<p>Hierarchical federated learning (HFL) has emerged as a promising paradigm by sinking model aggregation logic to edge servers nearer to the data source, thereby reducing latency and alleviating backbone network congestion. However, deploying HFL in wireless networks presents significant challenges, including cloud-edge communication overhead, highly heterogeneous communication traffic loads and data distribution, and energy shortage on terminal devices. To address these issues, we propose a noval Hierarchical Semi-Asynchronous Federated Learning (HSA_FL) framework optimized for wireless environments, where model aggregation updates are performed synchronously at the lower layer and asynchronously at the upper layer. This framework augments the frequency of lower-layer aggregation and introduces natural dithering compression to reduce upper-layer communication costs. We conduct a theoretical convergence analysis of this framework, highlighting the crucial impact of data distribution divergence on learning performance. Based on this insight, we model the system’s training latency, energy consumption, and data distribution divergence, with the goal of optimizing bandwidth allocation, device energy management, and device-to-edge server assignment strategies to reduce training costs and enhance learning quality. However, the optimization problem is a non-convex Mixed-Integer Nonlinear Programming (MINLP) problem, which is inherently difficult to solve. Leveraging the block coordinate descent approach, we simplify and decompose the problem, and develope a straightforward yet effective device assignment strategy based on greedy algorithm. Experimental results demonstrate that the proposed HSA_FL framework, along with the resource management and device assignment strategies, significantly reduces system energy consumption and latency while enhancing learning quality compared to baseline methods.</p>