We consider the problem of degradation in performance of multi-carrier multi-user massive MIMO systems when channel induced Doppler spread is high. Recently, Orthogonal Time Frequency Space (OTFS) modulation has been shown to be robust to channel induced Doppler spread. In OTFS based systems, information symbols are embedded in the delay-Doppler (DD) domain where they are jointly modulated to generate the time-domain transmit signal. Due to the multi-path delay and Doppler shifts, the DD domain information symbols need to be jointly demodulated at the receiver. For multi-carrier based communication (e.g., Orthogonal Frequency Division Multiplexing (OFDM)), massive MIMO systems have been shown to achieve high spectral and energy efficiency with low complexity multi-user precoding in the downlink. Extending the same to OTFS based downlink multi-user massive MIMO systems is challenging due to the requirement for joint demodulation of all information symbols at the user terminal (UT). In this paper, we solve this problem by proposing a novel OTFS based multi-user precoder at the base station (BS) and a corresponding low complexity detector (LCD) at the user terminals (UTs), which allows for separate demodulation of each DD domain information symbol at the UT. The complexity of the proposed precoder increases only linearly with increasing number BS antennas Q and the number of UTs. We show, through analysis, that as Q increases (with total transmitted power decreased linearly with Q), the proposed low complexity detector achieves a sum SE close to that achieved with optimal joint demodulation at each UT. Numerical simulations confirm our analysis and also show that the SE and error rate performance of the proposed OTFS based massive MIMO precoder and LCD detector is significantly more robust to channel induced Doppler spread when compared to OFDM based multi-user massive MIMO systems.

中文翻译：

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多用户大规模MIMO OTFS下行链路中的低复杂度预编码和检测

当信道感应多普勒扩展很高时，我们考虑了多载波多用户大规模MIMO系统性能下降的问题。最近，正交时频空间（OTFS）调制已被证明对信道诱导的多普勒扩展具有鲁棒性。在基于OTFS的系统中，信息符号嵌入到延迟多普勒（DD）域中，在该域中它们被联合调制以生成时域发射信号。由于多径延迟和多普勒频移，DD域信息符号需要在接收机处被联合解调。对于基于多载波的通信（例如，正交频分复用（OFDM）），大规模MIMO系统已显示出在下行链路中具有低复杂度的多用户预编码的情况下实现了高频谱和能量效率。由于需要在用户终端（UT）对所有信息符号进行联合解调，因此将其扩展到基于OTFS的下行链路多用户大规模MIMO系统具有挑战性。在本文中，我们通过在基站（BS）上提出一种基于OTFS的新型多用户预编码器并在用户终端（UT）上提出相应的低复杂度检测器（LCD）来解决此问题，从而可以对每个DD分别进行解调UT上的域信息符号。所提出的预编码器的复杂度仅随着数量增加的BS天线Q和UT的数量线性增加。通过分析，我们表明，随着Q的增加（总发射功率随Q线性降低），建议的低复杂度检测器获得的总和SE接近于每个UT的最佳联合解调所获得的总和。