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An innovative method has developed recently for biasing the varactors of a reconfigurable intelligent surface (RIS) by utilizing resonant standing waves on the “biasing transmission line (TL)” [E. Ayanoglu, F. Capolino, and A. L. Swindlehurst, “Wave-controlled metasurface-based reconfigurable intelligent surfaces,” IEEE Wireless Communications, vol. 29, no. 4, pp. 86-92,2022] located beneath the reflective surface. Using this approach, each RIS element does not require separate external biasing. For estimating the RIS reflection properties controlled by varactors, we analyze a planar array with phase gradient in one direction, of side length L, of reconfigurable elements. We employ the analytical model for predicting the reflection coefficients of the unit cells presented in [D. Hanna, M. Saavedra-Melo, F. Shan, and F. Capolino, “A versatile polynomial model for reflection by a reflective intelligent surface with varactors,” IEEE AP-S/URSI, 2022] and investigate how the standing wave biasing approach compares with the traditional way to generate field patterns of the reflected wave. 

A Reconfigurable Intelligent Surface (RIS) consists of many small reflective elements whose reflection properties can be adjusted to change the wireless propagation environment. Envisioned implementations require that each RIS element be connected to a controller, and as the number of RIS elements on a surface may be on the order of hundreds or more, the number of required electrical connectors creates a difficult wiring problem. A potential solution to this problem was previously proposed by the authors in which “biasing transmission lines” carrying standing waves are sampled at each RIS location to produce the desired bias voltage for each RIS element. This paper presents models for the RIS elements that account for mutual coupling and realistic varactor characteristics, as well as circuit models for sampling the transmission line to generate the RIS control signals. The paper investigates two techniques for conversion of the transmission line standing wave voltage to the varactor bias voltage, namely an envelope detector and a sample-and-hold circuit. The paper also develops a modal decomposition approach for generating standing waves that are able to generate beams and nulls in the resulting RIS radiation pattern that maximize either the Signal-to-Noise Ratio (SNR) or the Signal-to-Leakage-plus-Noise Ratio (SLNR). The paper provides five algorithms, two for the case of the envelope detector, one for the sample-and-hold circuit, one for pursuing the global minimum for both circuits, and one for simultaneous beam and null steering. Extensive simulation results show that while the envelope detector is simpler to implement, the sample-and-hold circuit has substantially better performance and runs in substantially less time. In addition, the wave-controlled RIS is able to generate strong beams and deep nulls in desired directions. This is in contrast with the case of arbitrary control of each varactor element and idealized RIS models.