  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 symbol-by-symbol (SBS) and
frame-by-frame (FBF) 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 long short-term memory (LSTM) and convolutional
neural network (CNN) networks are employed in the SBS and FBF, respectively.
However, their usage is not optimal, since LSTM suffers from long-term memory
problem, whereas, CNN-based estimators require high complexity. For this
purpose, we overcome these issues by proposing an optimized recurrent neural
network (RNN)-based channel estimation schemes, where gated recurrent unit
(GRU) and Bi-GRU units are used in SBS and FBF channel estimation,
respectively. The proposed estimators are based on the average correlation of
the channel in different mobility scenarios, where several
performance-complexity trade-offs are provided. Moreover, the performance of
several RNN networks is analyzed. The performance superiority of the proposed
estimators against the recently proposed DL-based SBS and FBF estimators is
demonstrated for different scenarios while recording a significant reduction in
complexity.
