Channel Estimation, Interpolation and Extrapolation in Doubly-dispersive Channels

The OTFS (Orthogonal Time Frequency Space) is widely acknowledged for its ability to combat Doppler spread in time-varying channels. In this paper, another advantage of OTFS over OFDM (Orthogonal Frequency Division Multiplexing) will be demonstrated: much reduced channel training overhead. Specifically, the sparsity of the channel in delay-Doppler (D-D) domain implies strong correlation of channel gains in time-frequency (T-F) domain, which can be harnessed to reduce channel training overhead through interpolation. An immediate question is how much training overhead is needed in doubly-dispersive channels? A conventional belief is that the overhead is only dependent on the product of delay and Doppler spreads, but we will show that it's also dependent on the T-F window size. The finite T-F window leads to infinite spreading in D-D domain, and aliasing will be inevitable after sampling in T-F domain. Two direct consequences of the aliasing are increased channel training overhead and interference. Another factor contributing to channel estimation error is the inter-symbol-carrier-interference (ISCI), resulting from the uncertainty principle. Both aliasing and ISCI are considered in channel modelling, a low-complexity algorithm is proposed for channel estimation and interpolation through FFT. A large T-F window is necessary for reduced channel training overhead and aliasing, but increases processing delay. Fortunately, we show that the proposed algorithm can be implemented in a pipeline fashion. Further more, we showed that data-aided channel tracking is possible in D-D domain to further reduce the channel estimation frequency, i.e., channel extrapolation. The impacts of aliasing and ISCI on channel interpolation error are analyzed.