## 4 Simulation Results  
In this section, simulation results are presented in terms of PAPR reduction and BER performance. The simulation of the proposed hybrid PAPR reduction scheme using phase rotation factors and dither signals on partial sub-carriers is implemented. Scenarios with different \(U\) (\(U\in\{2,4\}\)), \(\beta\) (\(\beta\in\{0.25,0.5\}\)), and \(V\) (\(V\in\{2,4\}\)) are simulated and the corresponding results are compared with the conventional PAPR reduction scheme with dither signals [17] (denoted as \"_Dither_\"). As reference, the PAPR performances of PTS, SLM, the S.1 scheme, and the original signal without any PAPR reduction scheme are also included. For the OFDM-IM system, we use \(N=128\), \(n=4\), and \(k=2\). QPSK symbols are applied. For fairness, we use \(R=0.5\) for all selected schemes.  
The PAPR reduction performance comparison among the proposed scheme, PTS scheme, SLM scheme, and _Dither_ scheme in [17] is shown in Figure 9. This figure also compares the proposed scheme with different \(U\) (\(U\in\{2,4\}\)), \(\beta\) (\(\beta\in\{0.25,0.5\}\)), and \(V\) (\(V\in\{2,4\}\)). This result highlights that all PAPR reduction schemes have significant PAPR reduction capabilities. It is shown that the S.1 scheme described in the last section  
Figure 8: The IER of the proposed hybrid PAPR reduction scheme using different \(U\), \(V\), and \(\beta\).  
achieves the worst PAPR reduction performance due to the unexplored idle sub-carriers. However, by introducing phase rotation factors, significant PAPR reduction performance enhancement can be obtained. The proposed hybrid scheme can achieve flexible performance achieved by the conventional PTS and SLM schemes designed for OFDM, the proposed hybrid scheme can achieve an impressive performance in most scenarios. Moreover, it is shown that when \(U=4\), \(V=4\), \(\beta=0.5\), the proposed hybrid scheme can achieve even better performance than that of the _Dither_ scheme, which utilizes all idle sub-carriers. Furthermore, it is obvious that the more idle sub-carriers are used (e.g., \(\beta=0.5\), \(\beta=0.25\)), the better the PAPR reduction performance of the system can be achieved.  
Figure 10 shows the BER performance among the proposed scheme with different parameters, the _Dither_ scheme in [17], and the original OFDM-IM signals. It is illustrated from Figure 10 that the proposed method achieves better BER performance than of the conventional dither signal-based scheme. When \(U=2\), \(V=2\), and \(\beta=0.5\), the proposed scheme can achieve 5 dB gain compared with the conventional method at error probability \(10^{-4}\). However, it is also shown in Figure 10 that although the proposed hybrid scheme owns better PAPR reduction performance, it still has BER degradation compared with the S.1 scheme, which achieves almost the same performance as that of the original OFDM-IM signals (the ideal case). Nevertheless, the proposed hybrid scheme can still obtain better BER performance results and higher energy efficiency compared with the _Dither_ scheme. Additionally, it is shown that \(U\) and \(V\) can affect the error performance because \(U\) and \(V\) affect the IEP of the energy-based detection utilized by the proposed PAPR reduction scheme.  
Figure 9: The CCDF performance comparison among the proposed scheme, the SLM scheme, the PTS scheme, the _Dither_ scheme [17], the S.1 scheme, and the original OFDM-IM signal.