The Software-Defined Radio (SDR) concept is emerging as a potential and efficient solution for designing flexible future-proof multi-standard systems. A way of realizing a multi-standard terminal is to identify the appropriate common functions and operators inside and between the standards. This is what's called the parametrization approach, which can be divided into two categories: the pragmatic approach which is a practical version to create and develop common operators, and the theoretical approach which represents a graphical exploration of the SDR multi-standard system at different levels of granularity accompanied with an optimization problem. It’s in this last approach where our thesis subject dwells. In this context, a suggested cost function (in previous work) has to be optimized in order to select the convenient common operators between the different standards, enabling to construct an optimal design. In our work, we theoretically model a previously proposed graph structure of an SDR multi-standard system as a directed hypergraph as well as provide an alternative mathematical formal expression of the suggested cost function, using various graph theoretical definitions and notations. Afterwards, we prove that the associated optimization problem is an NP-problem under a certain constraint, which entails a proof of exclusion of some particular design options when searching for a minimum cost design. This was the second contribution in this thesis before we finally present a new algorithm (which exploits various modelization aspects of directed hypergraphs) that can solve the optimization problem, whose interest is in it giving an exact-optimal solution to our problem instead of a near-optimal one provided by heuristics. A program code for this algorithm was developed in C-language, and then it was applied on several generic case examples in order to explore its performance skills.
