URLLC with Massive MIMO: Analysis and Design at Finite Blocklength

TL;DR

This paper develops a finite blocklength analysis framework for Massive MIMO systems, assessing error probabilities for URLLC with practical considerations like imperfect CSI and pilot contamination, and demonstrates the effectiveness of MMSE processing.

Contribution

It introduces a rigorous finite blocklength framework for Massive MIMO, including numerical evaluation methods and insights into processing techniques for URLLC.

Findings

Error probability approaches zero as antennas increase with MMSE processing.

Orthogonal pilots are necessary for ultra-reliable error rates at finite blocklength.

Maximum ratio processing is insufficient for URLLC requirements.

Abstract

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. On the other hand, 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.