  We consider the underwater acoustic channel which is time-variant and
doubly-spread in this work. Since conventional channel estimation and decision
feedback equalizer (DFE) can not work well for this type of channel, a
path-specific underwater acoustic channel tracking is proposed. It is based on
the framework of Kalman filter. We provide a simplified sound propagation model
as the state transition model. A multipath tracker is proposed which is
tolerant of the model-mismatch. Then we can obtain the time-variant path number
and path-specific parameters such as delay and Doppler scaling factor. We also
consider the application of the proposed path-specific underwater acoustic
channel tracking. We propose two types of passive time reversal mirror (PTRM)
with our path-specific parameters for time-variant and doubly-spread underwater
acoustic channel. With the path-specific parameters obtained by the proposed
channel tracking, the proposed PTRM can not only match the time dispersion as
conventional PTRM, but also the doubly-spread channel, since the path-specific
delay and Doppler scaler factor can help to match the channel in both time and
frequency domain. For extensive doubly-spread channel, we can further apply the
path-specific compensation to the PTRM. Both simulations and experimental
results by data from 2016 Qiandao Lake experiment show the efficiency of
proposed path-specific channel tracking and proposed PTRMs with path-specific
parameters.
