cation to tackle FL in heterogeneous networks. The above two works did not consider the constraint of the actual wireless communication process. The work presented in [6] exploited the medium access control (MAC) property and used both ana- log and digital communications to directly get the model average. However, they did not consider the effects from wireless fading channels. Besides, gradient projection transmitted over MAC directly leads to a higher bit error rate (BER). In this chapter we propose to use NOMA in the uplink FL communication by considering the fading channels and adaptively compresses the gradient for the optimal transmission. This chapter highlights the following research contributions. 5G and Beyond Wireless Communication Networks, First Edition. Haijian Sun, Rose Qingyang Hu, and Yi Qian. © 2024 John Wiley & Sons Ltd. Published 2024 by John Wiley & Sons Ltd. 9 Wireless Systems for Distributed Machine Learning We utilize NOMA-enabled adaptive FL model update to reduce the aggregation latency. The study shows that NOMA can achieve superior performance in terms of communi- cation latency compared with the traditional time division multiplexing access (TDMA) approach, which is commonly utilized in the existing FL schemes. Considering the capacity limitation in wireless fading channels, we further propose to apply adaptive quantization and sparsification to compress model updates in the uplink NOMA-based FL in order to save bandwidth. We demonstrate the effectiveness of the proposed scheme with several distinct datasets. Results show that the communication latency for the NOMA-based FL update with gradient compression is significantly reduced by at least 7X with no compromise on the test learning accuracy. This chapter is organized as follows. Section 9.2 introduces the system model, FL update mechanism, and two compression techniques. Section 9.3 presents the NOMA transmission scheme, user scheduling, and adaptive transmission scheme. Simulation results are shown in Section 9.4 to verify the pro