Theoretic Analysis on Deterministic Reliability of Finite Blocklength Massive MIMO Transmission

To meet the zero-tolerance requirement for performance collapse of key ultra-reliable low-latency communication (URLLC) services in the sixth generation (6 G), this paper formalizes a new notion of deterministic reliability, which requires a target decoding error probability (DEP) to be met even under extreme channel conditions. Leveraging the abundance of spatial links, massive multiple-input multiple-output (MIMO) is a natural enabler of such deterministic reliability, but the systematic theoretical support is urgently needed. By invoking the normal approximation in finite-blocklength regime, this study derives an explicit closed-form expression for the cumulative distribution function (CDF) of DEP in massive MIMO systems. Furthermore, approximate analyses and simulation results for the first and second moments of DEP demonstrate that, as either the spatial degrees of freedom (DoF) or the blocklength grows unboundedly, massive MIMO achieves ever-higher and more deterministic reliability. The analysis also reveals an interchangeability between spatial and temporal resources, which implies that reliability requirements can still be satisfied by increasing the DoF even when the temporal codeword length is further shortened. The theoretical derivations in this paper reveal the nature of deterministic transmission in massive MIMO systems and establish an essential theoretical basis for the continued advancement of 6 G URLLC.