Channel estimation and symbol detection for AFDM over doubly selective fading channels

In this paper, two receiver designs, each incorporating channel estimation and symbol detection, are presented for affine frequency division multiplexing (AFDM) over doubly selective fading channels. The first design unlocks the potential of deep learning in AFDM receivers. We first construct deep neural networks (DNNs), then train them offline by using training data, and finally deploy them online at the receiver to output transmitted information bits. This DNN receiver fails to achieve satisfactory bit error rate (BER) performance when there is no guard interval (GI) between the pilot and data. To solve this problem, we design a GI-free iterative AFDM receiver, which first performs coarse channel estimation and symbol detection, then implements interference cancellation by using the detected symbols, and finally proceeds channel estimation, symbol detection, and interference cancellation in an iterative manner until reaching a stop criterion. Moreover, a performance-enhancing method is proposed for the GI-free iterative AFDM receiver. In this enhanced scheme, the data interfered by the pilot is estimated by maximum-likelihood detection. Simulation results show that the DNN receiver is more robust than the existing scheme in the presence of pilot-data interference, and the performance-enhancing GI-free iterative receiver demonstrates excellent BER performance, achieving a gap of less than 0.5 dB compared to the scenario of perfect channel estimation, at a BER level of $10^{-3}$.