Joint Channel Estimation and Equalization Using Circular Convolution and DNN for ZP-OTFS

To combat the Doppler shift caused by high mobility, orthogonal time frequency space (OTFS) systems have been proposed to convert the timevarying channel into a nearly time-invariant channel in the delay-Doppler (DD) domain. Since the DD domain received signal can be expressed as a two-dimensional (2D) circular convolution of the transmitted signal and the channel impulse response in the DD domain, we propose a joint channel estimation and equalization method based on 2D circular convolution, called circular convolution based joint channel estimation and equalization (C-JCE), for zero-padding (ZP) OTFS systems. However, when the Doppler shift is severe and the subcarrier spacing is not large enough, the phase distortion may occur. As a result, we further propose a deep learning (DL)-based method, called pilot-aided phase distortion compensation network (PDCN), to compensate the phase distortion. The proposed C-JCE with PDCN achieves a bit error rate performance close to the minimum mean square error (MMSE) or message passing (MP) equalization with perfect channel state information (CSI) on the low earth orbit (LEO) satellite channel with an extremely large Doppler shift. Overall, the proposed C-JCE with PDCN for ZP-OTFS systems not only has a higher spectral efficiency but also achieves an outstanding performance.