Statistics of $\alpha-\mu$ Random Variables and Their Applications in Wireless Multihop Relaying and Multiple Scattering Channels

Exact results for the probability density function (PDF) and cumulative distribution function (CDF) of the sum of ratios of products (SRP) and the sum of products (SP) of independent
$\alpha-\mu$
random variables (RVs) are derived. They are in the form of 1-D integral based on the existing works on the products and ratios of
$\alpha-\mu$
RVs. In the derivation, generalized Gamma (GG) ratio approximation (GGRA) is proposed to approximate SRP. Gamma ratio approximation (GRA) is proposed to approximate SRP and the ratio of sums of products (RSP). GG approximation (GGA) and Gamma approximation (GA) are used to approximate SP. The proposed results of the SRP can be used to calculate the outage probability (OP) for wireless multihop relaying systems or multiple scattering channels with interference. The proposed results of the SP can be used to calculate the OP for these systems without interference. In addition, the proposed approximate result of the RSP can be used to calculate the OP of the signal-to-interference ratio (SIR) in a multiple scattering system with interference.