# Mechanism to Estimate Effective Spectrum Availability Inside Smart Buildings
## 4 Interference Model Validation
### Influence of Shadowing Phenomena  
During a measurement campaign, the instantaneous values vary very quickly, so the influence of shadowing phenomena on the average measured value and the simulated value should be considered.  
Considering that the values obtained with a propagation model are average values and because shadowing is a random process, the simulated values can vary within a range. The range is variable, so it is customary to represent it with a parameter called the confidence interval (CI).  
The standard deviation of a propagation model \(\sigma_{S}\) due to shadowing can be determined from the following expression for the case of macro-cells [27]:  
\[\sigma_{S}=0.65(\log f_{c})^{2}-1.3\log f_{c}+5.2. \tag{19}\]  
The value of the losses by shadowing \(L_{S}\) is found using  
\[L_{S}=\sigma_{S}t \tag{20}\]  
where \(t\) is the probability of being within the coverage of the macrocell, \(p_{cM}\).  
\[p_{cM}=1-Q(t) \tag{21}\]  
where \(Q\left(t\right)\) is the tail distribution function of the normal distribution. Due to shadowing, the received power may be higher or lower than the power value calculated by a propagation model; thus, the upper and lower limits of the power values obtained by simulation define a CI for the measured interference values with a probability \(p_{cM}\).  
Figure 9 shows a shaded area above and below the red line. This area indicates the probable zone of the interference levels of the EGLI model considering a probability of CI = 0.95, compared with the measurements made in the central apartment of the building. The graph shows that all the values obtained in the measurement campaign were entirely within the CI given by the simulation values.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Propagation Model** & **EGLI** & **FRIIS** & **COST-WI** \\ \hline small building measurements & 0.97 & 0.72 & 0.79 \\ long building measurements & 0.93 & 0.81 & 0.82 \\ \hline \end{tabular}
\end{table}
Table 1: Correlation coefficients for propagation models and measurements.  
The shadowing phenomena are multiplicative noise in the communication channel, where additive noises such as white noise and thermal noise also intervene. The power levels of the additive noise can influence to a greater or lesser extent the power level of the received signal. The white noise levels depend directly on the electromagnetic pollution of the study environment, while the level of noise produced in a receiver due to thermal noise can be calculated, considering a temperature of 27 \({}^{\circ}\)C, according to [27]:  
\[N_{dBm}=-174+10\log(B)+F_{dB} \tag{22}\]  
where \(B\) is the channel bandwidth in Hz and \(F_{dB}\) is the device noise figure in dB.  
Considering a 6 MHz bandwidth TV channel and a TV receiver with an average noise figure of 8 dB; using (22), a total noise of \(-98\) dBm is obtained in the receiver, which gives a margin of 23 dB with respect to the threshold level; this margin would also allow controlling the variations in the power level due to white noise. For these reasons, this study does not include a detailed study on the influence of additive noises since they present power levels much lower than the threshold power level.