The 60 GHz band compact-range communication is very promising for short-time, short distance communication. Unfortunately, due to the short wavelengths in this frequency band the shadowing effects caused by human bodies, furniture, etc are severe and need to be modeled properly. The numerical methods like the finite-difference time-domain method (FDTD), the finite-element method (FEM), the method of moments (MoM) are unable to compute the field scattered by large objects due to their excessive time and memory requirements. Ray-based approaches like the geometrical theory of diffraction (GTD), uniform geometrical theory of diffraction (UTD), uniform asymptotic theory of diffraction (UAT) are effective and popular solutions but suffer from computation of corner-diffracted field, field at the caustics. Fresnel zone number (FZN) adopted modified edge representation (MER) equivalent edge current (EEC) is an accurate and fast high frequency diffraction technique which expresses the fields in terms of line integration. It adopts distances, rather than the angles used in GTD, UTD or UAT but still provides uniform and highly accurate fields everywhere including geometrical boundaries. Previous work verified this method for planar scatterers. In this work, FZN MER EEC is used to compute field distribution in the millimeter-wave compact range communication in the presence of three dimensional scatterers, where shadowing effects rather than multi-path dominate the radio environments. First, circular cylinder is disintegrated into rectangular plate and circular disks and then FZN MER is applied along with geodesic path loss. The dipole wave scattering from perfectly conducting circular cylinder is discussed as numerical examples.

Radio channel modeling is fundamental for designing wireless communication systems. In millimeter or sub-millimeter wave short range communication, shadowing effect by electrically-large objects is one of the most important factors determining the field strength and thus the coverage. Unfortunately, numerical methods like MoM, FDTD, FEM are unable to compute the field scattered by large objects due to their excessive time and memory requirements. Ray theory like geometrical theory of diffraction (GTD) by Keller is an effective and popular solution but suffers various kinds of singularities at geometrical boundaries such as incidence shadow boundary (ISB) or reflection shadow boundary (RSB). Modified edge representation (MER) equivalent edge current (EEC) is an accurate and a fast high frequency diffraction technique which expresses the fields in terms of line integration. It adopts classical Keller-type knife-edge diffraction coefficients and still provides uniform and highly accurate fields everywhere including geometrical boundaries. MER is used here to compute the millimeter-wave field distribution in compact range communication systems where shadowing effects rather than multi-path ones dominate the radio environments. For further simplicity, trigonometric functions in Keller's diffraction coefficients are replaced by the path lengths of source to the observer via the edge point of integration of the scatterers in the form of Fresnel zone number (FZN). Complexity, Computation time and the memory were reduced drastically without degrading the accuracy. The dipole wave scattering from flat rectangular plates is discussed with numerical examples.

This paper presents the Physical Optics field calculation in terms of only line integrations by using the Modified Edge Representation technique (MER), the alternative way of the surface integration. Not only the diffracted fields as in the conventional method of equivalent edge currents (EEC) but also the scattering geometrical optics fields are expressed in terms of the MER line integrals. The far field patterns of parabolic reflector antennas with the defocused dipole feed are discussed and the satisfactory agreement with those obtained by the Physical Optics surface integration is demonstrated.

The Modified edge representation (MER) is the concept to be used in the line integral approximation for computing the surface radiation integrals of diffraction. The MER as applied to the physical optics (PO-MER), has remarkable accuracy in the surface-to-line integral reduction even for the curved surfaces and for sources very close to the scatterer. In the discussion of the mathematical foundation for this accuracy, the evaluation of the singularities in the integrand of the PO-MER line integration was left for further study.

Modified Edge Representation (MER) empirically proposed by one of the authors is the line integral representation for computing surface radiation integrals of diffraction. It has remarkable accuracy in surface to line integral reduction even for sources very close to the scatterer. It also overcomes false and true singularities in equivalent edge currents. This paper gives the mathematical derivation of MER by using Stokes' theorem; MER is not only asymptotic but also global approximation. It proves remarkable applicability of MER, that is, to smooth curved surface, closely located sources and arbitrary currents which are irrelevant to Maxwell equations.

The effects of finite ground plane upon the patterns of the GPS patch antennas are analyzed by EEC with modified edge representation (MER). The comparison with UTD and measurements shows that low elevation patterns including axial ratios are successfully predicted.