The increase in channel bandwidth and peak-to-average power ratio (PAPR) of modern communication standards poses a serious challenge to performing channel power (CP) and complementary cumulative distribution function (CCDF) measurements in real-time using standard measurement solutions based on spectrum analyzers (SA). Recently, Software Defined Radio (SDR) technology has become a viable alternative to the conventional real-time spectrum monitoring approach based on SA due to its reduced cost. Therefore, in this paper, we propose a novel, innovative, agile and cost-effective solution to enable both CP and CCDF measurements on a state-of-the-art SDR platform. The proposed solution exploits the ability of the SDR equipment to access signal samples in the time domain and defines both CP and CCDF-type measurements. The two measurement functions are software implemented in GNU Radio by designing customized blocks and integrated into a graphical user interface. The proposed system was first tested and parameterized in a controlled environment using emitted signals specific to the IEEE 802.11ax family of wireless local area networks. After parameterization, the SDR-based system was used for over-the-air measurements of signals emitted in the 4G+, 5G and 802.11ax communication standards. By performing the measurement campaign, we have demonstrated the capabilities of the measurement system in performing real-time measurements on broadband channels (up to 160 MHz for IEEE 802.11ax). Altogether, we have proved the usability of CP and CCDF measurement functions in providing valuable insights into the power distribution characteristics of signals emitted by the latest communication standards. By exploiting the versatility of SDR technology, we have enabled a cost-effective solution for advanced real-time statistical measurements of modern broadband signals.