Beyond $\lambda/2$: Can Arbitrary EMVS Arrays Achieve Unambiguous NLOS Localization?

Conventional radar array design mandates interelement spacing not exceeding half a wavelength ($\lambda/2$) to avoid spatial ambiguity, fundamentally limiting array aperture and angular resolution. This paper addresses the fundamental question: Can arbitrary electromagnetic vector sensor (EMVS) arrays achieve unambiguous reconfigurable intelligent surface (RIS)-aided localization when element spacing exceeds $\lambda/2$? We provide an affirmative answer by exploiting the multi-component structure of EMVS measurements and developing a synergistic estimation and optimization framework for non-line-of-sight (NLOS) bistatic multiple input multiple output (MIMO) radar. A third-order parallel factor (PARAFAC) model is constructed from EMVS observations, enabling natural separation of spatial, polarimetric, and propagation effects via the trilinear alternating least squares (TALS) algorithm. A novel phase-disambiguation procedure leverages rotational invariance across the six electromagnetic components of EMVSs to resolve $2\pi$ phase wrapping in arbitrary array geometries, allowing unambiguous joint estimation of two-dimensional (2-D) direction of departure (DOD), two-dimensional direction of arrival (DOA), and polarization parameters with automatic pairing. To support localization in NLOS environments and enhance estimation robustness, a reconfigurable intelligent surface (RIS) is incorporated and its phase shifts are optimized via semidefinite programming (SDP) relaxation to maximize received signal power, improving signal-to-noise ratio (SNR) and further suppressing spatial ambiguities through iterative refinement.