Wave propagation in curved tunnels: modelling and ...

Wave propagation in curved tunnels: modelling and measurements D. Didascalou, F. K uchen and W. Wiesbeck

Institut fur Hochstfrequenztechnik und Elektronik (IHE), Universitat Karlsruhe (TH) Kaiserstr. 12, 76128 Karlsruhe (Germany) Tel. +49-721-608-6256, Fax +49-721-69 18 65, E-mail [email protected] Abstract | Electromagnetic wave propagation in curved tunnels is treated in this paper. First, a novel deterministic modelling technique, based on stochastic ray launching (Monte-Carlo method) combined with ray density normalization is introduced, which is applicable to arbitrary tunnel geometries. The inclusion of moving vehicles inside tunnels can be considered, which allows investigating the in uence of trac on the propagation characteristics. The approach is validated by various measurements at 120GHz in scaled tunnel models. I. Introduction

Recently, several ray-based methods have been proposed to model the electromagnetic wave propagation in tunnels. Irrespective of their ray tracing technique (ray launching [1], imaging [2] or a combination of both [3]), they all have in common that they can only treat re ections at plane boundaries. As a consequence, either they only look at rectangular (piecewise) straight tunnel sections, or they tessellate more complex geometries into multiple plane facets. The proposed modelling technique is not restricted to plane surfaces so that e.g. curved tunnels of arched shape can be dealt with directly. It is based on Geometrical Optics (GO) [4] and contrary to classical ray tracing, where the one ray representing a locally plane wave front is searched, the new method requires multiple representatives of each physical electromagnetic wave at a time. The contribution of each ray to the total eldstrength level at the receiver is determined by the proposed ray density normalization. For the latter, an important prerequisite is a dense equal spatial distribution of the traced rays, which is accomplished by a Monte-Carlo ray launching. The model also handles moving vehicles inside of tunnel structures. Because of its ray nature, the prediction of broadband channel parameters like delay spread and doppler spread becomes directly possible. If analytically describable boundaries, like sections of elliptical toruses etc., are used to describe the geometry of the tunnel, the modelling becomes reasonably fast so that sets of time series can be generated automatically. These sets may then be used to evaluate the performance of dierent transmission schemes. The modelling approach has been veri ed theoretically at several ca-

nonical examples [5], [6]. In order to verify the model experimentally, comparisons with measurements at different scaled model tunnels at 120GHz are presented. All together, they show very good agreement with the prediction. II. Stochastic ray launching with ray density normalization

The employed ray-optical method is based on ray launching. In ray launching, a large number of rays is sent out from the transmitter in arbitrary directions. Each ray is then traced in space and wave propagation is calculated according to Geometrical Optics (GO) [4]. At the receiver, all incoming rays are combined coherently in order to determine the overall reception level. The decision, whether a ray hits a receiver or not is actually one of the biggest problems in ray launching. The two known methods to solve this problem are discrete ray tubes [7] or reception spheres [8]. Although discrete ray tubes perform well in urban or indoor environments, which are constituted by plane surfaces, they fail at curved geometries. This is because the delimitation of adjacent rays becomes ambiguous after re ection from a curved surface. Therefore only reception spheres are considered in the following. The diculty with the classical approach of reception spheres is the determination of their size: If the size is too small, only a few rays reach the receiver and the results are inaccurate because important propagation paths may not have been considered. On the other hand, if the size is too big, several physically \identical rays" reach the receiver so that the results become faulty without a correct normalization. This multiple ray problem is illustrated in Fig. 1, where receiver 1 is e.g. reached by multiple direct rays. In reality, there is only one direct ray representing the direct propagation path. Additionally Fig. 1 shows that the number of registered rays is also depending on the distance from the transmitter assuming constant receiver sizes. A means to overcome this problem is given by the proposed ray density normalization (RDN). Here, each discrete ray carries the density information along its path, so that the theoretical number of identical rays hitting a reception sphere can be calculated by simply multiplying the ray density with the area of the sphere. This number

receiver 2 receiver 1 transmitter

Fig. 1. The multiple ray problem using reception spheres in ray launching

is used to normalize the contribution of each ray to the total eldstrength. The method is also valid in curved geometry|contrary to the hitherto usual approach [8]. Prerequisites of the RDN are a high number of rays and their homogeneous distribution in space, both achievable by a stochastic (Monte Carlo) generation of the ray directions. The propagation itself and the calculation of the ray densities are based on GO. A detailed description of the calculation of the ray densities and the application of the RDN to ray tracing is given in [6].

placed in the center of the waveguide, the receivers are situated along the line center-to-outer-wall of the waveguide at 10m from the transmitter. Taking into account the ideal lossless surface of the corrugated waveguide, even rays with a high number of re ections are still contributing to the overall reception level. Therefore a sucient convergence of the ray-tracing is only possible with considerable computational eort. Despite this drawback, the very good agreement of the results validate the developed normalization. IV. Verification by measurements

To verify the RDN experimentally, measurements have been carried out at 120GHz in scaled model tunnels built of concrete and stoneware. A. Measurement setups Fig. 3 and 4 show the two measurement setups: transmitter: horn antenna

III. Theoretical validation in ideal corrugated cylindrical waveguide

In this section, the proposed modelling approach is compared to a theoretical \reference"-solution in an ideal geometry. To allow for curved boundaries, an ideal corrugated circular waveguide was chosen1. An ideal corrugated waveguide is a special waveguide with the re ection coecients Rp = Rs = ,1, which is e.g. used in microwave technology for power transmission. The reference-solution utilized in this geometry is based on fast mode decomposition [9]. Fig. 2 shows the com20

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Fig. 3. Measurement setup with concrete tube, diameter: 20cm, length: 1m, r  5, transmitter: horn antenna at tunnelentrance, receiver: wave-guide probe for 2D-scans at tunnelexit (resolution: 2mm2mm), f = 120GHz transmitter: horn antenna

mode decomposition ray density normalization

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parison of the two methods in a waveguide with radius 2m at f = 1GHz. An omnidirectional transmitter is 1 In a rectangular waveguide, image-theory and RDN deliver the same results [6]

receiver positions of waveguide probe

Fig. 4. Measurement setup with bent stoneware tube, angle of curvature: 45 , diameter: 20cm, length: 30cm, r  8, transmitter: horn antenna at tunnel-entrance, receiver: wave-guide probe for 2D-scans at tunnel-exit (resolution: 2mm2mm), f = 120GHz

A straight concrete tube with length of 1m and diameter of 20cm and a bent stoneware tube with angle of

curvature of 45, length of 30cm and diameter of 20cm. A vertically polarized horn antenna acts as transmitter at f = 120GHz. The receiver is a rectangular waveguide-probe, which can be displaced automatically to generate two dimensional (2D) scans with a resolution of 2mm2mm. The frequency of f = 120GHz in the scaled geometry is comparable to a frequency of 1{5GHz in real tunnels. The received power level was measured using a network analyzer. B. Comparisons of measurements and simulation For all simulations, 50 resp. 100 million rays are traced with up to 10 re ections. The permittivity of the concrete tube is taken to r = 5, the one of the stoneware bend to r = 8. The measured directional pattern of the horn antenna is considered in the simulations. The simulation time is between 1.5 to 5 hours on a HP C-series workstation with 240MHz clock rate. P/P0 (dB) 6

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represents the power level in free space at 1m distance from the transmitter. First, the straight concrete tube of Fig. 3 is examined. Fig. 5 shows the measured and simulated power level distribution (coherent analysis, vv-polarization) at the end of the tube for an eccentric transmitter position 5cm above the center at the tunnel entrance. The measurement and the simulation show almost identical results. Only in the lower regions of the gures small discrepancies occur, which might be due to a possible misalignment. Thereafter, a con guration with a road lane made of PVC (r  2:5) and a matchbox car (\London Sightseeing Bus") is used. The thickness of the lane is approx. 1cm. The vehicle resembles a rectangular box (length: 11.7cm, width: 3.6cm, height: 6.4cm, distance between lane and underbody of the car: 0.3cm) with various windows, whose dimensions are in the order of several wavelengths. Although the vehicle is only modelled as a oating metallic rectangular box, the measurement (Fig. 6(a)) and the simulation (Fig. 6(b)) are quite similar. The matchbox car is situated 5cm in front of the 0

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(b) Simulation at 120GHz Fig. 5. Measurement setup according to Fig. 3, transmitter 5cm above center, scanned area: 7171 points, resolution: 2mm

All results are normalized to a reference level P0 , which

(b) Simulation at 120GHz Fig. 6. Measurement setup according to Fig. 3 with PVC- oor (r  2:5) and square-like vehicle, centric transmitter position, scanned area: 8646 points, resolution: 2mm

tunnel exit so that a distinct shadow is visible in the analysis. In both gures the circular structures coincide as well as the horizontal stripes of high resp. low reception levels. Also the boundary condition for grazing incidence is visible at the surface of the lane, which

claims a minimum of the received power level. Finally, the bent stoneware tube of Fig. 4 is used as scaled model tunnel. The transmitter is situated at the entrance of the tube in an eccentric position 5cm from the center in the direction of the bend. Fig. 7 depicts the measurement and the simulation at the other end of the tunnel. The in uence of the relatively strong bend can be identi ed by the attening of the circular structure perpendicular to the direction of the bend. A simulation of the same scenario but without bend shows a shifted but more or less circular symmetrical pattern similar to that of Fig. 5. P/P (dB) 0 35 6 30 4

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(b) Simulation at 120GHz Fig. 7. Measurement setup according to Fig. 4, transmitter 5cm left of center, scanned area: 7171 points, resolution: 2mm

The great tolerances in the geometry of the bent tube, which is originally intended for the use in sewers, make the comparison quite dicult: the bend is neither

circular, nor constant over the whole length. Nevertheless, the simulation (Fig. 7(b)), which assumes piecewise constant and circular bends and the measurement (Fig. 7(a)) show a good agreement over a large area. V. Conclusions

A novel stochastic ray launching with ray density normalization is presented, which allows the prediction of the signal level in curved tunnels of dierent crosssections and shape. The method is veri ed theoretically and by various measurements at 120GHz using scaled tunnel models. Altogether, the simulation results are validated quite well by the measurements. Thus the proposed modelling approach is applicable for the simulation of wave propagation in curved tunnels. References [1] Y.P. Zhang, Y. Hwang, and R.G. Kouyoumjian, \Ray-optical prediction of radio-wave propagation characteristics in tunnel environments{part 2: Analysis and measurements," IEEE Transactions on Antennas and Propagation, vol. 46, no. 9, pp. 1337{1345, 1998. [2] P. Mariage, M. Lienard, and P. Degauque, \Theoretical and experimental approach of the propagation of high frequency waves in road tunnels," IEEE Transactions on Antennas and Propagation, vol. 42, no. 1, pp. 75{81, 1994. [3] Shin-Hon Chen and Shyh-Kang Jeng, \SBR image approach for radio wave propagation in tunnels with and without trac," IEEE Transactions on Vehicular Technology, vol. 45, no. 3, pp. 570{578, 1996. [4] Constantine Balanis, Advanced Engineering Electromagnetics, John Wiley & Sons, New York, 1989. [5] D. Didascalou, N. Geng, and W. Wiesbeck, \Ray optical wave propagation modelling in curved tunnels," in URSI XXVIth General Assembly, Toronto, Canada, August 1999. [6] D. Didascalou, F. Kuchen, and W. Wiesbeck, \A novel normalization technique for ray-optical wave propagation modelling in arbitrary shaped tunnels (in German)," Frequenz, accepted for publication in 1999. [7] Dieter J. Cichon, Thomas Zwick, and Jaakko Lahteenmaki, \Ray optical indoor modeling in multi- oored buildings: simulations and measurements," in IEEE AP-S'95, Newport Beach, California, USA, June 1995, pp. 522{525. [8] Scott. Y. Seidl and Theodore S. Rappaport, \Site-speci c propagation prediction for wireless in-building personal communication system design," IEEE Transactions on Vehicular Technology, vol. 43, pp. 879{891, 1994. [9] G. Michel and M. Thumm, \Spectral domain techniques for eld pattern analysis and synthesis," in Surveys on Mathematics for Industry, Special Issue on Scienti c Computing in Electrical Engineering. to be published in 1999.