Yasser Al-Eryani
Continuous-aperture and holographic MIMO systems motivate signaling that operates directly on large electromagnetic apertures rather than on a few antenna ports. This paper is the empirical companion to the operator-theoretic curvature-domain framework: a reproducible benchmark of curvature-domain signaling under a common scalar aperture-channel model, stress-testing the theory's dual-budget generalized water-filling law against the modal bases used in near-field and holographic MIMO. All methods share the same apertures, quadrature, Fresnel or Green-function propagation, phase-only constraints, power, phase-energy and curvature-energy budgets, receiver noise, phase quantization and training assumptions. The compared coordinates are curvature-regularized eigenmodes, raw phase coefficients, Fourier phase modes, polynomial and Zernike-like wavefront modes, near-field matched-focus profiles, random and optimized RIS phase codebooks, and SVD water-filling upper bounds. The claim is deliberately limited: curvature-domain signaling is a gauge-invariant, physically realizable coordinate system that can approach the phase-space SVD water-filling bound with fewer stable modes where derivative noise, phase quantization, sampling density or ill conditioning limit conventional bases. It is not a claim of new electromagnetic physics, nor that curvature modes dominate every baseline. We prove the SVD upper-bound relation for the discretized phase-control tangent space, derive pairwise-error and perturbation bounds, and report capacity, retained modes, symbol error, robustness, quantization, sampling, regularization, conditioning and cost, with 95% bootstrap confidence intervals on Monte Carlo results. A verdict table locates the regimes where curvature-domain signaling is engineering-relevant: moderate-to-high phase noise, coarse phase quantization, and non-Fourier-diagonal channels.