The Ratio of Independent Arbitrary α-μ Random Variables and its Application in the Capacity Analysis of Spectrum Sharing Systems

General, simple, exact, closed-form expressions for the ratio of independent non-identically distributed α-μ random variables are derived. These important results find applicability in several performance analysis of wireless communication systems, in particular those for which the ratio of signal powers is of relevance. One such application, currently of enormous interest, is the capacity analysis of spectrum sharing networks. Motivated by this, a comprehensive capacity study of spectrum sharing systems undergoing α-μ fading is performed, followed by insightful discussions.