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Orthogonal time frequency and space (OTFS) modulation is a promising technology that satisfies high-Doppler requirements for future mobile systems. OTFS encodes information symbols and pilot symbols into the two-dimensional (2D) delay-Doppler (DD) domain. The received symbols suffer from inter-Doppler interference (IDI) in fading channels with fractional Doppler shifts sampled at noninteger indices in the DD domain. The IDI has been treated as an unavoidable effect because the fractional Doppler shifts cannot be obtained directly from the received pilot symbols. This paper provides a solution to channel estimation for fractional Doppler channels with lower computational complexity than a conventional channel estimation method using a pseudo sequence. The proposed estimation provides new insight into the OTFS input-output relation in the DD domain as a 2D circular convolution with a small approximation. According to the input-output relation, we also provide a low-complexity channel equalization method using the estimated channel information. We demonstrate the error performance of the proposed channel estimation and equalization in a high-Doppler channel by simulations. The simulation results show that the proposed channel estimation method outperforms the conventional channel estimation. The results also show that the proposed equalization method has a similar performance to the minimum mean square error equalizer using matrix inversion.

Channel Estimation and Equalization for CP-OFDM-based OTFS in Fractional Doppler Channels