Parameter Estimation of Ultra Wideband (UWB) · PDF file162 Parameter Estimation of Ultra Wideband (UWB) GESTS-Oct.2005 p rameters can be applied to characterize the reflected pulse?

GESTS Int’l Trans. Computer Science and Engr., Vol.18, No.1 161

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Parameter Estimation of Ultra Wideband (UWB) Electromagnetic Pulses Reflected from a Lossy Half Space

Qingsheng Zeng1, 2 and Gilles Y. Delisle3

1 University of Ottawa, Ottawa, Ontario, Canada K1N 6N5 [email protected]

2 Communications Research Centre Canada, Ottawa, Ontario, Canada K2H 8S2 [email protected]

3 International Institute Telecommunications, Montreal, Quebec, Canada, H5A 1K6 [email protected]

Abstract. In this article, the definitions of waveform parameters are extended, so that they are applicable not only to a double exponential ultra-wide-band (UWB) incident pulse but also to the reflected pulse for both horizontal and vertical po-larizations. With numerical inversion of Laplace transform, the waveform pa-rameters of UWB electromagnetic pulses reflected from lossy interfaces are esti-mated for both horizontal and vertical polarizations. Based on the estimation, the relationships between the waveform parameters of reflected pulses and incident angles as well as material parameters of interfaces are discussed.

1 Introduction

Studies on pulse distortion are important in various areas including channel modeling, and analysis and design of modern communication systems, such as ultra-wide-band (UWB) radio systems. In a multipath channel, normally reflections from interfaces between different media have most significant impacts on pulse distortion. The tran-sient analysis of electromagnetic pulses reflected from lossy interfaces can be con-ducted in frequency domain first. Then the results in time domain may be obtained by carrying out a numerical Fourier transform of the frequency domain response. How-ever, it is preferable to solve the problems directly in the time domain under certain circumstances, in which time-varying media or nonlinear systems are involved, or the lossy interface causes the reflected pulse to persist very long time, thus creating diffi-culties with fast Fourier transform (FFT) aliasing.

The finite difference time domain (FDTD) technique can be applied to this prob-lem, while computation costs are still higher even combining surface impedance boundary conditions with the FDTD algorithm [1]. The approximate form of a fre-quency-domain reflection coefficient permits one analytical expression of the impulse response of a lossy half space [2], but makes the solutions inaccurate or even invalid in some cases, e.g., for small incident angles. One method based on numerical inver-

162 Parameter Estimation of Ultra Wideband (UWB)

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sion of Laplace transform is applied to the transient analysis of the reflected pulse from a lossy interface [3]. This method gets rid of the restrictions in [2] on the rela-tive dielectric constant and the incident angle, leads to good accuracy in both late and early time, and has a simple algorithm, short calculation time, small required memory size, readily controlled error and wide application range. In [3], the shapes of re-flected pulses from lossy interfaces with different material parameters for both verti-cal and horizontal incidence have been reproduced quite well. However, the relation-ships between some important waveform parameters of reflected pulses and incident angles as well as material parameters of interfaces have not yet been addressed.

In general, UWB pulses have steep edges and short durations. One type of com-monly used UWB electromagnetic pulses is double exponential pulses. These pulse shapes can be described with three waveform parameters, the peak value pE , the rise

time and the pulse length rt plt [4]. The interesting and meaningful questions arise: If

a double exponential pulse impinges on a lossy interface, the above waveform pa-rameters can be applied to characterize the reflected pulse? If they can, how will these parameters vary with incident angles and material parameters of interfaces? In this article, the definitions of waveform parameters are extended, so that they are applica-ble not only to a double exponential incident pulse but also to the reflected pulse for both horizontal and vertical incidence. With numerical inversion of Laplace transform, the waveform parameters of UWB electromagnetic pulses reflected from lossy inter-faces are estimated for both horizontal and vertical incidence. Based on the estimation, the relationships between the waveform parameters of reflected pulses and incident angles as well as material parameters of interfaces are discussed.

2 Waveform Parameters

In this article, the definitions of the waveform parameters are given as follows. The peak value pE is defined as the largest magnitude; The rise time is defined as the

time period for the pulse to change from 10% to 90% of rt

pE before reaching the peak

point; The pulse length plt is defined as the duration from the half of pE at the rising

(or falling) edge to the half of pE at the falling (or rising) edge, with both edges be-

ing nearest to the peak point. The three waveform parameters are indicated by pE ,

and rt

plt in Fig. 1 and Fig. 2, and by p nE , and r nt pl nt ( 1 2 3, ,n = ) in Fig. 3 and Fig. 4.

For horizontal polarization with any incident angle (Fig. 2) and for vertical polariza-tion with an incident angle not larger than the Brewster angle Bθ (solid line in Fig. 3), the shapes of reflected pulses are characterized by the above three waveform parame-ters. For vertical polarization with an incident angle larger than the Brewster angle

Bθ (dashed line in Fig. 3 and dash-dot line in Fig. 4), where 1 072 45.B rtanθ ε−= = ,

the reflected pulse alters sign once as a function of time and has a negative and posi-tive peak values. For this case, in addition to the above three waveform parameters, the fourth waveform parameter, the side peak value spE , is added and is defined as the


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other peak value than pE , so that the shape of reflected pulse is characterized by the

four parameters. The side peak value spE is shown in Fig. 4, but not in Fig. 3 since

spE appears beyond a time range of 0 – 0.3 µs, while this time range has to be used to

clearly illustrating p nE , and r nt pl nt ( 1 2n = , ).

Fig. 1. Double exponential incident pulse

Fig. 2. Reflected pulse for horizontal polarization ( rε = 10, σ = 10 mS/m and ) 00θ =


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Fig. 3. Reflected pulse for vertical polarization ( rε = 10, σ = 10 mS/m and ) 0 00 88θ = ,

Fig. 4. Reflected pulse for vertical polarization ( rε = 10, σ = 10 mS/m and ) 081θ =

3 Analysis and Results

A double-exponential pulse is shown in Fig. 1 and is given by

( )0( )inc t tE t A e eα β− −= −


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with (kV/m), (1/S), and 0 52 5.A = 64 10α = × β = 4.76 (1/S). It has three wave-

form parameters: peak value

810×

pE = 50 kV, rise time rt = 0.00415 µs and pulse length

0.1841 µs. This pulse is incident from free space onto an interface between free

space and a lossy material with the conductivity plt =

σ and the relative dielectric con-stant rε . The reflection coefficients in frequency-domain for vertical and horizontal polarizations are

2

0 0

2

0 0

( )r r

v

r r

cos sins s

R scos sin

s s

σ σε θ ε θε ε

σ σε θ ε θε ε

⎛ ⎞+ − + −⎜ ⎟

⎝ ⎠=⎛ ⎞

+ + + −⎜ ⎟⎝ ⎠

and

2

0

2

0

( )r

h

r

cos sins

R scos sin

s

σθ ε θε

σθ ε θε

− + −=

+ + −,

where 0ε is the permittivity of free space, θ is the incident angle with the normal to the interface, and s jω= is the complex frequency.

Using numerical inversion of Laplace transform, the reflected pulses can be given numerically for both horizontal and vertical polarizations [3], as shown in Figs. 2-4.

For vertical polarization, there exists some incident angle Jθ for each set of σ

and rε values, the magnitude of the negative peak of the reflected pulse is not larger

than that of the positive peak of the reflected pulse for B Jθ θ θ< ≤ , and is larger than

that of the positive peak for Jθ θ> . Jθ depends on both σ and rε , while Bθ de-

pends on rε value only. Fig. 4 plots the reflected pulse for B Jθ θ θ< ≤ , and the

dashed line in Fig. 3 plots the reflected pulse for Jθ θ> . In order to easily demon-strate shape distortion of a reflected pulse in terms of the incident pulse shape, wave-form parameters of a reflected pulse are scaled by the corresponding waveform pa-rameters of the incident pulse. Note that the side peak value of a reflected pulse is scaled by the peak value of the incident pulse.

Fig. 5 and Fig. 6 plot the scaled peak value as a function of the incident angle θ with conductivity σ as a parameter for horizontal and vertical polarizations, respec-tively, and indicate that the scaled peak value becomes -1 at for both polari-zations. Fig. 5 shows that, for horizontal polarization, the scaled peak value is nega-tive for all

90oθ =

θ values, the scaled peak magnitude increases when θ or σ increases, and the change rate of the scaled peak value with θ decreases when σ increases. From Fig. 6, the following points for vertical polarization can be observed: For


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Bθ θ≤ , the scaled peak is positive, the scaled peak magnitude decreases as θ in-

creases and increases as σ increases. For B Jθ θ θ< < , the scaled peak is positive while the scaled side peak is negative, the scaled peak magnitude decreases and the scaled side peak magnitude increases as θ increases, and the scaled peak magnitude increases and the scaled side peak magnitude decreases as σ increases. At Jθ θ= , the scaled peak value jumps down, the scaled side peak value jumps up and both change sign, but the peak values (or scaled side peak values) for B Jθ θ θ< <

smoothly connect with the scaled side peak values (or peak values) for Jθ θ> . For

Jθ θ> , the scaled peak is negative while the scaled side peak is positive, the scaled

peak magnitude increases and the scaled side peak magnitude decreases as θ in-creases, and the scaled peak magnitude decreases and the scaled side peak magnitude increases as σ increases. As σ increases, Jθ increases and the change rates of the

scaled peak and side peak values with θ decrease for Jθ θ≤ and increase for Jθ θ> .

Fig. 7 and Fig. 8 respectively illustrate the scaled rise time and the scaled pulse

length versus θ when σ = 1, 10, 100 mS/m for horizontal polarization, and indicate that the scaled rise time and pulse length decrease as θ increases, and are not smaller than 1 for all θ values. From Fig. 8 it is seen that the scaled pulse length and its change rate with θ decrease as σ increases.

Fig. 5. Scaled peak value as a function of the incident angle θ for horizontal polarization

( rε = 10 and σ = 1, 10, 100 mS/m)


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Fig. 6. Scaled peak and side peak values as functions of incident angle θ for vertical polariza-

tion ( rε = 10 and σ = 1, 10, 100 mS/m)

Fig. 7. Scaled rise time versus θ incident angle for horizontal polarization ( rε = 10 and σ = 1,

10, 100 mS/m)


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Fig. 8. Scaled pulse length versus θ incident angle for horizontal polarization ( rε = 10 and

σ = 1, 10, 100 mS/m)

Fig. 9. Scaled rise time versus θ incident angle for vertical polarization ( rε = 10 and σ = 1,

10, 100 mS/m)


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Fig. 10. Scaled pulse length versus θ incident angle for vertical polarization ( rε = 10 and

σ = 1, 10, 100 mS/m)

Fig. 9 and Fig. 10 respectively plot the scaled rise time and the scaled pulse length versus θ with σ = 1, 10, 100 mS/m for vertical polarization, and show the following points: The scaled rise time and pulse length increase with increase of θ for Jθ θ< ,

jump down at Jθ θ= , and increase again with increase of θ for Jθ θ> . The scaled

rise time and pulse length are larger than 1 for Jθ θ< and are not larger than 1 for

Jθ θ> . From Fig. 10 it is observed that the scaled pulse length decreases with in-

crease of σ for all θ values and its change rate with θ decreases for Jθ θ< and

increases for Jθ θ> with increase of σ .

4 Conclusions

The definitions of waveform parameters are extended. Waveform parameters of UWB electromagnetic pulses reflected from lossy interfaces are evaluated for both horizontal and vertical polarizations. The relationships between the waveform pa-rameters of reflected pulses and incident angles as well as material parameters of interfaces are addressed. It is found that the reflected pulse goes through less distor-tion for horizontal polarization than for vertical incidence.


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References

[1] S. Kellali, B. Jecko, and A. Reineix, “Implementation of a surface impedance for-malism at oblique incidence in FDTD method,” IEEE Trans. Electromagn. Compat., vol. 35, no. 3, pp. 347-356, August 1993.

[2] P. R. Barnes and F. M. Tesche, “On the direct calculation of a transient plane wave reflected from a finitely conducting half space,” IEEE Trans. Electromagn. Compat., vol. 33, no. 2, pp. 90-96, May 1991.

[3] Q. Zeng and G. Y. Delisle, “Characterization of a transient wave reflected from a lossy half space using numerical inversion of Laplace transform,” 10th International Symposium on Antenna Technology and Applied Electromagnetics and URSI Con-ference (Antem 2004/URSI), pp. 87-90, Ottawa, ON, July 20-23, 2004.

[4] M. Camp and H. Garbe, “Parameter estimation of double exponential pulses (EMP, UWB) with least squares and Nelder Mead Algorithm,” IEEE Trans. Electromagn. Compat., vol. 46, no. 4, pp. 675-678, Nov. 2004.

Biography

▲ Name: Qingsheng ZENG Address: Communications Research Centre Canada

3701 Carling Ave., Ottawa, Ontario Canada K2H 8S2

Tel: +1-613-9904920 E-mail: [email protected] Education & Work experience: Qingsheng ZENG received his B.Eng. from Taiyuan University of Technology, Taiyuan, China, in 1984, his M.Eng. from Xidian University, Xian, China, in 1987, and his M.Sc. from INRS – Telecommunica-

tions, University of Quebec, Montreal, Canada, in 2002, all in electrical engineer-ing. He is a PhD candidate in the School of Information and Technology Engineer-ing (SITE), University of Ottawa. During 1987-1992, he worked at the Second In-stitute, the Chinese Ministry of Electronic Industry, as an engineer, and at Taiyuan University of Technology, as a lecturer. From 1993 to 1995, he was a visiting scholar at the Institute of High Frequency Technology, Ruhr University, Bochum, Germany. Between 1996 and 1998, he was a graduate research assistant at Concor-dia University, Montreal. He joined Communications Research Centre Canada as a research engineer in 2001. He has undertaken research and teaching in several fields, including antennas, electromagnetics, optoelectronics, wireless and speech communications, authored and co-authored more than 20 technical publications, and reviewed some journal and conference articles in these fields. His current research interests contain analy-ses of electromagnetic compatibility / interference (EMC / EMI) in ultra wideband (UWB) and microwave communications, computational electromagnetics, antenna analysis and design, as well as establishment of a link between information theory and electromagnetism.


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▲ Name: Gilles Y. Delisle Address: International Institute of Telecommunications 800 de la Gauchetiere St West, suite 6700 Place Bonaventure, Montréal, Québec, Canada H5A 1K6 Tel: +1-514-395-1282 E-mail: [email protected] Education & Work experience: Gilles Y. Delisle received his Ph.D. from Laval University, Québec City, Canada, in 1973.

He is currently Vice-President Research at the International Institute of Telecom-munications in Montréal, Québec, Canada, since July 2004. Previously, he was Di-rector and Professor in the School of Information Technology and Engineering, University of Ottawa, Ottawa, Canada, from January 2002 to June 2004, and was a Professor of Electrical and Computer Engineering at Laval University, from 1973 to 2001, where he was Head of the department from 1977 to 1983. From June 1992 to June 1997, he was also Director of INRS – Telecommunications in Montréal, a research institute which is a part of the Université du Québec. He is involved in re-search work in intelligent antenna array, radar cross-section measurements and analytical predictions, mobile radio-channel propagation modeling, personal com-munications and industrial realization of telecommunication equipments. Dr. Delisle is a member of the Order of Engineers of the Province of Québec and Professional Engineers of Ontario, Past-President of the Canadian Engineering Accreditation Board, Member of the Canadian Academy of Engineering, Past Ca-nadian President of URSI (Union Radio Scientifique Internationale), Past President of ACFAS (Association Canadienne Francaise pour l’Avancement des Sciences ), and a Fellow of the Institute of Electrical and Electronics Engineers (IEEE), of the Canadian Engineering Institute, of the Canadian Academy of Engineering and of the Institution of Electrical Engineers (IEE). His work in technology transfer has been recognized by a Canada Award of Excellence in 1987. He has been a consult-ant in many countries, and he was awarded the J. Armand Bombardier prize of ACFAS for outstanding technical innovation in 1986. Dr. Delisle has supervised the work of over a hundred graduate and post-graduate students over the last 30 years.

mailto:[email protected]

Parameter Estimation of Ultra Wideband (UWB) · PDF file162 Parameter Estimation of Ultra Wideband (UWB) GESTS-Oct.2005 p rameters can be applied to characterize the reflected pulse?

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