## 9 A Novel Methodology for 5G-Enabled Broadband Connectivity Coverage of Smart Cities
It is often more useful to employ a formula that calculates the path loss, with the metric of distance expressed in meters. This proves more convenient when we consider limited-range networks, e.g., a municipal Wi-Fi in a city square. In addition, the trend for both small cells in deployed 4G networks and the expanding 5G system is for smaller-range cells, so that path loss models should be able to take as an input variable the transmitter-receiver distance directly in meters rather than in kilometers. The following equation provides the loss in dB when the transmitter-receiver distance is expressed in meters [40]:  
\[L_{total}=PL(d_{0})+N\log_{10}\left(d\mathord{\left/{\vphantom{d_{0}}}\right. \kern-1.2 pt}d_{0}\right) \tag{2}\]  
where \(P_{L0}(dB)\) is the reference path loss for the reference distance, \(d_{0}\), which is considered equal to 100 m or 1 km for outdoor environments and equal to 1 m for indoor environments; \(N\) equals 10\(n\), where \(n\) is the path loss exponent which equals 2 for the free space model. The frequency dependence is \"embedded\" in the coefficient \(PL(d_{0})\) (i.e., reference path loss), which is calculated from Equation (1), assuming a distance equal to the reference distance, \(d_{0}\). The local mean received power, according to the free space model, corresponds to the losses that depend on the distance between the transmitter and the receiver (T-R separation) and the operating frequency of the wireless system under consideration. Thus, the free space model assumes strictly deterministic losses. In realistic propagation environments, however, with many obstacles and complex electromagnetic propagation phenomena, the free space model is not reliable for the calculation (i.e., prediction) of the local mean received power, because it does not consider losses due to the fact of shadowing and other phenomena (reflection, scattering, and diffraction) [41]. The first simple way to incorporate these additional losses into the model of Equation (2) is to modify the value of the path loss exponent accordingly. This, in most cases, corresponds to a path loss exponent larger than 2 (i.e., the free space model value). When the shadowing losses are due to the fact of fixed (i.e., static) obstacles, their impact on the signal attenuation for a given location of the transmitter and receiver exceeds the time scale of seconds or minutes. These losses are then incorporated in the logarithmic formula, and the shadow loss is also included in the total path loss calculated (predicted) by the model, which leads to the Log-Distance path loss (shadow) model [42]. The mathematical expression of the log-distance path loss model is given by the expression [43]:  
\[L_{total}=PL(d_{0})+N\log_{10}\left(d\mathord{\left/{\vphantom{d_{0}}}\right. \kern-1.2 pt}d_{0}\right)+X_{\sigma} \tag{3}\]  
where \(PL(d_{0})\) is the path loss for the reference distance (as in the free space model, the reference distance is taken equal to 1 m for indoor environments); \(N\) is the path loss exponent (\(\times 10\)); and Xs is a Gaussian random variable with zero mean and a standard deviation equal to \(\sigma\ dB\). \(N\) and \(\sigma\) are calculated from empirical data (either from textbooks or other published works or hands-on measurements) [42]. Assuming a coverage rate equal to 95% (suboptimal scenario), the relationship between the Gaussian random variable and the shadowing deviation is equal to [42]:  
\[X_{\sigma}=z\times\sigma(dB)=1.645\times\sigma(dB) \tag{4}\]  
The main disadvantage of the logarithmic distance model is the need to concurrently provide reliable values for two parameters (path loss exponent and shadowing depth). Our method relies on assigning a fixed \(n=2\) value for the path loss exponent, as per free space specifications, and the \"transfer\" of all excess path losses (any path loss \"beyond\" the deterministic distance-dependent attenuation, meaning practically all shadow losses due to the fact of obstacles) to the shadow variable Xs (dB).