The performance of speech processing models trained on clean speech drops significantly in noisy conditions. Training with noisy datasets alleviates the problem, but procuring such datasets is not always feasible. Noisy speech simulation models that generate noisy speech from clean speech help remedy this issue. In our work, we study the ability of Generative Adversarial Networks (GANs) to simulate a variety of noises. Noise from the Ultra-High-Frequency/Very-High-Frequency (UHF/VHF), additive stationary and non-stationary, and codec distortion categories are studied. We propose four GANs, including the non-parallel translators, SpeechAttentionGAN, SimuGAN, and MaskCycleGAN-Augment, and the parallel translator, Speech2Speech-Augment. We achieved improvements of 55.8%, 28.9%, and 22.8% in terms of Multi-Scale Spectral Loss (MSSL) as compared to the baseline for the RATS, TIMIT-Cabin, and TIMIT-Helicopter datasets, respectively, after training on small datasets of about 3 minutes.