This thesis presents wideband scattering models of electromagnetic (EM) wave propagation, that aim to characterise reflections of complex structures found in walls and partitions of buildings in the sub-Terahertz (sub-THz) band for fixed link wireless communications. The sub-THz frequency range has attracted attention due to its potential for various applications, including high-capacity fixed links in indoor and outdoor locations to overcome difficulties with employing fibre.

This can be primarily accomplished by providing Line-of-Sight (LoS) fixed links that are comparable to Free Space Propagation (FSP). However, establishing directed Non-Line-of-Sight (NLoS) fixed links with substantial scattering at the single reflection point, is crucial for enabling effective communication and overcoming the limitations imposed by the high path loss and directivity of the antenna. Owing to the short wavelength, interactions with seemingly ``smooth'' surfaces with a complex internal structure exhibit spatial and angular varying frequency selective characteristics that exceed straightforward parametrisation. Such structures hold a great deal of randomness, requiring a huge extent of measurement and large amount of computational resources to be modelled accurately. Finding a balance between measurement extent and complexity, is therefore a necessity in modelling wireless propagation resulting from NLoS reflections of such structures in fixed link scenarios. Current Ray-Tracing (RT) simulators that are calibrated based on measurement data consider reflections that arise from homogenized surfaces, eclipsing any varying characteristics. While a significant amount of work has been conducted for characterising rough surfaces, there is a notable gap when it comes to the characterisation of surfaces with randomness in their internal structure. Modelling signal propagation through complex structures enables the development of more accurate path loss models for scattered reflection fixed NLoS links. 

 Within this context, extensive spatial measurements of scattered reflection coefficients at wideband frequencies in the sub-THz band are initially conducted and analysed for the specular case, where the angle of reflection equals the angle of incidence, and an auto-regressive filter-based approach is proposed to efficiently model statistically accurate spatial distributions resulting from reflections of complex structures. Angular resolved scattering measurements are then conducted for the non-specular case, where the angle of incidence does not equal the angle of reflection, i.e., $\theta_{\text{i}}$ $\not =$ $\theta_{\text{r}}$, to determine the extent at which scattering from such structures can be exploited at different locations for fixed link communications. This form of scattering can be efficiently modeled by polynomial regression using a small number of coefficients. These coefficients can then be used as a reference to efficiently approximate the power levels of each measured spatial distribution at each of the measured Receiver (Rx) angles for a given fixed Transmitter (Tx) angle. Based on the above, long range NLoS path loss measurements are further conducted in a realistic environment for the case where there is unequal angle of incidence to reflection, and a comprehensive wideband modelling framework is formulated based on the bi-static radar equation that specifically accounts for the the effect of distance and alignment angle on the frequency selective Radar Cross Section (RCS) of scatterers found in complex building structures. There isn't a single well-defined reflection point where the incidence angle and reflection angle align to form the shortest Tx to Rx path, meaning that the scattering effect of the reflective wall gives reason to search for the best Tx antenna distance placement and angular alignment of the Rx antenna given a specific angle from the Tx.