On the sum and sum-of-ratio of α−μ distributions and application

This research presents closed-form statistical functions for three sums and sum-of-ratios of correlated or uncorrelated $\alpha /2-\mu$ RVs. We evaluated the upper incomplete moment-generating function (UIMGF) and moment-generating function (MGF) of two sum-ratio distributions. The study offers an Erratum of [7] by extending the MGF and CDF of the sum $\alpha -\mu$ RVs to the unanalyzed case $\alpha >=2$. Using statistical features of signal-to-noise ratio (SNR) and signal-to-interference-to-noise ratio (SINR) at legitimate and wiretapper receiver outputs, we investigated the secrecy outage probability of two RF wireless communication schemes subject to $\alpha -\mu$ fading and channel state information. Both receivers are equipped with multiple antennas and use the maximal-ratio combining diversity technique. Additionally, artificial noise is supplied from the primary source or a separate jammer transmitter. Using SINR’s UIMGF and MGF, closed-form secrecy outage probability (SOP) and intercept probability (IP) formulas were derived. The monotonicity of all analytical results vs. system settings has been thoroughly investigated. From a security perspective, the first scenario works better with high artificial noise power. Nevertheless, the output SNR of the legitimate end-user combiner decreases dramatically, reducing channel capacity and the average error rate. The framework might be utilized in full-duplex cooperative or multi-user interference systems. Monte Carlo simulation supports all analytical findings in all scenarios.