Multi-antenna radio systems exploit spatial inhomogeneity to share wireless resources. Blind source separation is a powerful capability that can reduce many received signals into a salient estimate of independent transmitters. Performing blind source separation in the analog, physical layer promises significant performance improvements but presents a problem in that not all received signals can be observed at the same time. We propose a novel algorithm that synthesizes univariate statistics to reconstruct the multivariate statistical properties required for blind source separation. Using analog photonic hardware, we demonstrate experimental techniques for obtaining the required information while remaining true to realistic constraints on observability. Finally, we provide an example application for using the physical layer to preserve privacy in spectrum monitoring operations. The concepts and techniques developed lay a groundwork for further research in blind multivariate analysis in the high-performance analog domain.