  Flexible antenna arrays (FAAs), distinguished by their rotatable, bendable,
and foldable properties, are extensively employed in flexible radio systems to
achieve customized radiation patterns. This paper aims to illustrate that FAAs,
capable of dynamically adjusting surface shapes, can enhance communication
performances with both omni-directional and directional antenna patterns, in
terms of multi-path channel power and channel angle Cram\'{e}r-Rao bounds. To
this end, we develop a mathematical model that elucidates the impacts of the
variations in antenna positions and orientations as the array transitions from
a flat to a rotated, bent, and folded state, all contingent on the flexible
degree-of-freedom. Moreover, since the array shape adjustment operates across
the entire beamspace, especially with directional patterns, we discuss the
sum-rate in the multi-sector base station that covers the $360^\circ$
communication area. Particularly, to thoroughly explore the multi-sector
sum-rate, we propose separate flexible precoding (SFP), joint flexible
precoding (JFP), and semi-joint flexible precoding (SJFP), respectively. In our
numerical analysis comparing the optimized FAA to the fixed uniform planar
array, we find that the bendable FAA achieves a remarkable $156\%$ sum-rate
improvement compared to the fixed planar array in the case of JFP with the
directional pattern. Furthermore, the rotatable FAA exhibits notably superior
performance in SFP and SJFP cases with omni-directional patterns, with
respective $35\%$ and $281\%$.
