The Waveform Distortion Due to Antennas on Transmission Loss of Ultra Wideband Impulse Radio

Transcription

1 Proceedings of APCC28 copyright 28 IEICE 8 SB 83 The Waveform Distortion Due to Antenn on Transmission Loss of Ultra Wideband Impulse Radio Sathaporn Promwong,, and Jun-ichi Takada Department of Information Engineering, Faculty of Engineering, King Mongkut s Institute of Technology Ladkrabang, Bangkok 152, Thailand. Graduate School of Science and Engineering, Tokyo Institute of Technology O-okayama Minami 6 Bldg., , O-okayama, Meguro-ku, , Tokyo, Japan. kpsathap@kmitl.ac.th Abstract In this paper, we evaluated the transmission gain of ultra wideband radio by using the Friis transmission formula. However, it is not directly applicable to ultra wideband impulse radio (UWB-IR) transmission systems. This paper presents the link budget evaluation formula in the term of transmission gain for the UWB-IR systems that takes into account the transmitted waveform, its distortion due to the antenn, the channel and the correlation receiver. Since the antenn are significant pulseshaping filters in UWB-IR, the various kinds of the antenn are experimentally examined, especially focused on the effect of the received signal and the isotropic template waveforms. I. INTRODUCTION In the UWB-IR communication systems, any frequency selectivity causes distortion of the transmitting pulse shape. Therefore, antenn usually act significant pulse-shaping filters. In the narrowband wireless systems, Friis transmission formula is used for the line-of-sight (LOS) link budget evaluation [1]. However, it is not directly applicable to the UWB- IR system the bandwidth of the pulse is extremely wide. Moreover, the effect of the waveform distortion shall be quantitatively considered in the link budget evaluation. The special ces of constant gain and constant aperture antenn are treated [2], but no general discussion had been made. The antenna and the receiver template waveform are considered to evaluate the free space transmission property [3], but it only considered the relative performance. The inverse Fourier transform of the Friis transmission formula is considered to discuss the waveform distortion [4], but it did not consider the receiver. The framework for link budget analysis is proposed [5]. Although it considered the multipath environment in the comprehensive manner, it did not consider the optimum correlation receiver, and the channel impulse response is used for the modeling, which can not accurately reflect the antenna property. In this paper, we discuss the free space evaluation scheme in the term of transmission gain for the UWB-IR systems that takes into account the transmitted waveform, its distortion due to the antenn, the channel and the correlation receiver. This scheme is bed on the Friis transmission formula, adapted to the UWB-IR, in the sense that we derive the equivalent transmission gain of the UWB-IR systems. The transmission and the receiver template waveforms are the keys for the extension of the Friis transmission formula for the UWB- IR systems [6], [7]. Experimental investigations are done for different types of the antenn. II. THEORY A. Transmission Signal Analysis for UWB-IR The Friis transmission formula [1] h been widely used to evaluate the link budget for the narrowband LOS channels. The Friis transmission gain G Friis (f) is defined G Friis (f) = P r(f) P t (f), (1) = G f (f, d)g r (f, Ω r )G t (f, Ω t )η p (f), where P t (f) and P r (f) respectively are the input power to the transmitter (Tx) antenna and the output power from the receiver (Rx) antenna, G t (f, Ω t ) and G r (f, Ω r ), respectively and G f,d (f) is the free space propagation gain and η p (f) is the polarization matching efficiency. The free space propagation gain can be written ( ) 2 λ G f (f, d) =, (2) 4πd where λ = c/f is the wavelength, c is the velocity of light, f is the operating frequency and d is the separation between Tx and Rx antenn. It is noted, however, that Eq. (1) is satisfied only at some frequency, and is not directly applicable to UWB-IR systems. The formula shall be extended to take into account the transmitted waveform, its distortion due to the antenn, the channel and the correlation receiver [6], [7]. Free space channel response including the antenn is obtained by using the extension of Friis transmission formula H c (f) = H f (f, d)h r (f, Ω r ) H t (f, Ω t ), (3) where the free space transfer function H f (f, d) can be written H f (f, d) = λ exp( jkd), (4) 4πd k = 2π/λ is the propagation constant and effective gain of Tx and Rx antenn apply H a (f, Ω a ) (a = r or t) is a complex transfer function vector of the antenna relative to the isotropic antenna towards the Ω a = (θ a, ϕ a ) direction, i.e. H a (f, Ω a ) = H a (f, θ a, ϕ a ) (5) = ˆθ a H aθ (f, θ a, ϕ a ) + ˆϕ a H aϕ (f, θ a, ϕ a ),

2 Proceedings of APCC28 copyright 28 IEICE 8 SB 83 Fig. 1. Block diagram of transmission system model for UWB-IR signal. G f,d (f) is the free space propagation gain and and which h the relation 1 4π 2π π H a (f, θ a, ϕ a ) 2 sin θdθdϕ = η a, (6) where η a is the antenna efficiency, so that the value is normalized by that for isotropic antenna. Unit vectors ˆθ a, ˆϕ a express the polarization and are defined with respect to the local polar coordinates of the antenn. The following relations can be eily derived ˆθ r = ˆθ t, (7) ˆϕ r = ˆϕ t. (8) The spectral density of the receiver input V r (f) is given by V r (f) = H c (f)v t (f), (9) where V t (f) is the spectral density of the transmitted waveform. B. Received Signal Correlation Receiver Let us consider a correlation receiver shown in Fig. 1. The output SNR is dependent on the choice of the template waveform. The correlator output v o (τ) is therefore expressed v o (τ) = v r (t)h w (t τ)dt, (1) where v r (t) is the receiver input waveform which is the inverse Fourier transform of Eq. (9), h w (t) is the template waveform and τ corresponds to the timing of the template waveform. The optimum timing τ o is chosen Hereafter h w (t) is normalized τ o = arg max v o (τ). (11) τ h w (t) 2 dt = 2B, (12) where B is the signal bandwidth, so that the output noise power is a constant N B, where N o is the power spectral density 2 of AWGN. Under the constraint of Eq. (12), h wm (t) maximizes v o (τ o ) when h wm (t) is a time-reversed and scaled version of v r (t), i.e. 2Bvr (τ o t) h wm (t) =, (13) v r(t) 2 dt where τ o is usually chosen so that h wm (t) = for t < to satisfy the causality. h wm (t) is called the received signal template waveform hereafter. It is noted that the link budget evaluation is identical to that in [7] when h wm (t) is used the receiver template. C. Isotropic Correlation Receiver It is obvious from Eq. (13) that the received signal template waveform is not the simple time-reversed version of the transmitted waveform, but including the frequency characteristics of the antenn and the free space propagation. Therefore, it is not always feible to adapt the template waveform to the angulardependent antenna characteristics, since the waveform shall be generated at the clock rate of tens of gigahertz. Therefore, we consider a canonical template waveform h wc (t). In this paper we have chosen h wc (t) that is optimum for the isotropic and the constant gain antenn, i.e. 2Bvr-iso (τ o t) h wc (t) =, (14) v r-iso(t) 2 dt where the receiver input voltage for the ce of isotropic antenn used in both sides v r-iso (t) can be written v r-iso (t) = H f (f)v t (f) exp(j2πft)df (15) D. Transmission Gain The transmission gain in this paper is defined the peak amplitude of the correlator output with the considered antenn normalized by that with the isotropic antenn. Due to the normalization of template waveforms in Eqs. (13) and (14), this gain value represents the gain of signal-to-noise ratio. Therefore, the transmission gain of the received signal template ce G wm can be written G wm = v r(t)h wm (t τ)dt v r-iso(t)h wc (t τ)dt. (16) Similarly, the transmission gain of the isotropic template ce G wc can be written G wc = v r(t)h wc (t τ)dt v r-iso(t)h wc (t τ)dt. (17) The difference between the transmission gain of the received signal and the isotropic template ces indicates the distortion quantity of the waveform. Different from the original Friis transmission formula, the optimum transmission gain of UWB signal can not be simply expressed by the product of antenna indices. III. EXPERIMENTAL EVALUATION OF UWB CHANNELS In this section, the LOS links with the different kinds of the UWB-IR antenn are evaluated bed on the previous section. A. Transmitted Waveform The effect of the waveform distortion is more obvious when the bandwidth is wider. We considered the impulse radio signal that fully covers the FCC band [8], i.e., GHz. The center frequency and the bandwidth were therefore set to be f = 6.85 GHz and f b = 7.5 GHz, respectively. The transmitted waveform sumed in the simulation w a single ASK pulse with the carrier frequency f. To satisfy the bandwidth requirement of f b, the pulse length w set

3 Proceedings of APCC28 copyright 28 IEICE 8 SB 83 Amplitude Time (ns) Fig. 2. Transmitted waveform of UWB-IR signal. TABLE I EXPERIMENTAL SETUP PARAMETERS. Parameter Value Frequency range 3 GHz to 11 GHz Number of frequency points 161 Dynamic range 8 db Tx antenna height 1.75 m Rx antenna height 1.75 m Distance between Tx and Rx 1 m Rx rotation range to 36 Rx rotation step 5 Rx rotation cut E- or H-plane to be 2/f b. Then the signal w band-limited by a Nyquist roll-off filter with roll-off factor α = (rectangular window) and psband (f f b /2, f + f b /2). Figure 2 shows this transmitted pulse waveform. The frequency spectrum is given { [ ] sinc 2(f f) V t (f) = f b f f < f b 2. (18) otherwise B. Experimental Setup and Meurement Model The UWB-IR radio channel transfer function w meured S 21 in frequency domain by using a vector network analyzer (VNA) in an anechoic chamber. The VNA w operated in the response meurement mode, where Port-1 w the Tx port and Port-2 w the Rx port, respectively. Both Tx and Rx antenn were fixed at the height of 1.75 m and separated by 1 m. We used a biconical antenna the Tx antenna. We have chosen this antenna for ee of the fabrication, well its low distortion property. The geometry of the antenna is shown in Fig. 3. The upper cone is connected to the center conductor of a coaxial line while the lower cone is connected to the shield conductor. The maximum diameter is 65.3 mm and the length is 37 mm. We changed only the Rx antenn to compare the transmission gain properties. The experimental parameters are listed in Table I. It is noted that the calibration of VNA is done at the connectors of the cables to be connected to the antenn. Therefore, all the impairments of the antenna characteristics are included in the meurement results. C. Data Processing The waveform transmission w simulated by using V t (f) defined in Sec. 2.1, H c (f) meured in Sec. 3.2 and the correlation receiver presented in Sec. 2.2 and 2.3. As the template waveforms, we considered the received signal template waveform h wm (t) which w optimized for each transmission channel setup, i.e. antenn and their pointing directions, well the isotropic template waveform h wc (t) designed for the isotropic antenn and independent of antenna setup. Although the absolute transmission gain can be derived by using the proposed approach, the UWB-IR transmission gain presented in the next section w normalized by the transmission gain of the isotropic antenn at both Tx and Rx sides defined in Sec D. Results In this section, the two typical broadband antenn are used in the meurement for the link budget evaluation. One is the biconical antenna, which is with low dispersion. The other is the log periodic dipole antenna (LPDA), which is highly dispersive. 1) Biconical Antenna: First, the same biconical antenn were used both at Tx and Rx sides. The gain and group delay of antenna at, 3 and 6 pointing angles are shown in Figs. 4 and 5, respectively. Figure 6 shows the normalized UWB-IR transmission gain a function of the antenna pointing angle in the E-plane. Well-known 8-shaped patterns were obtained. Two template waveforms were used for comparison, and the difference w rather small. The phe center of the biconical antenna is the feed point and it h theoretically the frequency independent gain at the broadside direction, and that is why the waveform distortion effect is small compared with the isotropic template. 2) Log-Periodic Dipole Antenna: A log-periodic dipole antenna (LPDA) is also used at broadband. It also h a frequencyindependent gain. Different from the biconical antenn, however, the dispersion characteristic of the LPDA is rather big, since the phe center changes with frequency due to the resonance of the dipole elements [9]. We used a commercial LPDA, Watkins Johnson s AR7-15A, shown in Fig. 7. The antenna h been designed to operate in the range of 1 to 12.4 GHz. Figures 8 and 9 show the gain and group delay of antenna at, 3 and 6 pointing angles, respectively. Figure 1 shows the UWB-IR transmission gain pattern for biconical LPDA link in E-plane. As is known, an LPDA is uni-directional and its gain is higher than that of a biconical antenna. The degradation of the transmission gain is observed when the canonical isotropic template is used, since the waveform dispersion is obvious. IV. DISCUSSION From these results, the UWB-IR transmission gain, using both the eeereceived signal and the isotropic template waveforms, gives us the quantitative meurement of the link budget. Since we have chosen the broadband antenn, the trend of the narrowband gain is reflected in the UWB-IR transmission gain. Another issue is the distortion of the waveform. The difference between the optimum and the isotropic templates is the meurement of the waveform distortion. It is obvious that the use of LPDA caused the biggest distortion among the sample antenn, while its transmission gain characteristic is significantly large.

4 Proceedings of APCC28 copyright 28 IEICE 8 SB cm 8 x cm Fig. 3. Biconical antenna structure and dimensions. Group delay (degree/hz) pointing angle 3 pointing angle 6 pointing angle Fig. 5. UWB-IR transmission gain for biconical biconical link. Gain (db) Received Signal Template pointing angle 35 3 pointing angle 6 pointing angle Fig. 4. UWB-IR transmission gain for biconical biconical link. V. CONCLUSION This paper h presented how to evaluate the of UWB- IR transmission gain, which includes the transmit waveform, the antenn, the free space propagation, and the correlation receiver. By using the definition, we have evaluated two types of the broadband antenn. This scheme may be effective especially to evaluate the deployable antenna with non-ideal frequency characteristics of return loss and directivity, the overall performance can be evaluated only by the term of the UWB-IR transmission gain. Note that the formulation presented in [7] is a special ce for the optimum template waveform in this paper. Therefore, the IEEE a path loss model presented in [12] is also a special ce of the formulation presented in this paper, by considering the rectangular frequency spectrum, the frequency independent isotropic antenna and the received signal template. This approach can be eily extended to the multipath environment well. There are two key issues: One is the focus of this paper, i.e. the antenna transfer function is angulardependent. The other one is that the propagation channel is also angular dependent at both Tx and Rx. In the context of Isotropic Template Fig. 6. UWB-IR transmission gain for biconical biconical link. UWB-IR, just a few studies have been done with respect to the former pect, and almost none for the latter. Although Ref. [5] treated both antenna and multipath channels, it only considered the impulse response of the channel. However, the impulse response itself is influenced by the antenn, and the formulation for multipath environment is not sufficient. The authors are working on the double-directional modeling of the UWB-IR channel in parallel to this study [13], [14]. Due to this background, we are planning to treat the multipath environment by using this approach in future. ACKNOWLEDGEMENT The authors would like to thank Mr. Kimio Sakurai from Tokyo Institute of Technology for his help in the experiments, and Prof. Koichi Ito and Dr. Kazuyuki Saito of Chiba University for letting us use their LPDA.

5 Proceedings of APCC28 copyright 28 IEICE 8 SB x 1 5 Fig. 7. Log-periodic dipole antenna (Watkins Johnson AR7-15A). 1 Group delay (degree/hz) pointing angle.8 3 pointing angle 6 pointing angle Fig. 9. UWB-IR transmission gain for biconical LPDA link. Gain (db) Received Signal Template Isotropic Template pointing angle 2 3 pointing angle 6 pointing angle Fig. 8. UWB-IR transmission gain for biconical LPDA link. REFERENCES [1] H.T. Friis, A note on a simple transmission formula, Proc. IRE, vol. 34, no. 5, pp , May [2] United States of America, Path loss calculations for ultra-wideband signals in indoor environments, ITU-R Document 3K/3-E, pp. 1 14, Nov. 23. [3] J. McLean, H. Foltz, and R. Sutton, The quantitative sessment of the effects of dissipative loading on the time-domain performance of antenn, Proc. 6th European Conf. Wireless Tech. Munich, Germany, pp , Oct. 23. [4] A.H. Mohammadian, A. Rajkotia, and S.S. Soliman, Characterization of UWB transmit-receive antenna system, Proc. IEEE Conf. Ultra Wideband Syst. Tech. (UWBST) 23, Reston, USA, pp , Nov. 23. [5] A. Sibille, A Framework for Analysis of Antenna Effect in UWB Communications, Proc. 25 Spring IEEE Veh. Tech. Conf. (VTC), Tex, USA, vol. 1, pp , June 25. [6] J. Takada, S. Promwong and W. Hachitani, Extension of Friis transmission formula for ultra-wideband systems, IEICE Tech. Rep., WBS23-8/MW23-2, May 23. [7] S. Promwong, and J. Takada, Free space link budget estimation scheme for ultra wideband impulse radio with imperfect antenn, IEICE Electronics Express, vol. 1, no. 7, pp , July 24. [8] Radio Frequency Devices, Part 15, Federal Communications Commission Rules, Dec. 23. Fig. 1. UWB-IR transmission gain for biconical LPDA link. [9] H.G. Schantz, Dispersion and UWB antenn, Proc. 24 Int. Workshop Ultra Wideband Syst. / Conf. Ultra Wideband Syst. Tech. (Joint UWBST & IWUWBS 24), Kyoto, Japan, May 24. [1] S. Promwong, W. Hachitani, and J. Takada, Experimental evaluation scheme of UWB antenna performance, Tech. on Instrumentation and Meurements, IEE Japan, IM-3-35, June 23. [11] S. Promwong, W. Hachitani, and J. Takada, Free Space Link Budget Evaluation of UWB-IR Systems, Proc. 24 Int. Workshop Ultra Wideband Syst. / Conf. Ultra Wideband Syst. Tech. (Joint UWBST & IWUWBS 24), Kyoto, Japan, pp , May 24. [12] J. Foerster, Channel modeling sub-committee report final, IEEE P /368r5-SG3a, Nov. 22. [13] J. Takada, K. Haneda and H. Tsuchiya, Joint DOA/DOD/DTOA Estimation System for UWB double directional Channel Modeling, in S. Changran (eds.), Advance in Direction of Arrival Estimation, pp , Artech House, Norwood, MA, USA, 26. [14] K. Haneda, J. Takada and T. Kobayhi, Double Directional Ultra Wideband Channel Characterization in a Line-of-Sight Home Environment, IEICE Trans. Fundamentals, vol. E88-A, no. 9, pp , Sept. 25.