## 1 Introduction
Some authors analyze signals in the frequency domain and use metrics such as entropy in order to detect PU, rendering detectors less sensitive to noise and increasing the probability of detection (\(\mathrm{P_{D}}\)) [2; 7; 15; 16]. The Shannon entropy metric has been used to detect PU signals in the frequency domain showing better results in terms of noise uncertainty [2; 7; 15; 16]. In contrast, our research analyzes Renyi-Entropy and implements it on a Software Defined Radio (SDR) system through a MCRN protocol that emulates a real system, thus allowing to establish a comparison between simulated and real scenarios. In most of the previous work, results are analyzed in simulation settings, while this is the first research to focus on implementing it on real devices. Renyi Entropy is a measure of uncertainty and a generalized form of Shannon Entropy. Although used in information theory [17; 18; 19; 20], the measured data goes beyond said niche since Renyi-entropy can be applied in economics, finance, machine learning and statistics, among others [17; 21; 22; 23; 24]. For instance, Renyi Entropy has been used to distinguish different modulations [25], which is closer to a real MCRN. Compared with Shannon entropy, Renyi entropy can better reflect the difference between two distributions [26]. In this article, we propose to measure the power signal of a PU over time. The Discrete Fourier Transform (DFT) is calculated by translating the signal into the frequency domain while the Renyi Entropy detector is used to find a threshold to differentiate between noise and PU signals. The \(\mathrm{P_{FA}}\) and \(\mathrm{P_{D}}\) are calculated for some values of SNR and the results are compared with the work found in literature. We implement the detector on a SDR with a fully operational GSM system that allows a phone call service between two SU and an OFDM transmission system to deliver experimental results. The proposed component of this research regarding cognition consists in the implementation of a spectrum analyzer to measure the power of the frequency spectrum in real time. The Mobile Cognitive Base Station (MCBS) is implemented on an SDR NI-USRP2922, whose function is to read the power measured by the spectrum analyzer and, if the chosen frequency is available, it is assigned to the SU. If a PU needs to use this frequency, then the MCBS must change the SU frequency to another one within the corresponding range. If no other frequencies are available, the last option is to end transmission for the SU. The experiments include both GMSK and OFDM systems. The main contribution of this work is to implement a cognitive radio network protocol to enable frequency hopping on an SDR. GMSK and OFDM modulations are used to probe signals from 2G and 5G systems by comparing theoretical results, simulations and implementations. Renyi entropy detect signals from PU to improve the spectrum sensing system. In contrast with the literature, our research implements algorithms and takes real values from the spectrum in MCRN which makes it close to the real environment. The present paper is organized as follows: Section 2 presents the proposed method used for all experiments. In Section 3, the SDR testbed for experiments is shown followed by the results in Section 4. In Section 5, the discussion is shown and the conclusions are presented in Section 6.