Performance limits for FDMA cellular systems described by hypergraphs

Abstract

The authors present some preliminary material about hypergraphs, including a discussion of what they call random hypergraph multicolorings, a notion which is central to the analysis of frequency-assignment algorithms. They show that for any frequency-assignment algorithm, the carried traffic function must satisfy T(r)⩽T_0(r), where T_0(r) is a simple function that can be computed by linear programming. They give an asymptotic analysis of a class of 'fixed' frequency-assignment algorithms, and show that in the limit as n→∞, these algorithms achieve carried traffic functions that are at least as large as T_1( r), another simple function that can be computed by linear programming. They show that T_0(r)=T_1(r). This common value, denoted by T_(H,p)(r) is the function referred to above. They also describe some of the most important properties of the function TH,p(r), and identify the 'most favorable' traffic patterns for a given hypergraph H.