# Real-Time Statistical Measurement of Wideband Signals Based on Software Defined Radio Technology
## 2 Advanced Electromagnetic Spectrum Measurement Capabilities
In the same paper, the authors report that for levels close to the noise threshold, the HackRF one platform does not represent an efficient measurement solution. Therefore, a very important parameter of SDR platforms is the resolution of the analog-to-digital converter which impacts their ability to measure low-amplitude signals. To ensure the highest level of accuracy in measurements, spectrum monitoring systems must adapt to the evolving signal characteristics of advanced technologies, such as 5G NR and WLAN, mitigating for improved spectrum monitoring capabilities. A type of spectrum measurement used in wireless system networks is channel power (CP), performed to measure the power transmitted within a specified frequency or channel bandwidth. CP measurements serve multiple purposes, including validating the performance of transmitters, ensuring compliance with government regulations, and minimizing system interference. Modern SAs possess the capability to automatically compute CP by integrating power over the channel bandwidth. In the traditional approach using SAs, it is difficult to implement CP measurements on wideband signals from the latest communication standards due to the overwhelming hardware requirements. The high cost of SAs further limits high-bandwidth studies, and real-time implementations on the order of hundreds of MHz using SAs are currently available only at very high cost. CP measurements become an insufficient characterization of signals that have high temporal variability, like those used by new-generation communication devices. Additionally, these modern signals require a measurement tool capable of providing direct statistical insights and graphical representation for the amplitude variation in time. To this extent, the SA proves to be a valuable tool for obtaining an accurate and complex statistical assessment of signal variation. SAs enable evaluation and analysis of PAPR with a high degree of accuracy and can perform statistical analysis of measurements even over long periods of time, but are limited by the bandwidth, which in the case of new technologies is very high. In the context of OFDM signals, which are known for their high PAPR, it is essential to use advanced statistical measurements such as Probability Density Function (PDF), Cumulative Distribution Function (CDF), Complementary Cumulative Distribution Function (CCDF) or Amplitude Probability Density (APD). The use of these advanced statistical measurement functions proves to be of interest for designing power-efficient amplifiers [27]. The probability density function parameter describes the relative probability that the measured power will take a particular value. The information contained in a PDF is similar to that of a histogram but shows continuous rather than discrete values. Using a PDF function, it is possible to determine the probability of a measured power falling between two limits by integrating over that range. The PDF integration over the entire function becomes what we call the CDF. The CDF curve tells us the percentage of time that the signal power is below a given value, or more specifically, it is very useful when performing noise analysis because it highlights the minimum power values. Using the CDF function, it is also possible to obtain its complement, the CCDF curve. The values of the CCDF curve are calculated as follows: CCDF = 1 \(-\) CDF [28]. The CCDF curve is plotted as a graph, with the power level expressed in dB above the average signal power on the \(Ox\) axis and the percentage of time the amplitude reached the specific power value on the \(Oy\) axis. The CCDF function, unlike the CDF, focuses on the maximum or peak power values. More specifically, it provides information about the probability or percentage of time that a signal is at a particular value or exceeds the average value of the signal [29; 30]. The APD method, also a statistical measurement, is suitable for studying the characteristics of a signal's amplitude variations.