Modal transmission-line method applied to radio wave propagation through periodic walls

The Modal Transmission-Line (MTL) method is used to analyse the shielding effectiveness of building walls, which is an important parameter for the accurate planning of microcellular mobile networks. For that, the buildings walls are modelled as multi-layer periodic structures. After a description of the extended MTL-theory, the newly developed MTLmethod is applied to reinforced-concrete and block-concrete walls. From a comparison of MTL-results with previously published theoretical results, obtained by the Finite Element Method (FEM) for reinforced-concrete walls, it is concluded that the MTL-method is very well suited, because it is accurate as well as computational time efficient. INTRODUCTION For an accurate planning of cellular networks, new radiowave propagation models for the estimation of the losses on the radio path must be used. For the conventional macrocells usually the position of the base station is higher than the average height of the surrounding buildings, but for microcells this height is very often below the rooftops of the buildings. In the microcellular concept, the shielding properties of the surrounding buildings are used to confine the radiated power within a small coverage area. While in the case of macrocells there are simple empirical models for the estimation of the path losses, for microcells the problem becomes very site-specific. Therefore, more precise deterministic models must be used to represent better the physics of the propagation of the electromagnetic waves between the base station and the mobile station. There are several different mechanisms of propagation, such as line-of-sight propagation, reflection, and diffraction. These three mechanisms are included in most ray optics based methods [1] or physical optics based methods [2]. However at UHF frequencies, transmission of radiowaves through buildings can be the dominant propagation mechanism [3-4]. Neglecting the contributions of these waves in the planning of a network may result in an unacceptable degree of inter-cell interference. There are very few publications available on the shielding effectiveness of buildings and they are based on rather simplified models. In the present paper the transmission through walls is studied in more detail, using one special property typical for many of them: the periodicity. This property allows using a novel full-wave method, the so-called modal transmission-line (MTL) method, for an accurate and at the same time computationally efficient prediction of the transmitted field [5]. This paper starts with a description of the MTL-method following reference [6]. Then, the theory is applied to the computation of the electromagnetic wave transmission through reinforced-concrete and block-concrete walls. In order to apply the MTL-method to such walls, they are modelled as multi-layer periodic structures. Finally, the MTL-results are compared with previously published numerical and experimental results [7-8]. MTL-METHOD WITH PLANE WAVE EXCITATION The geometry of the two-dimensional scattering problem is shown in Fig. 1.a. In this paper only the TE-case will be considered, but the method can also be applied to the TM-case. A time-harmonic plane electromagnetic wave with unit amplitude is incident on a periodic lossy dielectric structure, with thickness h and period d , at an angle of incidence θ . The problem space consists of 3 regions (a, b and c) and region (b) is subdivided into L layers. In each region there are two types of solutions with respect to the z-direction namely incident and reflected waves. It is convenient to use a global x and a local l z co-ordinate for every layer. The tangential fields in the l -th region can be written in terms of periodic Floquet space-harmonics [6]