Application of the Parabolic Equation Method for Analyisis of Indoor Propagation Problems

With the rapid growth of indoor wireless communication systems, the need to accurately model radio wave propagation inside the building environments has increased. Many site-specific methods have been proposed for modeling indoor radio channels. Among these methods, the ray tracing algorithm and the finite-difference time domain (FDTD) method are the most popular ones. The ray tracing approach as a high frequency technique is efficient for calculating the received field at a small number of receiver locations. Application of FDTD method as a full wave technique for indoor propagation modeling is time consuming and requires large amounts of memory. The parabolic equation method (PEM) is a fast full-wave technique which allows accurate modeling of the propagation environment and its electrical parameters. This paraxial version of the wave equation can be solved by marching techniques which need far less computation resources than a full elliptic equation. The PEM has been extensively used as an efficient algorithm for outdoor propagation modeling. In this paper we propose an unprecedented application of PEM for indoor propagation problems. Depending on the required speed and accuracy of computations, two and three-dimensional versions of the PEM can be used for indoor problems. Without loss of generality, we restrict ourselves to the two-dimensional problems and use two-dimensional approximation of the parabolic equation for fast and accurate radio wave propagation modeling in indoor environments. The parabolic equation has been derived for lossless media where the refractive index is very close to unity. To the authors' best knowledge the paraxial version of the wave equation has not yet been derived for propagation in general lossy dielectric media. In this paper, we first derive the general form of the parabolic wave equation for lossy dielectric media where it can be used for modeling the radio wave propagation through walls. The special form of the parabolic equation for modeling wave propagation in free space can be derived from this general form. We then apply PEM to model propagation of radio waves through a row of windows, reinforced concrete walls and typical corridors inside buildings. As windows are one of the most prevailing architectural elements in buildings, the phenomenon of plane wave transmission through them is of interest. In this paper PEM is used to model the radio wave propagation through windows. The numerical simulation results are presented for both normal and oblique incidence and compared with some reported results. The transmission and reflection characteristics of inhomogeneous walls have been studied by many numerical and analytical methods such as the finite-element method (FEM) and FDTD. In this paper, we use PEM to characterize reflection and transmission properties of reinforced concrete walls under plane wave incidence. The effect of several parameters namely wall thickness, bar diameter and spacing on the transmission coefficients of reinforced concrete walls will be analyzed. Corridors are also popular elements of buildings, so that the analysis of radio wave propagation in corridors has involved many researchers. The PEM is an effective method for modeling wave propagation in these environments. The effect of obstacles such as cupboards and cabinets inside a corridor can be modeled by PEM. This method is also able to model the effects of variations of the corridor direction on the wave propagation. The numerical simulation results will be presented and compared with the available data in the literature.