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

Transcription

1 GESTS Int l Tans. Comute Science and Eng., Vol.18, No Paamete Estimation of Ulta Wideband (UWB) Electomagnetic Pulses Reflected fom a Lossy Half Sace Qingsheng Zeng 1, 2 and Gilles Y. Delisle 3 1 Univesity of Ottawa, Ottawa, Ontaio, Canada K1N 6N5 qzeng@site.uottawa.ca 2 Communications Reseach Cente Canada, Ottawa, Ontaio, Canada K2H 8S2 qingsheng.zeng@cc.ca 3 Intenational Institute Telecommunications, Monteal, Quebec, Canada, H5A 1K6 gilles.delisle@iitelecom.com Abstact. In this aticle, the definitions of wavefom aametes ae extended, so that they ae alicable not only to a double exonential ulta-wide-band (UWB) incident ulse but also to the eflected ulse fo both hoizontal and vetical olaizations. With numeical invesion of Lalace tansfom, the wavefom aametes of UWB electomagnetic ulses eflected fom lossy intefaces ae estimated fo both hoizontal and vetical olaizations. Based on the estimation, the elationshis between the wavefom aametes of eflected ulses and incident angles as well as mateial aametes of intefaces ae discussed. 1 Intoduction Studies on ulse distotion ae imotant in vaious aeas including channel modeling, and analysis and design of moden communication systems, such as ulta-wide-band (UWB) adio systems. In a multiath channel, nomally eflections fom intefaces between diffeent media have most significant imacts on ulse distotion. The tansient analysis of electomagnetic ulses eflected fom lossy intefaces can be conducted in fequency domain fist. Then the esults in time domain may be obtained by caying out a numeical Fouie tansfom of the fequency domain esonse. Howeve, it is efeable to solve the oblems diectly in the time domain unde cetain cicumstances, in which time-vaying media o nonlinea systems ae involved, o the lossy inteface causes the eflected ulse to esist vey long time, thus ceating difficulties with fast Fouie tansfom (FFT) aliasing. The finite diffeence time domain (FDTD) technique can be alied to this oblem, while comutation costs ae still highe even combining suface imedance bounday conditions with the FDTD algoithm [1]. The aoximate fom of a fequency-domain eflection coefficient emits one analytical exession of the imulse esonse of a lossy half sace [2], but makes the solutions inaccuate o even invalid in some cases, e.g., fo small incident angles. One method based on numeical inve- GESTS-Oct.25

2 162 Paamete Estimation of Ulta Wideband (UWB) sion of Lalace tansfom is alied to the tansient analysis of the eflected ulse fom a lossy inteface [3]. This method gets id of the estictions in [2] on the elative dielectic constant and the incident angle, leads to good accuacy in both late and ealy time, and has a simle algoithm, shot calculation time, small equied memoy size, eadily contolled eo and wide alication ange. In [3], the shaes of eflected ulses fom lossy intefaces with diffeent mateial aametes fo both vetical and hoizontal incidence have been eoduced quite well. Howeve, the elationshis between some imotant wavefom aametes of eflected ulses and incident angles as well as mateial aametes of intefaces have not yet been addessed. In geneal, UWB ulses have stee edges and shot duations. One tye of commonly used UWB electomagnetic ulses is double exonential ulses. These ulse shaes can be descibed with thee wavefom aametes, the eak value E, the ise time t and the ulse length t l [4]. The inteesting and meaningful questions aise: If a double exonential ulse iminges on a lossy inteface, the above wavefom aametes can be alied to chaacteize the eflected ulse? If they can, how will these aametes vay with incident angles and mateial aametes of intefaces? In this aticle, the definitions of wavefom aametes ae extended, so that they ae alicable not only to a double exonential incident ulse but also to the eflected ulse fo both hoizontal and vetical incidence. With numeical invesion of Lalace tansfom, the wavefom aametes of UWB electomagnetic ulses eflected fom lossy intefaces ae estimated fo both hoizontal and vetical incidence. Based on the estimation, the elationshis between the wavefom aametes of eflected ulses and incident angles as well as mateial aametes of intefaces ae discussed. 2 Wavefom Paametes In this aticle, the definitions of the wavefom aametes ae given as follows. The eak value E is defined as the lagest magnitude; The ise time t is defined as the time eiod fo the ulse to change fom 1% to 9% of E befoe eaching the eak oint; The ulse length t l is defined as the duation fom the half of E at the ising (o falling) edge to the half of E at the falling (o ising) edge, with both edges being neaest to the eak oint. The thee wavefom aametes ae indicated by E, t and t l in Fig. 1 and Fig. 2, and by E n, tn and t ln ( n = 123,, ) in Fig. 3 and Fig. 4. Fo hoizontal olaization with any incident angle (Fig. 2) and fo vetical olaization with an incident angle not lage than the Bewste angle θ B (solid line in Fig. 3), the shaes of eflected ulses ae chaacteized by the above thee wavefom aametes. Fo vetical olaization with an incident angle lage than the Bewste angle 1 θ B (dashed line in Fig. 3 and dash-dot line in Fig. 4), whee θb = tan ε = , the eflected ulse altes sign once as a function of time and has a negative and ositive eak values. Fo this case, in addition to the above thee wavefom aametes, the fouth wavefom aamete, the side eak value E, is added and is defined as the s cgests-oct.25

3 GESTS Int l Tans. Comute Science and Eng., Vol.18, No othe eak value than E, so that the shae of eflected ulse is chaacteized by the fou aametes. The side eak value E s is shown in Fig. 4, but not in Fig. 3 since E s aeas beyond a time ange of.3 µs, while this time ange has to be used to clealy illustating E n, tn and t ln ( n = 12, ). Fig. 1. Double exonential incident ulse Fig. 2. Reflected ulse fo hoizontal olaization ( ε = 1, σ = 1 ms/m and θ = ) GESTS-Oct.25

4 164 Paamete Estimation of Ulta Wideband (UWB) Fig. 3. Reflected ulse fo vetical olaization ( ε = 1, σ = 1 ms/m and θ =, 88 ) Fig. 4. Reflected ulse fo vetical olaization ( ε = 1, σ = 1 ms/m and θ = 81 ) 3 Analysis and Results A double-exonential ulse is shown in Fig. 1 and is given by α β ( ) E () t = A e e inc t t cgests-oct.25

5 GESTS Int l Tans. Comute Science and Eng., Vol.18, No with A = (kv/m), α = 4 1 (1/S), and β = (1/S). It has thee wavefom aametes: eak value E = 5 kv, ise time t =.415 µs and ulse length t l =.1841 µs. This ulse is incident fom fee sace onto an inteface between fee sace and a lossy mateial with the conductivity σ and the elative dielectic constant ε. The eflection coefficients in fequency-domain fo vetical and hoizontal olaizations ae and σ σ + + Rv () s = σ σ 2 ε cosθ ε sin θ sε sε 2 ε + cosθ + ε + sin θ sε sε R () s = h cos cos σ 2 θ ε + sin θ sε σ θ ε sin θ sε, whee ε is the emittivity of fee sace, θ is the incident angle with the nomal to the inteface, and s = jω is the comlex fequency. Using numeical invesion of Lalace tansfom, the eflected ulses can be given numeically fo both hoizontal and vetical olaizations [3], as shown in Figs Fo vetical olaization, thee exists some incident angle θ fo each set of σ and ε values, the magnitude of the negative eak of the eflected ulse is not lage than that of the ositive eak of the eflected ulse fo θ B < θ θ, and is lage than that of the ositive eak fo θ > θ. θ deends on both σ and ε, while θ B deends on ε value only. Fig. 4 lots the eflected ulse fo θ B < θ θ, and the dashed line in Fig. 3 lots the eflected ulse fo θ > θ. In ode to easily demonstate shae distotion of a eflected ulse in tems of the incident ulse shae, wavefom aametes of a eflected ulse ae scaled by the coesonding wavefom aametes of the incident ulse. Note that the side eak value of a eflected ulse is scaled by the eak value of the incident ulse. Fig. 5 and Fig. 6 lot the scaled eak value as a function of the incident angle θ with conductivity σ as a aamete fo hoizontal and vetical olaizations, esectively, and indicate that the scaled eak value becomes -1 at θ = 9 o fo both olaizations. Fig. 5 shows that, fo hoizontal olaization, the scaled eak value is negative fo all θ values, the scaled eak magnitude inceases when θ o σ inceases, and the change ate of the scaled eak value with θ deceases when σ inceases. Fom Fig. 6, the following oints fo vetical olaization can be obseved: Fo GESTS-Oct.25

6 166 Paamete Estimation of Ulta Wideband (UWB) θ θ B, the scaled eak is ositive, the scaled eak magnitude deceases as θ inceases and inceases as σ inceases. Fo θb < θ < θ, the scaled eak is ositive while the scaled side eak is negative, the scaled eak magnitude deceases and the scaled side eak magnitude inceases as θ inceases, and the scaled eak magnitude inceases and the scaled side eak magnitude deceases as σ inceases. At θ = θ, the scaled eak value jums down, the scaled side eak value jums u and both change sign, but the eak values (o scaled side eak values) fo θ B < θ < θ smoothly connect with the scaled side eak values (o eak values) fo θ > θ. Fo θ > θ, the scaled eak is negative while the scaled side eak is ositive, the scaled eak magnitude inceases and the scaled side eak magnitude deceases as θ inceases, and the scaled eak magnitude deceases and the scaled side eak magnitude inceases as σ inceases. As σ inceases, θ inceases and the change ates of the scaled eak and side eak values with θ decease fo θ θ and incease fo θ > θ. Fig. 7 and Fig. 8 esectively illustate the scaled ise time and the scaled ulse length vesus θ when σ = 1, 1, 1 ms/m fo hoizontal olaization, and indicate that the scaled ise time and ulse length decease as θ inceases, and ae not smalle than 1 fo all θ values. Fom Fig. 8 it is seen that the scaled ulse length and its change ate with θ decease as σ inceases. Fig. 5. Scaled eak value as a function of the incident angle θ fo hoizontal olaization ( ε = 1 and σ = 1, 1, 1 ms/m) cgests-oct.25

7 GESTS Int l Tans. Comute Science and Eng., Vol.18, No Fig. 6. Scaled eak and side eak values as functions of incident angle θ fo vetical olaization ( ε = 1 and σ = 1, 1, 1 ms/m) Fig. 7. Scaled ise time vesus θ incident angle fo hoizontal olaization ( ε = 1 and σ = 1, 1, 1 ms/m) GESTS-Oct.25

8 168 Paamete Estimation of Ulta Wideband (UWB) Fig. 8. Scaled ulse length vesus θ incident angle fo hoizontal olaization ( ε = 1 and σ = 1, 1, 1 ms/m) Fig. 9. Scaled ise time vesus θ incident angle fo vetical olaization ( ε = 1 and σ = 1, 1, 1 ms/m) cgests-oct.25

9 GESTS Int l Tans. Comute Science and Eng., Vol.18, No Fig. 1. Scaled ulse length vesus θ incident angle fo vetical olaization ( ε = 1 and σ = 1, 1, 1 ms/m) Fig. 9 and Fig. 1 esectively lot the scaled ise time and the scaled ulse length vesus θ with σ = 1, 1, 1 ms/m fo vetical olaization, and show the following oints: The scaled ise time and ulse length incease with incease of θ fo θ < θ, jum down at θ = θ, and incease again with incease of θ fo θ > θ. The scaled ise time and ulse length ae lage than 1 fo θ < θ and ae not lage than 1 fo θ > θ. Fom Fig. 1 it is obseved that the scaled ulse length deceases with incease of σ fo all θ values and its change ate with θ deceases fo θ < θ and inceases fo θ > θ with incease of σ. 4 Conclusions The definitions of wavefom aametes ae extended. Wavefom aametes of UWB electomagnetic ulses eflected fom lossy intefaces ae evaluated fo both hoizontal and vetical olaizations. The elationshis between the wavefom aametes of eflected ulses and incident angles as well as mateial aametes of intefaces ae addessed. It is found that the eflected ulse goes though less distotion fo hoizontal olaization than fo vetical incidence. GESTS-Oct.25

10 17 Paamete Estimation of Ulta Wideband (UWB) Refeences [1] S. Kellali, B. ecko, and A. Reineix, Imlementation of a suface imedance fomalism at oblique incidence in FDTD method, IEEE Tans. Electomagn. Comat., vol. 35, no. 3, , August [2] P. R. Banes and F. M. Tesche, On the diect calculation of a tansient lane wave eflected fom a finitely conducting half sace, IEEE Tans. Electomagn. Comat., vol. 33, no. 2,. 9-96, May [3] Q. Zeng and G. Y. Delisle, Chaacteization of a tansient wave eflected fom a lossy half sace using numeical invesion of Lalace tansfom, 1th Intenational Symosium on Antenna Technology and Alied Electomagnetics and URSI Confeence (Antem 24/URSI),. 87-9, Ottawa, ON, uly 2-23, 24. [4] M. Cam and H. Gabe, Paamete estimation of double exonential ulses (EMP, UWB) with least squaes and Nelde Mead Algoithm, IEEE Tans. Electomagn. Comat., vol. 46, no. 4, , Nov. 24. Biogahy cgests-oct.25 Name: Qingsheng ZENG Addess: Communications Reseach Cente Canada 371 Caling Ave., Ottawa, Ontaio Canada K2H 8S2 Tel: qingsheng.zeng@cc.ca Education & Wok exeience: Qingsheng ZENG eceived his B.Eng. fom Taiyuan Univesity of Technology, Taiyuan, China, in 1984, his M.Eng. fom Xidian Univesity, Xian, China, in 1987, and his M.Sc. fom INRS Telecommunications, Univesity of Quebec, Monteal, Canada, in 22, all in electical engineeing. He is a PhD candidate in the School of Infomation and Technology Engineeing (SITE), Univesity of Ottawa. Duing , he woked at the Second Institute, the Chinese Ministy of Electonic Industy, as an enginee, and at Taiyuan Univesity of Technology, as a lectue. Fom 1993 to 1995, he was a visiting schola at the Institute of High Fequency Technology, Ruh Univesity, Bochum, Gemany. Between 1996 and 1998, he was a gaduate eseach assistant at Concodia Univesity, Monteal. He joined Communications Reseach Cente Canada as a eseach enginee in 21. He has undetaken eseach and teaching in seveal fields, including antennas, electomagnetics, otoelectonics, wieless and seech communications, authoed and co-authoed moe than 2 technical ublications, and eviewed some jounal and confeence aticles in these fields. His cuent eseach inteests contain analyses of electomagnetic comatibility / intefeence (EMC / EMI) in ulta wideband (UWB) and micowave communications, comutational electomagnetics, antenna analysis and design, as well as establishment of a link between infomation theoy and electomagnetism.

11 GESTS Int l Tans. Comute Science and Eng., Vol.18, No Name: Gilles Y. Delisle Addess: Intenational Institute of Telecommunications 8 de la Gauchetiee St West, suite 67 Place Bonaventue, Montéal, Québec, Canada H5A 1K6 Tel: gilles.delisle@iitelecom.com Education & Wok exeience: Gilles Y. Delisle eceived his Ph.D. fom Laval Univesity, Québec City, Canada, in He is cuently Vice-Pesident Reseach at the Intenational Institute of Telecommunications in Montéal, Québec, Canada, since uly 24. Peviously, he was Diecto and Pofesso in the School of Infomation Technology and Engineeing, Univesity of Ottawa, Ottawa, Canada, fom anuay 22 to une 24, and was a Pofesso of Electical and Comute Engineeing at Laval Univesity, fom 1973 to 21, whee he was Head of the deatment fom 1977 to Fom une 1992 to une 1997, he was also Diecto of INRS Telecommunications in Montéal, a eseach institute which is a at of the Univesité du Québec. He is involved in eseach wok in intelligent antenna aay, ada coss-section measuements and analytical edictions, mobile adio-channel oagation modeling, esonal communications and industial ealization of telecommunication equiments. D. Delisle is a membe of the Ode of Enginees of the Povince of Québec and Pofessional Enginees of Ontaio, Past-Pesident of the Canadian Engineeing Acceditation Boad, Membe of the Canadian Academy of Engineeing, Past Canadian Pesident of URSI (Union Radio Scientifique Intenationale), Past Pesident of ACFAS (Association Canadienne Fancaise ou l Avancement des Sciences ), and a Fellow of the Institute of Electical and Electonics Enginees (IEEE), of the Canadian Engineeing Institute, of the Canadian Academy of Engineeing and of the Institution of Electical Enginees (IEE). His wok in technology tansfe has been ecognized by a Canada Awad of Excellence in He has been a consultant in many counties, and he was awaded the. Amand Bombadie ize of ACFAS fo outstanding technical innovation in D. Delisle has suevised the wok of ove a hunded gaduate and ost-gaduate students ove the last 3 yeas. GESTS-Oct.25