  Channel estimation is essential for precoding/combining in millimeter wave
(mmWave) communications. However, accurate estimation is usually difficult
because the receiver can only observe the low-dimensional projection of the
received signals due to the hybrid architecture. We take the high speed
scenario into consideration where the Doppler effect caused by fast-moving
users can seriously deteriorate the channel estimation accuracy. In this paper,
we propose to incorporate the nested array into analog array architecture by
using RF switch networks with an objective of reducing the complexity and power
consumption of the system. Based on the covariance fitting criterion, a joint
Doppler and channel estimation method is proposed without need of discretizing
the angle space, and thus the model mismatch effect can be totally eliminated.
We also present an algorithmic implementation by solving the dual problem of
the original one in order to reduce the computational complexity. Numerical
simulations are provided to demonstrate the effectiveness and superiority of
our proposed method.
