The concept of federated learning (FL) was first proposed by Google in 2016. Thereafter, FL has been widely studied for the feasibility of application in various fields due to its potential to make full use of data without compromising the privacy. However, limited by the capacity of wireless data transmission, the employment of federated learning on mobile devices has been making slow progress in practical. The development and commercialization of the 5th generation (5G) mobile networks has shed some light on this. In this paper, we analyze the challenges of existing federated learning schemes for mobile devices and propose a novel cross-device federated learning framework, which utilizes the anonymous communication technology and ring signature to protect the privacy of participants while reducing the computation overhead of mobile devices participating in FL. In addition, our scheme implements a contribution-based incentive mechanism to encourage mobile users to participate in FL. We also give a case study of autonomous driving. Finally, we present the performance evaluation of the proposed scheme and discuss some open issues in federated learning.