  In this paper, we propose an innovative learning-based channel prediction
scheme so as to achieve higher prediction accuracy and reduce the requirements
of huge amounts and strict sequential format of channel data. Inspired by the
idea of the neural ordinary differential equation (Neural ODE), we first prove
that the channel prediction problem can be modeled as an ODE problem with a
known initial value by analyzing the physical process of electromagnetic wave
propagation within a mobile environment. Then, we design a novel
physics-inspired spatial channel gradient network (SCGnet), which represents
the derivative process of channel varying as a special neural network and can
obtain the gradients at any relative displacement needed for the ODE solving.
With the SCGnet, the static channel at any location served by the base station
is accurately inferred through consecutive propagation and integration.
Finally, we design an efficient recurrent positioning algorithm based on some
prior knowledge of user mobility to obtain the velocity vector and propose an
approximate Doppler compensation method to make up the instantaneous
angular-delay domain channel. Only discrete historical channel data is needed
for the training, whereas only a few fresh channel measurements are needed for
the prediction, which ensures the scheme's practicability. Comprehensive
evaluations show that the proposed scheme is most efficient in representing,
learning, and predicting mobile wireless channels.
