DLCT-c3 Index Modulation via Modular-Permutation Signaling

Abstract

DLCT-<inline-formula> <tex-math notation="LaTeX">$c_{3}$ </tex-math></inline-formula> index modulation (DLCT-<inline-formula> <tex-math notation="LaTeX">$c_{3}$ </tex-math></inline-formula> IM) is presented as a single-parameter transform-domain index signaling scheme. The <inline-formula> <tex-math notation="LaTeX">$c_{3}$ </tex-math></inline-formula>-parameterized invertible modular-dilation state of a DLCT-inspired finite operator family is used as an information-bearing index resource. Under coherent scalar-flat channels, the common chirp–DFT–chirp factor can be removed by a shared inverse transform without changing Euclidean distances or ML decisions, enabling an exact structured implementation of joint index-and-symbol ML detection. Equal-rate <inline-formula> <tex-math notation="LaTeX">$E_{b}/N_{0}$ </tex-math></inline-formula> simulations under AWGN and Rician/Rayleigh flat fading compare the proposed scheme with DFT/QAM and OFDM-IM. The AWGN union bound approaches the simulated BER at high <inline-formula> <tex-math notation="LaTeX">$E_{b}/N_{0}$ </tex-math></inline-formula>, while the measured fading slopes agree with the predicted first-order behavior.