As a revolutionary generative paradigm of deep learning, generative adversarial networks (GANs) have been widely applied in various fields to synthesize realistic data. However, it is challenging for conventional GANs to synthesize raw signal data, especially in some complex cases. In this paper, we develop a novel GAN framework for radio generation called "Radio GAN". Compared to conventional methods, it benefits from three key improvements. The first is learning based on sampling points, which aims to model an underlying sampling distribution of radio signals. The second is an unrolled generator design, combined with an estimated pure signal distribution as a prior, which can greatly reduce learning difficulty and effectively improve learning precision. Finally, we present an energy-constrained optimization algorithm to achieve better training stability and convergence. Experimental results with extensive simulations demonstrate that our proposed GAN framework can effectively learn transmitter characteristics and various channel effects, thus accurately modeling for an underlying sampling distribution to synthesize radio signals of high quality.