Sensibility of Ray Tracing Methods to Reality Description: Macro Objects Positions

Luigi Valbonesi, Riccardo E. Zich, Thierry MeouchiDipartimento di Elettrotecnica, Politecnico di Milano

P.za Leonardo da Vinci 32, 20133 Milano, Italy luigi.valbonesi@etec.polimi.it

INTRODUCTION Ray tracing techniques are powerful methods used to predict electromagnetic field in complex environments such as cities. The problem is to know how confident we can be on results obtained from simulations. Usually all ray tracers presented in literature have been validated accurately, but are they possible to use in any kind of urban environment? Another problem is the data source for buildings details, position, shape etc. Sometimes it is possible to “measure” the site by direct observation, but most of the times we have to use buildings plans o raster maps of the city. How accurately can we model reality from such inaccurate data sources? In this paper we have investigated the problem of modeling the entire buildings positions (we could say blocks position). EXPERIMENT PARAMETERS In order to test ray tracing techniques, we have used a validated method called BRT (Beam Ray Tracing) [1][2] that performs a full 3 D ray tracing and considers direct, reflected and diffracted rays. This method can be set so to consider any order of interaction with the environment, in order to avoid truncation problems [3][5]. We have used a particular parameter defined in literature [4] to describe the sensibility of the method to a variation of the input data: relative variation (%). This parameter is calculated by dividing results difference, between two realizations, by results of one of them as it is shown in (1), where E(N) and E(N’) are the two results. The acceptable value for this parameter has been set at 3% [4].

%)(

)'()(100(%)NE

NENE −×=∆ (1)

We have used raster maps and onsite viewing to have the input data and to model properly at least buildings shapes and dimensions. In Fig. 1 the raster map that was used is shown and in Fig. 2 we have shown the reality model used (top view) with a center street marked in blue. As we are interested in the field outside blocks, we have not modeled inside macro objects. In Fig. 3, 4, 5 and 6 we have shown some buildings and their models used for this experiment.

Figure 1 – Raster map. Figure 2 – Reality model (top view).

Figure 3 – Building. Figure 4 – Model. Figure 5 – Building. Figure 6 – Model. RESULTS We have tried several cases with several distances; here we show the two most meaningful (results of other cases don’t differ much). First we have moved blocks randomly in direction and 6 wavelength in distance (2 m). Usually raster maps precision is 2 m or 1 m. In Fig. 7 we have shown the relative variation for fast fading (natural and log scale), the difference in position of buildings is marked with blue spots. In Fig. 8 we have shown the relative variation for slow fading. It appears clear that such values of relative variation are not affordable. It can be noticed that high values are distributed in the entire area and not only in precise spots as great values are.

Figure 7 – Relative variation for 6 wavelengths movements and for fast fading (natural scale and log scale).

Figure 8 – Relative variation for 6 wavelengths movements and for slow fading (natural scale and log scale).

As an error in blocks positions of 6 wavelength is not affordable, we have tried with 1 wavelength. Trying with smaller distances can be an exercise, because it is not possible to know buildings positions with such precisions and at an affordable cost. In Fig. 9 and 10 we have reported the calculated relative variation for both fast and slow fading (natural and log scale). It appears evident that is not possible to afford these variations in field values.

Figure 9 – Relative variation for 1 wavelength movements and for fast fading (natural scale and log scale).

Figure 10 – Relative variation for 1 wavelength movements and for slow fading (natural scale and log scale).

In order to reduce sensibility to blocks positions we can consider contributes (rays) without taking in account for their phases, as the most probable cause for these results is how different rays combine their field for the total field value (constructively or destructively). In a previous work [5] we had shown how changes in buildings positions had no real influence on final field value, especially if we consider places some wavelength away from walls, but that result was obtained with a simple micro cell. For this reason we can say that sensibility to macro objects positions increases with the increasing complexity of the environment. CONCLUSIONS We have investigated sensibility of ray tracing methods to macro objects position in a real case (a part of the city of Milano, North Italy) by imposing movements of them in random directions . We have found out that we cannot afford errors in determining blocks positions even greater than one single wavelength. We have found that this sensibility increases with the increasing of environment complexity. Further studies are needed to experiment if adding different rays fields “in power” (disregarding phase informations) reduces this sensibility and allows to use ray tracing techniques to calculate slow fading in different types of cities with different environments complexity. REFERENCES [1] L.Valbonesi, “A new approach for electromagnetic field evaluation in urban environments: Beam Ray Tracing” Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA 01), Torino, Italy, 10 – 14 September 2001. [2] L. Valbonesi “Beam Ray Tracing ( BRT ): validazione”, Atti della Quindicesima Riunione Nazionale di Elettromagnetismo, XV RiNEm, Cagliari, Italy, 13 – 16 September 2004, pp. 233 – 236.

[3] Luigi Valbonesi,”Una nuova tecnica per la previsione teorica di campo elettromagnetico con il metodo dei fasci illuminanti ( Beam Ray Tracing: BRT ): validazione ed analisi della sensibilità.”Rapporto Interno N° 2001.80, Dipartimento di Elettronica e Informazione, Politecnico di Milano, 2001. [4] Guiducci D., Passerini C., Falciasecca G., “ Studio sull’affidabilità degli algoritmi di Ray Tracing”, XIII RiNEm (Riunione Nazionale di Elettromagnetismo), Como, 25-28 Settembre 2000. [5] L. Valbonesi, R. E. Zich, “Sensibility of ray tracing methods to environment description in different urban scenarios” Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA 03), Torino, Italy, 8 – 12 September 2003.