# Simplified Welch Algorithm for Spectrum Monitoring
## 5 Laboratory Tests and Real-Time Validation
### Final Results  
The modified design was tested in the laboratory using the setup presented in Figure 16. The first result tries to show the capacity to detect every type of narrow band and wideband signals in different frequencies, like any other spectrum analyzer. A single tone at a frequency of 1.572 GHz and a modulated QAM signal with pulse shaping are selected as narrowband, and wideband signals in different center frequencies are then passed through the commercial spectrum analyzer and SDR equipped with the modified Welch algorithm. Table 1 briefly explains the parameters selected for this test. Figure 16: Laboratory setup and devices (signal generators, BEEcube SDR (Software Defined Radio), Tektronix and Rohde & Schwarz) used for real-time analysis. Figure 15: Test bench used to validate the modified algorithm. In regards to the fairness of competition, we considered the following points carefully:  
* It should be mentioned that the power transferred by the signal generator is equally divided between all devices with the help of a splitter. Thus, all devices (SDR and two other spectrum analyzers) are competing with similar input power. * Selected span for commercial devices is 10 MHz. The SDR that run the new design, has a sampling rate of 40 MHz, thus, the span of the SDR is equal to 20 MHz. Selected span for the two other devices is half of SDR, that allows them to have two times better resolution. * The attenuation gain for all three devices is equal to 0 dB. It allows the two other spectrum analyzers to have maximum sensitivity to the input signal. * Selected cables have the same attenuation gain. * During the test, we also changed the input signal of different devices to be sure that the obtained results were real. Table 2 provide more details about the commercial device settings. As it can be seen in Figure 17, the modified design can represent any spectral formation with accuracy for signal monitoring and interference detection. For both narrowband and wideband signals, the center frequencies detected match the transferred signals completely, and the bandwidth detected is equal to the bandwidth of the modulated QAM. \begin{table} \begin{tabular}{c c c c c c c} \hline \hline
**Single-Tone** & **Modulated** & **Modulated** & **Single-Tone** & **Modulated** & **SDR Sample** & \(a\) **Parameter** & **FFT Size** \\
**Center** & **QAM Center** & **QAM Bandwidth** & **Power** & **QAM Power** & **Rate** & \(a\) **Parameter** & **FFT Size** \\
1.574 GHz & 1.57542 GHz & 1 MHz & \(-\)48 dBm & \(-\)65 dBm & 40 MHz & 0.99 & 2048 \\ \hline \hline \end{tabular}   
* It is observed that the power transferred by the signal generator is equally divided between all devices with the help of a splitter. Thus, all devices (SDR and two other spectrum analyzers) are competing with similar input power. * Selected span for commercial devices is 10 MHz. The SDR that run the new design, has a sampling rate of 40 MHz, thus, the span of the SDR is equal to 20 MHz. Selected span for the two other devices is half of SDR, that allows them to have two times better resolution. * The attenuation gain for all three devices is equal to 0 dB. It allows the two other spectrum analyzers to have maximum sensitivity to the input signal. * Selected cables have the same attenuation gain. * During the test, we also changed the input signal of different devices to be sure that the obtained results were real. Table 2 provide more details about the commercial device settings. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Rohde \& Schwarz** & \\ \hline
**Span** & **Reference** & **Attenuation gain** & **Center frequency** & **Resolution bandwidth** \\ \hline
10 MHz & 0 dB & 0 dB & 1.57542 GHz & 30 kHz \\ \hline \hline \multicolumn{4}{c}{**Tektronix RSA600**} \\ \hline
**Span** & **Reference** & **Attenuation gain** & **Center frequency** & **Resolution bandwidth** \\ \hline
6.2 MHz & \(-\)20 dB & 0 dB & 1.57542 GHz & 1 kHz \\ \hline \hline \end{tabular}  
\end{table} 
Table 2: Commercial devices parameters.