Understanding beamshaping in reconfigurable intelligent surfaces (RIS) is crucial for practical deployment, especially with the recent emphasis on self-configuring RISs. However, accurate beamshaping must account for factors such as mutual coupling and structural scattering. This paper proposes a beamshaping framework for physically consistent RISs using a modified signal model that bridges communication theory and multiport network theory. By focusing on desired beam and null locations, we enable pre-calculation of RIS channel gain matrices, reducing computational complexity. The optimization problems are then solved using constrained simulated annealing (CSA). Numerical simulations validate the framework by demonstrating wide beam and null formation and the necessity of discrete optimization for accurate beamshaping with less than 7 bits of discrete control. Results also reveal that ignoring mutual coupling in structural scattering leads to a notable decline in null quality.

Terahertz (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. Recently, reconfigurable intelligent surface (RIS) has emerged as a potential technology to assist in THz communications by boosting signal power or providing virtual line-of-sight (LOS) paths. 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, this paper presents the first comparative investigation of the performance of an RIS-aided THz system under these two extreme re-radiation models. In particular, we first develop a novel parametric channel model that encompasses both models of the 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). The time complexities associated with the proposed approaches are explicitly derived. 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.

The use of reconfigurable intelligent surfaces (RIS) can improve wireless communication by modifying the wireless link to create virtual line-of-sight links, bypass blockages, suppress interference, and enhance localization. However, enabling the RIS to modify the wireless channel requires careful optimization of the RIS phase-shifts. Although discrete RIS is more practical given hardware limitations, continuous RIS phase-shift optimization has attracted significantly more attention than discrete RIS optimization, which suffers from issues like quantization error and scalability. To overcome these issues, we develop a comprehensive 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 gradient descent (GD) approach that employs closed-form approximations for the expectation. We have explicitly derived the worst-case computational complexities of the proposed algorithms. The numerical results demonstrate that the proposed technique is applicable to a variety of discrete RIS optimization problems and outperforms other general approaches, such as closest point projection (CPP) and semidefinite relaxation (SDR) methods.

Determining optimal phases for a discrete reconfigurable intelligent surface (RIS) in RIS-aided wireless systems is known to be a challenging problem. This paper develops a novel probabilistic reformulation technique to transform such discrete optimization problems into continuous domain problems. The idea is to treat optimization variables as a categorical random vector with independent but non-identically distributed (i.n.i.d.) entries and replace the objective function with its expectation. In the unconstrained case, we rigorously establish the equivalence between the original problem’s unique optimal solution and the corresponding degenerate probability density function (PDF) of the transformed problem. Furthermore, we derive key analytical moments and gradients associated with the quadratic form and binary random vectors that are useful in the optimization of RIS-aided wireless systems. In order to concretely demonstrate the benefits of the proposed technique, we reformulate a canonical discrete RIS-aided signal-to-interference-plus-noise ratio (SINR) maximization problem and solve the reformulated problem with the gradient descent (GD) technique. Our solution includes an analytical approach that relies on closed-form approximations for the expectation, incorporating moment results, and a stochastic sampling method based on a log-derivative gradient estimator. Numerical results show that our expectation-based algorithms outperform state-of-the-art conventional algorithms, thereby demonstrating the effectiveness of our approach.

The geometry-based stochastic channel models (GSCM), which can describe realistic channel impulse responses, often rely on the existence of both local and far scatterers. However, their visibility from both the base station (BS) and mobile station (MS) depends on their relative heights and positions. For example, the condition of visibility of a scatterer from the perspective of a BS is different from that of an MS and depends on the height of the scatterer. To capture this, we propose a novel GSCM where each scatterer has dual disk visibility regions (VRs) centered on itself for both BS and MS, with their radii being our model parameters. Our model consists of short and tall scatterers, which are both modeled using independent inhomogeneous Poisson point processes (IPPPs) having distinct dual VRs. We also introduce a probability parameter to account for the varying visibility of tall scatterers from different MSs, effectively emulating their noncontiguous VRs. Using stochastic geometry, we derive the probability mass function (PMF) of the number of multipath components (MPCs), the marginal and joint distance distributions for an active scatterer, the mean time of arrival (ToA), and the mean received power through non-line-of-sight (NLoS) paths for our proposed model. By selecting appropriate model parameters, the propagation characteristics of our GSCM are demonstrated to closely emulate those of the COST-259 model.

The operation of Terahertz (THz) communication can be significantly impacted by the interaction between the transmitted wave and the molecules in the atmosphere. In particular, it has been observed experimentally that the signal undergoes not only molecular absorption, but also molecular re-radiation. Two extreme modeling assumptions are prevalent in the literature, where the re-radiated energy is modeled in the first as additive Gaussian noise and in the second as a scattered component strongly correlated to the actual signal. Since the exact characterization is still an open problem, we provide in this paper the first comparative study of the performance of a reconfigurable intelligent surface (RIS) assisted THz system under these two extreme models of re-radiation. In particular, we employ an RIS to overcome the large pathloss by creating a virtual line-of-sight (LOS) path. We then develop an optimization framework for this setup and utilize the block-coordinate descent (BCD) method to iteratively optimize both RIS configuration vector and receive beamforming weight resulting in significant throughput gains for the user of interest compared to random RIS configurations. Our results reveal that a slightly better throughput is achieved under the scattering assumption for the molecular re-radiation than the noise assumption.