Comments on "Spatially Common Sparsity Based Adaptive Channel Estimation and Feedback for FDD Massive MIMO"

In the generalized multiple measurement vectors (GMMV) setup of compressive sensing, we consider the problem of jointly recovering multiple sparse signal vectors sharing a common sparsity pattern based on joint analysis of their linear measurements. The important aspect of the GMMV setup is that the linear measurements of different sparse signal vectors are acquired by using different sensing matrices. It is not yet well understood how the GMMV setup affects identifiability of sparse signal vectors from the measurements, in particular compared to the single measurement vector (SMV) setup wherein we perform recovery of each sparse signal vector independently. Gao et al. presented the first theorem on identifiability of sparse signal vectors in the GMMV setup, in which it is stated that the GMMV setup allows signal vectors with more nonzero rows to be identifiable compared to the SMV setup. In this correspondence, we aim to present a contrasting perspective on sparse signal identifiability in the GMMV setup. In particular, it is shown that the GMMV setup does not result in an improved identifiability condition for some signal vectors even when their entries are diverse.