On the Ratio of Generalized-$\mathcal{K}$ Random Variables with Application to BAC-NOMA-Enabled Mission-Critical IoBT Systems

Targeting the mission-critical Internet-of-Battlefield-Things (IoBT) applications in sixth-generation (6G) networks, in this paper, we study the non-orthogonal multiple access-based backscatter communication (BAC-NOMA)-enabled IoBT system under statistical delay quality-of-service (QoS) requirements. In particular, to facilitate the performance analysis, first, we derive the novel closed-form expressions for the probability distribution function (PDF), and the cumulative density function (CDF) of the ratio of generalized
$-\mathcal{K}(\mathcal{K}_{g})$
random variables. Then, by leveraging the obtained results, we derive the asymptotic expressions for the effective capacity of the BAC-NOMA system under Nakagami-
$m$
fading channels at a high signal-to-noise ratio (SNR). Our simulation results endorse the analytical analysis, and reveal that the stringent QoS constraint degrades the effective capacity; however, the system performance can be improved by adjusting the power reflection coefficients.