# Simplified Welch Algorithm for Spectrum Monitoring
## 5 Laboratory Tests and Real-Time Validation
### Final Results
The next part of the laboratory results represents the effect of \(\alpha\) on the spectrum smoothness and accuracy in frequency component recognition. Figure 17(a)-c represent a modulated QAM signal at 1.57542 GHz mixed with a CWI at 1.575 GHz compared to the two other spectrum analyzers. In this test, a very low-power CWI is used to make it harder to detect. In this situation, both of the commercial spectrum analyzers could not see the CWI and the modified design was able to detect the spike caused by the interference. Another important point observed in Figure 17 is that the spectrum displayed by the modified design is similar in shape to the two other spectrum analyzers with less noise, and the CWI can appear 4 dB higher than the modulated signal. Figure 17: (**a**) CWI (Carrier Wave Interference) represented and QAM (Quadrature Amplitude Modulation) modulated with the R&S (Rohde & Schwarz) spectrum analyzer; (**b**) CWI represented and QAM signal spectrum modulated with the modified Welch algorithm. Figure 18: (**a**) CWI and modulated QAM signal representation on the R&S spectrum analyzer; (**b**) CWI and modulated QAM signal representation with the modified Welch algorithm with \(\alpha=0.99\) (**c**) CWI and modulated QAM signal representation with the Tektronix spectrum analyzer. Figure 19 represents the results obtained from SDR by repeating the second tests using lower \(a\) parameters. As it can be seen, another spectrum is obtained for the larger a parameter. The lower the \(\alpha\) parameter, the harder it gets to detect the CWI mixed with the modulated QAM until for \(\alpha=0.70\) in Figure 19b, the CWI peak is covered by noise and is not visible. The last test tries to compare the ability of two commercial spectrum analyzers with the modified design in weak signal monitoring. In this test, only a wideband signal with low power is used. The signal power transmitted is decreased until the spectrum analyzers are unable to monitor it. As it can be seen in the Figure 20, with a transmitted power of \(-87\) dBm, both spectrum analyzers are unable to monitor the input power, and the transmitted spectrum is covered by noise; however, the SDR equipped with the modified design still clearly depicts signal with correct and reliable details. Figure 19: (**a**) CWI and modulated QAM signal representation with \(\alpha=0.85\); (**b**) CWI and modulated QAM signal representation with \(\alpha=0.7\). Figure 20: (**a**) PSD representation from the R&S spectrum analyzer at \(-87\) dBm; (**b**). PSD representation from the modified Welch algorithm at \(-87\) dBm; (**c**) PSD representation from the Tektronix spectrum analyzer at \(-87\) dBm. For both cases, narrow band and wide band, when other spectrum analyzers could not display the spectrum, the modified design could still display frequency component 5 dB higher than the noise level. With a narrow band signal such as a CWI, when its power is decreased until the point where other devices cannot see the CWI, the new design can see it 5 dB stronger than the QAM signal. As it has been explained before, \(\alpha=0.99\) can result in SNR improvement equivalent to averaging by N order of 100. Averaging reduces the noise level and improves the SNR by 20 dB gain. Thus, the frequency components can be visible clearly on top of the noise. Superiority over other spectrum analyzers is demonstrated with the SNR improvement. By decreasing the signal power, it will be fading in the background noise and commercial devices are not able to track it in the surrounding noise. However, the new design, benefiting from the SNR improvement, can display the desired signal in lower SNRs.