# Null Subcarrier Index Modulation in OFDM Systems for 6G and Beyond
## 1 Introduction  
Rapid technological advancements in industry have resulted in an exponential increase in the number of connected devices, causing a massive volume of data traffic that appears almost impossible to manage by the current wireless networks. The OFDM waveform has been used in several ways and adopted well in several existing wireless communication systems. However, OFDM has certain disadvantages, such as high out-of-band radiation, high peak-to-average power ratio (PAPR) problems [1], and the loss of orthogonality caused by synchronization errors. Thus, the OFDM system requires some improvements to be used for future wireless systems. The primary aim of future-generation wireless communication systems is to provide three generic services: enhanced mobile broadband (eMBB) aiming to improve the high data rate, massive machine-type communications (mMTCs) concentrating on establishing connectivity among a large number of Internet of things (IoT) devices, and ultra-reliable low-latency communications (URLCCs) focusing on providing a link that is extremely sensitive and has a very low latency [2]. In order to meet the requirements of the aforementioned services, in addition to improving the performance of the OFDM system, several types of candidate waveforms for next-generation networks (6G and beyond) have been developed and studied in various environments such as industrial testbeds and academic research labs. In order to improve the performance of wireless systems in terms of spectral efficiency, energy efficiency, etc., the new candidate waveformssuch as universal filtered multicarrier (UFMC) [3], generalized frequency division multiplexing (GFDM) [4], filter bank multicarrier (FBMC) [5], and filtered OFDM [6] have been studied. The key benefit of these candidate waveforms over the classical OFDM system is to improve the spectral efficiency losses caused by high out-of-band radiations. On the other hand, new types of modulation techniques are proposed for OFDM systems to increase the data transmission ability of each subcarrier used in the frequency spectrum, while studies on the aforementioned new waveforms have also been in progress to meet the requirements of the services in 6G and beyond wireless networks. In addition to modulating the subcarriers by the complex constellation mapper, new research on the transmission of additional information bits that are conveyed by the indices of the active subcarriers have recently become very attractive. This new modulation form, known as index modulation (IM), was presented in [7] and has rapidly gained a broad interest. The main idea of IM is to transmit the data not only by modulating the subcarriers, but also by the carrier indices [8], which are involved in transmission based on the incoming data stream. Although, in some configurations, OFDM-IM improves the spectral efficiency over the OFDM systems, the computational complexity of the OFDM-IM waveform remains an open issue. To tackle this issue, several studies have been carried out to reduce the complexity of the system at the transmitter and receiver. An energy-based greedy detection method was proposed with reduced complexity maximum likelihood (ML) in [9]. A modified frequency index modulation (FIM) scheme, which aims to reduce the transmitted energy, was suggested in [10]. This system has a lower complexity compared to the OFDM-IM scheme. By specifying a threshold for the likelihood probability, Reference [11] provided a simpler \"log-likelihood ratio (LLR)\" calculation approach for OFDM-IM that delivers near-optimal coded BER performance, with significantly less complexity. As for the low-complexity receiver design, two linear complexity detection schemes taking into account the minimum mean-squared error and zero-forcing receivers were proposed in [12]. A generalized time domain index modulation scheme (GTD-IM) with low complexity was introduced in [13], where the receiver uses a square-law envelope detector (SLED) to detect the active indices.