# Null Subcarrier Index Modulation in OFDM Systems for 6G and Beyond
## 1 Introduction
### Contributions and Organization  
The main goal of this research was to design a new scheme for reducing the computational complexity of the OFDM-IM systems by utilizing null subcarrier locations rather than active subcarriers. The major contributions of this paper are summarized as follows:  
* The proposed NSC-OFDM-IM scheme algorithm starts by assuming all the subcarriers as if they are active in the subgroup. Depending on the incoming bit substream, one subcarrier among them is set to inactive. On the other hand, conventional OFDM-IM first assumes all subcarriers as if they are inactive in the subgroup, and the index selector algorithm starts by targeting the combination (or sequences) of activated subcarriers based on lexicographic order in the complex subgroup;
* _Transmitter complexity and index selection:_ In conventional OFDM-IM, in order to determine the indices of the active subcarriers, the first step is to convert the index bits into their equivalent natural value, and then, the combination of k indices corresponding to this natural number is obtained using the combinatorial algorithm. The combinatorial (or combinatics) algorithm is used in existing methods to perform a one-to-one mapping between the decimal number of the index bits and k combinations. In other words, the OFDM-IM scheme requires a number of combinatorial processing in order for the index selector to be able to find the corresponding indices of the subcarriers within the complex subgroup. However, in our proposed method, the index bits are first converted to their corresponding decimal value, and then, the index selector in this scheme calculates the one greater than this decimal value. The new value is then set as the inactive carrier position in the frequency subgroup. In other words, the NSC-OFDM-IM index selector just functions by deactivating one of the active subcarriers in the complex subgroup based on the decimal value of the incoming index bits. By comparing the computational complexity of the index selection mechanisms of the conventional and the proposed schemes, it was found that in the proposed NSC-OFDM-IM, the index selection is performed very easily just by adding 1 to the corresponding decimal value of the index bits, and hence, the proposed method has a significantly reduced complexity at the transmitter;
* _Receiver complexity and index detection:_ At the receiver, after the signal is converted to frequency domain representation, the LLR processing is applied to both conventional OFDM-IM and the proposed NSC-OFDM-IM in the same way. However, the complexity reduction of the index detection algorithm in the proposed scheme comes from the following two aspects: 1. The first complexity reduction is eliminating the need to apply a sorting algorithm to the coefficients in the LLR subgroups. Hence, there is no sorting complexity in all LLR subgroups; 2. In comparison to the conventional scheme, the use of the combinadic ranking algorithm as part of the index detection process is no longer essential in the proposed method because no sorting in the LLR subgroups is required. Hence, there is no complexity in terms of finding the indices of the active carrier locations. The detection mechanism in the proposed method just finds the index of the minimum value of the coefficients in each LLR subgroup. The receiver detector then takes one less than the index number and uses it as the decimal number to convert to the binary value. The remainder of the paper is structured as follows: The conventional OFDM system is summarized in Section 2. The existing OFDM-IM technique is discussed in Section 3. The proposed novel NSC-IM for OFDM system (NSC-OFDM-IM) is introduced in Section 4. The multipath channel model as a transmission environment utilized in this study is given in Section 5. The complexity of the proposed NSC-OFDM-IM scheme is compared with the OFDM-IM scheme in Section 6. The computer simulation results are evaluated in Section 7.