Definition of nonspec Defining and as the fraction of the coherent power impinging on that is reflected as spec trans F specular (coherent) reflection and transmitted through the facet, respectively, a consistent model of the complete scatter process might be expected to conserve energy, giving: (9) Unfortunately, our semi-empirical model is not consistent, and different assumptions are made for each mechanism: the most theoretically based model is that for specular scatter. For a smooth facet, the spec: – reflected power is determined by the Fresnel reflection coefficients (which depend on the specular reflection angle, and the electrical properties of the facets). However there is no simple extension for surface scattering, and the model uses a semi-empirical term rough that modifies (reduces) the smooth surface Fresnel reflection coefficient. It is proposed that is defined as the power reduction factor due to the rough surface effect alone; that is, it spec does not take account of reflected power variation due to the Fresnel coefficient variation. The latter depends on the reflection angle and polarization, and therefore so would the nonspecular scattered power; this would be incompatible with the Lambertian assumption. in principle the transmitted component can also be calculated from Fresnel theory for – trans: a smooth surface, single interface. However, in practice, the situation is too complicated to model (rough surface, multiple interfaces and reflections) and an experimentally determined, empirical value for should be used. trans In principle each must satisfy the condition 0 1. There is no reason to believe that equation (9) will be satisfied, and if used to derive from and it is possible for to nonspec spec trans, nonspec become negative which is unphysical. It is proposed therefore that the non-specular fraction is derived directly from the specular fraction, ignoring the transmitted component: (10) In practice is likely to be quite small (e.g. 10 dB building penetration loss implies = 0.1). trans trans Calculation of spec is the reduction factor applied to the specular reflection coefficient to account for the spec power effect of surface roughness on specular reflection. It is: (11) When calculating the specular reflection coefficient, the effective reflection coefficient is R obtained by multiplying the Fresnel coefficient by RF s: (12) can be calculated from: s (13) where: (14)
Definition of nonspec Defining spec and trans as the fraction of the coherent power impinging on F that is reflected as specular (coherent) reflection and transmitted through the facet, respectively, a consistent model of the complete scatter process might be expected to conserve energy, giving: (9) Unfortunately, our semi-empirical model is not consistent, and different assumptions are made for each mechanism: – spec: the most theoretically based model is that for specular scatter. For a smooth facet, the reflected power is determined by the Fresnel reflection coefficients (which depend on the specular reflection angle, and the electrical properties of the facets). However there is no simple extension for rough surface scattering, and the model uses a semi-empirical term that modifies (reduces) the smooth surface Fresnel reflection coefficient. It is proposed that spec is defined as the power reduction factor due to the rough surface effect alone; that is, it does not take account of reflected power variation due to the Fresnel coefficient variation. The latter depends on the reflection angle and polarization, and therefore so would the nonspecular scattered power; this would be incompatible with the Lambertian assumption. – trans: in principle the transmitted component can also be calculated from Fresnel theory for a smooth surface, single interface. However, in practice, the situation is too complicated to model (rough surface, multiple interfaces and reflections) and an experimentally determined, empirical value for trans should be used. In principle each must satisfy the condition 0 1. There is no reason to believe that equation (9) will be satisfied, and if used to derive nonspec from spec and trans, it is possible for nonspec to become negative which is unphysical. It is proposed therefore that the non-specular fraction is derived directly from the specular fraction, ignoring the transmitted component: (10) In practice trans is likely to be quite small (e.g. 10 dB building penetration loss implies trans = 0.1). Calculation of spec spec is the power reduction factor applied to the specular reflection coefficient to account for the effect of surface roughness on specular reflection. It is: (11) When calculating the specular reflection coefficient, the effective reflection coefficient R is obtained by multiplying the Fresnel coefficient RF by s: (12) s can be calculated from: (13) where: (14)
R-REC-P.1410-5-201202-I!!MSW-E.docx