  Extremely large-scale array (XL-array) has emerged as a promising technology
to enable near-field communications for achieving enhanced spectrum efficiency
and spatial resolution, by drastically increasing the number of antennas.
However, this also inevitably incurs higher hardware and energy cost, which may
not be affordable in future wireless systems. To address this issue, we propose
in this paper to exploit two types of sparse arrays (SAs) for enabling
near-field communications. Specifically, we first consider the linear sparse
array (LSA) and characterize its near-field beam pattern. It is shown that
despite the achieved beam-focusing gain, the LSA introduces several undesired
grating-lobes, which have comparable beam power with the main-lobe and are
focused on specific regions. An efficient hybrid beamforming design is then
proposed for the LSA to deal with the potential strong inter-user interference
(IUI). Next, we consider another form of SA, called extended coprime array
(ECA), which is composed of two LSA subarrays with different (coprime)
inter-antenna spacing. By characterizing the ECA near-field beam pattern, we
show that compared with the LSA with the same array sparsity, the ECA can
greatly suppress the beam power of near-field grating-lobes thanks to the
offset effect of the two subarrays, albeit with a larger number of
grating-lobes. This thus motivates us to propose a customized two-phase hybrid
beamforming design for the ECA. Finally, numerical results are presented to
demonstrate the rate performance gain of the proposed two SAs over the
conventional uniform linear array (ULA).
