  Doubly-selective channel estimation represents a key element in ensuring
communication reliability in wireless systems. Due to the impact of multi-path
propagation and Doppler interference in dynamic environments, doubly-selective
channel estimation becomes challenging. Conventional channel estimation schemes
encounter performance degradation in high mobility scenarios due to the usage
of limited training pilots. Recently, deep learning (DL) has been utilized for
doubly-selective channel estimation, where convolutional neural network (CNN)
networks are employed in the frame-by-frame (FBF) channel estimation. However,
CNN-based estimators require high complexity, making them impractical in
real-case scenarios. For this purpose, we overcome this issue by proposing an
optimized and robust bi-directional recurrent neural network (Bi-RNN) based
channel estimator to accurately estimate the doubly-selective channel,
especially in high mobility scenarios. The proposed estimator is based on
performing end-to-end interpolation using gated recurrent unit (GRU) unit.
Extensive numerical experiments demonstrate that the developed Bi-GRU estimator
significantly outperforms the recently proposed CNN-based estimators in
different mobility scenarios, while substantially reducing the overall
computational complexity.
