  Given the high degree of computational complexity of the channel estimation
technique based on the conventional one-dimensional (1-D) compressive sensing
(CS) framework employed in the hybrid beamforming architecture, this study
proposes two low-complexity channel estimation strategies. One is two-stage CS,
which exploits row-group sparsity to estimate angle-of-arrival (AoA) first and
uses the conventional 1-D CS method to obtain angle-of-departure (AoD). The
other is two-dimensional (2-D) CS, which utilizes a 2-D dictionary to
reconstruct the 2-D sparse signal. To conduct a meaningful comparison of the
three CS frameworks, i.e., 1-D, two-stage and 2-D CS, the orthogonal match
pursuit (OMP) algorithm is employed as the basic algorithm and is expanded to
two variants for the proposed frameworks. Analysis and simulations demonstrate
that when the 1-D CS method is compared, two-stage CS has somewhat lower
performance but significantly lower computational complexity, while 2-D CS is
not only the same as 1-D CS in terms of performance but also slightly lower in
computational complexity than two-stage CS.
