# Wireless Communications with Reconfigurable Intelligent Surfaces

**In this thesis, we explore the utilization of Reconfigurable Intelligent Surfaces (RIS) in wireless communication systems. A RIS comprises of a grid of reflective elements which are constructed using metasurfaces. Semiconductor devices such as a varactor diode is a typical example of a RIS reflective element. In general, one can tune the phase of each RIS element to alter the propagation medium of the transmitted signals in order to enhance performance metrics such as sum-rate, coverage, etc. The philosophy behind RIS technology is that due to its near passive nature, it is more efficient to operate in terms of power usage and functionality compared to massive multiuser multiple-input multiple-output (MU-MIMO) technology. However, it has become evident in the literature that analyzing and optimizing RIS-aided wireless systems is difficult due to the complexity of the optimization problems. The RIS introduces many constraints on the optimization problems leading to many non-closed form results and many complex optimization algorithms.**

The thesis is divided into two main research areas; a performance analysis of RIS-aided wireless systems and the development of efficient techniques to improve system performance of RIS-aided systems. In the analysis portion of the thesis, we consider a single user (SU) uplink (UL) transmission and develop a closed form optimal RIS matrix to maximize the UL signal to noise ratio (SNR). Utilizing the closed form optimal RIS matrix, exact optimal mean SNR expressions are derived for systems where the RIS- base station (BS) channel is rank-1 line of sight (LOS) and the user (UE)-BS and UE-RIS channels are correlated Rayleigh channels. In addition, we utilise the gamma distribution to derive tight approximations to the SNR variance and mean rate. Leveraging the mean SNR expression, we explore the impact of correlation on the mean SNR and conclude that system performance benefits from having independent paths in the UE-BS channel and full correlation in the UE-RIS channel. The analysis is extended to scenarios where the UE-BS and UE RIS channels are correlated Ricean where the impact of correlation and K-factor on the mean SNR is now investigated. Analysis shows that system performance benefits from having scattering in the UE-BS channel and correlation/LOS in the UE-RIS channel. These observations are also applicable for downlink (DL) systems through UL-DL reciprocity.

The SU analysis thus far assumes perfect reflection of the RIS elements. That is, each RIS element can be tuned to the desired optimal RIS phase and constant amplitude attenuation is present. In practical systems, we need to investigate system imperfections, which for RISs are present in the setting of the RIS phases. Phase dependent loss (PDL) is a real and measured phenomenon where the signals reflected from the RIS elements are attenuated by varying amounts depending on the phase rotation implemented by the element. We derive exact mean SNR expressions for systems where the RIS experiences PDL, whilst the RIS-BS channel is rank-1 LOS and the UE-BS and UE-RIS channels are correlated Rayleigh channels. Leveraging the derived mean SNR expression, we explore the impact of parameters in the loss function on the mean SNR.

We also derive an exact mean SNR expression in the presence of imperfect channel state information (CSI). The derived mean SNR expression is leveraged to analytically characterise the impact of error variances from the channel estimation process on the mean SNR. It is shown that as the error variances increase, the mean SNR reduces to that of a system with randomly selected RIS phases. Consequently, the growth in mean SNR reduces from O(N2) for the perfect CSI case to O(N) for the imperfect case.

In the second portion of the thesis, we conduct research for systems with multiple users, where efficient optimization techniques are developed to improve the typical sum rate metric of various precoding schemes. In this context, optimization refers to finding the best RIS matrix to improve performance metrics. Here, the UE-BS and UE-RIS channels are not restricted to any particular channel model, however, we maintain the assumption that the RIS-BS channel is rank-1 LOS. Through this assumption, we introduce a novel technique called channel separation which provides a new understanding of how the RIS phases affect the different sum-rate metrics. Channel separation significantly reduces the complexity of the related optimization problems. However, these efficient optimization techniques assume continuous RIS phases. That is, each RIS element has an infinite resolution for its phase range. Hence, we propose an efficient algorithm to optimize the identical sum-rate metrics but for discrete RIS phases (i.e. quantized RIS phases). Results show that our efficient optimization techniques obtain sum-rates close to values obtained through a numerical optimization approach (interior-point). Sub-optimal sum-rate results can be achieved with low-level quantization of the RIS phases. To investigate the robustness of the developed techniques, we also apply these techniques when the RIS-BS channel has a dominant LOS path, but some scattering is present. Results show that our techniques are fairly robust to the presence of scattering, even though channel separation was originally designed for LOS RIS-BS channels only. Multiple iterations of the proposed algorithm are shown to improve performance but a single run of the algorithm remains a high-performance, low complexity solution.