Bounds on Shaping Partially Coherent Microwaves with Programmable Scattering Systems

Abstract

We derive bounds on manipulating partially coherent microwaves with programmable scattering systems. We first consider the concentration of power from a partially coherent input into a single output port and derive a prototype-aware bound by combining multiport network theory (MNT) with semidefinite relaxation (SDR). We then address general coherency-matrix synthesis, deriving architecture-independent bounds on fidelity and useful strength, prototype-specific scalar refinements thereof, and fully prototype-aware SDR bounds on the useful-strength--fidelity Pareto frontier. The prototype-aware formulations account for mutual coupling, loss, discrete tunability, and static scattering. We evaluate the bounds on four experimental RIS-parametrized MIMO systems with up to 100 1-bit-programmable elements, using proxy-MNT models estimated from measurements. The resulting bounds are generally tight compared with feasible discrete-optimization outcomes. Interestingly, for coherency synthesis, the simpler bounds can in some cases be tighter than the fully prototype-aware bounds, highlighting their complementarity. Our results provide certified limits for wave-domain processing and harvesting of partially coherent microwaves.