  We consider the problem of accurate channel estimation for OTFS based systems
with few transmit/receive antennas, where additional sparsity due to large
number of antennas is not a possibility. For such systems the sparsity of the
effective delay-Doppler (DD) domain channel is adversely affected in the
presence of channel path delay and Doppler shifts which are non-integer
multiples of the delay and Doppler domain resolution. The sparsity is also
adversely affected when practical transmit and receive pulses are used. In this
paper we propose a Modified Maximum Likelihood Channel Estimation (M-MLE)
method for OTFS based systems which exploits the fine delay and Doppler domain
resolution of the OTFS modulated signal to decouple the joint estimation of the
channel parameters (i.e., channel gain, delay and Doppler shift) of all channel
paths into separate estimation of the channel parameters for each path. We
further observe that with fine delay and Doppler domain resolution, the
received DD domain signal along a particular channel path can be written as a
product of a delay domain term and a Doppler domain term where the delay domain
term is primarily dependent on the delay of this path and the Doppler domain
term is primarily dependent on the Doppler shift of this path. This allows us
to propose another method termed as the two-step method (TSE), where the joint
two-dimensional estimation of the delay and Doppler shift of a particular path
in the M-MLE method is further decoupled into two separate one-dimensional
estimation for the delay and for the Doppler shift of that path. Simulations
reveal that the proposed methods (M-MLE and TSE) achieve better channel
estimation accuracy at lower complexity when compared to other known methods
for accurate OTFS channel estimation.
