Unit Cell Phase-Frequency Profile Optimization in RIS-Assisted Wide-Band OFDM Systems

The reflection characteristics of a reconfigurable intelligent surface (RIS) depend on the reflection response of the constituent unit cells, which are necessarily frequency dependent. This paper investigates the role of an RIS comprised of unit cells with different phase-frequency profiles in improving the achievable rate of a wide-band orthogonal frequency division multiplexing (OFDM) system. Specifically, we propose phase-frequency profiles with both variable phase and variable slope that enable improvements in the spectral efficiency of a channel. We first propose a mathematical model for the frequency response of the reflection coefficient of a realizable RIS unit cell and parameterize the phase-frequency profile by its slope and by its resonance center frequency. Then, modelling each RIS element with b control bits, we propose a method for selecting the parameter pairs to obtain a set of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{b}$ </tex-math></inline-formula> reflection profiles. We then use a low-complexity optimization algorithm to maximize the data rate through the joint optimization of (a) the reflection profile for each RIS unit cell from the available sets and (b) the power allocations across the sub-carriers. We show that the resulting RIS outperforms existing designs over a wide range of user locations in single-input single-output and multi-user multiple-input single-output OFDM systems.