We investigate multiuser uplink communication from multiple single-antenna users to a base station (BS), which is equipped with a movable-antenna (MA) array and adopts zero-forcing receivers to decode multiple signals. We aim to optimize the MAs' positions at the BS, to minimize the total transmit power of all users subject to the minimum rate requirement. After applying transformations, we show that the problem is equivalent to minimizing the sum of each eigenvalue's reciprocal of a matrix, which is a function of all MAs' positions. Subsequently, the projected gradient descent (PGD) method is utilized to find a locally optimal solution. In particular, different from the latest related work, we exploit the eigenvalue decomposition to successfully derive a closed-form gradient for the PGD, which facilitates the practical implementation greatly. We demonstrate by simulations that via careful optimization for all MAs' positions in our proposed design, the total transmit power of all users can be decreased significantly as compared to competitive benchmarks.

翻译：我们研究从多个单天线用户到配备可移动天线阵列且采用迫零接收机解码多路信号的基站的多用户上行通信。以用户最低速率需求为约束，我们旨在优化基站处可移动天线的位置以最小化所有用户的总发射功率。经过变换后，我们证明该问题等价于最小化某矩阵各特征值倒数之和——该矩阵是所有可移动天线位置的函数。随后采用投影梯度下降法求解局部最优解。特别地，与最新相关工作不同，我们利用特征值分解成功推导出投影梯度下降法的闭式梯度，这极大地促进了实际实现。仿真结果表明，通过我们提出的方案对所有可移动天线位置进行精细优化，相较于竞争基准方案，所有用户的总发射功率可显著降低。