  Recently, channel extrapolation has been widely investigated in frequency
division duplex (FDD) massive MIMO systems. However, in time division duplex
(TDD) fifth generation (5G) new radio (NR) systems, the channel extrapolation
problem also arises due to the hopping uplink pilot pattern, which has not been
fully researched yet. This paper addresses this gap by formulating a channel
extrapolation problem in TDD massive MIMO-OFDM systems for 5G NR, incorporating
imperfection factors. A novel two-stage two-dimensional (2D) channel
extrapolation scheme in both frequency and time domain is proposed, designed to
mitigate the negative effects of imperfection factors and ensure high-accuracy
channel estimation. Specifically, in the channel estimation stage, we propose a
novel multi-band and multi-timeslot based high-resolution parameter estimation
algorithm to achieve 2D channel extrapolation in the presence of imperfection
factors. Then, to avoid repeated multi-timeslot based channel estimation, a
channel tracking stage is designed during the subsequent time instants, in
which a sparse Markov channel model is formulated to capture the dynamic
sparsity of massive MIMO-OFDM channels under the influence of imperfection
factors. Next, an expectation-maximization (EM) based compressive channel
tracking algorithm is designed to jointly estimate unknown imperfection and
channel parameters by exploiting the high-resolution prior information of the
delay/angle parameters from the previous timeslots. Simulation results
underscore the superior performance of our proposed channel extrapolation
scheme over baselines.
