Analysis of Massive Ultra-Reliable and Low-Latency Communications Over the κ-μ Shadowed Fading Channel

We investigate the performance of massive ultra-reliable and low-latency communications (mURLLC) under massive active users, and non-uniform small-scale and shadow fading in the uplink (UL) of a next-generation multiple access (NGMA) system that integrates massive multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA) techniques. We first derive new closed-form expressions to accurately approximate the probability density function (PDF) and cumulative distribution function (CDF) of the channel gains in MIMO systems under the $\kappa $ - $\mu $ shadowed fading. Then, we derive the post-processing signal-to-noise ratio (SNR) and its closed-form PDFs and CDFs in the NGMA system, under both perfect and imperfect channel state information of the $\kappa $ - $\mu $ shadowed fading channel. Given the post-processing SNRs and their PDFs, the general expressions are established for the error probability (EP) to analyze the mURLLC of NGMA by applying finite blocklength information theory. Corroborated by extensive simulations, our analysis reveals that with the increasing reliability requirements of the users, the relative gaps in EPs enlarge between users experiencing different fading channels, and the feasible system configurations (i.e., the transmit powers of the users, and the numbers of antennas, active users, and subcarriers) also increasingly differ between the users. The impact of different fading on mURLLC implementations cannot be overlooked, and the research of mURLLC under the $\kappa $ - $\mu $ shadowed fading model is indispensable. The NGMA system considered in this paper is capable of achieving mURLLC under non-uniform small-scale and shadow fading.