###### Abstract  
While the effect of rainfall and other environmental phenomena on a link budget in microwave wireless communication has been well studied for network design, it has usually been done for each microwave-link separately. Recently, attenuation in multiple microwave-links is being used simultaneously for rainfall mapping over specific areas, and consequently, rain-induced attenuation fields can be constructed. Dedicated algorithms have been designed to relate attenuation in multiple microwave-links to its corresponding rain-field. Their performance depends significantly on the structure of the network. As the topology of a cellular microwave network (CMNs) is region-dependent, general theory for its effect on performance can only be developed statistically. In this paper we study the statistical nature of CMNs and lay the groundwork for such models based on empirical results. cellular microwave-links; rainfall mapping; rain-field estimation; network statistics; non-linear regression +
Footnote †: journal:  
0000-0002-4819-7000]H.G.M. Micro factors would be those that have a minor impact on the chosen position of the BS. For instance, after deciding to position a BS on a specific street block, one would consider micro factors for positioning that BS on a specific building's roof-top rather than another's. The macro factors, on the other hand, will inform the CMN architect what should be the amount of CMLs to deploy in an area, how to spatially distribute them, and how their lengths (i.e., distances between linked BS) should vary. Insights regarding the design of backhaul networks can be found in [7]. We suggest that there is a random factor in the spread of CMLs. This claim, which is the basis of this paper, relies on both the micro and macro factors. However, in this paper we focus on the macro factors as they impact the spatial distribution of CMLs globally. As will be demonstrated, CMLs' spatial distribution can be divided into subsets of distribution categories, each corresponding to characteristic population density and topography. As pointed out in [8], CMLs tend to be distributed in clusters. This means that not only is their spatial distribution observed to be non-uniform, it also leaves regions with little or no coverage. We will make the case that these clusters correspond in their locations to population densities. As this hypothesis will be supported, it provides an intuition for the macro factors of CMLs' distribution and volume. We analyze CMLs in the context of distribution categories, namely being urban (most dense), suburban, and rural (least dense) [9; 10]. In [11] one may also find a connection between population density and perspective BS service capacity. Population volumes may be high so as to saturate BS service capacity, thus calling for the allocation of additional BS to share the load. Table 1 shows results of BS density studies. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Region** & **Area (km2)** & **BS Amount** & **BS Density (1/km2)** \\ \hline Most Dense City & 60 \(\times\) 40 & 6251 & 2.604 \\ Second Densest City & 30 \(\times\) 50 & 1911 & 1.274 \\ Third Densest City & 40 \(\times\) 40 & 977 & 0.611 \\ Rural & 200 \(\times\) 200 & 12,691 & 0.317 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical base station (BS) densities [10]. BS densities depend on population densities. Since cellular microwave-links (CMLs) topologies are such that the number of CMLs is nearly identical to the number of BS, this table also reflects spatial densities of CMLs. Figure 1: A single cellular microwave–link (CML) [6]. Figure 2: Typical cellular microwave-link (CML) topologies. All four are such that the number of CMLs is approximately identical to the number of BS [6]. BS densities project on CML densities. To witness this relationship, Figure 2 presents the four common CML topologies. One can see that for each of these, the number of edges is similar to the number of nodes, as they symbolize the CMLs and BS, respectively.