A very important task in Mobile Cognitive Radio Networks (MCRN) is to ensure that the system releases a given frequency when a Primary User (PU) is present, by maintaining the principle to not interfere with its activity within a cognitive radio system. Afterwards, a cognitive protocol must be set in order to change to another frequency channel that is available or shut down the service if there are no free channels to be found. The system must sense the frequency spectrum constantly through the energy detection method which is the most commonly used. However, this analysis takes place in the time domain and signals cannot be easily identified due to changes in modulation, power and distance from mobile users. The proposed system works with Gaussian Minimum Shift Keying (GMSK) and Orthogonal Frequency Division Multiplexing (OFDM) for systems from Global System for Mobile Communication (GSM) to 5G systems, the signals are analyzed in the frequency domain and the Rényi-Entropy method is used as a tool to distinguish the noise and the PU signal without prior knowledge of its features. The main contribution of this research is that uses a Software Defined Radio (SDR) system to implement a MCRN in order to measure the behavior of Primary and Secondary signals in both time and frequency using GNURadio and OpenBTS as software tools to allow a phone call service between two Secondary Users (SU). This allows to extract experimental results that are compared with simulations and theory using Rényi-entropy to detect signals from SU in GMSK and OFDM systems. It is concluded that the Rényi-Entropy detector has a higher performance than the conventional energy detector in the Additive White Gaussian Noise (AWGN) and Rayleigh channels. The system increases the detection probability (PD) to over 96% with a Signal to Noise Ratio (SNR) of 10dB and starting 5 dB below energy sensing levels.