Electromagnetic waves in the Radio Frequency (RF) spectrum are used to convey wireless transmissions from one radio antenna to another. Spectrum utilisation factor, which refers to how readily a given spectrum can be reused across space and time while maintaining an acceptable level of transmission errors, is used to measure how efficiently a unit of frequency spectrum can be allocated to a specified number of users.
The demand for wireless applications is increasing exponentially, hence there is a need for efficient management of the RF spectrum. However, spectrum usage studies have shown that the spectrum is under-utilised in space and time. A regulatory shift from static spectrum assignment to DSA is one way of addressing this. Licence exemption policy has also been advanced in Dynamic Spectrum Access (DSA) systems to spur wireless innovation and universal access to the internet. Furthermore, there is a shift from homogeneous to heterogeneous radio access and usage of the same spectrum band. These three shifts from traditional spectrum management have led to the challenge of coexistence among heterogeneous wireless networks which access the spectrum using DSA techniques.
Cognitive radios have the ability for spectrum agility based on spectrum conditions. However, in the presence of multiple heterogeneous networks and without spectrum coordination, there is a challenge related to switching between available channels to minimise interference and maximise spectrum allocation. This thesis therefore focuses on the design of a framework for coexistence management and spectrum coordination, with the objective of maximising spectrum utilisation across geographical space and across time. The amount of geographical coverage in which a frequency can be used is optimised through frequency reuse while ensuring that harmful interference is minimised. The time during which spectrum is occupied is increased through time-sharing of the same spectrum by two or more networks, while ensuring that spectrum is shared by networks that can coexist in the same spectrum and that the total channel load is not excessive to prevent spectrum starvation.
Conventionally, a graph is used to model relationships between entities such as interference relationships among networks. However, the concept of an edge in a graph is not sufficient to model relationships that involve more than two entities, such as more than two networks that are able to share the same channel in the time domain, because an edge can only connect two entities. On the other hand, a hypergraph is a generalisation of an undirected graph in which a hyperedge can connect more than two entities. Therefore, this thesis investigates the use of hypergraph theory to model the RF environment and the spectrum allocation scheme.
The hypergraph model was applied to an algorithm for spectrum sharing among 100 heterogeneous wireless networks, whose geo-locations were randomly and independently generated in a 50 km by 50 km area. Simulation results for spectrum utilisation performance have shown that the hypergraph-based model allocated channels, on average, to 8% more networks than the graph-based model. The results also show that, for the same RF environment, the hypergraph model requires up to 36% fewer channels to achieve, on average, 100% operational networks, than the graph model. The rate of growth of the running time of the hypergraph-based algorithm with respect to the input size is equal to the square of the input size, like the graph-based algorithm. Thus, the model achieved better performance at no additional time complexity.