Achievable Rate of $N$-Continuous Precoded SIM-OFDM

$N$-continuous (NC) precoder is a class of efficient sidelobe suppression techniques by smoothing the consecutive multicarrier symbols at the cost of additional interference to the transmit signals. In this paper, we firstly investigate the $N$-continuous precoder in recently developed Subcarrier-Index Modulation Orthogonal Frequency Division Multiplexing (SIM-OFDM) systems, when the channel is modeled by frequency-selective fading. On the one hand, the Signal to Interference Plus Noise Ratio (SINR) is derived through theoretical analysis. Furthermore, with the quantified SINR, the achievable rate is first acquired for evaluating the performance of NC precoded SIM-OFDM. We also show that the above-mentioned performance analysis matches well with the simulation results.