Practical Configuration of a Discrete RIS With Phase-Dependent Amplitude Response

We consider configuring discrete reconfigurable intelligent surfaces (RIS) with phase-dependent amplitude responses. The problem is formulated as a constrained virtual-channel selection problem. When considered over subsets with maximum phase-variation <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\theta _{\max }}\lt \pi $ </tex-math></inline-formula>, the solution is shown to be bounded between two matroid-constrained problems. We illustrate configuration problems whose optimal solution lies within such subsets and show that a greedy framework guarantees a worst-case <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$|2\log _{2}\cos (\theta _{\max }/2)|$ </tex-math></inline-formula> optimality gap uniformly over all system parameters. Subsequently, a low-complexity framework is proposed for general discrete configuration problems. Numerical experiments show that the framework performs within 4% of the optimal binary-RIS configuration and achieves at least 90% of the continuous phase-shift performance using a 3-bit configuration.