Non-binary coded CCSK and Frequency-Domain Equalization with simplified LLR generation

In this paper, we investigate the performance of Single-Carrier (SC) transmission with Non-Binary Low-Density Parity-Check (NB-LDPC) coded Cyclic Code-Shift Keying (CCSK) signaling in a multipath environment and we show that the combination of CCSK signaling and non-binary codes results in two key advantages, namely, improved Log-Likelihood Ratio (LLR) generation via correlations and reduced implementation complexity. We demonstrate that Maximum Likelihood (ML) demodulation can be expressed by two circular convolution operations and thus it can be processed in the frequency domain. Then, we propose a joint Frequency-Domain Equalization (FDE) and LLR generation scheme that aims at reducing the complexity of the receiver. Finally, we demonstrate through Monte-Carlo simulations and histogram analysis that this proposed CCSK signaling scheme gives more robustness to SC-FDE systems than commonly employed Hadamard signaling schemes (a gap of ≈ 1.5dB in favor of CCSK signaling is observed at BER = 10⁻⁵, assuming perfect Channel State Information).