# Null Subcarrier Index Modulation in OFDM Systems for 6G and Beyond
## 8 Discussion  
Computational complexity is one of the open issues in the existing OFDM-IM systems. In this paper, we proposed a new method for mapping and detecting the index bits with the reduced computational complexity algorithms. With the aim of overcoming the problems mentioned in the Introduction, the proposed method tackles the complexity problem by eliminating the need for using either a look-up table or a combinatorial algorithm for the index mapper and detector. Different from the existing studies [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17] on the OFDM-IM scheme, in the frequency domain subgroup, this novel transmission technique incorporates the index of a null subcarrier rather than the indexes of active subcarriers. The additional data bits (the index bits) are conveyed by the index of the null subcarrier in the subgroup.  
We showed that the computational complexity of the proposed method was significantly reduced as compared with the known OFDM-IM scheme, as shown in Table 5. The proposed NSC-OFDM-IM also maintains the spectral efficiency of the existing OFDM-IM scheme, as depicted in Table 3. Moreover, this new method does not suffer from any performance degradation and expresses the same BER performance, as illustrated in Figures 8, 10, and 13, but it differs from the existing studies [11; 14] in terms of the need to use the combinadic algorithms and the way of conveying the index bits through the indices of the subcarrier locations. Furthermore, while these existing studies express the computational complexity of the index selection/detection algorithms (the combinatorial algorithms), the proposed method in our study does not require using the combinatorial method.  
At the transmitter side, the complex subgroup in the frequency domain was designed in such a way that the proposed method first assumes all subcarriers as if they are all in the active state in the frequency domain, and then, based on the incoming index bits, it starts by deactivating one of the active subcarriers within the subgroup. In other words, we were interested in finding the location of the subcarrier that will be left empty in the frequency domain, which means there will be no carrier generated at that frequency point. The remaining active subcarriers were used for the complex data modulation, as in the conventional OFDM-IM systems. In contrast to the existing OFDM-IM methods, the proposed method is not concerned with the order of the active subcarrier indices in the complex subgroup, since these indices are not taken into account for data transmission.  
At the receiver side, the proposed NSC-OFDM-IM has the same LLR processing as the existing OFDM-IM, but the detection of the subcarrier index is performed in a different  
Figure 15: Performance of the proposed NSC-OFDM-IM without applying the LLR detection.  
way in comparison to the work in [13; 17]. In more detail, in the traditional OFDM-IM scheme, the LLR algorithm is used to find the arrangement of the indices of the active subcarriers in the complex subgroup. However, in the proposed NSC-OFDM-IM scheme, the index detector algorithm is only interested in finding the null subcarrier location in the subgroup since the extra information bits are mapped to the inactive subcarrier index. In other words, the minimum value of the LLR coefficients in each subgroup indicates that the probability of occurrence of an active subcarrier at that location (the index of minimum value) is extremely small, and hence, it means the occurrence of a null subcarrier.