Channel Estimation for Hybrid mmWave Systems Using Generalized Kronecker Compressive Sensing (G-KCS) With Successive Decision-Aided Recovery

It is known that compressive sensing (CS) techniques are useful for the estimation of millimeter wave (mmWave) channels. When uniform planar arrays (UPA) are used, four dictionaries, two for angles of departure (AoD) and two for angles of arrival (AoA), are constructed and mmWave channel estimation becomes a four-dimensional CS problem. The sensing matrix in the CS formulation, containing the Kronecker product of four dictionary matrices, becomes very large. The complexity is extremely high even when efficient orthogonal matching pursuit (OMP) is used. In this paper, we view the channel estimation problem for mmWave systems as a generalized Kronecker compressive sensing (G-KCS) problem that also arises in multidimensional signal processing. We show that we can solve G-KCS using successive recovery, one dimension at a time. In each one-dimensional recovery, the sensing matrix is of a much smaller size, which greatly reduces the complexity of OMP. The recovery result of a particular dimension, called decisions, can be utilized for successive decision-aided recovery (SDAR) of subsequent dimensions. The exploitation of earlier decisions allows us to have not only a more relaxed recovery condition but also further reduction in complexity. The proposed SDAR-OMP can be applied to G-KCS problems, e.g., channel estimation for mmWave channels and multidimensional signal processing. Simulations demonstrate that when SDAR-OMP is applied to channel estimation for hybrid mmWave systems, the estimation error is comparable to that of conventional OMP but the complexity is much lower.