  In this paper, we aim to efficiently and accurately predict the static
channel impulse response (CIR) with only the user's position information and a
set of channel instances obtained within a certain wireless communication
environment. Such a problem is by no means trivial since it needs to
reconstruct the high-dimensional information (here the CIR everywhere) from the
extremely low-dimensional data (here the location coordinates), which often
results in overfitting and large prediction error. To this end, we resort to a
novel physics-inspired generative approach. Specifically, we first use a
forward deep neural network to infer the positions of all possible images of
the source reflected by the surrounding scatterers within that environment, and
then use the well-known Gaussian Radial Basis Function network (GRBF) to
approximate the amplitudes of all possible propagation paths. We further
incorporate the most recently developed sinusoidal representation network
(SIREN) into the proposed network to implicitly represent the highly dynamic
phases of all possible paths, which usually cannot be well predicted by the
conventional neural networks with non-periodic activators. The resultant
framework of Cosine-Gaussian Radial Basis Function network (C-GRBFnet) is also
extended to the MIMO channel case. Key performance measures including
prediction accuracy, convergence speed, network scale and robustness to channel
estimation error are comprehensively evaluated and compared with existing
popular networks, which show that our proposed network is much more efficient
in representing, learning and predicting wireless channels in a given
communication environment.
