AI 中文总结
研究不完美信道状态信息下无线传输联邦学习的长期均方误差最小化问题，通过收敛分析建立上界，开发优化框架联合设计发射系数与接收合并向量，引入基于李雅普诺夫的方法处理因果CSI，实验验证算法可减少精度下降及优越性。
AI 中文摘要
无线传输（OTA）计算作为提高无线联邦学习（FL）通信效率的有效方法，近来备受关注。OTA-FL能同时传输和聚合本地模型更新，减少延迟和带宽消耗。但信道状态信息（CSI）不确定性导致全局模型聚合不完美，影响最终学习性能。本文研究不完美CSI条件下OTA-FL的长期均方误差（MSE）最小化问题。通过收敛分析建立时间平均MSE的上界，揭示多轮通信中聚合误差对整体训练性能的影响。基于此分析，开发了一个优化框架，通过联合设计本地设备的发射系数和参数服务器（PS）的接收合并向量来最小化长期MSE。由于交替优化方法需要非因果CSI，进一步引入基于李雅普诺夫的优化方法来处理因果CSI场景。通过纳入虚拟队列来表征长期能耗，该方法有效解耦时间依赖性，允许根据每个聚合轮的因果CSI优化发射系数。在Fashion-MNIST、CIFAR-10和CIFAR-100数据集上的综合评估表明，所提算法能显著减少由不完美CSI导致的测试精度下降。与其他基准方案的比较进一步验证了所提算法的优越性。
英文摘要
Over-the-air (OTA) computation has recently gained significant attentions as an effective approach to enhance the communication efficiency of wireless federated learning (FL). By enabling simultaneous transmission and aggregation of local model updates, OTA-FL can substantially reduce both latency and bandwidth consumption. However, a key challenge lies in the imperfect aggregation of global models caused by channel state information (CSI) uncertainty, which introduces distortion to the final learning performance. To address this issue, we study the long-term mean squared error (MSE) minimization problem for OTA-FL under imperfect CSI conditions. Through convergence analysis, we establish an upper bound for the time-averaged MSE, thereby revealing the effect of aggregation errors accumulated throughout multiple communication rounds on the overall training performances. Based on this analysis, an optimization framework is developed to minimize the long-term MSE via the joint design of (i) transmit coefficients at the local devices and (ii) receive combining vectors at the parameter server (PS). Since this alternating optimization approach requires non-causal CSI, a Lyapunov-based optimization method is further introduced to handle causal CSI scenarios. By incorporating virtual queues to characterize long-term energy consumption, the proposed method effectively decouples temporal dependencies and allows transmit coefficients to be optimized based on the causal CSI of each aggregation round. Comprehensive evaluations on Fashion-MNIST, CIFAR-10 and CIFAR-100 datasets have demonstrated that the proposed algorithms can significantly reduce the degradation of test accuracy caused by imperfect CSI. Comparisons with other benchmark schemes further verify the superiority of our proposed algorithms.
