Over-the-Air (OtA) Federated Learning (FL) refers to an FL system where multiple agents apply OtA computation for transmitting model updates to a common edge server. Two important features of OtA computation, namely linear processing and signal-level superposition, motivate the use of linear compression with compressed sensing (CS) methods to reduce the number of data samples transmitted over the channel. The previous works on applying CS methods in OtA FL have primarily assumed that the original model update vectors are sparse, or they have been sparsified before compression. However, it is unclear whether linear compression with CS-based reconstruction is more effective than directly sending the non-zero elements in the sparsified update vectors, under the same total power constraint. In this study, we examine and compare several communication designs with or without sparsification. Our findings demonstrate that sparsification before compression is not necessary. Alternatively, sparsification without linear compression can also achieve better performance than the commonly considered setup that combines both.

翻译：空中联邦学习（OtA FL）是指多个智能体利用空中计算技术将模型更新传输至共用边缘服务器的联邦学习系统。空中计算的两个重要特性——线性处理与信号级叠加——推动了基于压缩感知（CS）方法的线性压缩技术发展，从而减少信道中传输的数据样本数量。现有关于在OtA FL中应用压缩感知方法的研究通常假设原始模型更新向量具有稀疏性，或已在压缩前进行了稀疏化处理。然而，在相同总功率约束下，尚不明确基于CS重建的线性压缩是否比直接传输稀疏化更新向量中的非零元素更有效。本研究考察并比较了多种含或不含稀疏化的通信设计方案，结果表明压缩前的稀疏化并非必要。相反，不采用线性压缩的稀疏化方案，其性能也能优于当前普遍采用的联合处理方案。