## 4 Results
### Simulation Results  
In the simulations, Monte Carlo experiments were conducted with the configuration shown in Table 1. The parameters were selected to compare them with the results of an entropy detector found in [11]. A random bits generator was used to generate the date and it is modulated in GMSK. The additional noise is added depending on channel fading (AWGN or Rayleigh). The DFT is then calculated and the histogram method is used to calculate Renyi-entropy. The threshold is calculated depending on the SNR values and figures of the PD, PFA and ROC curves are finally generated. The P\({}_{\text{FA}}\) is an input of the system, the target that P\({}_{\text{FA}}\) will be less than 0.1 (10%) so the P\({}_{\text{D}}\) will be over 90% [11]. The proposed method is compared with energy detection in two possible scenarios: AWGN channel and Rayleigh Channel. The performance of the algorithms is evaluated by calculating receiver operation characteristics (ROC) curves, the P\({}_{\text{FA}}\) and P\({}_{\text{D}}\) over some SNR values. In the AWGN scenario, the parameters shown in Table 1. are used for SNR values ranging from -25 dB to 0 dB. ROC curves are shown in Figure 3. comparing the P\({}_{\text{D}}\) of the proposed Renyi-Entropy detector against the energy detector from [11]. Figure 4 shows the ROC curve of P\({}_{\text{FA}}\) versus the P\({}_{\text{D}}\) compared to the energy detection method from [11] for SNR = -18 dB. The parameters from Table 1. were used for experiments. Results show that the SNR needed is SNR = -16 dB for the proposed Renyi-Entropy detector and SNR= -8 dB for the energy detector. The proposed scheme has an 8 dB performance improvement compared with the energy detector in the AWGN channel. As N increases, also does the P\({}_{\text{D}}\) increase, yet it needs more time to make a decision. Samples are stored to compare them with [11]. The Rayleigh scenario was chosen because it offers the worst performance in detectors [35]. Experiments include SNR values from \(-\)25 dB to 0 dB, ROC curves are shown in Figure 5, comparing the P\({}_{\text{D}}\) of the proposed Renyi-Entropy based detector against the energy detector from [11]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Description** \\ \hline Number of samples & 10,000 \\ PU & 2 \\ SU & 2 \\ Number of bins L & 15 \\ Estimated P\({}_{\text{FA}}\) & \textless{}0.1 \\ Objective P\({}_{\text{D}}\) & \textgreater{}0.9 \\ Signal Noise & AWGN/Rayleigh \\ Primary Signal & GMSK /OFDM \\ Bandwidth & 12 kHz \\ Symbol Ratio & 10 kbps \\ Carrier Frequency & 40 kHz \\ Sampling Frequency & 100 kHz \\ DFT size & 128 \\ Average Noise Power & \(-\)90 dBm \\ \(\alpha\) & 2.5 \\ Confidence level & 95\% \\ Error & 5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. Figure 4: ROC curves for the Rényi-entropy and energy detector for AWGN channel. Figure 5: PD vs SNR for Rényi-entropy and energy detector for Rayleigh channel. Figure 3: PD vs SNR for Rényi-entropy and energy detector for AWGN channel. Figure 6 shows the ROC curve of \(\mathrm{P_{FA}}\) versus the \(\mathrm{P_{D}}\) compared to energy detection from [11] for SNR = \(-\)18 dB and \(-\)11 dB. To obtain the ROC curves, an SNR must be defined. This value is close to \(-\)11 dB in practice. The \(\mathrm{P_{FA}}\) is an input to the system, the target that \(\mathrm{P_{FA}}\) will be less than 10% so the \(\mathrm{P_{D}}\) will be over 90%. The simulation results shows a PFA and PD close to energy detection, but better for Renyi-entropy [11]  
The parameters from Table 1 were used for experiments. Results show that the SNR needed is SNR = \(-\)11 dB for the proposed Renyi-Entropy based detector and SNR= \(-\)3 dB for the energy detector. The proposed scheme has an 8 dB performance improvement compared with energy detector [11]. After comparing the AWGN and Rayleigh channels, a 5 dB difference is noticed because of additional fading losses. The Renyi-entropy detector must have a SNR of \(-\)11 dB compared to \(-\)16 dB in the AWGN channel.