PROPAGATION OF UWB SIGNAL OVER CONVEX SURFACE MEASUREMENTS AND SIMULATIONS

8 Poznańskie Warsztaty Telekomunikacyjne Poznań grudnia 8 PROPAGATION OF UWB SIGNAL OVER CONVEX SURFACE MEASUREMENTS AND SIMULATIONS Piotr Górniak, Wojciech Bandurski, Piotr Rydlichowski, Paweł Szynkarek Abstract The paper deals with frequency domain (FD) modelling of diffraction of a signal, by conducting convex objects and its verification through the measurements. The proposed FD model, which is under the test in this paper, was worked out by means of Uniform Theory of Diffraction (UTD) formulated in the frequency domain. The experimental verification of the model has been proposed. The measurements of amplitude of the received signal were compared with calculation based on frequency domain UTD model. Measurements were performed indoors the building. Conducting convex object under the test was a metallic cylinder. The purpose of the experimental verification of the FD model is the ultra wide band - UWB channel modelling and prediction of electromagnetic pulse wave propagation in a given scenario. Index Terms UTD Uniform Theory of Diffraction, UWB Ultra Wide Band, TD Time Domain, FD Frequency Domain, PSD Power Spectral Density. I. INTRODUCTION The UWB communication has received a great deal of attention in recent years [5-7]. The large bandwidth of UWB signals offers rapid increase in data transmission speed on the one hand, and greater accuracy of positioning and object detection on the other hand. However, this large bandwidth of UWB signals introduces some problems nonexistent or negligible in narrowband data transmission. The distortion of an UWB pulse is one such problem. Since the propagation loss is frequency dependent, the frequency spectrum of the transmitted UWB signal is significantly changed during propagation. This phenomenon has been discussed in a number of papers, e.g. [8-]. Pulse distortion is mainly caused by scattering objects such as walls, edges and rounded surfaces []. The propagation between scattering objects does not affect pulse shapes, but rather involves pulse delays []. The scattering object, which we investigate, is an obstacle with a rounded shape, as rounded pillar, which are the objects of measurements presented in this article. Such a scattering object has its own frequency response and equivalent impulse response. In the case of UWB propagation, using the impulse response of a scattering object is more convenient for analyzing the propagation of the transmitted UWB pulse. If the impulse response of the scattering object is known, the time domain characteristics of the distorted UWB pulse can be found through an operation of convolution. In particular, time domain results can give more insight in baseband data transmission, which is an option in an UWB communication system. It is also helpful in determining time delay parameters of the channel in such areas as synchronization, positioning and detection. The impulse response of a shadowing conducting rounded D object was derived by the authors of this article and was presented in []. After working out the time domain deterministic model of diffraction on convex D conducting object the key task to do is to verify this model with the reality. An obvious way of performing it is making relevant measurements. The main goal of the measurements is to verify the UTD frequency response of a particular convex object (cylinder), with theoretical model. In the case when measurements confirm calculation results in frequency domain, the time domain model will be also experimentally verified, because the TD and FD models are related to each other through the frequency-time transforms. The paper is organized as follows. In Section we describe the measurements. In Section 3 we show the transformations which we used on the measurements results in order to get the desired comparison. We also signify the limitations of the measurements. Section 4 gives the measurements results. We make the comparison of the measurements results with he results calculated with the usage of the deterministic model. We present the summary and conclusions in Section 5. II. THE MEASUREMENTS SETUP The scenario of our measurements was the following. UWB signal were propagated between two antennas which were shadowed by one metallic cylinder. For the place of the measurements we chose the downstairs hall of the Department of Electronics and Telecommunication of Poznań University of Technology. The geometrical parameters of the cylinder followed the parameters of the pillars in the hall. In order to make the measurements we collected all necessary devices. The list of the devices used by us is as follows: scalar spectrum analyzer AGILENT E447B with the 9 khz to 6.5 GHz frequency range and the 3 db ultra wide band amplifier, which were borrowed from ERA Company, arbitrary waveform generator AWG 7 borrowed from TEKTRONIX Company through the TESPOL Company, two directional panel antennas with gain 4 db, and operating frequency range 5.-5.9 GHz, manufactured by INTERLINE Company from Wroclaw

and a set of MRC-4 connectors for the 5GHz band. The block diagrams of the measurements setup are shown in Fig. and. The first diagram is related to the antennas Figure. Antennas measurements. measurement without cylinder between them. The distance between the antennas was. m. This distance was established in the way that the Figure 3a. The antennas measurement setup from diagram in Fig. Figure. Cylinder measurements. measurements could be done in radiation zone of the transmitting antenna. The heights of the positions of the transmitting and receiving antenna were the same, to ensure the D propagation case. The heights of the antennas positions were also determined by one path propagation condition, which was dependent from the distance between the antennas and their radiation patterns. The power spectral density (PSD) of received signal was captured on the screen of the spectrum analyzer. The measurements were made for different angles (positions) of transmitting antenna. We have to do more antenna measurements, because we were not able to measure accurate angle of radiation direction. Because of it we had to examine the half power settings of the antennas, and then make a comparison with a radiation pattern of the antennas given by their manufacturers. The second diagram is related to the case of the metallic cylinder between the antennas. The radius of the cylinder was cm. The distances from the transmitting antenna to the cylinder and from the cylinder to the receiving antenna were established to.6 m and. m respectively. These distances fulfilled the radiation zone requirements. As in the case of antennas measurementa, the heights of the antennas positions ensure the D propagation conditions. We tried to set a desirable placement of the antennas with respect to the cylinder, which meant that the symmetry axes of the antennas and the symmetry axis of the cylinder were supposed to be the same. The illustration of the measurement setup, used devices, cylinder and the measurements scenario are shown in Fig 3. Figure 3b. The measurement setup (cylinder measurements) from diagram in Fig. The transmitted UWB signal was created by the AWG7 generator in compliance with the UWB WiMedia standard []. We used RFXpress software. The center frequency of the signal was 5.5 GHz. The band of the signal was 5 MHz wide. The shape and the spectrum of generated UWB pulse is shown in Fig. 4. Figure 4a.The shape of the generated UWB pulse in time domain.

IV. RESULTS OF THE MEASUREMENTS In this section we compare performed frequency domain measurements with the data calculated through the expression formulated using UTD directed to convex objects. This formula is given by (3), and is the frequency domain equivalent of the UWB time domain model of a convex obstacle [], which is under test in this paper. Figure 4b.The shape of the generated UWB pulse in frequency domain. III. THE MEASUREMENTS The goal of the measurements was to find the D frequency response of the cylinder H(ω). However with the usage of the available spectrum analyzer we could only measure H(ω). The phase of H(ω) couldn t been obtained. We derived H(ω) in the following steps: The first step was making the measurements using the scheme from Fig.. The next step we perform the measurements according to the diagram from Fig.. After finalizing the measurements we made the transformations on antennas measurement results, Fig.. The goal of these transformations was to find the products of the PSD of the transmitted signal and the squared spectrums (the square of the amplitude part of the transmittance) of antennas, connectors and squared spectrums of the propagation path excluding the air path. This was achieved by dividing the PSDs captured by the spectrum analyzer by theoretical squared spectrum of the air path, as in (). S( ω, S D = () S where φ relates to the transmitting antenna angle, S (ω, is the PSD captured by the spectrum analyzer (each related to a given transmitting antenna position) when scheme from Fig. is applied and S A (ω, is the squared spectrum of the air path of first measurements scenario. After deriving S D (ω, functions for separate antenna positions, related to a specific φ, we could obtain H(ω) by using measurement results gathered from applying the scheme from Fig.. The measured PSD were divided by the product of a squared spectrum of the air path and properly chosen S D (ω,, as in (). The result was multiplied by the factor S (ω). H where ( ω) = S A A S S S φ( θ = θ D φmax ) )) S φ( θ = θ )) (a) S ( ) φmax ) S ω = (b) S φ( θ = θ )) H ( ω) = H θ ) + H θ ) A A A ( X ( θ)) ) π j 4 jβθr F d * H (, ) = ( ) A ω θ m e e + q ξd ( θ) (3) β ξ d ( θ) π We can see, that H A (ω) comprises two ray UTD components. The goal to reach is to compare H(ω) and H A (ω). The results of the measurements are assigned to two main groups. The first of these groups are the antenna measurements. The results of the measurements are shown in Fig. 5, 6 and 7. - - -3-4 -5-6 -7-8.4...8.6.4.. a) 5. 5.3 5.4 5.5 5.6 5.7 5.8 pos pos b) 5. 5.3 5.4 5.5 5.6 5.7 5.8 f[ghz] pos pos and S A (ω, is the squared spectrum of the air path of second measurements scenario related to Fig. and S (ω,φ max ) is the maximum PSD from (). 3

c) Average attenuation [db]..9.8.7.6.5.4.3... 5.4 5.45 5.5 5.55 5.6 f[ghz] pos 6 pos d) - - -3-4 -5-6 -7 3 4 5 6 7 8 9 Antenna position number Average attenuation Figure 6. The averaged PSD of the received signal with respect to maximum averaged PSD with respect to transmitting antenna position...9.8.7.6.5.4.3... 5.4 5.4 5.44 5.46 5.48 5.5 5.5 5.54 5.56 5.58 5.6 f[ghz] pos 9 pos Figure 5. PSDs of the received signal for antenna measurements for position and (pos, pos ) in dbm (a) and in mw (b), for positions and 6 (pos, pos 6) (c), position and 9 (pos, pos 9) (d) in mw. From Fig. 6 we can see that the half power angle is passed in between 9th and th position of the transmitting antenna. Keeping in mind this, we can estimate the position of the transmitting antenna which relates to θ =θ from Fig.. For the parameters of placement of the antennas with respect to the cylinder described in section II we can calculate the angles θ.3 rad and φ(θ ),6 rad 9,4. We can estimate then, that φ(θ ),6 rad 9,4 relates to the 6th or 7th position of the antenna. Standard deviation of average attenuation (Fig. 7), confirms that antennas can be used with good results for transmission of UWB signal in 5 GHz band. This may be concluded from sufficiently small variety of the standard deviation value for separate transmitting antenna positions. This signifies that for all radiation directions of the antennas the transmitted UWB pulse would be distorted by the antenna in the same manner. The plot of the standard deviation of average attenuation suggests also, that for antenna measurements one path condition was fulfilled.,5,4,3,, Standard deviation of average attenuation [db] 3 4 5 6 7 8 9 Antenna position number Stand. dev. Figure 7. Standard deviation from the normalized averaged PSD of the received signal with respect to transmitting antenna position The second measurement results group concerns the cylinder measurements. In Fig. 8 and 9 there are compared the squared spectrums which are calculated by using () and (3)....8.6.4. a) 5.5 5.35 5.45 5.55 5.65 5.75. m dev. m dev.3 m dev.4 m dev measurement 4

...8.6.4. b) 5.5 5.35 5.45 5.55 5.65 5.75. m dev. m dev.3 m dev.4 m dev measurement Figure 8 Comparison of H A (ω) with H(ω) (a) and with averaged H(ω) (b) for assumption of occurrence of the rays related to the 6th position of transmitting antenna....8.6.4...8.6.4. a) 5.5 5.35 5.45 5.55 5.65 5.75.. m dev. m dev.3 m dev.4 m dev measurement b) 5.5 5.35 5.45 5.55 5.65 5.75. m dev. m dev.3 m dev.4 m dev measurement Figure 9 Comparison of H A (ω) with H(ω) (a) and with averaged H(ω) (b) for assumption of occurrence of the rays related to the 7th position of transmitting antenna. Fig. 8 and 9 show the comparisons of the H A (ω) calculated from UTD theory - formula (3), with measurements of squared amplitude spectrum of the transfer function containing cylinder H(ω), averaged and not averaged. The function H(ω) is obtained from formulas () and (). In Fig. 8 and 9 on each plot there are 5 squared amplitude spectrums H A (ω) obtained from formula (3) and one from measurements H(ω). The first curve from the top on each plot was calculated by means of formula (3) with the following assumptions: the symmetry axis of antennas setup and symmetry axis of cylinder are collinear (see Fig.), the distances between transmitter, cylinder and receiver are respectively cm and 6 cm. The next 4 curves on each plot were obtained with assumption that symmetry axes of transmitter was moved down with respect to the receiver and cylinder symmetry axes. The values of the described above movements (position deviations) were set by us to. m,.4 m,.3 m and.4m respectively. One can notice that our measurements confirm the calculations results, with admissible error, by the curve with position deviation equal to.4m (fifth from the top). This fact may be explained as a mistake, done by us, in positioning of the transmitting antenna with respect to common symmetry axis of the cylinder and receiving antenna. V. CONCLUSIONS. The goal of the paper was to verify the UWB diffraction model of convex object (conducting cylinder) in frequency domain experimentally by performing the relevant measurements. We obtained sufficient agreement of the theoretical model results with the measurements. The measurement error was in admissible range. The irregularities of the measured characteristic may result from non-uniform value of the cylinder radius and its dielectric constants and from the possible occurrence of signal echos coming to the receiving antenna from the other paths than the two considered by us. The second cause may be other differences between the noises which occurred during the two antennas and cylinder measurements. Unfortunately we hadn t a vector analyzer, so we couldn t perform the phase measurements, which would be the supplement to H(ω) results. The knowledge of amplitude and phase characteristics will permits for creating the transfer function H(ω) of the channel containing the cylinder. Having this in mind we are now working on calculating of the phase characteristics of the cylinder transfer function from the H(ω) of the cylinder what is possible in some cases []. The good agreement between H A (ω) with H(ω) is the sufficient confirmation of the thesis, that UTD theory is a good choice, when we want to investigate the propagation of the UWB electromagnetic wave on convex objects, and supposedly on other obstacles. This suggest, that the work which was done on deriving the UWB time domain model of diffraction on convex objects can be used for extending this model for other obstacles and other phenomena. We are also working on it. 5

REFERENCES [] P. Górniak, W. Bandurski, "Direct Time Domain Analysis of an UWB Pulse Distortion by Convex Objects with the Slope diffraction Included, IEEE Transactions on Antennas and Propagation, vol. 56, no. 9, September 8, pp. 336-344. [] Standard ECMA-368, nd edition, December 7 [3] P. H. Pathak, W. Burnside, R. Marhefka, A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface, IEEE Transactions on Antennas and Propagation, vol. 8, no. 5, September 98, pp. 63-64. [4] D. A. McNamara, C. W. I. Pistorius, Introduction to the uniform geometrical theory of diffraction, Artech House, Boston 99. [5] M.Z. Win, R.A. Scholtz, Impulse radio: How it works, IEEE Commun. Lett., Vol., pp. 36-38, Feb 998 [6] D. Porcino, W. Hirt, Ultra-wideband radio technology: potential and challenges ahead, IEEE Commun. Mag., pp. -, July 3 [7] A. F. Molisch, Ultra-wideband propagation channels theory, measurement and modeling, IEEE Transactions on Vehicular Technology, vol. 54, no. 5, September 5, pp. 58-545 [8] R. C. Qiu, I. -T. Lu, Wideband wireless multipath channel modeling with path frequency dependence, Conference Record, International Conference on Converging Technologies for Tomorrow s Applications, 3-7 Jun 996, pp 77-8 vol. [9] R. C. Qiu, A study of the ultra-wideband wireless propagation channel and optimum UWB receiver design, IEEE Journal on Selected Areas in Communications, vol., no. 9, December, pp. 68-637 [] R. C. Qiu, A Generalized Time Domain Multipath Channel and its Application in Ultra-Wideband (UWB) Wireless Optimal Receiver Design - Part III: System Performance Analysis, IEEE Transactions on Wireless Communications, vol. 5, no., October 6, pp. 685-695 [] R. C. Qiu, Chenming Zhou, Qingchong Liu, Physics-based pulse distortion for ultra-wideband signals, IEEE Transactions on Vehicular Technology, vol. 54, no. 5, September 5, pp. 546-555 [] J. Yang, J. Jinhwan, T. P. Sarkar, Reconstructing a Nonminimum Phase Response from the Far-Field Power Pattern of an Electromagnetic system, IEEE Transactions on Antennas and Propagation, vol. 53, no., February 5, pp. 833-84 AUTHORS NOTE Piotr Górniak, Wojciech Bandurski, Piotr Rydlichowski Poznań University of Technology, Department of Electronics and Telecommunications, Paweł Szynkarek ERA Company. 6