Electromagnetic Bounds on Realizing Targeted MIMO Transfer Functions in Real-World Systems with Wave-Domain Programmability

A key question for most applications involving reconfigurable linear wave systems is how accurately a desired linear operator can be realized by configuring the system's tunable elements. The relevance of this question spans from hybrid-MIMO analog combiners via computational meta-imagers to programmable wave-domain signal processing. Yet, no electromagnetically consistent bounds have been derived for the fidelity with which a desired operator can be realized in a real-world reconfigurable wave system. Here, we derive such bounds based on an electromagnetically consistent multiport-network model (capturing mutual coupling between tunable elements) and accounting for real-world hardware constraints (lossy, 1-bit-programmable elements). Specifically, we formulate the operator-synthesis task as a quadratically constrained fractional-quadratic problem and compute rigorous fidelity upper bounds based on semidefinite relaxation. We apply our technique to three distinct experimental setups. The first two setups are, respectively, a free-space and a rich-scattering $4\times 4$ MIMO channel at 2.45 GHz parameterized by a reconfigurable intelligent surface (RIS) comprising 100 1-bit-programmable elements. The third setup is a $4\times 4$ MIMO channel at 19 GHz from four feeds of a dynamic metasurface antenna (DMA) to four users. We systematically study how the achievable fidelity scales with the number of tunable elements, and we probe the tightness of our bounds by trying to find optimized configurations approaching the bounds with standard discrete-optimization techniques. We observe a strong influence of the coupling strength between tunable elements on our fidelity bound. For the two RIS-based setups, our bound attests to insufficient wave-domain flexibility for the considered operator synthesis.