Ultra Wide Band Signal Simulations Using FDTD Method · Kai Siwiak: 15 September 2001 3 UWB...

Kai Siwiak: 15 September 20011

Ultra Wide Band Signal Simulations Using FDTD Method

Kazimierz “Kai” SiwiakTime Domain Corporation

Tadeusz M. BabijFlorida International University

27-28 September 2001

The Boston Marriott Hotel Newton, Massachusetts


Introduction

4 UWB signals generally more complex than sinusoids [1, 2]4 Sinusoids remains sinusoidal throughout link4 UWB waveforms and spectra change from transmitter,

to radiation, to the receiver

4 FDTD method used to study waveforms across link4 Compared with measurements4 Receiver efficiency predicted

4 UWB Wireless link characterized


UWB Wireless LinkWaveform pulses st(t) sent at rate R pulses per second

Pt = transmitter powernf = receiver noise factorHy(t) = copolarized transverse magnetic fieldst(t), s(t) = transmitter and received voltage waveformsp(t) = template waveformh(t) = receiver filter impulse response

Template p

DataTransmitter

Eb /N0 in

Eb/N 0 out

n f

SNR out

Filter h(t)

P t

s t(t)

Template p

DataTransmitter

Eb /N0 in

Eb/N 0 out

n f

SNR out

Filter h(t)

P t

s t(t)

s

Integrate

Template p

DataTransmitter

Eb /N0 in

Eb/N 0 out

n f

SNR out

Filter h(t)

P t

s t(t)

Template p(t)

DataTransmitter

Eb /N0 in

Eb/N 0 out

n f

Hy(t) SNR out

Filter h(t)

P t

s t(t)

s(t) sc(t)

FDTD

RX analysis


FDTD Simulations

4Radiation between UWB dipole pair [3] simulated [4] with Finite Difference Time Domain (FDTD) method [5]

Transmitting dipole

Receiving dipole


Waveform “A”:Stimulus and Response

0 0.35 0.7 1.05 1.4 1.75 2.1 2.45 2.8 3.15 3.51

0.80.60.40.2

0

0.20.40.60.81

time

A(t)

Calculated: Measured:

00.35 0.7 1.05 1.4 1.75 2.1 2.45 2.8 3.15 3.5

0.02

0.0150.01

0.0050

0.005

0.010.0150.02

0.025

0.03

time

s(t)

TX

RX


XFDTD Simulations of UWB Waveforms and their Spectra

In time:

In frequency:

“A” at TX antenna: H-field: RX antenna load:

0 2 4 6 8 10 12 14-100

-75

-50

-25

0

Frequency(GHz)

dB

0 2 4 6 8 10 12 14Frequency(GHz)

-100

-75

-50

-25

0dB

Frequency(GHz)0 2 4 6 8 10 12 14

-100

-75

-50

-25

0dB


Waveform “B”:Stimulus and Response

Calculated: Measured:

0 0.35 0.7 1.05 1.4 1.75 2.1 2.45 2.8 3.15 3.5

0

0.04

0.08

0.12

0.20

0.24

0.28

0.32

0.16

B(t)

time

0 0.35 0.7 1.05 1.4 1.75 2.1 2.45 2.8 3.15 3.50.015

0.012

0.009

0.006

0.003

0

0.003

0.006

0.009

0.012

0.015s(t)

time

TX

RX


Transmitted Power Spectral Density

4 “Sine wave equivalent” power density at distance d is

PDENSITY,CW = Pt Gt ( fc )/(4πd 2)

4 Power spectral density is

PD( f ) = |F {Hy (t)}|2 η0

4 Which integrates to PDENSITY and includes transmit antenna gain Gt ( f )


Receive Antenna Aperture

4 Received co-polarized signal is:

4 And |F {Hy(t)}|2η0 = PD( f ) power spectral density of Hy(t) integrates to PDENSITY;

η0= µ0c = 376.73 ohms

4 Aperture factor for a unity gain antenna is:Ae(f ) = (c/f )2/4π

PRX = |F {Hy(t)}|2 η0 Ae(f ) df⌠⌡

∞

−∞


UWB Propagation

4UWB transmissions analyzed, for convenience, by free space propagation at a “center frequency” fc

4Propagation assumed to be “sine wave equivalent” at the center frequency

4For a given EIRP=PtGt , the CW or sine-wave equivalent is:

PRX, CW = PDENSITY,CW Ae(fc)


The “Sine Wave Equivalent” Propagation

4 Actual received signal relative to the sine-wave equivalent signal is

4 Value of AF is waveform dependent, but generally close to 1; hence “sine wave equivalent” propagation usually justified

η0 |F {Hy(t)}|2 Ae(f ) df⌠⌡

∞

−∞

Ae(fc ) Pt Gt ( fc )/(4πd 2)AF =


Example:Gaussian Derivative H-Field4 If: magnetic field at distance d in time

domain can be represented by

4Then: magnetic field at distance d in frequency domain is

Hy(t) = t2

τ21−

exp1−

2

t2

τ2

4

τ 3 π

exp1−

2(2π f τ)2

τ 83

6 π

94

Hy( f ) = (f τ)2


Example: AF for Gaussian Derivative H-field

-200 -100 0 100 200

-15

-10

0

5

10

-20

Time, picoseconds

Sig

nal

leve

l, µA

/m

0 2 4 6 8 10

-160

-140

-120

-100

-80

Frequency, GHz

Sig

nal

leve

l, d

B µ

A/m

= 1.15η0 |F {Hy(t)}|2 Ae(f ) df

⌠⌡

∞

−∞

Ae(fc ) Pt Gt ( fc )/(4πd 2)AF =


UWB Path Link

4 Receive antenna gain is constant over bandwidth of pulse

4 Path attenuation between unity gain antennas:

4 AF = antenna “sine-wave equivalent” aperture factor

4 Lw = in-building attenuation, dB/m4 dw = distance to first wall

( ) dw)(dw4log20 >−−

= ddL

dfc

c AFP wL Φπ


Bit Energy to Noise Density Ratio

4At receiver antenna load: [independent of wave shape!]

4At correlator output:

4Efficiency:

4Optimum for:

Eb

s t( )2⌠⌡

dt

=N0nf

inN0

p(t) dt

2

Eb =

c:out⌠⌡

N0N0 nf

s(τ)h(τ-t) dτ⌠⌡

⌠⌡

p(τ)h(τ-t) dτ⌠⌡

2

dt

ec = (Eb/N0)c:out / (Eb/N0)in

p(τ)h(t-τ) dτ = Cs(t)⌠⌡


Signal “A” and Pulse Template

4Red: Signal at correlator input: sc(t)4Blue: Optimum width template: p(t)

Rectangular pulse is optimally centered at signal amplitude peak,[better templates possible]

t fc

0 0.5 1 1.5 2 2.5-1

0.5

0

0.5

1

p(t)p(t)

s(t)s(t)


Sampler Cell Efficiency “A” Waveform

4Efficiency ec vs. template width tfc with rectangular template pulse p(t)

0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

t fc

ec

Efficiency: -2.8 dB


Signal “B” and Pulse Template

4Red: Signal at correlator input: sc(t)4Blue: Optimum width template: p(t)

Template pulse is optimally centered at signal amplitude peak

0 0.5 1 1.5 2 2.5 3 3.5 41

0.5

0

0.5

1

s(t)

p(t)

0 0.5 1 1.5 2 2.5 3 3.5 41

0.5

0

0.5

1

s(t)

p(t)

t fc


Sampler Cell Efficiency “B” Waveform

t fc

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

ec

Efficiency: -4.5 dB

4Efficiency ec vs. template width tfc with rectangular template pulse p(t)


Signal Waveform “B” and Bipolar Sampler

4Red: Signal4Blue: Optimum width bipolar template

s t( ) sin 2 π fc t t0−( ) exp t t0−−π fc

QR

Φ t( )=

0 0.5 1 1.5 2 2.5 3 3.5 41

0.5

0

0.5

1

s(t)

p1(t)

0 0.5 1 1.5 2 2.5 3 3.5 41

0.5

0

0.5

1

s(t)

p1(t)

t fc

Efficiency: -1.6 dB


Receiver System SNR

4Received power [6] is:

PRX= PEIRP (Af c/4πdfc)2 10-Lw(d-dw)Φ(d >dw)

4 Input signal to noise at impulse rate R:

SNRin= (Eb /N0)in R/BRF = PRX / nf kTBRF

4Receiver implementation losses:Lsys= -10 log(ec /nf)


Receiver System SNR

4 Integrating I impulses per bit a R bps:

R I = Bdata

4System signal to noise at output:

SNRout= (Eb /N0)out R/Bdata= (ec /nf )PRX /kTBdata

4Finally, processing gain is:

PG = SNRout / SNRin = ec BRF / Bdata


Receiver Sensitivity

4Receiver sensitivity S is:

S = 10log(kTB)+SNR+NF+ ec

4Assuming a needed SNR=7 dB, noise figure NF=3 dB and loss ec = 2 dB

S = -104 dBm/MHz

4System gain is –S dB/mWEIRP


Summary

4 Impulse transmissions studied using FDTD method

4 Link performance impacted by UWB wave forms

4 UWB Receiver performance characterized4 Watch future IEEE VTS News for:

UWB Radio: an Emerging PAN and Positioning Technology


References1. K. Siwiak, “Ultra-Wide Band Radio: Introducing a New Technology,”

Invited Plenary Paper, Conference Proceedings of the IEEE VTC-2001, Rhodes, Greece, May 6-9, May 2001.

2. Robert A. Scholtz, Moe Z. Win, “Impulse Radio”, Invited Paper, IEEE PIMRC'97, 1997, pp. 245-267.

3. Hans Gregory Schantz, Larry Fullerton, “The Diamond Dipole: A Gaussian Impulse Antenna”, IEEE APS Conf., Boston MA., July 2001.

4. Zhong Yang, “Finite Difference Time Domain Analysis of Antennas Used in Personal Communications,” Florida International University, M.S.E.E. Thesis Defense, 22 June 2001.

5. K. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, CRC Press Inc., 1993.

6. K. Siwiak, A. Petroff, “A Path Link Model for UWB Pulse Transmissions,” Conference Proceedings of the IEEE VTC-2001, Rhodes, Greece, May 6-9, May 2001.


Kai Siwiak, Vice President – Strategic [email protected]+1(954)-755-6828 +1(256)-990-9062Time Domain Corporation7057 Old Madison PikeHuntsville, AL 35806

Tadeusz M. Babij, Professor Department of Electrical and Computer Engineering

[email protected]+1(305)-348-2683Florida International UniversityUniversity Park Campus, Miami, Florida 33199

Ultra Wide Band Signal Simulations Using FDTD Method · Kai Siwiak: 15 September 2001 3 UWB...

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