Kronecker-structured Sparse Vector Recovery with Application to IRS-MIMO Channel Estimation

We study the recovery of a sparse vector with a Kronecker structure from an underdetermined linear system with a Kronecker-structured dictionary. This problem arises in several applications, such as the channel estimation of an intelligent reflecting surface-aided wireless system. Existing work only exploits the Kronecker structure in support of the sparse vector and solves the entire linear system jointly with high complexity. Instead, we decompose the original sparse recovery problem into multiple independent subproblems and solve them individually. We obtain the sparse vector as the Kronecker product of individual solutions, retaining its Kronecker structure. Besides, the subproblems exhibit reduced effective measurement noise. Our simulations demonstrate that our method has superior estimation accuracy and runtime compared to the existing work. We attribute the low complexity to the reduced dimensionality of the subproblems and improved accuracy to the denoising effect of the decomposition step.