Hybrid BP-EP based iterative receiver for faster-than-nyquist with index modulation

Faster-than-Nyquist (FTN) signaling with index modulation (IM) is an attractive non-orthogonal transmission scheme characterized by high spectral efficiency and energy efficiency. In this paper, we develop a hybrid belief propagation (BP) and expectation propagation (EP) based iterative receiver for FTN-IM systems. To approach the optimal maximum a posteriori (MAP) receiver, we derive the factorization of marginal posterior probability and construct the corresponding factor graph by ignoring trivial interferences. To address the inherent colored noise imposed by FTN signaling, we employ autoregressive (AR) model to approximate the correlated noise samples. To further design low-complexity parametric message passing receiver, we resort to expectation propagation (EP) to derive Gaussian approximation of discrete transmitted symbols containing specific inactivated zeros. As a result, the overall complexity grows linearly with the number of transmitted symbols. Simulation results show that the coded FTN-IM system relying on the proposed iterative receiver can improve the spectral efficiency up to 43% without performance loss. For identical spectral efficiency with the Nyquist counterpart, FTN-IM signaling achieves 0.80 dB performance gain with proper packing factor and coding rate.