Low-Complexity Multi-Slot Cross-Domain MAMP Receiver and Coding Principle for MIMO-OTFS

This paper investigates a coded multiple-input multiple-output (MIMO) orthogonal time frequency space (OTFS) system in high-mobility channels. Existing coding schemes are limited by the strong assumption that the codeword length is equal to the dimension of the modulation length. Moreover, the design of low-complexity and high-reliability receivers remains a critical challenge for MIMO-OTFS systems. Therefore, this paper proposes a multi-slot cross-domain memory approximate message passing (MS-CD-MAMP) receiver as well as develops its information-theoretic (i.e., achievable rate) limit and optimal coding principle for MIMO-OTFS. The proposed MS-CD-MAMP receiver can exploit not only the time domain channel sparsity for low complexity but also the constellation constraints in DelayDoppler (DD) domain for performance enhancement. Meanwhile, limited by the high-dimensional complex state evolution (SE), a simplified single-input single-output variational SE is proposed to derive the achievable rate of MS-CD-MAMP and the optimal coding principle with the goal of maximizing the achievable rate. Numerical results show that the finite-length performances of MS-CD-MAMP with optimized low-density parity-check (LDPC) codes are about <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1.1 \sim 1.4 \mathbf{d B}$</tex> away from the associated constrained information-theoretic limit and has <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.9 \sim 4.7 \mathbf{d B}$</tex> gain over the well-designed point-to-point LDPC codes.