  The technology of Reconfigurable Intelligent Surfaces (RISs) has lately
attracted considerable interest from both academia and industry as a low-cost
solution for coverage extension and signal propagation control. In this paper,
we study the downlink of a multi-cell wideband communication system comprising
single-antenna Base Stations (BSs) and their associated single-antenna users,
as well as multiple passive RISs. We assume that each BS controls a separate
RIS and performs Orthogonal Frequency Division Multiplexing (OFDM)
transmissions. Differently from various previous works where the RIS unit
elements are considered as frequency-flat phase shifters, we model them as
Lorentzian resonators and present a joint design of the BSs' power allocation,
as well as the phase profiles of the multiple RISs, targeting the sum-rate
maximization of the multi-cell system. We formulate a challenging distributed
nonconvex optimization problem, which is solved via successive concave
approximation. The distributed implementation of the proposed design is
discussed, and the presented simulation results showcase the interplay of the
various system parameters on the sum rate, verifying the performance boosting
role of RISs.
