As a promising solution to achieve efficient learning among isolated data owners and solve data privacy issues, federated learning is receiving wide attention. Using the edge server as an intermediary can effectively collect sensor data, perform local model training, and upload model parameters for global aggregation. So this paper proposes a new framework for resource allocation in a hierarchical network supported by edge computing. In this framework, we minimize the weighted sum of system cost and learning cost by optimizing bandwidth, computing frequency, power allocation and subcarrier assignment. To solve this challenging mixed-integer non-linear problem, we first decouple the bandwidth optimization problem(P1) from the whole problem and obtain a closed-form solution. The remaining computational frequency, power, and subcarrier joint optimization problem(P2) can be further decomposed into two sub-problems: latency and computational frequency optimization problem(P3) and transmission power and subcarrier optimization problem(P4). P3 is a convex optimization problem that is easy to solve. In the joint optimization problem(P4), the optimal power under each subcarrier selection can be obtained first through the successive convex approximation(SCA) algorithm. Substituting the optimal power value obtained back to P4, the subproblem can be regarded as an assignment problem, so the Hungarian algorithm can be effectively used to solve it. The solution of problem P2 is accomplished by solving P3 and P4 iteratively. To verify the performance of the algorithm, we compare the proposed algorithm with five algorithms; namely Equal bandwidth allocation, Learning cost guaranteed, Greedy subcarrier allocation, System cost guaranteed and Time-biased algorithm. Numerical results show the significant performance gain and the robustness of the proposed algorithm in the face of parameter changes.
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