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：我们研究了从多个单天线用户到基站（BS）的多用户上行链路通信，其中基站配备可移动天线（MA）阵列并采用迫零接收机解码多个信号。我们旨在优化基站处MA的位置，在满足最小速率要求的条件下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矩阵各特征值倒数之和，而该矩阵是所有MA位置的函数。随后，采用投影梯度下降（PGD）方法寻找局部最优解。值得注意的是，与最新相关工作不同，我们利用特征值分解成功推导出PGD的闭式梯度，这极大便利了实际实现。仿真结果表明，通过精心优化所提设计中所有MA的位置，相比于竞争基准方案，所有用户的总发射功率可显著降低。