In this paper, we investigate the movable antennas (MAs)-enabled multiple-input-single-output (MISO) systems, where the base station (BS) equipped with multiple MAs serves multiple single-antenna user. The delay-sensitive scenario is considered, where users refrain from periodically sending training signals to the BS for channel estimations to avoid additional latency. As a result, the BS relies solely on the statistical channel state information (CSI) to transmit data with a fixed rate. Under this setup, we aim to maximize the outage-aware sum rate of all users, by jointly optimizing antenna positions and the transmit beamforming at the BS, while satisfying the given target outage probability requirement at each user. The problem is highly non-convex, primarily because the exact cumulative distribution function (CDF) of the received signal-to-interference-plus-noise ratio (SINR) of each user is difficult to derive. To simplify analysis and without comprising performance, we adopt the statistical CSI based zero-forcing beamforming design. We then introduce one important lemma to derive the tight mean and variance of the SINR. Leveraging these results, we further exploit the Laguerre series approximation to successfully derive the closedform and tight CDF of the SINR. Subsequently, the outageaware sum rate expression is presented but still includes complex structure with respect to antenna positions. Facing this challenge, the projected gradient ascent (PGA) method is developed to iteratively update antenna positions until convergence. Numerical results demonstrate the effectiveness of our proposed schemes compared to conventional fixed-position antenna (FPA) and other competitive benchmarks.

翻译：本文研究了基于可移动天线（MAs）的多输入单输出（MISO）系统，其中配备多个MA的基站（BS）为多个单天线用户提供服务。考虑时延敏感场景，用户为避免额外延迟，不向基站周期性发送训练信号进行信道估计。因此，基站仅依赖统计信道状态信息（CSI）以固定速率传输数据。在此设置下，我们旨在通过联合优化天线位置和基站发射波束成形，在满足每个用户给定目标中断概率要求的同时，最大化所有用户的中断感知和速率。该问题具有高度非凸性，主要因为每个用户接收信号与干扰加噪声比（SINR）的精确累积分布函数（CDF）难以推导。为简化分析且不影响性能，我们采用基于统计CSI的迫零波束成形设计。随后引入一个重要引理来推导SINR的紧致均值和方差。利用这些结果，我们进一步借助拉盖尔级数逼近，成功推导出SINR的闭式紧致CDF。继而给出中断感知和速率表达式，但其仍包含关于天线位置的复杂结构。针对这一挑战，我们开发了投影梯度上升（PGA）方法以迭代更新天线位置直至收敛。数值结果表明，相较于传统固定位置天线（FPA）及其他竞争基准方案，我们提出的方案具有显著有效性。