Fluid antenna-enabled multiple-input multiple-output (FA-MIMO) systems hold significant application potential; however, they also introduce substantial costs in channel state information (CSI) acquisition. In this paper, we propose a novel FA-assisted rectangular differential index modulation (FA-RDIM) scheme for MIMO systems, aiming to achieve high spectral efficiency while addressing the problem of the increased CSI acquisition cost. The transmitted information is mapped to modulation symbols and cyclic shifts of FA pattern indices. A multi-stage detection method is introduced, which reduces computational complexity by identifying the most likely candidates for FA pattern indices. We derive a closed-form expression for the bit error rate (BER) theoretical performance considering error propagation, and present an optimization algorithm based on rank and determinant criterion (RDC), Hamming distance (HD), and gradient descent (GD) to optimize the FA pattern vector set. Simulation results demonstrate that the proposed scheme exhibits a minimal performance loss compared to conventional coherent modulation schemes under static channel conditions, while offering a performance advantage in time-varying channels with outdated CSI.

The reconfigurable intelligent surface (RIS) aided index modulation (IM) is a promising technology for next-generation wireless communications. However, acquiring channel state information (CSI) for RIS-based IM requires expensive pilot overhead, especially for the IM in multiple domains. In this paper, a novel rectangular differential reflecting spatial modulation (RDRSM) system is proposed for the RIS-aided multiple-input multiple-output (MIMO) system. Specifically, the proposed multi-antenna-activated RDRSM (M-RDRSM) scheme utilizes a rectangular dispersion matrix (DM) to jointly map a digital beamforming (DBF) weight vector and a RIS reflection pattern to perform the rectangular differential modulation. A thorough analysis presents that the proposed M-RDRSM scheme can achieve high-spectral efficiency, low complexity of the system, and noncoherent decoding without prior knowledge of CSI in the space-reflection dual-domain IM. Further, the proposed M-RDRSM scheme is simplified to a single-antenna-activated RDRSM (S-RDRSM) scheme, which can reduce the hardware cost and avoid the inter-antenna synchronization problem more effectively. Simulation results demonstrate that the proposed RDRSM scheme performs better in terms of bit error rate performance and achieve a lower decoding complexity than the existing correlated differential IM schemes with the same achievable spectral efficiency.