Low Complexity Doubly Fractional OTFS Channel Estimation Based on L-BFGS Method

A low complexity doubly fractional orthogonal time-frequency space (OTFS) channel estimation method is proposed in this paper. In order to deal with the channel spread caused by fractional delay and Doppler frequency shift, and to make full use of channel sparsity in the delay Doppler (DD) domain, the channel response is estimated in the fractional DD domain. In the fractional DD domain, the channel state information (CSI) could be approximately represented by several impulse responses and their corresponding delay Doppler information. Thus, we do not process the whole responses corresponding to the entire DD domain, but find only several impulse responses iteratively. To alleviate the coupling effect between the fractional delay and Doppler dimension, mixed one- and two-dimensional (1&2D) fractional models are used, and then these models are combined in an optimization problem to get the final CSI. To further reduce the complexity, limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method is employed in this paper, thus resulting much reduced complexity, i.e., $\mathcal{O}\left( {\lambda {M_0}{N_0}} \right)$, compared with baseline schemes. Our simulation results show that, despite the quite low complexity, the NMSE performance of the proposed scheme is still superior to several classic methods.