A large population of radar-measured ground rain cells is used to devise and assess a rain cell model for use in some of the future telecommunication applications. The model is based on cells of exponential profile (which is shown to reproduce best the point rain rate CDF); both rotational and biaxial symmetries are considered for the horizontal cross sections. Furthermore, the proposed model contains analytical expressions for the joint probability densities of the parameters which define the cell, i.e., peak rain intensity, cell size and axial ratio. Finally, an algorithm is given for adapting the model to the characteristics of any given site: this algorithm requires as input the local cumulative distribution of point rainfall and provides the spatial number densities (i.e., the average number of cells per square kilometer and per unit range of the parameters) which this distribution would produce. The model offers the possibility of predicting the statistics of many propagation parameters (such as attenuation or interference by rain scattering) which are determined by the rain cell characteristics and their frequency of occurrence. assumption is made that the same types of precipi-during 1980 near Milan, Italy. tation occur in different locations' what varies is the The model is based on a distribution of cells each frequency of their occurrence. Yet propagation pre-one characterized by an exponential profile of the diction models become a powerful tool in predicting rain rate (in the following referred to as "model statistics of the quantities of interest only if the model cells"). parameters can be derived from local meteorological The statistical properties of the population of data [Rogers, !976]. "model cells" are presented and discussed together with the procedure for linking the parameters of the •Dipartimento di Elettronica, Centro di Studio per le Telecom-model to the meteorological data. rnunicazioni Spaziali CNR Politeenico di Milano, Milano, Italy. A rain cell is defined as any connected region of aFondazione Ugo Bordoni, Rome, Italy. space composed of points where the rain rate exceeds aCentro di Studio per le Telecomunicazioni Spaziali CNR Poli-a given intensity threshold. tecnico di Milano, Milano, Italy. The "model cell" is identified by forcing some of Copyright 1987 by the American Geophysical Union. its integral parameters to correspond with those of Paper number 6S0709. the observed cell. 0048-6604/87/006s-0709508.00 Two models of cell are dealt with' a monoaxial 395 in the range 6-150 mm/h is given by (19). Konrad, T. G., Statistical models of summer rainshowers derived rom fine-scale radar observations, J. Appl Meteorol., 17(2), 171-4. No(R•t ), the number density of R u, in Figure 199,1978. 8, is given in the form of a cumulative distribution Lane, S. O., and W. L. Stutzman, Spatial rain rate distribution normalized to the total number of cells exceeding 5 modeling for earth-spaoe link propagation calculations, paper 404 CAPSONI ET AL.: RAIN CELL MODELING FOR PROPAGATION APPLICATIONS pr...

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This paper presents a new approach for the prediction of propagation parameters (such as rain attenuation, site diversity gain, interference by rain scattering, etc.) in telecommunication applications beyond 10 GHz. It consists of a comprehensive theory allowing the full exploitation of the large amount of meteorological data available today. The method is based on a recently devised statistical model of the rain horizontal structure (Capsoni et al., this issue), whose parameters can be determined on the basis of the local statistical distribution of the point rainfall intensity. A test of the ability of this method in predicting attenuation statistics is performed using data collected in Europe with the satellites SIRIO and OTS (COST 205, 1985). The excellent results obtained encourage the application of the model to the statistical prediction of other parameters pertaining to propagation. 1. FOREWORD This paper presents a new approach for the prediction of propagation parameters (such as rain attenuation, site diversity gain, interference by rain scattering, etc.) in telecommunication applications beyond 10 GHz. It consists of a comprehensive theory allowing the full exploitation of the many meteorological These considerations are here applied to the rain cell model proposed by Capsoni et al. [this issue]. It is shown how they lead to a very accurate attenuation prediction method which is described in detail step by step and assessed against data collected during the COST 205 project in Europe [COST 205, 19853.It is noted that this is only an example of an applidata acquired by radars and rain gauges. cation of the principles here presented, which areThe basic concept underlying this theory is that more general and, due to their applicability to many the rain structures causing "events" of interest for parameters, they offer a tool for linking these parampropagation of radio waves (rain cells, stratified rain, eters to each other (which is necessary when data etc.) are quite similar at each site, at least in their must be extrapolated to different conditions or corngeneral characteristics, and what characterizes the bined in order to evaluate an overall system perlocal behavior is the different probabilities of oc-formance). currence of these structures. It follows that, if we know them with sufficient 2. THE SUPERPOSITION PRINCIPLEaccuracy and possess good models for their description, the problem of predicting propagation parame-Let us suppose that the random process describing ters reduces to that of determining their probability a given propagation parameter is generated by the of occurrence. movement of the abovementioned rain structures in

For accurate frequencj estimation, principal component autoregressive spectral estimation methods habe received considerahle attention in the recent literature. Explicit computation of the eigendecomposition of the autocorrelation matrix is required to obtain the principal component solution. An alternative approach called the eigenvalue filtering method, which does not require explicit computation of the eigenvalues and the eigenvector%, is proposed in thi5 paper. The proposed method applie5 a transformation to the autocorrelation matrix which has the effect of truncating the undesired eigenbalue5 5o that the corresponding matrix function closely approximate5 the pseudoinverse. It is shown via computer simulation that compared to the forward-backward method, the proposed method enhances the threshold in SNR by about 6-8 dB. Further improvement is obtained h j a simple subset selection method and a second eigenvalue filtering iteration.

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