Six-dimensional movable antenna (6DMA) has emerged as a promising new technology for future wireless networks, which can adaptively adjust the three-dimensional (3D) positions and 3D rotations of antennas/antenna arrays for performance enhancement. This paper proposes a novel cost-effective 6DMA-based base station (BS) architecture, termed the \textit{flexible-sector} BS, which allows the deployed antennas to flexibly rotate and move along a circular track, thus enabling common sector rotation and flexible antenna allocation across sectors to adapt to the spatial user distribution efficiently. In particular, we focus on the uplink transmission in a single-cell system, where the flexible-sector BS receives independent messages from multiple users. We introduce an angular-domain user distribution model, which captures the users' spatial clustering or hot-spot distribution effectively. Assuming the zero-forcing (ZF) based receiver applied at the BS to decode multiuser signals, we derive the average sum rate achievable for the users as a function of the common rotation of sectors and the antenna allocation over them. Moreover, we develop a two-step algorithm to jointly optimize the common sector rotation and antenna allocation to maximize the average sum rate of all users. It is shown that the optimal antenna number in each sector linearly increases with the number of users in it. It is also revealed that under the most favorable user distribution, the achievable sum rate gain increases in the order of $\log_{2}(B)$ in the regime of asymptotically large number of antennas, where $B$ denotes the number of sectors. Numerically results also show that as $B$ increases, the proposed flexible-sector BS achieves higher sum rate, and it outperforms other benchmark schemes, such as the traditional fixed-sector BS as well as the BS with sector rotation or antenna allocation optimization only.

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