A Joint Optimization Method for Trajectory and Power of Unmanned Aerial Vehicle assisted Over-the-Air Computation
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摘要: 无人机(UAV)辅助的空中计算(AirComp)系统为大范围、分布式数据的快速聚合提供了有效的解决方法。该文研究了通过无人机辅助空中计算系统联合轨迹规划与功率优化方法。UAV作为移动基站，通过调整其运动轨迹和地面传感器节点发射功率，实现AirComp系统聚合数据均方误差的最优化。在UAV轨迹、传感器功率限制下，联合优化UAV轨迹、去噪因子和传感器功率，使时间平均均方误差最小化。基于块坐标下降和逐次凸逼近方法，提出无人机飞行轨迹与功率联合优化算法，并通过仿真验证了所提算法的性能。Abstract: The Unmanned Aerial Vehicle (UAV)assisted over-the-Air Computation(AirComp) system provides an effective solution for the fast aggregation of large-scale and distributed data. In this paper, a joint trajectory planning and power optimization method through UAV-assisted AirComp system is investigated. As a mobile base station, UAV is used to optimize the mean square error of the aggregated data of the AirComp system by adjusting its trajectory and transmitting power of the ground sensors. Under the limitations of UAV trajectory and sensor power, the UAV flight trajectory, the scaling factor and sensor power are jointly optmized to minimize the time-averaged mean square error. Based on the block coordinate descent and successive convex approximation methods, the joint optimization algorithm of UAV flight trajectory and power is proposed. Simulation results verify the performance of the proposed algorithm.
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算法1 无人机飞行轨迹与功率优化算法 定义无人机飞行时间N；传感器的最大发射功率$\{ {P_k}[n]\} $；传感
器的平均发射功率$\{ \overline {{P_k}} [n]\} $；收敛精度$\xi $；环境参数u和v；误差
幅度参数A。(1) 定义$r = 0$,${R^0} = 1$；初始化无人机的飞行轨迹$ \{ {{\boldsymbol{q}}^0}[n]\} $；传
感器初始发射功率$\{ p_k^0[n]\} $；(2) 循环 (3) r=r+1 (4) 利用$ \{ {{\boldsymbol{q}}^{r - 1}}[n]\} $和$ \{ p_k^{r - 1}[n]\} $，根据式(16)求解$\{ {\eta ^r}[n]\} $并且
更新$\{ \eta [n]\} $；(5) 利用$ \{ {{\boldsymbol{q}}^{r - 1}}[n]\} $和$\{ {\eta ^r}[n]\} $，根据式(18)求解$ \{ p_k^r[n]\} $并且更
新$ \{ p_k^{}[n]\} $；(6) 利用$\{ {\eta ^r}[n]\} $和$ \{ p_k^r[n]\} $，根据式(26)求解$ \{ {{\boldsymbol{q}}^r}[n]\} $并且更新
$ \{ {\boldsymbol{q}}[n]\} $；(7) 根据式(10)和式(11)计算${\overline {{\text{MSE}}} ^r}$，并赋值${R^r} = {\overline {{\text{MSE}}} ^r}$； (8) 若${{({R^r} - {R^{r - 1}})} \mathord{\left/ {\vphantom {{({R^r} - {R^{r - 1}})} {{R^r}}}} \right. } {{R^r}}} \le \xi $，认为算法收敛，退出循环； (9) 问题得以求解得到次优解：去噪因子$\{ \eta [n]\} $，传感器发射功
率$\{ p_k^{}[n]\} $和UAV最优飞行轨迹$\{ {\boldsymbol{q}}[n]\} $；
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