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Smart radio environments (SREs) are seen as a key rising concept of nextgeneration wireless networks, where propagation channels between transmittersand receivers are purposely controlled. One promising approach to achieve suchchannel flexibility relies on semipassive reflective Reconfigurable intelligentsurfaces (RISs), which can shape the bouncing multipath signals for enhancingcommunication quality of service, making localization feasible in adverseoperating conditions, or reducing unwanted electromagnetic emissions. Thispaper introduces a generic framework that aims at optimizing the end-to-endprecoder controlled by RISs, so that arbitrary beam patterns can be generated,given a predefined lookup table of RIS element-wise complex reflectioncoefficients. This method is validated and illustrated for different targetedbeam patterns in both the far-field and the near-field regimes, whileconsidering the prior characterization of real-life RIS hardware prototypes.These results show how, and to which extent, RIS configuration optimization canapproximate the desired beams under realistic hardware limitations andlow-complexity implementation practicability, or conversely, which RISelements' lookup tables would be more suitable. The latter can provide usefulguidelines for future RIS hardware designs.

Arbitrary Beam Pattern Approximation via RISs with Measured Element Responses