The orthogonal time frequency space (OTFS) modulation proposed in recent years is considered to have superior performance than orthogonal frequency division multiplexing (OFDM) for the doubly selective (DS) channels. The works in the existing literature on OTFS mainly focus on the cases where the channels are underspread (i.e.

the product of the delay spread and the Doppler spread is less than 1). In the scenario of overspread DS channel

which has large delay spread and severe Doppler spread

such as underwater acoustic (UWA) channel

the channel model in delay-Doppler (DD) Domain derived by existing work is no longer applicable. In this paper

we derive a more generalized expression of the channel model in delay-Doppler domain

which allows the product of the delay spread and Doppler spread to be larger than 1. The result shows that the existing channel model is just a special case of the one we proposed. Using the proposed channel matrix in DD domain

we build the OTFS detectors with the minimum mean square error (MMSE) and message passing (MP) algorithms on overspread doubly selective channel. Finally

simulation results are presented to verify the theoretical derivation and the effectiveness of the detectors.