Enhanced Carrier Mode Shift Keying

Carrier mode shift keying (CMSK) is a recently proposed waveform-domain index modulation scheme that improves the spectral efficiency (SE) of hybrid carrier (HC) communication systems. This innovative scheme simultaneously transmits information bits mapped to the traditional constellation symbols as well as information bits mapped to the index of the weighted-type fractional Fourier transform (WFRFT) parameter. In this paper, we propose an enhanced version of CMSK (E-CMSK) that introduces a subblock precoding module at the transmitter side. Compared with CMSK, E-CMSK conveys index information through subblock-level parameter mapping, thereby further improving the SE. Furthermore, E-CMSK provides enhanced system flexibility, enabling trade-offs among the SE, reliability and detection complexity through subblock size adjustment. To address the prohibitive complexity of the maximum likelihood (ML) detector, a low-complexity sequential detector based on linear frequency domain equalization (FDE) is developed, which reduces the computational complexity from exponential to linear. Furthermore, to compensate for the performance loss inherent in linear equalization, an enhanced iterative block decision feedback equalization (IB-DFE) detector is proposed. This iterative scheme effectively suppresses residual interference, enabling the system to approach the global ML performance. An analytical expression for the average overall bit error rate (BER) is derived to provide theoretical performance insights. While this expression reveals the impact of key parameters like Euclidean distance, its complexity makes it intractable for direct optimization. Therefore, we directly analyze the Euclidean distance distribution of the E-CMSK constellation as an intuitive yet effective tool for system design. This analysis guides the design of a Gray-coded bit-parameter mapping scheme and an equally spaced WFRFT parameter selection strategy, which aims to improve the overall BER performance. Simulation results demonstrate that the proposed E-CMSK scheme outperforms the conventional HC system in multi-path fading channels, particularly at high SNRs.