Sixth-generation (6G) wireless communication scenarios are complex and diverse. Small-scale fading is a key part of wireless channels and its impact on performance in scenarios with time sensitivity and 6G ultrareliable and low latency communications (URLLC) quality-of-service requirements cannot be ignored. Therefore, it is necessary to accurately characterize small-scale fading when designing wireless communication systems. In this paper, we derive approximate closed form expressions for the probability density function, cumulative distribution function and moment-generating function of the postprocessing signal-to-noise ratio following the zero-forcing detector in a cell-free massive multiple-input multiple-output (CF mMIMO) system. CF mMIMO system is a nonorthogonal multiple access (NOMA) system that enables users to share all channel uses and can ensure the fairness of the communication quality experienced by different users. Our key contributions include the extension of the κ-μ shadowed fading model to a CF mMIMO system and the proposal of theoretical tools (the derived closed-form expression) to improve its mathematical tractability. By exploiting the statistical characterizations of the arrival and service processes, another important contribution is the exploitation of the upper bound of the queuing delay violation probability (UB-QDVP) over the Mellin transforms of the arrival and service processes in the proposed CF mMIMO system under the κ-μ shadowed fading model. Corroborated by extensive simulations, our analyses validate that the CF mMIMO system outperforms the orthogonal multiple access and power-domain NOMA systems and reveal the relationships among different small-scale fading types, energy efficiency, delay and the UB-QDVP, as well as the accuracy and effectiveness of the proposed theoretical tools based on the κ-μ shadowed fading model.
Keywords: cell-free massive multiple-input multiple-output (CF mMIMO); statistical delay quality-of-service (QoS); ultrareliable and low latency communications (URLLC); κ–μ shadowed fading model.