This paper is an analysis of the generalized PHASE (norm) RETRIEVAL problem, which aims to reconstruct a signal from its quadratic measurements. We provide some connections between PHASE (norm) RETRIEVAL $G$-frames and generalized PHASE (norm) RETRIEVAL Hermitian matrices $\left\lbrace A_{j}\right\rbrace_{j=1}^{n}$ with real entries. In particular, we investigate some characterizations of PHASE RETRIEVAL $G$-frames by using their induced frames on real Hilbert spaces. With regard to PHASE (norm) RETRIEVAL frames, the study uncovers new aspects of $G$-frames that possess PHASE (norm) RETRIEVAL properties and concludes with a detailed consideration of a PHASE RETRIEVAL dual $G$-frames. Finally, we obtain some sufficient conditions under which PHASE RETRIEVAL $G$-frames are stable under small perturbations.