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.

翻译：双选择性信道估计是确保无线系统通信可靠性的关键要素。由于动态环境中多径传播和多普勒干扰的影响，双选择性信道估计变得具有挑战性。传统的逐符号（SBS）和逐帧（FBF）信道估计方案因使用有限训练导频而在高移动性场景中性能下降。近年来，深度学习（DL）被用于双选择性信道估计，其中在SBS和FBF中分别采用长短期记忆（LSTM）和卷积神经网络（CNN）。然而，这些方法并非最优，因为LSTM存在长期记忆问题，而基于CNN的估计器复杂度较高。为此，我们通过提出优化的基于循环神经网络（RNN）的信道估计方案来克服这些问题，其中在SBS和FBF信道估计中分别使用门控循环单元（GRU）和双向GRU（Bi-GRU）。所提出的估计器基于不同移动性场景下信道的平均相关性，并提供了多种性能-复杂度权衡方案。此外，还分析了多种RNN网络的性能。在不同场景下，所提估计器相对于近期基于深度学习的SBS和FBF估计器展现出性能优势，同时显著降低了复杂度。