Statistical Delay Performance Analysis for URLLC in Uplink Cell-Free Massive MIMO Systems: A Stochastic Network Calculus Perspective

Cell-free (CF) massive multiple-input multiple-output (mMIMO), which has been considered as a promising technology to achieve ultra-reliable low latency communications (URLLC), emphasizes extreme and rare events instead of well studied average performance. In this paper, we analyze the statistical delay performance in uplink CF mMIMO-aided URLLC systems, specifically characterizing the tail of the delay distribution. Firstly, we derive the SINR distribution in a user-centric uplink CF mMIMO system using moment-matching techniques and log-normal approximation. Subsequently, the average decoding error probability (DEP) with finite blocklength coding is studied based on the derived distribution, and an upper bound on the delay violation probability (DVP) is analyzed using stochastic network calculus (SNC). To provide a clearer representation of the bound on DVP, a closed-form upper bound for the average DEP is derived. Furthermore, we propose a rate adaptive scheme based on SNC to minimize the DVP. Numerous numerical results validate the accuracy of the derived SINR distribution and the upper bound on average DEP. Besides, CF mMIMO systems exhibit significant gains compared to mMIMO systems in terms of statistical delay performance, as the distributed deployment of numerous APs can effectively compensate for performance degradation caused by interference and increased arrival rates.