphysical layer candidate for low cost, short rangewireless personal area networks.

• Estimating the UWB multipath channel andcollecting multipath energy pose challenges toUWB receiver design.

• Transmitted reference (TR) systems employautocorrelation receiver and waive the need toestimate channel path gains and path delays[Hoctor and Tomlinson, UWBST’2002].


Introduction (Cont’d)

• The TR system is simple and robust. Its variantshave been proposed in various literature [Chaoand Scholtz, Franz and Mitra, Zhang and Goeckel,Nekoogar and Dowla].

• Differential detection [Ho et.al.] and pilot waveformassisted modulation [Yang and Giannakis]

• We propose a novel dual pulse (DP) system thatdoubles the data rate of the TR system.


Features of the DP System

• The data rate of the DP system doubles the TR system, while achieving similarperformance.

• The delay unit in the receiver is only half the dual-pulse width, Tw/2 and muchshorter than the frame delay Tf in the TR system. Implementing accurate shortdelays is easier than long delays.

• The DP system is less sensitive to time variation of the channel. Within a fixedchannel coherence time, there are more received reference sub-pulses to beaveraged over to reduce the noise effect.

• The DP system retains the merits of the TR system, such as robust performance,simple implementation and easy timing acquisition.

• Inter-pulse interference in the DP system is not severe.

• The improved dual pulse (iDP) system eliminates the inter-pulse interference inthe DP system.


The UWB Channel Model

• The UWB channel characterization is a subjectarea requiring extensive experiments and research

• The IEEE 802.15.3a task group gathered differentUWB characterisation attempts and proposed theIEEE UWB channel model

• The IEEE UWB channel model can berepresented by

h(t) = X

L∑l=0

K∑k=0

αk,lδ(t − Tl − τk,l) (1)


Sample of the IEEE channel model

0 50 100 150 200 250 300−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Time (ns)

Cha

nnel

Am

plitu

de


The Transmitted Reference (TR)System

• A coherent rake receiver must estimate thechannel tap gains and tap delays.

• The shape of a UWB pulse may be altered afterpassing through the channel.

• The TR system uses a doublet

Td=T

f

Td=T

f

2Tf

2Tf

Binary PAM b=1

Binary PAM b=−1


TR System (con’t)

The autocorrelation receiver uses the reference pulseto demodulate the data pulse.

Output of the autocorrelator is represented as

D =

Ns−1∑j=0

∫ (2j+1)Tf +Ttr

(2j+1)Tf

ri(t)ri(t − Tf )dt (2)


The Novel Dual Pulse (DP) System

• The DP system transmits a reference sub-pulsefollowed by a data sub-pulse as one pulse unit.

• The binary PAM modulated DP pulse isrepresented as

gdp(t) = p(t) + b · p(t −Tw

2), 0 ≤ t ≤ Tw (3)

• The DP system requires only one time frame totransmit a data pulse, effectively doubles thetranmission rate when compared with the TRsystem.


Illustration of the DP pulse

OOK

Tf

Tf

b="1" "1"

b="1"

"−1"

"−1"

Binary PAM


DP System Receiver

• The receiver design for DP system can beillustrated as follows

• Where T (Dl) is the test function defined by thedifferent combining schemes• Generalized Selection Combining (GSC)

• Absolute Threshold GSC (AT-GSC)

• Normalised Threshold GSC (NT-GSC)


General Selection Combining (GSC)

• This method selects L largest |Dl|’s to form D

• The test function T (Dl),

T (Dl) =

8

<

:

Dl, if |Dl| ≥ |D(L)|0, if |Dl| < |D(L)|

(4)

• The conditional probability of error given by

P (e|α, τ) = P (D < 0|b = +1, α, τ) =1

2πj

Z c+j∞

c−j∞

ΦGSC(s)

sds (5)


GSC (con’t)

• Moment generating function (MGF) of GSC

ΦGSC(s) =

Lt−1X

i=0

Z ∞

−∞

fi(Di)esDi

X

all Ii

Y

l∈Ii

Ψl(s, Di)Y

l′ /∈Ii

l′ 6=i

[Fl′(|Di|)−Fl′(−|Di|)]dDi

(6)

where

Ψl(s, x) =1

2esµl+

σ2

l2

s2

"

erfc

|x| + (µl + σ2l s)√

2σl

!

+ erfc

|x| − (µl + σ2l s)√

2σl

!#

(7)

Ii ⊂ {0, 1, · · · , Lt − 1} − {i}


Effect of L on GSC

0 2 4 6 8 10 12 14 16 18

10−4

10−3

10−2

10−1

100

Average Eb/N

0 (dB)

Bit

Err

or P

roba

bilit

y

GSC (CM3) (Lt = 110, L = 10, N

p = 50)

GSC (CM3) (Lt = 110, L = 20, N

p = 50)

GSC (CM3) (Lt = 110, L = 30, N

p = 50)

GSC (CM3) (Lt = 110, L = 40, N

p = 50)

GSC (CM3) (Lt = 110, L = 60, N

p = 50)

GSC (CM3) (Lt = 110, L = 110, N

p = 50)


Absolute Threshold GSC (AT-GSC)

• This method combines Dl that has absolute valuegreater than Dth to form the decision variable

yl = T (Dl) =

8

<

:

Dl, if |Dl| ≥ Dth

0, if |Dl| < Dth

(8)

• The MGF of AT-GSC is presented by

ΦAT−GSC(s) =

Lt−1Y

l=0

Φyl(s) =

Lt−1Y

l=0

[Fl(Dth) − Fl(−Dth) + Ψl(s, Dth)]. (9)


Effect of Dth on AT-GSC

0 2 4 6 8 10 12 14 16 18

10−4

10−3

10−2

10−1

100

Average Eb/N

0 (dB)

Bit

Err

or P

roba

bilit

y

DP, AT−GSC (CM3) (Dth

= 5, Np = 50)


= 3, Np = 50)


= 1.5, Np = 50)


= 1, Np = 50)


= 0.6, Np = 50)


= 0.1, Np = 50)


Normalised Threshold GSC (NT-GSC)

• Like the AT-GSC, NT-GSC selects Dl that has absolutevalue higher than threshold Dth = ηthDmax whereDmax = max|Dl|

T (Dl) =

8

<

:

Dl, if |Dl| ≥ ηthDmax

0, if |Dl| < ηthDmax

. (10)


NT-GSC (con’t)

• The MGF of NT-GSC is represented by

ΦNT−GSC(s) =

Lt−1X

i=0

Z ∞

−∞

fi(Di)esDi

×Lt−1Y

l=0l6=i

h

Ψ̃l(s, ηthDi, Di) + Fl(ηth|Di|) − Fl(−ηth|Di|)i

dDi

(11)

• whereΨ̃l(s, x, y) = Ψl(s, x) − Ψl(s, y) (12)


Effect of ηth on NT-GSC

0 2 4 6 8 10 12 14 16 18

10−4

10−3

10−2

10−1

100

Average Eb/N

0 (dB)

Bit

Err

or P

roba

bilit

y

DP, NT−GSC (CM3) (ηth

= 0.9, Np = 50)


= 0.7, Np = 50)


= 0.5, Np = 50)


= 0.4, Np = 50)


= 0.2, Np = 50)


= 0.1, Np = 50)


Simple autocorrelation receiver forDP system

• Receiver of the DP system can also berepresented by a simple autocorrelator

• Decision variable given by

D =

Ns−1X

j=0

Z jTf + Tw2

+Tdp−int

jTf + Tw2

r(t)r(t − Tw

2)dt (13)

• The autocorrelation receiver design for the DPsystem is similar to the TR system receiver design,thus providing similar receiver complexity


Comparison between TR system andDP system, CM1

0 2 4 6 8 10 12 14 16 18 20 22

10−4

10−3

10−2

10−1

100

Average Eb/N

0 (dB)

Bit

Err

or P

roba

bilit

y

TR (Ttr=28ns, N

p=1)

DP, GSC (Lt=40, L=20, N

p=1)

DP, AT−GSC (Dth

=1.5, Np=1)

DP, NT−GSC (ηth

=0.1, Np=1)

DP, Int (Tdp−int

=28ns, Np=1)

TR (Ttr=28ns, N

p=50)

DP, GSC (Lt=40, L=20, N

p=50)

DP, AT−GSC (Dth

=0.1, Np=50)

DP, NT−GSC (ηth

=0.1, Np=50)

DP, Int (Tdp−int

=28ns, Np=50)


Comparison between TR system andDP system, CM4

0 2 4 6 8 10 12 14 16 18 20 22

10−4

10−3

10−2

10−1

100

Average Eb/N

0 (dB)

Bit

Err

or P

roba

bilit

y

TR (Ttr=126ns, N

p=1)

DP, GSC (Lt=180, L=100, N

p=1)

DP, AT−GSC (Dth

=1.5, Np=1)

DP, NT−GSC (ηth

=0.1, Np=1)

DP, Int (Tdp−int

=126ns, Np=1)

TR (Ttr=126ns, N

p=50)

DP, GSC (Lt=180, L=100, N

p=50)

DP, AT−GSC (Dth

=0.1, Np=50)

DP, NT−GSC (ηth

=0.1, Np=50)

DP, Int (Tdp−int

=126ns, Np=50)


The Improved DP (iDP)System

• The performance of DP system is worse than theTR system due to the interference between thereference pulse and the data pulse

• The iDP system is designed to eliminate theperformance degradation of the DP system

• The iDP system requires two pulse transmissionfor each data bit

• The iDP pulses are given by

g1(t) = p(t) + b1 · p(t − Tw

2), 0 ≤ t ≤ Tw

g2(t) = −p(t) + b1 · p(t − Tw

2), 0 ≤ t ≤ Tw. (14)


Illustration of the iDP signal

Binary PAM Ns=2 b=1

Binary PAM Ns=2 b=−1

Tf

Tf

g1(t) g

2(t)

g2(t) g

1(t)


iDP system receiver design

• The block diagram for iDP receiver design

• whereDl =

Z l Tw2

+Tw

l Tw2

+ Tw2

rref (t − Tw

2)rdat(t)dt. (15)

rref (t) = r1(t − Tf ) − r2(t)

rdat(t) = r1(t − Tf ) + r2(t)


Performance comparison betweenTR, DP and iDP systems, CM1

0 2 4 6 8 10 12 14 16 18

10−4

10−3

10−2

10−1

100

Average Eb/N

0 (dB)

Bit

Err

or P

roba

bilit

y

TR (Ttr=28ns, N

p=1)

DP, GSC (Lt=40, L=20, N

p=1)

DP, AT−GSC (Dth

=1.5, Np=1)

DP, NT−GSC (ηth

=0.1, Np=1)

DP, Int (Tdp−int

=28ns, Np=1)

TR (Ttr=28ns, N

p=50)

DP, GSC (Lt=40, L=20, N

p=50)

DP, AT−GSC (Dth

=0.1, Np=50)

DP, NT−GSC (ηth

=0.1, Np=50)

DP, Int (Tdp−int

=28ns, Np=50)

Ns=2

TR & improved DP

Ns=1

CM1


Performance comparison betweenTR, DP and iDP systems, CM4

0 2 4 6 8 10 12 14 16 18

10−4

10−3

10−2

10−1

100

Average Eb/N

0 (dB)

Bit

Err

or P

roba

bilit

y

TR (Ttr=126ns, N

p=1)

DP, GSC (Lt=180, L=100, N

p=1)

DP, AT−GSC (Dth

=1.5, Np=1)

DP, NT−GSC (ηth

=0.1, Np=1)

DP, Int (Tdp−int

=126ns, Np=1)

TR (Ttr=126ns, N

p=50)

DP, GSC (Lt=180, L=100, N

p=50)

DP, AT−GSC (Dth

=0.1, Np=50)

DP, NT−GSC (ηth

=0.1, Np=50)

DP, Int (Tdp−int

=126ns, Np=50)

CM4N

s=1

Ns=2

TR & improved DP


Effect of IPI, CM1

0 2 4 6 8 10 12 14 16 18

10−4

10−3

10−2

10−1

100

Average Eb/N

0 (dB)

Bit

Err

or P

roba

bilit

y

TR (Ttr=28ns, N

p=1)

DP, GSC (Lt=40, L=20, N

p=1)

DP, AT−GSC (Dth

=1.5, Np=1)

DP, NT−GSC (ηth

=0.1, Np=1)

DP, Int (Tdp−int

=28ns, Np=1)

TR (Ttr=28ns, N

p=50)

DP, GSC (Lt=40, L=20, N

p=50)

DP, AT−GSC (Dth

=0.1, Np=50)

DP, NT−GSC (ηth

=0.1, Np=50)

DP, Int (Tdp−int

=28ns, Np=50)

Grey Marker −> DP, Ns=2

Black Marker −> iDP, Ns=2


Effect of IPI, CM2

0 2 4 6 8 10 12 14 16 18

10−4

10−3

10−2

10−1

100

Average Eb/N

0 (dB)

Bit

Err

or P

roba

bilit

y

TR (Ttr=42ns, N

p=1)

DP, GSC (Lt=60, L=30, N

p=1)

DP, AT−GSC (Dth

=1.5, Np=1)

DP, NT−GSC (ηth

=0.1, Np=1)

DP, Int (Tdp−int

=42ns, Np=1)

TR (Ttr=42ns, N

p=50)

DP, GSC (Lt=60, L=30, N

p=50)

DP, AT−GSC (Dth

=0.1, Np=50)

DP, NT−GSC (ηth

=0.1, Np=50)

DP, Int (Tdp−int

=42ns, Np=50)

Grey Marker −> DP, Ns=2

Black Marker −> iDP, Ns=2


Thank you!


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