L’électromagnétisme, 150-1 Une Science En Pleine Action

Shadow fading is a well known problem in wireless sensor networks (WSN) and ad hoc networks since the communicating devices often are at street-level where the surrounding buildings often obstruct incoming radio waves. Therefore, accurately modeling shadow fading is an important requirement for the optimal design of such networks. Because the height of building is the most important parameter to calculate diffraction loss, the correlation of building heights on two close paths may influence the correlation of shadow-fading. In this paper, we first assume that the building heights follow an exponentially correlated Gaussian distribution, and then investigate shadow-fading correlation through the uniform theory of diffraction (UTD). The result shows that the correlation of shadow-fading stems from multiple exponential decay functions. Considering that the buildings near RX and TX are dominant contributors to shadow fading, a multiple (double in particular) exponential decay function is expected to better model the correlation than a single exponential. Introduction Shadow fading is a well known problem in wireless sensor networks (WSN) and ad hoc networks since the communicating devices often are at street-level where the surrounding buildings often obstruct incoming radio waves. Therefore, accurately modeling shadow fading is an important requirement for the optimal design of such networks. The radio paths between a transmitter (TX) and a receiver (RX) rarely match the condition of line of sight (LOS), implying severe shadowing effect, which indirectly provides an advantage for the frequency reuse that can be exploited in cognitive radio (CR) systems as well as other in distributed wireless peer-to-peer systems (e.g. ad hoc networks, wireless local area networks), leading to the enhancement of spectrum efficiency. Given this context, the purpose of the present work is to develop simple and suitably accurate models of shadow fading in urban environments. In early studies, for the sake of simplicity, the statistical distribution of shadow-fading was approximated as a lognormal distribution (Gaussian in dB), spatially correlated in an ad hoc manner, typically with a distance dependent exponential decay (Gudmundson model [1]). Recent works showed that correlated shadow-fading has a detrimental influence on the performance of wireless systems. In [2][3], the performance of collaborative spectrum sensing for opportunistic access in correlated shadow-fading environment degrades as the decorrelation distance increases. Another author asserts that highly correlated shadow-fading results in a large positioning error when applying a localization algorithm such as the weighted centroid localization algorithm in a WSN [4]. In order to obtain 2-dimensional results, several algorithms to generate 2-dimentional correlated shadow fading have been derived by expanding Gudmundson’s 1-dimensional model [5][6]. Other researchers report that a high correlation has been observed within a certain angular separation between the directions going from the mobile stations to the base station [7]. Even though the exponential decay model or other angular correlation models are well-known and proved by a large amount of measurements, there is no elaborated impact on physical layer aspects of such model and the decorrelation distance. In this paper, we first investigate shadow-fading correlation through the uniform theory of diffraction (UTD), which is a technique of reference to treat the diffraction by building edges in simulation tools of the propagation by deterministic methods. In urban areas, shadow-fading is indeed mainly caused by obstruction from buildings. In ray-tracing, when the TX and RX are far enough from each other (implying more than 3 reflections and 1 diffraction), the rays along streets URSI-France Journées scientifiques 26/27 mars 2013