Micro-Doppler analysis has become increasingly popular in recent years owning to the ability of the technique to enhance classification strategies. Applications include recognising everyday human activities, distinguishing drone from birds, and identifying different types of vehicles. However, noisy time-frequency spectrograms can significantly affect the performance of the classifier and must be tackled using appropriate denoising algorithms. In recent years, deep learning algorithms have spawned many deep neural network-based denoising algorithms. For these methods, noise modelling is the most important part and is used to assist in training. In this paper, we decompose the problem and propose a novel denoising scheme: first, a Generative Adversarial Network (GAN) is used to learn the noise distribution and correlation from the real-world environment; then, a simulator is used to generate clean Micro-Doppler spectrograms; finally, the generated noise and clean simulation data are combined as the training data to train a Convolutional Neural Network (CNN) denoiser. In experiments, we qualitatively and quantitatively analyzed this procedure on both simulation and measurement data. Besides, the idea of learning from natural noise can be applied well to other existing frameworks and demonstrate greater performance than other noise models.