# Null Subcarrier Index Modulation in OFDM Systems for 6G and Beyond
## 7 Simulation Results
Figure 8 depicts the bit error rate performance of the conventional and the proposed waveforms by using the BPSK complex modulation. The proposed NSC-OFDM-IM was tested with different sizes of complex subgroups. Each simulation result was compared with the conventional OFDM and OFDM-IM systems. The complex subgroups with the sizes of \(n=\widetilde{M}=4\) and \(n=\widetilde{M}=8\) were simulated. Along the frequency spectrum, the number of total subgroups (K) were 32 and 16 for \(\widetilde{M}=4\) and \(\widetilde{M}=8\), respectively. In the low SNR values, the proposed system struggled to achieve the null carrier indices due to the significant amount of noise, which caused the signal to be distorted, at the position of the null subcarriers in the frequency domain. However, the performance of the system was significantly improved by the increasing SNR values while maintaining the same BER as OFDM-IM. In Figure 9, the spectral efficiencies of the waveforms in the BPSK modulation are illustrated. Theoretically, in terms of the spectral efficiency, as shown in Table 3, the proposed scheme outperformed the conventional OFDM while having the same spectral efficiency as the existing OFDM-IM. Experimentally, we showed that the proposed NSC-OFDM-IM scheme had an improved performance over the increasing SNR values as compared to the conventional OFDM scheme. From Table 3, we also observed that the NSC-OFDM-IM scheme had the same spectral efficiency in different complex subgroup configurations, which consisted of three and four subcarrier locations. However, according to the simulation results of each NSC-OFDM-IM configuration, the system designed with the complex subgroups having four subcarrier locations reached the maximum spectral efficiency earlier than the other configuration consisting of eight subcarrier locations in the complex subgroups. Figure 8: BER performance comparison between the proposed NSC-OFDM-IM and conventional OFDM-IM/OFDM, where the BPSK modulation was adopted. Figure 10 shows the comparison of the bit error rates by using the 4-QAM complex modulation. The proposed system was tested by configuring the complex subgroups with 4, 8, and 16 subcarriers. Theoretically, in the design of the complex subgroups with four subcarriers, the proposed system had the same spectral efficiency as the classical OFDM system. However, according to the simulation results, the proposed waveform exhibited better BER performance than the OFDM system. Most probably, the reason for this behavior was that the proposed waveform successfully captured the null carrier locations; however, conventional  
Figure 10: BER performance comparison between the proposed NSC-OFDM-IM and conventional OFDM-IM/OFDM, where 4-QAM modulation was adopted. Figure 9: Comparison of the proposed NSC-OFDM-IM with conventional OFDM/OFDM-IM in terms of spectral efficiency, where the BPSK modulation was adopted. OFDM failed to obtain the complex data, which coincided at the same location as the NSC-OFDM-IM null carriers along the frequency axis. It was also observed that the proposed scheme achieved the same error performance as the OFDM-IM scheme. The succession rate of the null subcarrier indices was also affected by the low SNR values and the size of the subgroups. Figure 11 shows the succession rate of capturing the correct null carrier positions in the complex subgroups. The system configured by using four subcarrier locations in each subgroup had better succession performance than the other subgroup configurations consisting of eight and sixteen subcarrier locations, in lower SNR values. However, with the increasing SNR regimes, all the inactive carrier positions along the frequency spectrum were successfully captured in all 4-QAM modulated subgroup configurations.