In this paper, we introduce and study novel operator-valued frames, called operator-valued metaplectic Gabor frames, which is a natural extension of operator-valued Gabor frames in the framework of metaplectic Wigner distributions. We first show that there exists an operator-valued metaplectic Gabor frame over any full-rank lattice of \({\mathbb {R}}^{2d}\) . Then we prove that the canonical dual operator-valued frame of a given operator-valued metaplectic Gabor frame is also an operator-valued metaplectic Gabor frame. Moreover, Janssen’s representation for the frame operators, Wexler-Raz biorthogonality relations and density theorems for operator-valued metaplectic Gabor frames are provided. Finally, equivalent norms for the weighted modulation spaces are obtained in terms of operator-valued metaplectic Gabor frames generated by operators from some Banach subspaces of the Hilbert-Schmidt operators on \(L^2({\mathbb {R}}^d)\) .
