## 3 Materials and Methods
### Measured Signal Processing  
The measured signals were recreated in the MATLAB environment to investigate their characteristics. The first step was determining the sampling rate. It is assumed that the offset frequency is the start frequency for each band. Since the spectrums are plotted as a one-sided spectrum, the sampling rate (f\({}_{\text{s}}\)) of the input signal is as given in Equation (1).  
\[\text{f}_{\text{s}}=2\text{f}_{\text{s}} \tag{1}\]  
where F\({}_{\text{s}}\) is the frequency span.  
Thus, the sampling frequencies are obtained as 1.2 GHz, 0.8 GHz, and 1.2 GHz for the 6 GHz, 7 GHz, and 8 GHz frequency bands.  
Figure 3: Experimental setup for the frequency scan measurements.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline Frequency Band & Start Frequency & Stop Frequency & Frequency Span \\ \hline
6 GHz & 5.9 GHz & 6.5 GHz & 600 MHz \\
7 GHz & 7.4 GHz & 7.8 GHz & 400 MHz \\
8 GHz & 7.7 GHz & 8.3 GHz & 600 MHz \\ \hline \hline \end{tabular}
\end{table}
Table 3: Frequency usage plan for the three different frequency bands tested.  
The signals are generated as sine waves and colored noise. Figure 4 shows the process of generating colored noise. The signals are fed as inputs to the random stream generator. The output of the random stream generator is white noise, which could be Gaussian or uniform. This is fed to the coloring filter, and the colored noise is evolved after applying the appropriate gain factor.  
The random stream generator generates a white noise that is either a Gaussian or uniform distribution. Uniform white noise has its amplitude bounded between +1 and \(-1\), while Gaussian noise amplitude is not bounded between +1 and \(-1\). This boundary is enforced by the gain \(g\). A coloring filter is then applied to the generated white noise, with a power spectral density (PSD) given in Equation (2).  
\[S(f)=\frac{L(f)}{|f|^{\alpha}} \tag{2}\]  
where \(\alpha\) is the inverse frequency power in the interval \(-2\leq\alpha\leq 2\). \(\alpha\) is a real number. \(L(f)\) is a positive, slowly varying, or constant function. If \(\alpha=0\), then no coloring filter is applied to the generated white noise, and \(L(f)\) is a constant proportional to the process variance. If \(\alpha>0\), \(S(f)\) goes to infinity as the frequency, \(f\), approaches 0. If \(\alpha<0\), the process is anti-persistent and exhibits a negative correlation between increments.  
The sine waves were generated with the trigonometric function method, which computes the sinusoid in the \(i\)th channel, \(y_{i}\) by sampling the continuous function as expressed in Equation (3).  
\[y_{i}=A_{i}\sin(2\pi f_{i}t+\varphi_{i}) \tag{3}\]  
where \(A_{i}\) is the amplitude of the \(i\)th channel, \(f_{i}\) is the \(i\)th channel frequency, and \(\varphi_{i}\) is the phase offset. Each band and polarization for all of the scans can then be generated by adding all of the signals at different frequencies, as given in Equation (4).  
\[S_{b,p}=\sum_{i}^{N}y_{i} \tag{4}\]  
Equation (5) expresses the power of the signal concerning its standard deviation (\(\sigma\)) [53]. Therefore, the standard deviation (\(\sigma\)) can be described, as shown in Equation (6). It is assumed that the default Gaussian noise in the environment has the standard deviation as calculated in Equation (6) with zero mean. Otherwise, if a particular frequency is used, a signal is generated and added to the Gaussian noise. The step-by-step procedure for the analysis of the scanned frequencies is given in Table 4.  
\[\text{p}=10\log_{10}\sigma^{2} \tag{5}\]  
\[\sigma=\sqrt{10^{\frac{p}{10}}} \tag{6}\]  
Figure 4: Process of generating colored noise.