# Hard Fusion Based Spectrum Sensing over Mobile Fading Channels in Cognitive Vehicular Networks
## 5 Numerical and Simulation Results  
In this section, both theoretical and simulated results are provided through numerical and Monte Carlo simulations to illustrate spectrum sensing performance in cognitive vehicular networks. We run the Monte Carlo simulation results over \(10^{4}\) independent trials to verify the accuracy of the developed analytical results. Note that the arbitrary parameters, \(L\), \(N\), \(\eta_{0}\) and \(\gamma_{0}\) are fit for the developed analytical results of the local (global) probability of misdetection. Therefore, for all simulation cases, we choose some simple parameters, \(L\), \(N\), \(\eta_{0}\) and \(\gamma_{0}\) to plot the local (global) probability of misdetection, and observe how they affect the system sensing performance. Without losing generality, we consider a fixed PU case where the PU accesses channel with probability \(p=0.5\). The PU signal is assumed to have unit power and be any kind of modulated signal with carrier frequency of 900 MHz and bandwidth of 6 MHz. The sampling frequency in energy detector is equal to the bandwidth of PU signals, at the same time, the number of sampling observations during a sensing interval is \(L=50\). We consider a Rayleigh multi-path propagation model. For all simulation cases, the channel vector can be modeled as a zero-mean, complex Gaussian random vector with correlation matrix \(\rho\) (\(F_{d}T_{s}=0.01\)). In addition, the average SNR of sensing/reporting channels are assumed to be the same for all SVUs, e.g., \(\eta_{0}=-8\) dB (as it is typically assumed in CVNs) and \(\gamma_{0}=5.5\) dB (as it makes the error probability of reporting channel equal to 0.1). The performances with respect to the local (global) probability of misdetection is estimated to meet the constraint on the local (global) probability of false alarm of \(P_{f}\) (\(Q_{f}\)) = 0.1. First of all, let us consider spectrum sensing with energy detector in non-cooperative scenarios. In Figure 3, the local \(\overline{P}_{m}\) is shown as a function of the number of samples for various SNR. The simulations are performed in the case of \(\mathcal{M}_{2}\) with the parameters \(F_{d}T_{s}\) = 0.01 and \(P_{f}\) = 0.1. As expected, the local \(\overline{P}_{m}\) decreases along with the increasing number of samples. And the decrease of the local \(\overline{P}_{m}\) in the case of high SNR is very rapid compared with low SNR. In Figure 4, the local \(\overline{P}_{m}\) is shown as a function of Doppler shift \(F_{d}T_{s}\). The simulation parameters are \(L=50/500\), \(N=1\), \(\eta_{0}=-8\) dB and \(P_{f}\) = 0.1. With the carrier frequency and the sampling interval fixed, \(F_{d}T_{s}\) value varies at a rate linearly proportional to the speed of the SVU. In addition, a larger \(F_{d}T_{s}\) results in a smaller correlation coefficient (\(\rho\)). The results show clearly that, the probability of misdetection is a decreasing function of the speed of the SVU for all the system configurations. In addition, the local \(\overline{P}_{m}\) with 500 samples declines drastically compared with 50 samples. This reason is that high mobility and a greater number of samples give us an opportunity to achieve more received signal information, thereby enables SVUs to obtain higher sensing performance. In Figure 5, the local \(\overline{P}_{m}\) is shown as a function of the average SNR of sensing channels for various values of \(F_{d}T_{s}\). The simulation parameters are \(L=50\), \(N=1\) and \(P_{f}=0.1\). The capability of energy detector decreases quickly with the reduction of the average received SNR from 10 dB to \(-10\) dB. It can be seen that the simulating results show good or very good agreement with the theoretical analysis for both cases \(\mathcal{M}_{1}\) and \(\mathcal{M}_{3}\), confirming the validity of the developed theoretical analysis. Figure 5 also indicates that these asymptotic results (17) and (11) (18) serve as a upper and lower bounds for the local \(\overline{P}_{m}\) for spectrum sensing over correlated Rayleigh fading channel.