Development of a Stochastic Geometry Framework for Heterogeneous Cellular Network Optimisation in Nigerian Urban Areas

The deployment of heterogeneous cellular networks combining macro base stations, small cells, and emerging millimetre-wave access points in densely populated Nigerian urban environments including Lagos, Kano, and Abuja presents mathematically complex coverage, capacity, and interference management challenges that classical deterministic planning tools cannot address tractably. This dissertation develops an original stochastic geometry framework for the analysis and optimisation of heterogeneous cellular networks operating in the Nigerian regulatory and propagation environment. The theoretical foundation employs Poisson point process models for base station and user equipment locations, with original extensions to capture the spatial clustering structure of Nigerian urban morphology characterised by dense compounds, informal settlements, and unplanned street layouts. A novel cluster point process model for base station deployment is introduced and its coverage probability functional is derived analytically in closed form using probability generating functionals, constituting a theoretical advance beyond existing Poisson approximations. The framework incorporates a new propagation model calibrated to field measurement data from Lagos and Kano urban cores, accounting for the specific building density, material characteristics, and street grid irregularity of Nigerian urban fabric. An original optimisation theorem characterises the tier association policy that maximises area spectral efficiency in the heterogeneous network under the calibrated spatial model. Numerical validation against field measurement data confirms coverage probability prediction accuracy within 3.8 percent. Keywords: stochastic geometry, heterogeneous cellular network, Poisson point process, Nigerian urban, spectral efficiency.