Fast Ray Tracing Propagation Prediction Model For Indoor Environments 1, 2
Chiya Saeidi1, Manouchehr Kamyab2, Azim Fard 3 Department of Electrical Engineering,Khajeh-Nasir-Toosi University of Technology, Tehran, Iran 3 Department of Engineering, Shahed University, Tehran, Iran
[email protected],
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Abstract A fast brute force ray tracing method employed to analyze indoor radio communication environment. To speed up the numerical calculation, several improved techniques are applied. The achieved overall enhancement, measured by verification of obtained results for three indoor case studies. Significant improvements observed in terms of calculation time and estimated field strength values have good agreement with recorded measurements. 1.
and ϕ (∆θ and ∆ϕ) in local spherical coordinates centered at the antenna as shown in Figure 1.
INTRODUCTION
The proficient evaluation, design and installation of a radio network in indoor environment needs an accurate characterization of the radio propagation channel. Ray tracing technique has been verified to be promising for indoor radio propagation modeling by many researchers [1-6]. There are two types of ray tracing methods: one is called the “image” method, and the other is the “brute force” ray tracing method. The first one is well suited for analysis of radio propagation associated with geometries of low complexity involving small number of reflections. The brute force method shoots a bundle of ray tubes, which may or may not reach the receiver. When the indoor environment is large and complex, second one is preferable, however, it will take a lot of CPU time to calculate the propagation characteristics. It is therefore important to reduction the prediction time. This paper presents a fast three-dimensional brute force ray tracing model, based on geometrical optics (GO), which integrates several intelligent techniques, including geometrical simplification and approximation, to improve calculation time without losing accuracy. 2.
distance 1m from the transmitter [2]. Therefore, in the developed ray tracing program, any ray tube is composed of four rays defined by the increments of θ
SOURCE MODELING
The transmitter is modeled as a point source inside the building. In order to determine all possible ray tubes that leave the transmitter and may arrive at the receiving point, it is necessary to consider all possible angles of departure as well as arrival at the transmitter as well as at the receiver. Antenna pattern is incorporated to include the effects of antenna in both azimuthal and elevation planes. To have a global ray manipulation routines, it is desirable that each ray tube occupy the same solid angle, and all wavefronts have an identical shape and size at the
Fig. 1: A ray tube shooting from a point source
To generate those ray tubes, an imaginary unit sphere centered at the antenna is divided into quadrilateral cells by selecting fixed angular resolution ∆θ and corresponding ∆ϕ = ∆θ / sin θ where θ is the elevation angle of any ray of each ray tube. The ray tubes along the local z axis are been neglected. For simplicity of calculation, in case of dipole antenna, the axis of the antenna is chosen to be the z axis of the spherical coordinates. The field strengths of the initial ray tubes, consequently, are symmetry along ϕ. Each ray tubes have to be stored for further application in procedure. The data set for each stored ray tube includes the direction vectors, shooting point locations, total path lengths and E-field phasors of the four rays. To describe the ray tracing method an important parameter which is to be chosen according to the environmental features is the ∆θ of the transmitted ray tubes. The ∆θ is given by: D (1) ∆θ = 2 × arctan min Lmax
Where Dmin is the minimum feature size of the indoor environment under consideration and Lmax is maximum path length that a ray tube may travel, before its power drops below the receiving threshold Pth. Considering transmitting power on unit sphere, Pt , and receiving threshold Pth , the Lmax could be calculated easily by free space loss formula: (2) Pt λ Lmax =
4π
Pth
Where is the wavelength.
3.
MODELING OF INDOOR GEOMETRY
A model of plane facets as tetragons is used to describe the indoor geometry. All the elements of an indoor emplacement such as walls, doors, etc., are represented by facets with four vertices. Each tetragon is characterized by complex dielectric constant r, normal vector of each facet and location of vertices. Even for a moderate indoor environment, because of large number of facets to model and accordingly the large number of intersection tests, a geometrical pre-processing is essential to prevent unnecessary computation. By employing the key criteria nˆ ⋅ rˆ ≤ 0 , where nˆ is the normal vector of facet and rˆ is the vector of source ray tube direction, only half of the facets which are in front of source ray tube need to be intersected [3]. Since, the facets near to the shooting point have higher chance to intersect ray tube; it is convenient to start intersection tests by the facets which have been sorted according to their distance from the shooting point of ray tube, as the second step of geometrical pre-processing. The computational complexity of the ray tube calculation grows exponentially with reflections and transmissions regarded. If all types of these ray tubes have to be traced, the computation time of the ray tracing method would be cumbersome. In this paper, therefore, “thin-wall” assumption used and ray tubes generated by multiple reflections inside walls have been ignored. Consequently, incident ray tubes and corresponding transmitted ray tubes have the same directions. The thinwall assumption will affect the calculation of the spreading factor and the length of the ray path. It is then important to verify the accuracy of mentioned assumption before ray tracing can be employed. It is found that when the wall thickness is 1/3 wavelength, the standard deviation of error of received power is 1.98 dB. When the wall thickness increases to one wavelength, the standard deviation reaches to 3.7 dB which is well blow 6 dB; the criteria for determining measurement accuracy for indoor propagation environments [8]. At most, it is reasonable to ignore the offset between the refracted and the incident ray, as has been done in most papers [6]. 4.
FAST RAY TRACING METHOD
The energy of those rays diffracted from the edges and corners evanesces at a small distance from the diffraction location [5] [8]. Therefore, no significant influence can have this mode of propagation on overall field strength value at the receiving point. This paper, therefore, does not take diffracted wave influence into account. After provision of the indoor model, ray tracing starts by manipulation of first ray tube, according to the following procedure. First, line of sight (LOS) propagation
possibility has to be checked and in case, received field strength value would be calculated. Next, the source ray tubes are traced, in their corresponding directions, to detect any intersecting facet. If no intersection occurred, the tracing of first ray tube stops and process re-starts for the new ray tube. Once an intersection detected, the corresponding transmitted and reflected ray tubes would be generated. The overall reflection and transmission coefficients are calculated for both polarizations using the conventional method for layered media [9] and calculated coefficients are employed for determination of decayed E-field of derived ray tube, directly. In any case of intersection, the reflected ray tube is stored for tracing in future and the transmitted ray tube is traced in a similar fashion explained above. This continues until the ray tube intensity falls below a specified threshold or the ray tube exits the building. A convergence test should be performed to set the proper threshold value, which is defined as the one percent of the reference field strength value of the primary ray tube on unit sphere centered at the transmitting point. It is observed that with lower threshold value, there is no notable change in the resulting field distribution. A ray tube deemed as a received ray tube if the receiving point fall inside the tetragon shaped by vertices which are intercepting points of four rays of considered ray tube with the plane perpendicular to one of them. For each received ray tubes based on GO, the E-field can be determined by using:
{
} { } {∏ e }⋅ SF
Er = E0 ⋅ ∏ Ri ⋅ ∏Ti ⋅
− j β 0 li
(3)
Where E 0 is the field on unit sphere, Ri and Ti are, respectively, the reflection and transmission coefficient dyads along the whole ray path, e − j β 0li is the product of the propagation phase variations for this ray contribution starting from unit sphere, and SF = A0 / Ar is the spreading factor. A0, and Ar are the cross-sectional areas at the unit sphere and at the receiving point, respectively [1]. To calculate received signal strength at a given receiving point, generally, there are two methods; summing the individual ray tube’s power (PS), and, summing individual ray tube’s electric field (FS). FS method is more accurate than PS method at UHF frequencies, especially in an indoor environment, where there are more conveniences to provide the precise database of environment and dielectric constant of materials [10]. 5.
VALIDATION
To verify the numerical accuracy of presented ray tracing method, the simulated E-field components for the half-wave dipole has been compared with the results presented in [11] (antenna factor is unknown) for a test
structure in free space. A half-wave dipole antenna, with 30dB ampere maximum current, is used for setting simulation up. It has been observed that the co-polarized component (Ez) is much stronger than the cross-polarized components (Ex and Ey). also, all of the components are decaying away from the source, and varies discontinuously because of GO approximation. A good agreement achieved between the calculated field strength envelopes of this paper and those presented in [11]. For measuring acceleration of calculation, moreover, ray tracing method of this paper applied to a corridor in a building of National Taiwan University of Science and Technology [1]. Calculation time improved more than 10%, considering same processing capability for both ray tracing methods. Furthermore, the accuracy of the ray tracing method examined for real structure of Figure 2. First, the “scale level” of the comparison must be defined. In actual condition, for the transmitter location chosen, a field prediction model is very rarely to result an accurate prediction of a given propagation parameter on a single receiver position, that is, at “point level.” Instead, if a “location” is defined as a set of receiver positions arranged on a cube vertices which centred at the receiver position, it is possible to obtain a good mean value of a given parameter over that location, i.e., at “location level.” The location spot must be several wavelengths wide but small enough in order for the propagation environment to be constant over the spot [4]. Therefore, the mentioned location level used.
The simulation model was applied to the hall room of 8th floor of Communication Regulatory Authority (Figure 2). The building is 7.7m × 6m in size with plasterboard walls and 6 wooden doors. Electrical parameters for the indoor construction materials in Figure 2, extracted from frequency dependent electrical properties of materials at microwave frequencies have published in [7] on 2.14 GHz. However, the fresnel reflection and transmission coefficients are not sensitive to small changes in the dielectric constant so that ray tracing method may be used with enough confidence even when the optimal effective building materials are unknown [2]. Ten points selected for conducting field strength measurement, using two 12cm wall mount wire transmitting antennas, mounted at a fixed height of 2.14m with 30cm distance between them. Points selected in such a way to have some Non Line of Sight (N-LOS) possibility. To take both transmitting antennas into account, superposition theory applied in calculation of field strength value at all test points. The simulation results are presented in Figure 3 and Figure 4.
Fig. 3: The results of the simulation and of the measurements
(a)
(b) Fig. 2: View of the 8th floor of Communications regulatory Authority for performing field measurements. (a) 3-D view. (b) Top view (point 5 to 10 are in N-LOS situation)
Fig. 4: Scatter plot of measured(x axis) and simulated electrical field strength(y axis) for the three sets of simulation. The average values are evaluated from single locations.
The differences between the measurements and simulations may be due to the following reasons: 1) Application of thin-wall model instead actual dimensions which affects simulation results. 2) Ignoring diffractions from the edges and corners as well as from the equipments and furniture situated inside the hall including portable measurement tool. 3) Inclusion only electrically large building structures in simulation. 4) Ignoring received noise from the outside of measuring hall which alters results, especially at N-LOS points. 5) Ignoring rooms surrounding the measuring hall. Table 1 the averages and standard deviations over the differences between the simulations and measurements in dB for three different 's. Table 1: Errors for the case given in figure 2 Stand. Div. Ave. Errors Stand. Div. Ave. Errors ,LoS points ,LoS points ,N-LoS ,N-LoS compared compared points points with meas. with meas. compared compared dB dB with meas. with meas. dB dB 2
3.2
-3.07
6.6
-0.9
3
4.72
-4.15
7.4
-2.2
4
7.31
-5.67
8.6
-1.85
As can be seen, the simulation is good for the LOS but is not so close in the N-LOS points. That may be because of ignored contribution which explained above and deep fading of measured signal level. Predicted values appear to be reliable for engineering purposes in all the cases considered. It has been observed that different values of affects the required running time significantly and should be kept small enough to obtain convergent results. 6.
CONCLUSION
A brute force ray tracing method developed for modeling indoor propagation. All reflections and transmissions of ray tubes among walls, ceilings/floors and other building structures are traced to determine the GO contributions. The presented method verified by comparison with two published results, in addition to the comparison with an indoor field measurement. The scale-level concept employed to assess some criteria for a useful comparison between measurement and ray tracing simulation. In both cases acceptable conformity observed. The computational efficiency of applied techniques proofed
by 10% calculation time improvement without losing accuracy, compared to conventional ray tracing methods. Additionally, accuracy of the presented method confirmed by comparison of simulated results with a real indoor measurement. Finally, the developed ray tube tracing method is applicable to model the wave propagation through arbitrary shapes of electrically large building structures that do not excite significant diffracted fields to the receiving locations. ACKNOWLEDGEMENT The authors would like to thank Communications Regulatory Authority for provision of measuring equipment and location. REFERENCES [1]
C. F. Yang, B.C.Wu, C.J. Ko, “A ray-tracing method for modeling indoor wave propagation and penetration”, IEEE Trans. Antenn. Propagat., vol. 46, pp. 907–919, June 1998. [2] S. Y. Seidel, T. S. Rappaport, “Site-specific propagation prediction for wireless in-building personal communication system design”, IEEE Trans. Veh. Technol., vol. 43, pp. 879– 891, Nov. 1994. [3] F. S. de Adana, O. G. Blanco, I. G. Diego, J. P. Arriaga, M. F. Cátedra, “Propagation Model Based on Ray Tracing for the Design of Personal Communication Systems in Indoor Environments”, IEEE Trans. Veh. Technol., vol. 49, pp. 21052112, Nov. 2000. [4] V. Degli-Esposti, G. Lombardi, C.Passerini, G. Riva, “Wide band measurement and ray tracing simulation of the 1900-MHz indoor propagation channel: comparison criteria and results , IEEE Trans. Antenn. Propagat. , vol. 49, July, 2001. [5] D.I. Laurenson, S. McLaughlin A.U.H. Sheikh, “The Application of Ray Tracing and the Geometrical Theory of Diffraction to Indoor Channel Modeling”, IEEE Trans. Antenn. Propagat, pp. 1242-1246, 2001. [6] Z. Ji, B. H. Li, H. X. Wang, H. Y. Chen, T. K. Sarkar, “Efficient Ray-Tracing Methods for Propagation Prediction for Indoor Wireless Communications”, IEEE Antenn. Propagat. Mag. , Vol. 43, pp. 41-49, Apr. 2001 [7] V.V. Varadan, R.D. Hollinger, D.K. Ghodgaonkar and V.K. Varadan, “Free-space broad band measurements of hightemperature, complex dielectric properties at microwave frequencies”, IEEE Trans. Instrum. Meas. vol 40, pp.842-846, Oct. 1991. [8] Z. Yun, M. F. Iskander, “Characterization of Angle of Arrival Based on Ray Tracing for an Indoor Wireless Communications Environment”, in IEEE/ACES, April 2005. [9] C. A. Balanis, Advanced Engineering Electromagnetics, John Wiley & Sons, New York, 1989. [10] Y. li, Z. W. du, K. gong, comparison of different calculating methods for path loss in Ray Tracing method at 2GHz , Inter. Conf. on Microwave and Millimetre Wave Tech. Proc. ,pp. 182184,2004. [11] C. F. Yang, C. J. KO, “A Ray Tracing Method for Modeling Indoor Wave Propagation and Penetration”, 0-7803-3216-4/96 IEEE 1996.
