Prediction of Rain Attenuation Series with Discretized Spectral Model

The rain attenuation plays a major role in the design of satellite-to-earth links operating at high frequencies such as Ka band and Ku band. The signal suffers from a strong attenuation during the propagation path as raindrops absorb and scatter radio waves, which results in an increase of transmission error and reduction of the system availability [1]. Predicting rain attenuation is one of the vital steps to be considered when analyzing a satellite communication link. Adaptive code mechanism or adaptive power control can be used to increase the transmission efficiency and to reduce the transmission power, on condition that the attenuation is predicted in some way. Several models of the rain attenuation were introduced in [2] : spectral (SPL) model, two-sample model (TSM), secondorder Markov chain (2MC) model, N-states Markov chain model, ITALSAT data-based model and synthetic storm technique (SST). Among these models the spectral model has a good correspondence with known properties of rain and its simplicity allows simulations of communication link performance under the influence of rain attenuation. In [3], the conditional probability distribution of the predicted attenuation based on the analog model was given, which allows an optimal prediction in the statistical sense. However, simulators often operate with the discretized model during the analysis of communication system. Predictions based on the discretized model were also studied in literature based on the filter design method [4] or on the online prediction method [5]. In this paper, we derive the conditional distribution of the predicted attenuation and give the optimal estimation bound based on the discretized model. The results can also be used for other systems with the similar model.