Frequency Model of Ultrawideband Antennas - IEEE Xplore

0 downloads 0 Views 728KB Size Report
Abstract—A new approach to model ultrawideband (UWB) antennas is proposed. A mathematical analysis of transmission through an UWB system in terms of ...
2342

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 8, AUGUST 2007

A Time/Frequency Model of Ultrawideband Antennas Yvan Duroc, Tan-Phu Vuong, Member, IEEE, and Smail Tedjini, Senior Member, IEEE

Abstract—A new approach to model ultrawideband (UWB) antennas is proposed. A mathematical analysis of transmission through an UWB system in terms of transfer function and impulse response is proposed. The analysis allows the separation of the transmitting and receiving antenna characteristics, using a consistent treatment with other UWB and earlier narrowband analysis techniques. A parametric modeling is added to provide efficient directional time-frequency models of UWB antennas. The technique is demonstrated through simulation and experiment. Index Terms—Parametric modeling, transient response, ultrawideband (UWB) antennas.

I. INTRODUCTION

S

INCE 2002, the Federal Communications Commission (FCC) has authorized the use of several frequency bands [0–960 MHz], [3.1–10.6 GHz], and [22–29 GHz] for new ultrawideband (UWB) transmissions. UWB signal is defined as a signal with a fractional bandwidth greater than 0.2 or a signal that occupies more than 500 MHz of spectrum. Thanks to the large bandwidth, UWB is a very promising technology for short-range wireless communications with high data rates as well as radar and geolocation applications, unrealizable in narrowband systems [1]. However compared to traditional systems, there are many new challenges involved in designing UWB systems, such as antenna design, interference, propagation, channel effects, modulation and coding methods, etc. [2]. One of the main difficulties relies on the emission limits stipulated by the FCC (e.g., 41.3 dBm/MHz within the frequency range [3.1–10.6 GHz]). As the transmitter design must comply with the spectral masks and the receiver design must be able to collect efficiently the emitted energy, the role of the transmitting and receiving antennas is preponderant in UWB systems. This study focused on the characterization of UWB antennas. In UWB, the classical design parameters of antennas and radio frequency front-end circuits (i.e., power, gain, reflection coefficient, etc.) become strongly frequency dependent complicating the analysis of the link budget via Friis transmission formula [3]. In addition, UWB antennas act as major pulse shaping filters. New parameters have then been introduced to take into consideration the transient radiation and to reveal phase variation effects. The common approach is to consider the antenna as a linear time invariant system described by its transfer function

Manuscript received January 9, 2006; revised March 12, 2007. The authors are with the LCIS-INPGrenoble, ESISAR, 26902 Valence, France (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2007.901834

Fig. 1. Conventional modeling for the radio frequency channel UWB.

(gain and phase) and its associated impulse response [4]–[6]. As the antenna characteristics also depend on the signal propagation direction (i.e., are spatial dependent), the transfer functions and the impulse responses modeling UWB antennas are spatial vectors [7]. Moreover the use of parametric modeling can allow the enhancement of the modeling. Analytical and compressed expressions of the transfer functions and the impulse responses can be achieved from measurement [8]–[10]. In this paper, we present a mathematical analysis of transmission through an UWB system in terms of transfer function and impulse response. In Section II, we review previously proposed models. In Section III, we suggest a new approach which allows the separation of the transmitting and receiving antenna characteristics from the channel characteristics, using a consistent treatment with other UWB and earlier narrowband analysis techniques. A parametric modeling is added to provide efficient directional time-frequency models of UWB antennas. Section IV demonstrates the interest of the method through simple experiments. Finally, conclusions and perspectives are presented in the last section. II. CONVENTIONAL UWB ANTENNA MODEL A. Approach of the Modeling Fig. 1 presents the classical approach, commonly used in the literature to characterize an ideal UWB channel, i.e., a radio link made up of two antennas in free space and under the approximation of far-field and line-of-sight propagation. The emission model takes into account the TX antenna and the channel jointly, while in reception only the RX antenna is considered. The transfer {input-radiated field} is modeled in frequency defined domain with a vectorial transfer function such as (1) where is the radiated electric far field at a space point defined by and : polar and azimuth angles respectively. is the considered input (e.g., voltage, current, or amplitude . wave). is the pulsation In a similar way, the transfer {incident field-output} is characterized by the vectorial transfer function between

0018-926X/$25.00 © 2007 IEEE

DUROC et al.: A TIME/FREQUENCY MODEL OF UWB ANTENNAS

2343

for , (5) is written as

or

, respectively. In the time domain,

(6)

Fig. 2. Equivalent circuits of antennas in the transmitting and receiving modes.

the output variable as

and the incident field

such

(2)

B. Analytical Expressions of Vectorial Transfer Functions The equivalent circuits of antennas in the transmitting and receiving modes are considered to determine the analytical expressions of vectorial transfer functions. They are represented on Fig. 2 according to [11]. The equivalent circuit in the transmitting mode is composed of a Thevenin generator which models the source and the TX input impedance antenna, . In the receiving mode, reception model is represented and by the load by a second Thevenin generator impedance, . is the open-circuit voltage of the termiis its impedance.1 nals of the RX antenna and According to the definition of the radiated field, can be written as

The transfer function of an antenna is generally assimilated to its effective length because these quantities are proportional as shown by (5). Moreover, supposing that e and s are voltages, the units of the transfer functions and the impulse responses2 are the following: , , and . C. Model of Transient Transmission From Sections II-A and II-B, the model of the full transfer {input-output}, i.e., the model of the transient transmission, can be deduced both in frequency and time domains. The funcand the associated impulse response tion transfer of the transmission are written as (7) (8) With the assumption that the radiated incident fields are equal (i.e., same modulus and same direction), (7), and (8) become

(9)

(10)

(3) is the effective length of the TX antenna, where is the speed of light, is the free space characteristic , is the observation distance impedance must be adapted to from the antenna. The coefficient , the input taken into account as follows: or for , or , respectively. The transposition of (3) in the time domain, applying the inverse Fourier transform, gives the following: (4)

Considering voltages for input and output, is in . without dimension and

appears

D. Analysis of the Transmission in Terms of Powers Considering the input and the output and introducing the reflection coefficients

, and defined as (11)

and the conjugate complex impedance of with , (9) can then be rewritten as

and

where “ ” denotes the convolution product and is the Dirac distribution. As a consequence of the reciprocity principle, the transfer is given by function

(5) (12) where ficient

is the effective length of the TX antenna. The coefis such as , or

1The currents (I ; I ) and the voltages (V are peak amplitudes and complex numbers.

;V

) in the following equations

where

is the wavelength

.

2The inverse Fourier transform involves the multiplication of the unit by s due to its definition.

2344

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 8, AUGUST 2007

where the free space channel transfer function is given by (19) Fig. 3. New modeling for the radio frequency channel UWB.

Otherwise the transmitted power are given by the following:

and the normalized effective lengths fined by the following relations:

and

are de-

and the received power (20) (13)

Combining (13) and (14), the transmission model in terms of powers is given by the relation

(21) Then, the proposed identification for the transfer functions (18) allows the verification of the Lorentz reciprocity, i.e., (22)

(14) represents the polarization loss factor and the gains where and are defined by (15)

Moreover supposing that the generator impedance and the are equals at the reference impedance , load impedance (20) provides the TX and RX antennas normalized transfer functions. The normalized effective lengths are then written using S-parameters as

Equation (14) is the known Friis transmission equation. Therefore compared to Friis formula, (9) in the frequency domain or (10) in the time domain provide a most complete model without loss of the phase which is a very relevant information for UWB antennas.

(23) (24)

III. NEW APPROACH OF THE UWB ANTENNA MODEL C. Analysis Results A. Presentation We propose another approach illustrated in Fig. 3, considering three blocks: the TX antenna, the free space channel and the RX antenna. Each block is characterized by a transfer func, and , and an assocition , and , ated impulse response respectively. In the case of a free space channel, the transient transmission is written in the frequency domain and the time domain, respectively, as (16) (17) B. Definition of the Transfer Functions From this intuitive description, each transfer function can be identified. An analysis in the frequency domain implies simple and (arcomputations. Indeed considering the voltages bitrarily chosen for the example), the transmission equation (9) can be rewritten as

1) Relation Between TX Antenna and RX Antenna: A first remark is to notice that the characterization of the TX and RX antennas must be necessarily distinguished as a consequence of the reciprocity (25) (26) 2) Dimension Analysis: This approach presents the drawback of forgetting a physical aspect in term of dimension for the transient radiation. Indeed, the transfer functions are expressed for TX and for RX. Then the impulse rein for TX sponses have the following dimensions and for RX. Otherwise, it can be seen that the free space channel transfer function and transmission transfer function are dimensionless. Although these first comments are a priori rather negative, the next points will present several advantages even for a physical point of view. 3) IEEE Standard Antenna Gain: The definition of the IEEE standard antenna gain, which excludes the losses due to mismatching, is given by the following relation [11]:

(18) (27)

DUROC et al.: A TIME/FREQUENCY MODEL OF UWB ANTENNAS

2345

In addition, once a reference antenna (TX antenna) is characterized, the transfer function of the unknown antenna (RX antenna) can be deduced for multiples orientations by (35)

Fig. 4. Characterization of the transmission in the frequency domain.

where is the reflection coefficient. As a consequence, assuming two identical antennas, the IEEE gain is written as (28) where the effective continuous wave gain pattern return loss are given by

and the

Equation (25) allows the determination of the corresponding TX transfer function. Then, the impulse responses are easily deduced by inverse Fourier transform after some cautions, i.e., either appropriate zero padding and forming conjugate frequency , or directly obtaining a complex analytical time response response. E. Parametric Modeling

(29) Then, this gain can also be expressed in several manners according to or/and

(30)

The previous parts have shown that UWB antennas could be modeled as multidimensional linear filters (for each direction of space). The last step of the proposed modeling is to look for an analytical model that can be integrated into a simulation system and used as “antenna block.” An interesting way, currently used in Electromagnetics, is to compute a parametric model based on the singularity expansion method (SEM) which extracts poles is based on a projection and residues [12], [13]. The model in a base of exponential functions defined by

(31)

(36)

Moreover (as expected) the gain is dimensionless. These relations show rightly both the difference and the duality aspect of the emission and reception transfers. 4) Friis Formula: An interesting propriety of this approach is its similitude with the fundamental Friis formula

, and , is the observed time response, is the noise (model error, additive noise, etc.). The parameters of the , the poles and the order. model are the residues Noticing that

(32)

(37)

and are the transmitted and received powers, rewhere spectively, and are the gains of TX and RX antennas respectively. It should be noticed that these gains correspond . Thus, considering the square of (16), the identification to with (31) is straightforward. 5) Case of Multipath Channels: Although the model given in (16) does not work for multipath channels, the proposed modeling of the antennas will be possible to use for multipath channels. In this aim, it is necessary to add a polarized transmission matrix for each single path and a summation over all paths.

this solution has the advantage of describing through a minimal couples of and , the responses both in data set, time domain and frequency domain. In general, simultaneous estimation of these parameters is nonlinear problem. However, it is possible to split the problem into two stages and thus to transform it to the resolution of two -by-N linear systems. Historically, Prony has established such an approach in 1795 to explain the expansion of various gases. Nowadays various variants of this polynomial approach improve it, particularly in order to fight the sensitivity to noise. In particular, Tufts and Kumaresan proposed several techniques based on linear prediction and singular value decomposition (SVD), giving more accurate estimates of the parameters [14]. More recently, the matrix pencil technique, whose roots go back to the pencil-of-functions (PoF) approach, led to better performance. This method is more computationally efficient because is a one-step process (instead the determination of the poles of two) and the variance of the estimate is improved. Generwill not be known and it will be necessary to ally the order estimate it. However, there is no straightforward method. In the presence of noise or considering an on-dimensioned system, the SVD can help to estimate using the most significant singular values [15].

D. Practice Approach to Determine the Transfer Functions In practice from simulation or measurement of the scattering in frequency domain, the transfer function of the parameter TX and RX antennas can be deduced (Fig. 4). Indeed using two identical antennas with equal orientation and considering (18), the following relations are achieved: (33) (34)

where

2346

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 8, AUGUST 2007

Fig. 5. (a) Geometry of the reported antenna and (b) fabricated antenna. Fig. 7. Simulated scattering parameter in the time domain.

S

: (a) in the frequency domain; (b)

TABLE I SUMMARY OF THE RESULTS OBTAINED WITH PRONY METHOD

Fig. 6. (a) Voltage standing wave ratio. (b) Radiation pattern in the xz plane.

The accuracy of the fit model can be achieved by calculating the “mean square error” of the difference between the model and the measured impulse responses (or transfer functions). In the following analysis, a signal to noise ratio (SNR) parameter is introduced to identify a “better” model from the set of possible and the models. It is deduced from the power of the error as power of the reference data (38) IV. APPLICATIONS AND RESULTS A. Presentation of the Studied Antenna The studied antenna is a compact band-rejected U-slotted planar antenna for impulse radio (IR) UWB systems. This antenna was designed using a co-design approach (i.e., antenna and filter) to cover the UWB band 3.1 to 10.6 GHz and also to reject the narrow band allocated to WiFi at 5 GHz; it is composed of a rectangular patch on a partial ground plane under microstrip configuration and of a U-Slot allowing the rejection of the limited band (Fig. 5). Some of the main conventional characteristics of this antenna are shown below. Fig. 6(a) presents the voltage wave standing ratio (VWSR) and shows that the antenna has a measured bandstarting at 3.7 GHz and going beyond the width 11 GHz, with a rejected band between 5.3 and 5.8 GHz. Fig. 6(b) plane at 4 plots the directional realized gain (in dBi) on the GHz and illustrates its omnidirectional pattern. In the case of UWB antennas, such a traditional characterization is not sufficient. As shown in Section III, the scattering paallows the improvement of the description allowing rameter the computation of the transfer function of the TX antenna and the RX antenna. The associated impulse responses can be deduced and used to obtain parametric models which, if possible,

are accurate with a small order . From a particular example, the following part illustrates some experiments to acquire an efficient parametric model. B. Characterization of the Antenna and Parametric Modeling Considering two identical antennas with same orientation and within a free space propagation channel, the complex scattering is simulated with the CST Microwave software. parameter in the frequency domain [Fig. 7(a)] and the Fig. 7 illustrates time domain [Fig. 7(b)]. , the impulse reFrom the simulated scattering parameter sponse of the RX antenna is computed and a relevant parametric model is defined.3 The following results show how this model is obtained. The objective of the modeling is to provide a model with a minimum set of data and a SNR larger that 25 dB (chosen arbitrarily to have an accurate model). For that with Prony analysis, several alternatives can be chosen: the number of data samples taken into account, the interval between two successive samples, the order of the model defined a priori and the possibility to use a SVD. Table I summarizes some results showing the effects of these choices. For the column 3The RX antenna is considered but the methodology is general and could be applied for the TX antenna or the TX/RX antenna system.

DUROC et al.: A TIME/FREQUENCY MODEL OF UWB ANTENNAS

2347

Fig. 8. Singular value decomposition (12th line of the Table I).

“SVD,” “no” means that the SVD is not applied; if the SVD is used, the number indicates the selection threshold compared to corresponds to the order of the obthe larger singular value. tained model. Initially, the impulse response is defined with 600 of 48 GHz. The samples and a sampling frequency direct application of the Prony method (1st line) provides a very but also an important order of precise model . With the same accuracy, it is possible to this model reduce and as the impulse response tends towards zero (2nd and 3rd line). Considering the 200 first samples, the decrease of the order implies that the SNR reduces (3rd to 6th line). The effect of a decimation (via the parameter ) shows that the order of the model can be reduced with an excellent SNR: and (7th line). Some tests (7th to 11th line) are presented. Considering this possibility, a good compromise is attained (9th and . Then, a possible option is to row): apply a SVD allowing the selection of the most significant singular values (11th to 15th line). Fig. 8 illustrates the SVD in the case of the 12th line. The singular values below the threshold are not taken into account in the model. The order of the model is reduced to 12 compared to 20. Then, the use of SVD improves the sensibility to noise of the model error. Fig. 9 shows the effect of the order (chosen a priori) on the impulse response and the and associated transfer function (12th to 15th line). For 30, the modeling is correct , i.e., the references and the models are similar in the time domain and the frequency decreases ( and 10), the modeling is domain. When inexact. For example in the time domain, the impulse responses become more and more dissimilar for the last samples. In the frequency domain, the rejected band does not appear any more in the gain. Finally, the Prony method associated to the SVD provides and , i.e., a model cona model such as stituted of 18 complex couples of residues and poles (12th line). Table II illustrates some results with the matrix pencil and are fixed according to the method. The parameters previous study.4 The three first lines give the obtained results for 25, 15, 12. Especially when , this model is better that the model obtained with the Prony 4The pencil parameter is chosen in the interval [K/3; 2K/3] as recommended in [15].

Fig. 9. Parametric model with SVD-prony (12th at 15th line of Table I): (a) impulse response; (b) transfer function. TABLE II SUMMARY OF THE RESULTS OBTAINED WITH MATRIX PENCIL METHOD

analysis ( , ). The use of the SVD also improves the model (4th line): and . Finally, the retained model for this example is obtained using conjointly the matrix pencil method and the SVD (last line of the Table II). The six conjugate and complex couples of residues and poles related to this model are given by the Table III. Noticing that the imaginary parts of the poles and the real parts are the damping coefare the pulsations , and that the residues are the amplitudes of the harficients monics, a relevant representation is to plot these parameters in three dimensions (Fig. 10). Three couples seem less significant. However if they are not taken into account the SNR decreases at 7 dB. This representation has to be utilized with caution.

2348

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 8, AUGUST 2007

TABLE III COMPLEX RESIDUES AND POLES (OPTIMAL CASE M = 12)

Fig. 11. Measured directional complex scattering parameter of the system made up of the two identical antennas separated by free space.

Fig. 10. Poles (pulsation and damping coefficient) and residues (amplitude) of the model.

Fig. 12. Modeling of the TX antenna for several orientations: (a) transfer function; (b) impulse response.

The modeling was presented for the RX antenna (positioned in one direction) but the approach can be generalized. In the following part, directional time-frequency parametric models of the TX antenna and the RX antenna are determined from measurement. C. Directional Time-Frequency Parametric Model The conventional characterization shows that the gain of the antenna not only depends on the frequency but also significantly on the direction (Fig. 7). Therefore the transfer function and the associated impulse response of the antenna are directional dependent. As mentioned in Section III, several orientations of the antennas can be considered using adequate scattering parameter . The simulation time being very important to determine (several hours), the presented results come from experiments. Two identical antennas was positioned in anechoic chamber and connected to the ports of a Vector Network Analyzer which provided the frequency dependent S-parameters for several orientations of the antennas. Fig. 11 represents the gain of the meaparameter made in the azimuth plane sured directional for several angles: 45, 0, 45 and 90 degrees. Applying the method described in Section III-D, Figs. 12 and 13 show the obtained responses in the frequency domain and the time domain for the antenna considered in transmission and in reception. The gains reveal the rejected frequency band. In the lower frequency band, the directional gains are relatively becomes smaller similar. In the upper band, the gain for that for the other directions. For the two symmetrical angles , the responses are relatively similar, as expected due

Fig. 13. Modeling of the RX antenna for several orientations: (a) transfer function; (b) impulse response.

to the symmetry of the antenna. Otherwise, it can also be noticed is the derivative of . that The parametric modeling can be applied for the different orientations of the antennas to obtain compact time-frequency directional models. From techniques described in Section IV-B, four models described by 12 complex conjugate couples of poles and residues, are achieved. An improvement of the complexity of models can be realized because whatever is the considered directional impulse response, the preponderant poles are the same and only the residues are adapted. Thus the poles are calculated (chosen arbitrarily) and also used for for the direction the others orientations. This option implies a little decrease of the accuracy (demonstrated by Table IV) but allows the diminution of the complexity because the 12 couples of poles are identical for the different models. Using identical poles for the modeling, Fig. 14 shows the obtained results considering the impulse response of the RX antenna. The measured and modelled curves match. The precision of the models is indicated on Table IV.

DUROC et al.: A TIME/FREQUENCY MODEL OF UWB ANTENNAS

TABLE IV SIGNAL NOISE RATIO OF THE DIRECTIONAL MODEL

Fig. 14. Directional impulse responses of the RX antenna.

2349

[4] S. Zwierzchowski and P. Jazayeri, “Derivation and determination of the antenna transfer function for use in ultra-wideband communications analysis,” in Wireless Proc., Jul. 2003, pp. 533–543. [5] A. H. Mohammadian, A. Rajkotia, and S. S. Soliman, “Characterization of UWB transmit-receive antenna system,” in IEEE Conf. Ultra Wideband Systems and Technology, Nov. 2003, pp. 157–161. [6] Z. N. Chen, X. H. Wu, H. F. Li, N. Yang, and M. Y. W. Chia, “Considerations for sources pulses and antennas in UWB radio systems,” IEEE Trans. Antennas Propag., vol. 52, no. 7, pp. 1739–1748, Jul. 2004. [7] W. Sörgel and W. Wiesbeck, “Influence of the antennas on the ultra-wideband transmission,” EURASIP J. App. Signal Processing, pp. 296–305, 2005. [8] S. Licul and W. A. Davis, “Unified frequency and time-domain antenna modeling and characterization,” IEEE Trans. Antennas Propag., vol. 53, no. 9, pp. 2882–2888, Sep. 2005. [9] Y. Duroc, T. P. Vuong, and S. Tedjini, “Realistic modeling of antennas for ultra wideband systems,” in Proc. IEEE Radio and Wireless Symp., Jan. 2006, pp. 347–350. [10] C. Roblin, “Ultra compressed parametric modeling of UWB antenna measurements,” in Proc. 1st Eur. Conf. on Antennas and Propagation, Nice, France, Nov. 6–10, 2006. [11] C. A. Balanis, Antenna Theory: Analysis and Design. New York: Wiley, 1997. [12] E. K. Miller and T. K. Sarkar, “Model-order reduction in electromagnetics using model-based parameter estimation,” in Frontiers in Electromagnetics, ser. IEEE Press Series on RF and Microwave Technology, D. H. Werner and R. Mittra, Eds. Piscataway, NJ: IEEE Press, 1999, ch. 9. [13] C. E. Baum, “On the singularity expansion method for the solution of electromagnetic interaction problems” AWFL Interaction Note 88, Dec. 1981. [14] D. W. Tufts and R. Kumaresan, “Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. 30, no. 6, pp. 833–840, Dec. 1982. [15] T. K. Sarkar and O. Pereira, “Using the Matrix Pencil method to estimate the parameters of a sum of complex exponentials,” IEEE Antennas Propag. Mag., vol. 37, no. 1, pp. 48–55, Feb. 1995.

V. CONCLUSION This paper emphasizes a new approach for modeling UWB antennas. From the determination of directional impulse responses (and associated transfer functions) and using singularity expansion methods (i.e., Prony and matrix pencil methods), compact time-frequency models of TX and RX antennas has been established. The reported technique was applied in the modeling of a small band-rejected U-slotted UWB antenna and is general. It should be noted that for antennas with less large bands, the impulse responses would be spreaded and then the order of associated models will increase.

Yvan Duroc was born in Angoulême, France in 1971. He received the Master degree from the National Polytechnic Institute, Grenoble, France, in 1994 and the teaching degree “Agrégation” in applied physics in 1995. In 1997, he joined the engineering school ESISAR, Institut National Polytechnique de Grenoble (INPG), France, as an Associate Professor. In parallel to his teaching activities, he is currently pursuing a Ph.D. degree at the research laboratory LCIS, INPG. His general research interests lie in the area of signal processing and digital communications especially UWB technology and antennas modeling.

ACKNOWLEDGMENT The authors wish to thank the Region Rhone-Alpes for its support for this topic under the FITT procedure. REFERENCES [1] FCC Notice of Proposed Rule Making, Revision of Part 15 of the Commission’s Rules Regarding Ultra-Wideband Transmission Systems Federal Communications Commission, ET-Docket 98-153. [2] L. Yang and G. B. Giannakis, “Ultrawideband communications: An idea whose time has come,” IEEE Signal Processing Mag., pp. 26–54, Nov. 2004. [3] Z. Irahhauten, A. Yarovoy, H. Nikookar, G. J. M. Janssen, and L. P. Ligthart, “The effect of antenna and pulse waveform on ultra wideband link budget with impulse radio transmission,” in Proc. 34th Eur. Microwave Conf., Oct. 2004.

Tan-Phu Vuong (S’98–M’01) was born in Saigon, Vietnam. He received the Ph.D. degree in electrical engineering, from the National Polytechnic Institute, Toulouse, France, in 1999. From January 1999 to August 2001, he was an Assistant Research Scientist and Teaching Assistant at the Electrical Engineering department of ENSEEIHT, Toulouse, France. Since September 2001, he has been an Associate Professor of microwave and wireless systems at the engineering school ESISAR, Institut National Polytechnique de Grenoble (INPG), France. His research interest is in the modeling of passive microwave and millimeter-wave integrated circuits by integral equations formulation and by variational approaches. Currently, his research activities include design of small antennas and printed antennas for communication mobile, RFID and UWB. Since 2006, he has been the head of the Radiofrequency and Systems (ORSYS) research team at the research laboratory LCIS, INPG.

2350

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 8, AUGUST 2007

Smail Tedjini (S’82–M’86–SM’92) was born in Algeria in 1956. He received the “Doctorat d’Etat” in physics from the National Polytechnic Institute, Grenoble, France, in 1985. From 1986 to 1993 he was a member of the Centre National de la Recherche Scientifique (CNRS). From 1993 to 1996, he was a Professor at Joseph Fourier University of Grenoble. Since 1996, he has been a Professor at the engineering school ESISAR, Institut National Polytechnique de Grenoble (INPG), France, where he founded the research lab LCIS. Since 2006,

he has been the Head of ESISAR. He is in charge of lectures in applied electromagnetism, radiofrequency and optoelectronics, for undergraduate, graduate and Ph.D. students, and he has supervised 21 Ph.D. thesis students. He has authored/coauthored more than 210 scientific papers and communications. He conducted research in microwave, guided optics and high-speed optoelectronics. His actual research interest concerns RF Wireless and optoelectronic systems with special attention to RFID and ultrawideband technologies. Prof. Tedjini is the Chapter Chair of the French CPMT/IEEE, Vice-president for France at CNFRS/URSI Commission D, and is a member of the French Societies SEE, EEA.