## 4 Simulation Results  
### Detection Results  
As discussed above, JSR is the most effective parameter in the detection process. Ideal detectors must be able to detect very low power CWI; however, the capability and precision of the detector depends on the downsampling factor, input signal type, interference characters, and adjusted parameter for the detector. The precision of the detected center frequency directly affects the efficiency of notch filters in CWI mitigation. When the mitigation stage has a precise estimation of CWI center frequency, a narrow notch filter can be utilized for interference cancelation. When the notch filter deviates from the exact center frequency, interference power will leak to the receiver, the notch must then utilize a wider notch for complete removal. The following condition helps to measure the detector precision:  
\[ \begin{split}& if\ \left(\left|f_{detected}-f_{interference}\ \right|>\varepsilon_{T}\right)\Longrightarrow\ \text{{Incorrect Detection}}\\ & if\ \left(\left|f_{detected}-f_{interference}\ \right|\leq \varepsilon_{T}\right)\Longrightarrow\ \text{{Correct Detection}}\end{split} \, \tag{15}\]  
where \(f_{detected}\) is the detected center frequency by the detector, \(f_{interference}\) is the real center of interference, and \(\varepsilon_{T}\) is the desired precision: if the detector deviates more than this value, its detection is not acceptable. Table 1 displays utilized parameters for simulation tests. For the comparison target, performance of the detector with the original Welch power spectrum estimation is also presented. Figure 12 displays the percentage of correct detection based on the input JSR. Minimum detectable JSR for the original Welch algorithm depends on two important factors: number of involved FFT packets in arithmetic average (averaging order) and downsampling factor. Clearly, by increasing the average order, more FFT packets are involved in PSD estimation and as the result, the system with a higher order has an outstanding result in precise center detection. When the system benefits from the average of 80 past FFT packets, it detects weak power CWI with JSR = \(-\)22 dB. It can be seen that increasing the downsampling factor from two to four, approximately increases the system performance by 3 dB. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**FFT Size**} & **Transmitted** & **Transmitted** & **Threshold** & **Number of** & **Desired** & **Downsampling** \\  & **Signal Power** & **Signal Type** & **Level** & **Detectors** & **PRECISION** & \(\varepsilon_{T}\) & **Factor** \\ \hline \multirow{2}{*}{2048} & \multirow{2}{*}{Normalized to 0 dB} & QPSK with & \multirow{2}{*}{3 dB} & \multirow{2}{*}{3 dB} & \multirow{2}{*}{3} & \multirow{2}{*}{0.001} & \multirow{2}{*}{2.4} \\  & & pulse shaping & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used for the simulation tests. Figure 11: Input JSR estimation based on the measured interference power in detector. System performance of the simplified Welch algorithm is controlled by the \(\alpha\) parameter. Compared to the original Welch method, \(\alpha\) parameter plays the same role as the averaging order. By increasing \(\alpha\) parameter, the estimated spectrum has more dependency on past calculated frequency samples and is smoother and more accurate. Based on Figure 13, changing the \(\alpha\) parameter can improve the detector system performance in weak signal detection to the JSR = \(-25\) dB. Downsampling again plays the same role and by increasing down sapling factor from two to four, a 3 dB improvement is observed in system performance. It can be seen that detector with \(\alpha=0.99\) can excel the original Welch that benefits from averaging of 80 previous packets. As it is mentioned before, benefiting from the averaging, the proposed design has a unique capability in weak signal detection. Machine learning and artificial intelligence techniques are able to classify the type of interference and they cannot estimate the center frequency.