 functions, respectively. By using them we can effectively reduce the compression accumulation errors. Algorithm 9.1 summarizes the proposed scheme. Algorithm 9.1 Adaptive FL Update with Uplink NOMA and Gradient Compression 1: Initialization: PS gives initial 00, maximum rounds T. 2: for each FL update round t do PS selects K = CN users and calculates their maximum achievable data rates Mk. Then sends synchronous pilots, Mk, and Ot to users. for each selected user k in parallel do Update local gradient one or multiple times: according to time budget. Based on Mk and size of gradient, apply either sparsification GS() or quantization GQ(A) Gradient residual , will be kept locally for next round update. Send gradients to the PS at the beginning of synchronous time slot. end for PS applies SIC to decode gradient from K users. PS performs weighted average: 12: end for 1 Intuitively, some residuals can be accumulated to exceed the minimum threshold and can be used to help speed up the model convergence. 9.4 Scheduling and Power Optimization Note: Compared with the TDMA-based scheme, our proposed NOMA-based scheme achieves a lower latency performance. However, at the PS side, the signal decoding complexity is elevated as NOMA requires a multi-user detection (MUD) receiver to decode user messages successively. 9.4 Scheduling and Power Optimization In Section 9.3, each round chooses K users randomly, and their transmission power is fixed. A careful user scheduling and power allocation can further improve system performance. In the following, we provide problem formulation and its solution [122]. 9.4.1 Problem Formulation Here we provide the formulated optimization problem with the following three constraints considered in our system model. C1: Each device can be scheduled at most once across different rounds. C2: At most K devices are allowed to participate the FL update in each round under NOMA. C3: Transmission power of each device in each round is bounded by a maximum value. We aim to maximize a weighted sum rate of al