Deterministic 5G mmWave Large-Scale 3D Path Loss Model for Lagos Island, Nigeria

5G millimeter wave (mmWave) application in mobile connectivity to realize high-speed, reliable communication is attributed with high path loss. This paper presents a detailed 3D ray-tracing technique at 28 GHz for Lagos Island to investigate five unique path loss scenarios: path loss, free space path loss with antenna pattern, free space path loss without antenna pattern, excess path loss with antenna pattern, and the excess path loss without antenna pattern for an urban environment. The Close-In (CI) model, Floating Intercept (FI) path loss model, and a root mean square error (RMSE) are used to model and evaluate the best path loss model for Lagos Island. The average achieved FI ( $\alpha,\beta, \sigma $ ) parameters were 189.92352, 0.1654, and 0.66948, While the average CI ( $\eta,X\sigma $ ) parameters were 2.309355 and 56.236425. From all the scenarios evaluated, the lowest path loss exponent achieved was 0.45, while the highest path loss exponent was 3.8. We have established that the FI path loss model accurately characterizes path loss for the Lagos Island environment with the lowest RMSE of 0.0359 dB and the highest RSME of 0.0997 dB. In contrast, the CI model over-predict the path loss at 28 GHz with the lowest RMSE of 0.0495 dB and the highest RMSE of 2.2547 dB. This work opens up a new area of research on mm-Wave at 28 GHz in Lagos Island, and the results obtained from this work can be used to benchmark future studies on mmWave in a similar environment