Message Passing Algorithm for GFDM-IM Detection

The generalized frequency division multiplexing with index modulation (GFDM-IM) is a recently developed multi-carrier technique, which has the signal feature that only part of subcarriers are activated. In this paper, the message passing (MP)-based signal detection of GFDM-IM is studied, and two MP detectors are presented. In the first MP detector, MP algorithm is performed directly in the factor graph constructed by the product of GFDM modulation matrix and channel matrix. In the second MP detector, the received signal is first frequency-domain equalized, and then MP algorithm is performed based on a sparse factor graph by utilizing the structured sparsity of the modulation matrix. In both MP detectors, an additional pattern node is introduced to leverage the relation in the variable nodes belonging to the same IM block introduced by activation pattern constraint. Simulation results show that, the proposed MP detectors show some superiority over conventional linear detectors in terms of error performance and/or complexity.