Reconfigurable intelligent surfaces (RISs) have recently attracted attention in the implementation of smart radio environment. In this paper, RISs are realized by the near-field focused antennas (NFF). A near-field channel gain model of RIS-assisted wireless communications is developed for an NFF reflectarray antenna based on the physics and electromagnetic nature of the RISs. The developed model entails the computation of the reflectarray aperture efficiency. Also, it takes into account reflectarray reconfigurablility to cope with varying environment, physical factors like the physical dimensions of the RISs, and the radiation patterns of the unit cells. Moreover, it is characterised by a reduction in the complexity. This model is further used in computing the positioning performance bounds and estimating the RIS optimal beamformer weights. For a validation purpose, the model is simulated by using Matlab software, and the results are compared to the simulation results of a near-field model discussed in literature. The comparison shows a very good agreement. Finally, the reflectarray antenna is thinned to achieve a performance comparable to a fully populated reflectarray antenna case using the full wave 3D electromagnetic solver CST Microwave Studio (CST MWS).
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