The traditional channel estimation for OFDM systems suffers from big overheads caused by pilots. Current channel estimation methods only consider the correlation among pilots within a time-frequency grid, which is a kind of local channel information. In this article, we propose a Generative Adversarial Network (GAN) based channel estimation method to utilize not only local channel information but also correlation across multiple frames, thus much fewer pilots are needed. We propose to explore GAN to establish a mapping from a low dimensional space to a high dimensional channel space. Then based on very few pilots, we solve an optimization problem to localize the low dimensional vector corresponding to the specified channel and generate the corresponding channel. Furthermore, we propose an improved conditional GAN (cGAN), which takes the multi-path number as conditional information, making the proposed generative channel model more robust in various scenarios. Experiments demonstrate that the proposed cGAN-based method can be applied to multiple channel profiles once trained offline, and it is robust to the mismatch of multi-path number. Besides, the proposed method outperforms the ideal ALMMSE and ChannelNet methods under the same pilot density. In the best case, it can achieve comparable performance with only about half the number of pilots.
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