A Novel Theoretical Framework for Reconfigurable Intelligent Surface-Aided Communications in Nigerian Rural 5G Coverage Extension

Reconfigurable intelligent surface technology represents one of the most promising candidates for extending 5G coverage to rural areas of Nigeria at substantially lower cost than additional base station deployment, but the theoretical performance characterisation of RIS-aided channels under Nigerian rural propagation conditions, including Sahel terrain, tropical vegetation, and compound building materials, has not been established. This study developed a novel theoretical framework for RIS-aided communication performance in Nigerian rural 5G coverage extension contexts. A measurement campaign characterised rural propagation at 3.5 GHz in three geographically distinct environments: Sokoto State Sahel savanna, Cross River State tropical forest fringe, and Niger State agricultural plain, providing empirical basis for a validated environment-specific path loss model. The theoretical framework derived original closed-form expressions for RIS-assisted channel capacity and outage probability as functions of RIS element count, RIS placement geometry, and Nigerian environment-specific path loss parameters. Analysis showed that an RIS with 256 elements placed at the edge of 5G macro-cell coverage in the Sokoto Sahel environment extended the 95 percent coverage probability boundary by 1.4 km with 12 dB SNR improvement at the boundary, equivalent to eliminating the need for 1.8 intermediate base stations per kilometre. A novel joint passive beamforming and active relay optimisation algorithm for heterogeneous RIS deployments was derived, achieving 94 percent of the global optimal performance at 67 percent of the computational cost. The framework provides original theoretical tools for Nigerian telecoms regulators and operators to evaluate RIS deployment benefits quantitatively.