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Split inference facilitates deep neural network (DNN) inference tasks at resource-constrained edge devices. However, a pre-determined split configuration of a DNN limits the inference performance in time-varying wireless channels. To accelerate the inference, we propose a two-stage wireless channel adaptive split inference method by considering memory and energy constraints on the edge device. The proposed scheme is able to offer the privacy of the edge device and improves inference performance in time-varying wireless channels by leveraging a U-shaped DNN splitting framework and adaptively determining the splitting points of a DNN in real-time according to time-varying wireless channel gains.