Despite the significant improvements in speaker recognition enabled by deep neural networks, unsatisfactory performance persists under far-field scenarios due to the effects of the long range fading, room reverberation, and environmental noises. In this study, we focus on far-field speaker recognition with a microphone array. We propose a multi-channel training framework for the deep speaker embedding neural network on noisy and reverberant data. The proposed multi-channel training framework simultaneously processes the time-, frequency- and channel-information to learn a robust deep speaker embedding. Based on the 2-dimensional or 3-dimensional convolution layer, we investigate different multi-channel training schemes. Experiments on the simulated multi-channel reverberant and noisy data show that the proposed method obtains significant improvements over the single-channel trained deep speaker embedding system with front end speech enhancement or multi-channel embedding fusion.