Fluid Antenna-Assisted Rectangular Differential Index Modulation: A Non-Coherent System Design, Optimization, and Performance Analysis

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schemes under static channel conditions, while offering a performance advantage in time-varying channels with outdated CSI.