多输入多输出多载波系统中跨域MAMP接收机的可实现速率与编码原理
Achievable Rate and Coding Principle for MIMO Multicarrier Systems With Cross-Domain MAMP Receiver Over Doubly Selective Channels
AI总结：
本文提出了一种多槽跨域记忆近似消息传递接收机，用于MIMO多载波系统，实现了可实现速率的理论极限和最优编码原理，提升了在双选择性信道中的性能。
摘要：
多载波调制与多输入多输出（MIMO）的结合对于在复杂环境中可靠传输无线信号至关重要，这显著提高了频谱效率。现有研究表明，流行的正交时频空（OTFS）和仿射频分复用（AFDM）在未编码的双选择性信道中相对于正交频分复用（OFDM）具有显著优势。然而，这些优势是否适用于编码系统仍存疑问。同时，编码MIMO多载波系统的信信息论极限分析及相应的低复杂度接收机设计仍不明确。为克服这些挑战，本文提出了一种多槽跨域记忆近似消息传递（MS-CD-MAMP）接收机，并开发了其信息论（即可实现速率）极限和最优编码原理，适用于MIMO-多载波调制（如OFDM、OTFS和AFDM）系统。所提出的MS-CD-MAMP接收机不仅可以利用时间域信道稀疏性以实现低复杂度，还可以利用相应的符号域星座约束以提升性能。同时，受限于高维复杂数状态演变（SE），提出了一种简化的单输入单输出变分SE，以推导MS-CD-MAMP的可实现速率和最优编码原理，目标是最大化可实现速率。数值结果表明，使用MS-CD-MAMP的编码MIMO-OFDM/OTFS/AFDM在双选择性信道中实现了相同的最大可实现速率，其有限长度性能与实际优化的低密度奇偶校验（LDPC）码的理论极限仅相差0.5～1.8 dB，并且在精心设计的点对点LDPC码上具有0.8～4.4 dB的增益。
英文摘要：
The integration of multicarrier modulation and multiple-input-multiple-output (MIMO) is critical for reliable transmission of wireless signals in complex environments, which significantly improve spectrum efficiency. Existing studies have shown that popular orthogonal time frequency space (OTFS) and affine frequency division multiplexing (AFDM) offer significant advantages over orthogonal frequency division multiplexing (OFDM) in uncoded doubly selective channels. However, it remains uncertain whether these benefits extend to coded systems. Meanwhile, the information-theoretic limit analysis of coded MIMO multicarrier systems and the corresponding low-complexity receiver design remain unclear. To overcome these challenges, 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-multicarrier modulation (e.g., OFDM, OTFS, and AFDM) systems. The proposed MS-CD-MAMP receiver can exploit not only the time domain channel sparsity for low complexity but also the corresponding symbol domain constellation constraints 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 coded MIMO-OFDM/OTFS/AFDM with MS-CD-MAMP achieve the same maximum achievable rate in doubly selective channels, whose finite-length performance with practical optimized low-density parity-check (LDPC) codes is only 0.5 $\sim$ 1.8 dB away from the associated theoretical limit, and has 0.8 $\sim$ 4.4 dB gain over the well-designed point-to-point LDPC codes.
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