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The reflection characteristics of a reconfigurable intelligent surface (RIS)depend on the phase response of the constituent unit cells, which isnecessarily frequency dependent. This paper investigates the role of an RISconstituting unit cells with different phase-frequency profiles in a wide-bandorthogonal frequency division multiplexing (OFDM) system to improve theachievable rate. We first propose a mathematical model for the phase-frequencyrelationship parametrized by the phase-frequency profile's slope andphase-shift corresponding to a realizable resonant RIS unit cell. Then,modelling each RIS element with $b$ control bits, we propose a method forselecting the parameter pairs to obtain a set of $2^b$ phase-frequencyprofiles. The proposed method yields an RIS design that outperforms existingdesigns over a wide range of user locations in a single-input, single-output(SISO) OFDM system. We then propose a low-complexity optimization algorithm tomaximize the data rate through the joint optimization of (a) power allocationsacross the sub-carriers and (b) phase-frequency profile for each RIS unit cellfrom the available set. The analysis is then extended to a multi-usermultiple-input single-output (MISO) OFDM scenario. Numerical results show animprovement in the coverage and achievable rates under the proposed frameworkas compared to single-slope phase-frequency profiles.

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