  This paper considers near-field multiuser communications based on sparse
arrays (SAs). First, for the uniform SAs (USAs), we analyze the beam gains of
channel steering vectors, which shows that increasing the antenna spacings can
effectively improve the spatial resolution of the antenna arrays to enhance the
sum rate of multiuser communications. Then, we investigate nonuniform SAs
(NSAs) to mitigate the high multiuser interference from the grating lobes of
the USAs. To maximize the sum rate of near-field multiuser communications, we
optimize the antenna positions of the NSAs, where a successive convex
approximation-based antenna position optimization algorithm is proposed.
Moreover, we find that the channels of both the USAs and the NSAs show uniform
sparsity in the defined surrogate distance-angle (SD-A) domain. Based on the
channel sparsity, an on-grid SD-A-domain orthogonal matching pursuit (SDA-OMP)
algorithm is developed to estimate multiuser channels. To further improve the
resolution of the SDA-OMP, we also design an off-grid SD-A-domain iterative
super-resolution channel estimation algorithm. Simulation results demonstrate
the superior performance of the proposed methods.
