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 ${\theta _{\max }}\lt \pi $ , 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 $|2\log _{2}\cos (\theta _{\max }/2)|$ 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.