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 $281\%$.

翻译：柔性天线阵列凭借其可旋转、可弯曲和可折叠的特性，在柔性无线电系统中被广泛用于实现定制化的辐射方向图。本文旨在阐明，能够动态调整表面形状的柔性天线阵列，可以在多径信道功率和信道角度克拉美-罗界方面，提升全向与定向天线方向图的通信性能。为此，我们建立了一个数学模型，该模型阐明了天线阵列从平坦状态转变为旋转、弯曲和折叠状态时，天线位置和方向变化的影响，所有这些变化均取决于柔性自由度。此外，由于阵列形状调整在整个波束空间内进行，特别是在定向方向图的情况下，我们讨论了覆盖$360^\circ$通信区域的多扇区基站的和速率。特别地，为了深入探究多扇区和速率，我们分别提出了分离式柔性预编码、联合柔性预编码和半联合柔性预编码。在将优化后的柔性天线阵列与固定均匀平面阵列进行比较的数值分析中，我们发现，在采用定向方向图的联合柔性预编码情况下，可弯曲柔性天线阵列相比固定平面阵列实现了高达$156\%$的和速率提升。此外，可旋转柔性天线阵列在全向方向图的分离式柔性预编码和半联合柔性预编码情况下表现出显著更优的性能，提升幅度分别为$35\%$和$281\%$。