Low-Complexity Successive Decision-Aided Estimation for Hybrid mmWave Systems

It is known that the estimation of millimeter wave (mmWave) channels can be formulated as a sparse recovery problem that can be solved elegantly using compressed sensing (CS) techniques. In typical CS-based methods, the dictionary is a Kronecker product of two dictionaries, one for angle of departure (AoD) and one for angle of arrival (AoA). The complexity increases with the product of two dictionary sizes. In this paper, we propose a new and efficient successive algorithm that breaks down the angle estimation problem of each path into two sub-problems, one for AoD and one for AoA. When the AoD estimate of a particular path has been estimated, the AoD decision provides information of the path being estimated. In particular, we can exploit the AoD estimate so that the estimation of the corresponding AoA becomes a problem of recovering a 1-sparse vector. In each angle estimation sub-problem, only one dictionary is involved and the overall complexity grows linearly with dictionary sizes. A significant reduction in computations can be achieved. Simulations are given to show that the estimation accuracy of the proposed successive algorithm is comparable to that of a full-search method that estimates the angle jointly but the complexity is much lower.