  Achieving high-rate communication with accurate localization and wireless
environment sensing has emerged as an important trend of beyond-fifth and sixth
generation cellular systems. Extension of the antenna array to an extremely
large scale is a potential technology for achieving such goals. However, the
super massive operating antennas significantly increases the computational
complexity of the system. Motivated by the inherent advantages of lens antenna
arrays in reducing system complexity, we consider communication and
localization problems with an \uline{ex}tremely large \uline{lens} antenna
array, which we call "ExLens". Since radiative near-field property emerges in
the setting, we derive the closed-form array response of the lens antenna array
with spherical wave, which includes the array response obtained on the basis of
uniform plane wave as a special case. Our derivation result reveals a window
effect for energy focusing property of ExLens, which indicates that ExLens has
great potential in position sensing and multi-user communication. We also
propose an effective method for location and channel parameters estimation,
which is able to achieve the localization performance close to the
Cram\'{e}r-Rao lower bound. Finally, we examine the multi-user communication
performance of ExLens that serves coexisting near-field and far-field users.
Numerical results demonstrate the effectiveness of the proposed channel
estimation method and show that ExLens with a minimum mean square error
receiver achieves significant spectral efficiency gains and complexity-and-cost
reductions compared with a uniform linear array.
