Advancing RIS Optimization: From Ideal to Realistic Models

Abstract

Owing to the ability of reconfigurable intelligent surfaces (RISs) to control the propagation environment in their vicinity, they have emerged as an appealing solution to enhance the performance of next-generation wireless networks. These surfaces consist of low-cost, energy-efficient reflecting elements that can dynamically alter the electromagnetic properties of the wireless channel. The ability to dynamically control the wireless channel enables exciting applications such as creating virtual line-of-sight (LoS) links, enhancing localization, improving channel rank, and beam shaping. However, realizing these benefits necessitates careful optimization of the RIS configuration. While the conventional strategy simplifies the optimization process by assuming ideal RIS, this approach leads to inaccuracies when compared with real-world measurements, particularly in more sophisticated applications. This, in principle, requires developing optimization strategies for physically consistent models of RISs which are efficient and largely independent of the problem structure.

In this dissertation, we begin our investigation with the robust optimization of the ideal RIS with continuous control on its configurable phase-shifts in a terahertz (THz) channel. THz communication signals are susceptible to severe degradation because of the molecular interaction with the atmosphere in the form of subsequent absorption and re-radiation and RISs emerge as a potential solution. However, the re-radiated energy has either been modeled as a scattering component or as additive Gaussian noise in the literature. Since the precise characterization is still a work in progress, we first develop a novel parametric channel model that encompasses two models of the THz re-radiation through a simple parameter change, and then utilize that to design a robust block-coordinate descent (BCD) algorithmic framework which maximizes a lower bound on channel capacity while accounting for imperfect channel state information (CSI). In this framework, the original problem is split into two sub-problems: a) receive beamformer optimization, and b) RIS phase-shift optimization. As the latter sub-problem (unlike the former) has no analytical solution, we propose three approaches for it: a) semi-definite relaxation (SDR) (high complexity), b) signal alignment (SA) (low complexity), and c) gradient descent (GD) (low complexity). We analytically demonstrate the limited interference suppression capability of a passive RIS by deriving the stationary points of signal-to-interference and noise ratio (SINR) of a one-element RIS system with one interferer. Our numerical results also demonstrate that slightly better throughput is achieved when the re-radiation manifests as scattering.

Second, we optimize discrete RIS configurations, which are more practical given hardware constraints. In particular, we develop a probabilistic technique to transform discrete optimization problems into optimization problems of continuous domain probability parameters by interpreting the discrete optimization variable as a categorical random vector and computing expectations with respect to those parameters. We rigorously establish that for the unconstrained case, the optimal points of the reformulation and the original problem coincide. For the constrained case, we prove that the transformed problem is a relaxation of the original problem. We apply the proposed technique to two canonical discrete RIS applications: SINR maximization and overhead-aware rate and energy efficiency (EE) maximization. The reformulation enables both stochastic and analytical interpretations of the original problems, as we demonstrate in our RIS applications. The former interpretation yields a stochastic sampling technique, whereas the latter yields an analytical GD approach using closed-form approximations for the expectation. The numerical results show that the proposed technique is applicable to various discrete RIS optimization problems and outperforms other general approaches, such as closest point projection (CPP) and SDR methods.

Next, we optimize the RIS for coexistence in wireless networks with minimal channel information. Although RIS performance is well-documented with complete CSI, including our own contributions to RIS-aided THz networks and discrete RIS optimization, its effectiveness with limited data in non-cooperative networks, where acquiring CSI is challenging, is less explored. In particular, we examine the interference suppression capabilities of an RIS for coexisting secondary and primary users (SUs and PUs) using angular information, achievable even with non-cooperating PUs. We address the coexistence challenge by employing SDR and inner majorization minimization (iMM) for RISs with continuous phase control, and propose an enhanced SDR tailored for discrete RISs. Numerical results reveal both SDR and iMM require at least five bits of discrete phase control for moderate interference suppression. They also indicate that interference suppression weakens if the PUs are inside certain angular regions, a limitation that varies with the algorithm but can be mitigated by increasing number of RIS elements. Ultimately, the coexistence performance of the RIS with a non-cooperative network is validated through full-wave simulations.

Building on our insights into RIS performance with limited channel knowledge, particularly using angular information, we next extend the beamshaping principles from the previous work to develop a beamshaping framework suited for physically consistent RIS models. This aims to enable coexistence and many other applications by tackling the practical challenge of acquiring precise channel state information and reducing control channel overhead. Our framework uses a multiport network model to develop a physically consistent beamshaping framework for RISs, explicitly including mutual coupling and structural scattering, factors often overlooked in conventional communication models. This allows us to pre-compute average RIS gain matrices, significantly lowering computational complexity. We propose both parametric and non-parametric optimization formulations, solved using constrained simulated annealing and gradient descent. These methods demonstrate robust and accurate beam and null formations, validated through full-wave electromagnetic simulations. We also present a full-wave optimization pipeline that considers quantization for discrete RIS phase-shifts, underscoring the capability and the effectiveness of the framework for large-scale RIS optimization under realistic operational constraints.

Finally, we characterize the THz point-to-point link utilized at the first part of the dissertation as an aside. In particular, we introduce a novel LoS $beta-gamma$ THz channel model that closely mirrors physical reality by considering radiation trapping. Our channel model provides an exhaustive modeling of the physical phenomena including the amount of re-radiation available at the receiver, parametrized by $beta$, and the balance between scattering and noise contributions, parametrized by $gamma$, respectively. Our findings indicate a nontrivial relationship between average limiting received signal-to-noise ratio (SNR) and distance. We further propose new maximum likelihood (ML) thresholds for pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) schemes, resulting in analytical symbol error rate (SER) expressions that account for different noise variances across constellation points. The results confirm that the analytical SER closely matches the true simulated SER when using an optimal detector. As expected, under maximum molecular re-radiation, the true SER is shown to be lower than that produced by a suboptimal detector that assumes equal noise variances.