The demand for mobile data is growing exponentially. More devices than ever are connecting to mobile broadband, and new applications are continually being developed. It is expected that technologies such as holographic telepresence, digital twins and selfdriving cars will become available in the coming decades, requiring more higher data rates and lower latency than current mobile generations can provide. 6G is expected to utilise millimetre wave (mmWave) band (30 - 300 GHz) and terahertz band (300 GHz - 3 THz) carrier frequencies to provide these, with initial deployment planned for 2030. However, significant propagation challenges occur at such high frequencies, such as increased path loss and attenuation, and limited reflection, diffraction and random scattering, resulting in shorter possible transmission distances.

Traditional solutions to extend coverage range, including the installation of additional base stations (BS) or relays, would be expensive to implement and consume a large amount of power. Reconfigurable intelligent surfaces (RIS) are proposed as a new technology to overcome some of these challenges. A RIS is a mostly passive array of metamaterial elements with the ability to change the phase of an incoming signal. Each RIS element can be tuned independently, allowing for controlled reflections directly influencing the signal path. Therefore, RIS offer a new way to increase channel capacity.

A key challenge of RIS design is the selection of reflection coefficients for each element, due to the multidimensionality of the problem. While an optimal design is believed to be intractable in a multi-user (MU) scenario, an optimal design has been derived for the single-user (SU) case. A number of near-optimal methods have been designed for MU situations, however most are iterative, complex and custom, making implementation challenging.

Therefore, the first part of this thesis focuses on designing a sub-optimal but very low complexity phase selection method for a MU RIS scenario by adapting the SU optimal design. An equal number of the N RIS elements are designed to serve each of the K users (referred to as a subsurface) on a separate frequency band. This means matched filtering can be used at the receiver. Elements not designed for a given user provide additional random scattering, something that is lacking in high-frequency environments. The analytical mean signal-to-noise ratio (SNR) of a system employing the subsurface design (SD) with a line-of-sight (LoS) RIS-BS channel, and Rayleigh fading user equipment (UE)-RIS and UE-BS channels is derived. An upper bound of the mean data rate is also found. This analysis is verified by simulation and is used to gain insights into system performance. When compared to the lowest complexity MU method known to us, a design that minimises the total mean-squared error (TMSE), the SD method leads to a rate loss due to each UE having only 1 K of the bandwidth of the MU case. However, this difference decreases as correlation increases. Similarly, it is found that spacing RIS elements closer together improves the mean SNR, as this increases correlation. Importantly, the SD leads to a K fold reduction in required channel state information and a N(K2 + K(N + 2)) computational complexity reduction when compared to the TMSE design.

In the next section, the analytical mean SNR of a system employing the SD is significantly extended to cover Ricean fading channels, a more realistic and flexible scenario. The SD is also extended to a low-complexity iterative subsurface design (ISD). The ISD sets each subsurface sequentially, using previously set subsurfaces to improve the design. This process can be done once, or repeated until the total SNR increases by less than a specified tolerance (referred to as the converged ISD (CISD)). The analysis is verified and the performances of the ISD and CISD are investigated by simulation. The impact of Ricean K-factor is assessed, and despite the bandwidth restrictions, the SD outperforms the TMSE method at high UE-RIS and RIS-BS link K-factors. The mean rate of the TMSE method falls dramatically when the K-factor nears 1, as the channel cannot support the spatial multiplexing required to support multiple UEs in one frequency band. This is not an issue for the SD design. The impact of clustering UEs at the same location is also considered. Again, the mean rate of the MU method decreases, as channel diversity is reduced, but the SD is unaffected. These are realistic scenarios where the SD offers significant advantages over MU designs.

Another key challenge facing RIS is channel state information acquisition. Passive RIS cannot generate pilot signals or process data. Therefore, rapid temporal changes in the channel would be problematic for a RIS system. The final section of this thesis uses second order statistics to investigate the temporal behaviour of a fundamental SU RIS system. Assuming a LoS RIS-BS link, we derive an exact expression for the level crossing rate (LCR) of the RIS link (UE-RIS-BS path) and propose a numerically stable approximation for the LCR of the UE-BS channel. Each LCR expression attained is then utilised to find the corresponding average fade duration (AFD). The mean SNR correlation is also derived for this scenario. Assuming a Ricean RIS-BS link, expressions for the system’s mean spatial correlation matrix and the mean SNR loss due to channel ageing are derived. All analysis is verified by simulation, and the impact of key system parameters is investigated. Crucially, it was found that RIS do not significantly amplify temporal changes in the channel, an important result.