The fast adoption of Massive MIMO for high-throughput communications was enabled by many research contributions mostly relying on infinite-blocklength information-theoretic bounds. This makes it hard to assess the suitability of Massive MIMO for ultra-reliable low-latency communications (URLLC) operating with short-blocklength codes. This paper provides a rigorous framework for the characterization and numerical evaluation (using the saddlepoint approximation) of the error probability achievable in the uplink and downlink of Massive MIMO at finite blocklength. The framework encompasses imperfect channel state information, pilot contamination, spatially correlated channels, and arbitrary linear spatial processing. In line with previous results based on infinite-blocklength bounds, we prove that, with minimum mean-square error (MMSE) processing and spatially correlated channels, the error probability at finite blocklength goes to zero as the number $M$ of antennas grows to infinity, even under pilot contamination. However, numerical results for a practical URLLC network setup involving a base station with $M=100$ antennas, show that a target error probability of 10 ⁻⁵ can be achieved with MMSE processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. Maximum ratio processing does not suffice.

中文翻译：

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具有大规模 MIMO 的 URLLC：有限块长度的分析和设计

许多研究贡献主要依赖于无限块长度信息理论界限，因此在高吞吐量通信中快速采用大规模 MIMO。这使得很难评估大规模 MIMO 是否适用于使用短块长度代码运行的超可靠低延迟通信 (URLLC)。本文提供了一个严格的框架，用于在有限块长度下大规模 MIMO 的上行链路和下行链路中可实现的错误概率的表征和数值评估（使用鞍点近似）。该框架包含不完善的信道状态信息、导频污染、空间相关信道和任意线性空间处理。与之前基于无限块长度边界的结果一致，我们证明， 百万美元 即使在飞行员污染的情况下，天线数量也会增长到无穷大。然而，涉及基站的实际 URLLC 网络设置的数值结果 $M=100$ 天线，表明只有在将正交导频序列分配给网络中的所有用户时，才能通过 MMSE 处理均匀地在每个小区上实现10 ^-5的目标错误概率 。最大比率处理是不够的。