Neighboring Mutual-Coupling Channel Model and Tunable-Impedance Optimization Method for Reconfigurable-Intelligent-Surface Aided Communications

ObjectiveReconfigurable Intelligent Surfaces (RIS) attract increasing attention due to their ability to controllably manipulate electromagnetic wave propagation. A typical RIS consists of a dense array of Reflecting Elements (REs) with inter-element spacing no greater than half a wavelength, under which electromagnetic mutual coupling inevitably occurs between adjacent REs. This effect becomes more pronounced when the element spacing is smaller than half a wavelength and can significantly affect the performance and efficiency of RIS-assisted systems. Accurate modeling of mutual coupling is therefore essential for RIS optimization. However, existing mutual-coupling-aware channel models usually suffer from high computational complexity because of the large dimensionality of the mutual-impedance matrix, which restricts their practical use. To address this limitation, a simplified mutual-coupling-aware channel model based on a sparse neighboring mutual-coupling matrix is proposed, together with an efficient optimization method for configuring RIS tunable impedances.MethodsFirst, a simplified mutual-coupling-aware channel model is established through two main steps. (1) A neighboring mutual-coupling matrix is constructed by exploiting the exponential decay of mutual impedance with inter-element distance. (2) A closed-form approximation of the mutual impedance between the transmitter or receiver and the REs is derived under far-field conditions. By taking advantage of the rapid attenuation of mutual impedance as spacing increases, only eight or three mutual-coupling parameters, together with one self-impedance parameter, are retained. These parameters are arranged into a neighboring mutual-coupling matrix using predefined support matrices. To further reduce computational burden, the distance term in the mutual-impedance expression is approximated by a central value under far-field assumptions, which allows the original integral formulation to be simplified into a compact analytical expression. Based on the resulting channel model, an efficient optimization method for RIS tunable impedances is developed. Through impedance decomposition, a closed-form expression for the optimal tunable-impedance matrix is derived, enabling low-complexity RIS configuration with computational cost independent of the number of REs.Results and DiscussionsThe accuracy and computational efficiency of the proposed simplified models, as well as the effectiveness of the proposed impedance optimization method, are validated through numerical simulations. First, the two simplified models are evaluated against a reference model. The first simplified model accounts for mutual coupling among elements separated by at most one intermediate unit, whereas the second model considers only immediately adjacent elements. Results indicate that channel gain increases as element spacing decreases, with faster growth observed at smaller spacings (Fig. 4). The modeling error between the simplified models and the reference model remains below 0.1 when the spacing does not exceed λ/4, but increases noticeably at larger spacings. Error curves further show that the modeling errors of both simplified models become negligible when the spacing is below λ/4, indicating that the second model can be adopted to further reduce complexity (Fig. 6). Second, the computational complexity of the proposed models is compared with that of the reference model. When the number of REs exceeds four, the complexity of computing the mutual-coupling matrix in the reference model exceeds that of the proposed neighboring mutual-coupling model. As the number of REs increases, the complexity of the reference model grows rapidly, whereas that of the proposed model remains constant (Fig. 5). Finally, the proposed impedance optimization method is compared with benchmark method (Fig. 7, Fig. 8). When the element spacing is no greater than λ/4, the channel gain achieved by the proposed method approaches that of the benchmark method. As the spacing increases beyond this range, a clear performance gap emerges. In all cases, the proposed method yields higher channel gain than the coherent phase-shift optimization method.ConclusionsThe integration of a large number of densely arranged REs in an RIS introduces notable mutual coupling effects, which can substantially influence system performance and therefore must be considered in channel modeling and impedance optimization. A simplified mutual-coupling-aware channel model based on a neighboring mutual-coupling matrix has been proposed, together with an efficient tunable-impedance optimization method. By combining the neighboring mutual-coupling matrix with a simplified mutual-impedance expression derived under far-field assumptions, a low-complexity channel model is obtained. Based on this model, a closed-form solution for the optimal RIS tunable impedances is derived using impedance decomposition. Simulation results confirm that the proposed channel model and optimization method maintain satisfactory accuracy and effectiveness when the element spacing does not exceed λ/4. The proposed framework provides practical theoretical support and useful design guidance for analyzing and optimizing RIS-assisted systems under mutual coupling effects.