Telecommunications provides a rich source of interesting and often challenging optimisation problems. This thesis is concerned with a series of mixed-integer non-linear optimisation problems that arise in mobile wireless communications systems.
The problems under consideration arise when mobile base stations have an Orthogonal Frequency-Division Multiple Access (OFDMA) architecture, where there are subcarriers for data transmission and users with various transmission demands. In such systems, we simultaneously allocate subcarriers to users and power to subcarriers, subject to various constraints including certain quality of service (QoS) constraints called rate constraints. These problems can be modelled as Mixed Integer Non-linear Programmes (MINLP).
When we began the dissertation, we had the following main aims:
To design an exact algorithm for the subcarrier and power allocation problem with rate constraints (SPARC), the objective of which is to maximise total data transmission rate of the entire system.
To design an exact algorithm for the fractional subcarrier and power allocation problem with rate constraints (F-SPARC) problem in order to maximise system efficiency, i.e.: total data transmission rate divided by total power supplied to the system.
To design a heuristic algorithm for the F-SPARC problem.
To design a heuristic algorithm for the SPARC problem in dynamic settings, where user demand changes very frequently.
Along the way, however, we discovered a new approach to a broad family of problems, which includes the F-SPARC as a special case. These problems are called mixed-integer fractional programs with indicator variables, and they are dealt with in Chapter 3.