3-D Rain Rate Estimation from Integrated Measurements of Commercial Wireless and Satellite Links

In the last decade, various algorithms have been developed to provide accurate rainfall maps from measurements of rain-induced attenuation on commercial wireless links (CWLs), such as [1]. These solutions provide precise results but they also require dense terrestrial microwave networks, which have non negligible installation and operating costs. A cheaper alternative for rainfall estimation is represented by broadcast satellites links (BSLs). However, to the best of authors’ knowledge, these approaches are able to estimate the rainfall rate on a single point only [2]–[4]. To gain all the benefits provided by both the cited schemes, we propose an adaptation of the state-of-the-art algorithm in [1] which is able to integrate the data provided by both the CWLs and BSLs, yielding a three-dimensional (3-D) rain rate map of a monitored area. Our contribution lies in the technical description of the data processing schemes developed to retrieve these maps, with particular interest in the 3-D system model. In the following, we summary the machinery of our approach. Let us consider a monitored zone, where N = Nw + Ns communication links are active, with Nw and Ns are the number of CWLs and BSLs, respectively. It is worth noting that rain is assumed only present below the 0 C isotherm height. We divide then the vertical dimension into H fixed heights, from ground level up to the 0 C isotherm height. Hence, by implementing the algorithm in [1] for each height, we obtain a set of H rain maps, one for each height value, yielding to a 3-D description of the phenomena. The effectiveness of novel approach is assessed using a simulator able to set up a configuration of the coordinates for both CWL and BSL terminals, and an instance of a simulated rain in a randomly-generated position. Preliminary results are given in Figures 1 and 2 which illustrate different scenarios in the presence of the same rain conditions. In the scenario of Fig. 1, the estimation is performed using only 21 CWLs, while Fig. 2 presents the estimation results using 13 BSLs and 8 CWLs. Though the position of the rain column with diameter 3 km is correctly estimated in both cases, it can be nevertheless noted that the joint utilization of both CWL and BSL provides a more accurate estimation of the rain intensity. To show a more general prove of effectiveness, the near-to-the-ground RMSE between actual and estimated rain rate is plotted for different scenarios. In Fig. 3, the RMSE is shown as a function of the number of wireless links, randomly chosen from the arrangement presented in Fig. 1. The curves are plotted for different numbers of satellite receivers, i.e., 0, 4, 8 and 16 randomly-positioned on the maps. It is apparent that even a few number of satellites can be of great help in reducing the RMSE.