Orthogonal time frequency space (OTFS) modulation is a recently proposed delay-Doppler (DD) domain communication scheme, which has shown promising performance in general wireless communications, especially over high-mobility channels. In this paper, we investigate DD domain Tomlinson-Harashima precoding (THP) for downlink multiuser multiple-input and multiple-output OTFS (MU-MIMO-OTFS) transmissions. Instead of directly applying THP based on the huge equivalent channel matrix, we propose a simple implementation of THP that does not require any matrix decomposition or inversion. Such a simple implementation is enabled by the DD domain channel property, i.e., different resolvable paths do not share the same delay and Doppler shifts, which makes it possible to pre-cancel all the DD domain interference in a symbol-by-symbol manner. We also study the achievable rate performance for the proposed scheme by leveraging the information-theoretical equivalent models. In particular, we show that the proposed scheme can achieve a near optimal performance in the high signal-to-noise ratio (SNR) regime. More importantly, scaling laws for achievable rates with respect to number of antennas and users are derived, which indicate that the achievable rate increases logarithmically with the number of antennas and linearly with the number of users. Our numerical results align well with our findings and also demonstrate a significant improvement compared to existing MU-MIMO schemes on OTFS and orthogonal frequency-division multiplexing (OFDM).

翻译：正交时频空（OTFS）调制是近期提出的一种延迟-多普勒（DD）域通信方案，在一般无线通信（特别是高移动性信道）中展现出优越性能。本文针对下行链路多用户多输入多输出OTFS（MU-MIMO-OTFS）传输，研究DD域Tomlinson-Harashima预编码（THP）方法。我们提出一种无需任何矩阵分解或求逆的THP简化实现方案，避免直接对庞大等效信道矩阵应用THP。该简化方案的可行性源于DD域信道特性——不同可分辨路径不具有相同延迟与多普勒频移，这使得逐符号预消除所有DD域干扰成为可能。通过利用信息论等效模型，本文进一步研究了所提方案的可达速率性能。特别地，我们证明该方案在高信噪比（SNR）条件下可实现接近最优的性能。更重要的是，推导了可达速率关于天线数与用户数的标度律：可达速率随天线数呈对数增长，随用户数呈线性增长。数值仿真结果与理论分析高度吻合，且相比现有基于OTFS与正交频分复用（OFDM）的MU-MIMO方案，所提方法性能显著提升。