Comparison of Heuristic UTD Coefficients in an Outdoor Scenario Diego Tami 1 , Cássio G. Rego 1 , Dinael Guevara 2 , Andrés Navarro 3 , Fernando J. S. Moreira 1 , Narcís Cardona 4 , Jordi Giménez 4 1 Graduate Program in Electrical Engineering, Federal University of Minas Gerais, Belo Horizonte, MG, Brazil, diegotami@ufmg.br 2 Francisco de Paula Santander University, Cúcuta, Colombia, dinaelgi@ufps.edu.co 3 Universidad Icesi, Cali, Colombia, anavarro@icesi.edu.co 4 Universitat Politècnica de València, Valencia, Spain, ncardona@iteam.upv.es Abstract—This paper presents a comparison of three heuristic coefficients for the Uniform Theory of Diffraction (UTD), used to characterize the radiowave scattering in typical urban scenarios. The coefficients were implemented in a propagation model based on 3D ray-tracing techniques for a Digital Video Broadcasting (DVB) service. In order to evaluate each coefficient we analyze the statistical behavior of the mean and standard deviation of the absolute errors between the estimated values and the measured data of path loss in a large number of receptor points in an outdoor scenario. Index Terms—Heuristic diffraction coefficients, ray tracing, uniform theory of diffraction. I. INTRODUCTION The continued development of wireless technologies, particularly in urban environment, leads to investigate methods to estimate, with high precision, the propagation parameters of wide-band channels in order to minimize the error with respect to on-site measurements. In recent years, methods based on ray tracing and UTD have shown accuracy and efficiency in the simulation of path-loss in complex environments. This accuracy depends mainly on the ray physical model in realistic environments and the numerical model used for estimating the scattered field. Therefore, the choice of the diffraction coefficients is important to accurately predict the signal amplitude obtained from the diffraction process. Initially, UTD coefficients were developed for perfectly conducting wedges [1]. Then, Luebbers established heuristic diffraction coefficients for lossy conducting wedges [2]. Luebbers' contributions have triggered a large number of studies to improve the accuracy of the heuristic coefficients. Among the most recent researches, Schettino et al [3] proposed a heuristic UTD coefficients combining features of previously investigated heuristic coefficients [2, 4-6], ensuring reciprocity and providing superior performance in arbitrary source and observer locations. Guevara et al [8] used Luebbers' coefficients in union with a physical technique that model the edge where diffraction occurs to obey reciprocity and adopt two types of permittivity to characterize the building materials. These two studies estimated propagation path loss in urban scenarios and compared them with measurements. Since the results indicated a good accuracy, this paper will present a comparison between these and the Luebbers' formulation in a common scenario. For this purpose, we use a 3D ray-tracing model based on optic rays to simulate the multipath propagation and so to evaluate the UTD in a realistic scenario that has been previously validated in [8]. The novelty in this paper is the implementation of three heuristic UTD coefficients applied to predict path loss in the realistic outdoor environment in order to evaluate the precision of the 3D ray-tracing model with respect to measurements. The paper is organized as follows: in section II we describe the heuristic UTD coefficients used for the comparison, in section III we describe the channel modeling process, in section IV we mentioned the characteristics of the propagation, the simulated outdoor scenario and the measurement campaign, in section V we discuss the results obtained and in section VI, conclusions and further work. II. HEURISTIC UTD COEFFICIENTS The UTD electric field at the observer (see Fig. 1) is defined as [1]: ܧ ௗ ሺሻ ൌ ܧ ௜ ሺሻ · ܦ ഥ ܣ·ሺ ݏ ௗ ሻ· ௝௞௦ ೏ (1) where ܧ ௜ ሺሻ is the incident electric field at the wedge, ܣሺ ݏ ௗ ሻ is the amplitude factor, ݏ ௗ is the distance between wedge and observer, and ܦ ഥ is the dyadic diffraction coefficient. Adopting the classical notation of [1], Luebbers’ soft and hard heuristic diffraction coefficients are given by: ܦ ഥ ௦,௛ ൌ ܩ ଴ ௦,௛  ܦ ଶ ൅ ଴ ௦,௛ ሺ ߙ ଴ ሻ ܦ ସ ൧൅ ܩ ௡ ௦,௛ ሾ ܦ ଵ ൅ ௡ ௦,௛ ሺ ߙ ௡ ሻ ܦ ଷ ሿ (2) where ܦ ௜ , for  ൌ 1, … ,4, are the UTD diffraction coefficients, ܩ ଴ and ܩ ௡ , are grazing incidence factors,  ଴ and  ௡ are Fresnel reflection coefficients, for the 0 and n faces, respectively, as defined in [2]. The angular definition ߙ ଴ and ߙ ௡ , used to calculate  ଴ and  ௡ respectively, are given by: ߙ ଴ ൌ min ሾ ௜ ,  ߨെ ௜ ሿ, ߙ ௡ ൌ min ሾ ௗ ,  ߨെ  ௗ ሿ (3) where,  ௜ is the angle of the incident wave, and  ௗ is the angle of the diffracted wave, both with respect to face 0, and  ߨis the wedge exterior angle (see Fig. 1). Luebbers’