# Real-Time Statistical Measurement of Wideband Signals Based on Software Defined Radio Technology
## 3 Materials and Methods
### Parameterization and Test System Implementation

Table 4: Noise power for 802.11 ax channels with different bandwidths. Figure 8: Setting parameters on the signal generator for an 802.11 ax channel. instrument compared to the SA. The following settings of the SA were used for the channel power measurements: Central frequency = 2400 MHz; SWT = 10.9 ms; N points = 860; SPAN = 80 MHz; channel bandwidth = 40 MHz; RBW = 30 kHz, number of measurements: 2740 (equivalent to 10 802.11 ax frames). The SA settings were implemented in such a way as to ensure the accuracy of the measurements, especially with respect to sweep time and number of pixels (interpixel time was calculated according to the symbol duration). In contrast to CP measurements, the SWT is replaced by the number of samples to be measured for CCDF measurements performed by the FSVR SA. Since only independent samples affect the statistical measurement, the acquisition time (AQT) is automatically determined and expressed as the ratio of the number of samples (N) to the resolution bandwidth (RBW): AQT = N/RBW. Another restrictive setting of the SA is the limitation of the resolution bandwidth in CCDF mode. This must be equal to the bandwidth of the WLAN channel. Therefore, measurements were performed in the laboratory for a maximum RBW of 40 MHz. To set up the statistical measurement and obtain the CCDF curve (Figure 9), the SA was configured with the following parameters: center frequency = 2400 MHz; acquisition time of a CCDF measurement was set equal to the duration of a symbol specific to the IEEE 802.11 ax standard (12.8 \(\upmu\)s); RBW equal to the bandwidth: 40 MHz; number of measurements: 4284 (for the measurement of 10 frames). In addition, all calculations for both CP and CCDF measurements were performed taking into account the PPDU transmission time (PSDU and its preamble), which is limited to 5484 \(\upmu\)s [38]. Both CP and CCDF mode settings of the USRP instrument were made in comparison with the analyzer. An application implemented in Phyton was used to extract channel power and CCDF data from the analyzer (mean and peak power, crest factor and percentage parameters above mean power for 10%, 1%, 0.1%, 0.01%). This application runs on a computer so that the spectrum analyzer is accessed remotely and, depending on the number of measurements and the time specified, returns the relevant information resulting from the measurements. Figure 9: CCDF display on the spectrum analyzer. Regarding the calculation of channel power, it should be noted that the vector signal analyzer uses frequency domain evaluation based on the expression [26]:  
\[L_{ch}=10\cdot\lg\bigg{(}\frac{B_{ch}}{B_{NIF}}\cdot\frac{1}{n_{2}-n_{1}}\cdot \sum\
olimits_{n_{1}}^{n_{2}}10^{\frac{P_{i}}{10}}\bigg{)} \tag{1}\]  
where \(L_{ch}\) represents the channel power level expressed in dBm; \(B_{ch}\) is the channel bandwidth in Hz; \(B_{NIF}\) is the intermediate frequency filter band expressed in Hz; \(P_{i}\) represents the measured power value for pixel \(i\). In comparison, SDR platforms provide access to samples acquired in the time domain, and the channel power calculation is performed according to the following mathematical expression:  
\[L_{ch}=10\cdot\lg\bigg{(}\ \frac{1}{n_{2}-n_{1}}\cdot\sum\
olimits_{m_{1}}^{n_{2}} \big{[}S_{n}\cdot S_{n}^{\prime}\big{]}\bigg{)} \tag{2}\]  
where \(L_{ch}\) is the channel power reading in dBm, \(S_{n}\) represents the current signal sample, and \(S_{n}\)' is the complex conjugate of the current sample. Accordingly, the channel power calculation is performed by averaging the product of the current time domain sample and its complex conjugate (the number of samples is between \(n_{1}\) and \(n_{2}\)) and applying the logarithmic operation to transform the final result into dBm. A critical component of an SDR platform is the analog-to-digital converter (ADC). Converter characteristics that can limit the performance of SDR receivers are sample rate and resolution. The sample rate limits the maximum bandwidth that can be processed in real-time.