# Superimposed Training Combined Approach for a Reduced Phase of Spectrum Sensing in Cognitive Radio
## 6 Results and Discussion
However, the simplified version of the SCAR-Phase is in the sense of computational complexity, which is analyzed in terms of the number of real operations in what follows. The computational complexity of the proposed approaches is shown in Figure 9 in terms of the required number of real operations as a function of the SNR. The results are obtained for a target pair of probabilities \(\beta_{d}=0.9\) and \(\beta=0.1\) using (44) for the SCAR-Phase sensing and (46) for the simplified version. It can be seen that, as the SNR decreases, the required number of real operations of the simplified SCAR-Phase also decreases in comparison to those required by the other approach. This is due to the fact that in the low SNR, the energy detector in the first sample processing period of the SCAR-Phase sensing decides more frequently the absence of the PU's signal. In consequence, the enhanced ST-based detection in the second sample processing period is executed. Since in the simplified version, the first sample processing period is omitted, the required number of real operations is reduced. For example, in SNR equal to \(-15\) dB, the SCAR-Phase sensing requires \(2.551\times 10^{5}\) real operations whereas the simplified version needs \(2.434\times 10^{5}\) real operations. The reduction is more noticeable in lower SNR  
Figure 7: Comparison of the (overall) probability of detection against SNR for different spectrum sensing schemes. values. For example, in SNR equal to \(-20\) dB, the SCAR-Phase sensing requires \(2.955\times 10^{5}\) real operations whereas the simplified version needs \(2.697\times 10^{5}\) real operations. Figure 8: Comparison of the required number of samples to achieve a probability of detection \(\rho_{d}=0.9\) for a target probability of false alarm \(\rho=0.1\) for different spectrum sensing schemes. Figure 9: Comparison of the required number of real operations to achieve a probability of detection \(\beta_{d}=0.9\) for a target probability of false alarm \(\beta=0.1\) for the proposed spectrum sensing schemes. Furthermore, in Figure 10 the performance of the proposed approaches is compared to the energy detector with a constraint on the level of protection for the PU. Therefore, the overall probability of a false alarm is obtained against different number of samples to satisfy a \(\beta_{d}=0.9\). The results show that with \(N=2000\), the probability of false alarm for the proposed approaches is approximately 0.0052, whilst for the energy detector, it is equal to 0.4633. This difference increases with the number of samples used for spectrum sensing, impacting the SU's achievable throughput. Finally, the maximum SU's achievable throughput against the number of samples is compared in Figure 11 for the proposed methods and the energy detector. The results are obtained using (45) for a frame size of \(N_{f}=60,000\) samples, \(\gamma_{s}=15\) dB and \(\gamma_{p}=-15\) dB. Moreover, different values of \(\Pr\{\mathcal{H}_{0}\}\) are considered to show the dependency of the SU's achievable throughput on the value of the prior probability of absence of the PU. It can be seen that for the proposed approaches the maximum throughput is achieved with \(N=2000\) samples, whereas for the energy detector it is achieved with \(N\approx 8500\) samples. Note that these number of samples are equal for both prior probabilities, but the achievable throughput varies accordingly since there are more opportunities to carry out SU's transmissions when the probability that the PU is inactive is greater. Figure 10: Probability of false alarm against sensing time.