Error Rate Analysis for Grant-free Massive Random Access with Short-Packet Transmission

Grant-free massive random access (RA) is a promising protocol to support the massive machine-type communications (mMTC) scenario in 5G and beyond networks. In this paper, we focus on the error rate analysis in grant-free massive RA, which is critical for practical deployment but has not been well studied. We consider a two-phase frame structure, with a pilot transmission phase for activity detection and channel estimation, followed by a data transmission phase with coded data symbols. Considering the characteristics of short-packet transmission, we analyze the block error rate (BLER) in the finite blocklength regime to characterize the data transmission performance. The analysis involves characterizing the activity detection and channel estimation errors as well as applying the random matrix theory (RMT) to analyze the distribution of the post-processing signal-to-noise ratio (SNR). As a case study, the derived BLER expression is further simplified to optimize the pilot length. Simulation results verify our analysis and demonstrate its effectiveness in pilot length optimization.