## 4 Simulation Results
### Detection Results
The utilized algorithm in [1] is capable of classifying the interference with JSR larger than 5 dB. As an example of time domain algorithm, Figure 14 displays the performance of the LMS algorithm [19] in CWI detection mixed with the narrowband signal. After downsampling by factor 4, this algorithm can detect the interference down to JSR = \(-6\) dB. The wavelet algorithm is mainly used to detect the interferences with JSR between 10 to 55 dB [22; 23]. Figure 12: Correct detection percentage based on the input JSR (detector with the original Welch method); (a) downsampling = 2; (b) downsampling = 4. Figure 13: Correct detection percentage based on the input JSR (detector with the simplified Welch method); (a) downsampling = 2; (b) downsampling = 4. Based on the previous results, utilizing more packets from the past increases the system capability in weak interference detection; however, the cost of this improvement is more convergence time and slower reaction to interferences with the variable center frequencies. Consider that the target of the system is to track the interference with hopping center frequency. Depending on the variation speed of center frequency, large dependency on the past can decrease the system performance. Let us consider that the sample rate of the system is large enough and during one FFT window, the interference has a constant center frequency. Now, the period of the variation of interference center frequency is an integer multiply of window duration. For simplicity, we normalize a window duration to one second. Figure 15 displays the detector performance in hopping CWI tracking based on the variation speed of the center frequency. In this test, the power of interference is constant (JSR = \(-\)15 dB and downsampling = 2). Clearly, the detector with large dependency on the past (larger \(\alpha\) parameter) is not able to track the fast variations in signal PSD. In this case, the \(\alpha\) parameter must be selected carefully. The amount of dependency must be large enough to make the interference visible but it must not filter the fast variation of center frequency hopping. By comparing Figures 13a and 15, detector behavior can be explained. In Figure 13a, at JSR = \(-\)15 dB, the detector has a detection rate = [71%, 90%, 98%, and 100%], respectively, for \(\alpha\)= \(\{\)0.6 0.7 0.8 0.9\(\}\). For \(\alpha\)\(\leq\) 0.9 and \(frequency\)\(variation\)\(\leq\) 10\({}^{-1}\), the spectrum estimator can convergence and obtain the presented performance in Figure 13a; however, for \(\alpha\)\(>\) 0.9, the system needs more convergence time and it cannot track the hopping center of interference. Moreover, detection rate of the system with larger \(\alpha\) degrades faster when increasing the variation speed. Figure 14: Least Mean Square (LMS) detector [19] performance based on the input JSR ( \(\varepsilon_{T}=10^{-3}\)). Figure 15: Detector performance in hopping Continues Wave Interference (CWI) detection. A robust monitoring system needs to have a variable dependency on the past to adjust itself from time to time based on the situation. For example, if the target is to detect a weak frequency component under noisy conditions, larger dependency (Larger \(\alpha\)) can help the monitoring system to recognize it more clearly. In other situations, when the system is trying to track a fast-hopping carrier frequency, smaller \(\alpha\) values are more useful because the averaging over time can filter fast variations. The proposed detector has a unique simplicity and flexibility of the averaging control. The \(\alpha\) parameter is a flexible control in the user's hand and allows the PSD parameters to be adjusted based on the current situation.