We consider a broadband over-the-air computation empowered model aggregation approach for wireless federated learning (FL) systems and propose to leverage an intelligent reflecting surface (IRS) to combat wireless fading and noise. We first investigate the conventional node-selection based framework, where a few edge nodes are dropped in model aggregation to control the aggregation error. We analyze the performance of this node-selection based framework and derive an upper bound on its performance loss, which is shown to be related to the selected edge nodes. Then, we seek to minimize the mean-squared error (MSE) between the desired global gradient parameters and the actually received ones by optimizing the selected edge nodes, their transmit equalization coefficients, the IRS phase shifts, and the receive factors of the cloud server. By resorting to the matrix lifting technique and difference-of-convex programming, we successfully transform the formulated optimization problem into a convex one and solve it using off-the-shelf solvers. To improve learning performance, we further propose a weight-selection based FL framework. In such a framework, we assign each edge node a proper weight coefficient in model aggregation instead of discarding any of them to reduce the aggregation error, i.e., amplitude alignment of the received local gradient parameters from different edge nodes is not required. We also analyze the performance of this weight-selection based framework and derive an upper bound on its performance loss, followed by minimizing the MSE via optimizing the weight coefficients of the edge nodes, their transmit equalization coefficients, the IRS phase shifts, and the receive factors of the cloud server. Furthermore, we use the MNIST dataset for simulations to evaluate the performance of both node-selection and weight-selection based FL frameworks.

翻译：针对无线联邦学习系统，我们提出一种基于宽带空中计算赋能模型聚合方法，并建议利用智能反射面来对抗无线衰落与噪声。首先研究传统节点选择框架，在此框架中，模型聚合时舍弃部分边缘节点以控制聚合误差。我们分析该节点选择框架的性能，推导其性能损失的上界，结果表明该上界与所选边缘节点相关。随后，通过优化所选边缘节点、其传输均衡系数、IRS相移及云服务器接收因子，最小化期望全局梯度参数与实际接收参数之间的均方误差。借助矩阵提升技术和凸差规划，成功将所构建的优化问题转化为凸问题，并利用现成求解器求解。为提升学习性能，进一步提出基于权重选择的联邦学习框架。在该框架中，模型聚合时为每个边缘节点分配适当权重系数而非直接丢弃节点，以降低聚合误差（即无需对齐不同边缘节点接收的局部梯度参数幅值）。我们同样分析该权重选择框架的性能并推导其性能损失上界，随后通过优化边缘节点权重系数、传输均衡系数、IRS相移及云服务器接收因子最小化均方误差。最后，使用MNIST数据集进行仿真，评估基于节点选择与权重选择的两种联邦学习框架性能。