Doubly-Iterative Sparsified MMSE Turbo Equalization for OTFS Modulation

Currently, orthogonal time frequency space (OTFS) modulation has drawn much attention to reliable communications in high-mobility scenarios. This paper proposes a doubly-iterative sparsified minimum mean square error (DI-S-MMSE) turbo equalizer, which iteratively exchanges the extrinsic information between a soft-input-soft-input (SISO) MMSE estimator and a SISO decoder. Our proposed equalizer does not suffer from short loops and approaches the performance of the near-optimal symbol-wise maximum a posteriori (MAP) algorithm. To exploit the inherent sparsity of OTFS system, we resort to graph theory to investigate the sparsity pattern of the channel matrix, and propose two sparsification guidelines to reduce the complexity of calculating the matrix inverse at the MMSE estimator. Then, we apply two iterative algorithms to MMSE estimation, i.e., the Generalized Minimal Residual (GMRES) and Factorized Sparse Approximate Inverse (FSPAI) algorithms. The former is used at the initial turbo iteration, whose global convergence is proven in our equalizer, while the latter is used at the subsequent turbo iterations with the help of our proposed guidelines. Simulation results demonstrate that our equalizer has a linear order of complexity while the performance loss incurred by the sparsification is only 0.2 dB at $10^{-4}$ bit error rate.