To effectively handle impulse noise in narrowband power line communication (NB-PLC) transceivers, a comprehensive statistical analysis of aperiodic asynchronous impulse noise (APIN) is crucial. Existing mathematical noise generation models only capture a subset of the noise characteristics. In this study, we propose a novel generative adversarial network (GAN), the noise-generating GAN (NGGAN), which performs data synthesis by learning the complex characteristics of real-world measured noise samples. To closely match the complex noise statistics of NB-PLC systems, we constructed a realistic dataset by measuring NB-PLC noise through the analog coupling and bandpass filtering circuits of a commercial NB-PLC modem. To train the NGGAN, we designed the input signal length to facilitate the generation of cyclic stationary noise in the NGGAN model. We used the Wasserstein distance as a loss function to improve the similarity between the generated noise and the training data. We analyzed the similarity performance of the GAN-based model quantitatively and qualitatively based on mathematical and real-world measured datasets. The training dataset includes actual measurements of the piecewise spectral circular stationary Gaussian model (PSCGM), the frequency-shifted (FRESH) filter, and the NB-PLC system. Simulation results show that the noise samples generated by NGGAN are very close to real noise samples. PCA scatter plots and FID analysis demonstrate that NGGAN outperforms other GAN-based models by generating noise samples with excellent fidelity and high diversity.