In this study, product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for κ-μ fading distribution and α-μ fading distribution is considered. The novel exact series formulas for the product of two i.n.i.d. fading distributions κ-μ and α-μ are derived instead of Fox H-function to solve the problem that Fox H function with multiple RVs cannot be implemented in professional mathematical software packages as MATHEMATICA and MAPLE. Exact close-form expressions of probability density function (PDF) and cumulative distribution function (CDF) are deduced to represent provided product expressions and generalized composite multipath shadowing models. At last, these analytical results are validated with Monte Carlo simulations, it shows that for provided κ-μ/α-μ model nonlinear parameter has more important influence than multipath component in PDF and CDF when the ratio between the total power of the dominant components and the total power of the scattered waves is same.

Although Cooperative Communications (CC) already exists in 4G LTE/5G, performance improvement is just not enough, hence, how to apply collaborative technology in 6G to achieve Internet of Everything and improve communication quality significantly is one of most important issues. As 5G communications standard has gradually established recently, CC has been one of most critical communication technologies which plays a founding role on Internet of Everything in 6G networks. Thus, in this study we propose new 6G enabled ultra-massive Machine Type Communication (mMTC) framework based on space-ground integrated networks, and consider that collaborative ideology has been regarded as foundation theory which widely exists in future multiple hybrid scenarios, such as, Cognitive-Internet of Things (C-IoT) networks, UAVs (Unmanned Aerial Vehicles) communications, air-space-ground integrated networks, underwater acoustic communication and so on. Besides, we discuss other key communication technologies that are closely combined with unique communication scenes, and elaborate critical problems that shall be solved in 6G ultra-mMTC Internet of Everything networks. Furthermore, we discuss extreme low-complexity and fast ultra-massive relays selection algorithm to apply in all sorts of future 6G scenarios. At last, it is concluded that for arbitrary two communication points (source/destination devices, sensors, relays, IoT nodes and so on), ideology of nodes selection of collaborative communication is theory of foundation to realize and optimize communication transmission in 6G Internet of Everything ultra-mMTC networks.