Wireless signal recognition (WSR) is crucial in modern and future wireless communication networks since it aims to identify the properties of the received signal in a no-collaborative manner. However, it is challenging to accurately classify signals in low signal-to-noise ratio (SNR) conditions and distributed network settings. In this paper, we propose a novel distributed multi-task learning framework for joint wireless signal enhancement and recognition (WSER), addressing the crucial need for non-collaborative signal identification in modern wireless networks. Our approach integrates a wireless signal enhancement and recognition network (WSERNet) with FedProx+, an enhanced federated learning algorithm designed for heterogeneous data distributions. Specifically, WSERNet leverages an asymmetric convolution block (ACBlock) to capture long-range dependencies in the input signal and improve the performance of the deep learning model. FedProx+ introduces a proximal term to the loss function to encourage the model updates to be closer to the previous model, enhancing the convergence speed and robustness of federated learning. Extensive experiments demonstrate the effectiveness of the proposed framework for joint WSER, achieving superior performance compared to state-of-the-art methods under both centralized and distributed settings including independent and identically distributed (IID) and non-IID data distributions.