A Graph-Based Theoretical Framework and Performance Analysis of Pattern Division Random Access

This paper investigates the theoretical foundations and practical benefits of pattern division random access (PDRA) within the massive multiple input multiple output (MIMO) assisted grant-free paradigm. PDRA leverages the superposition or finite-field operations of orthogonal/quasi-orthogonal structural building blocks to provide substantial pilot diversity, thereby effectively mitigating pilot collisions. We characterize PDRA through a random uniform graph process, establishing a novel connection between PDRA and decoding of graph-based codes. Theoretical performance limits are derived for the per-user probability of error (PUPE), quantifying user distinguishability during channel estimation. Furthermore, we conduct a detailed PUPE performance analysis of the PDRA scheme with successive interference cancellation (PDRA-SIC) in the finite-blocklength regime, demonstrating its capability to efficiently resolve collisions and mitigate interference. The analysis shows that PDRA-SIC achieves significantly improved PUPE performance compared to conventional single-pilot schemes in massive ultra-reliable low-latency communication (mURLLC) scenarios, underscoring its practical potential for next-generation wireless systems.