  In this paper, we investigate channel acquisition for high frequency (HF)
skywave massive multiple-input multiple-output (MIMO) communications with
orthogonal frequency division multiplexing (OFDM) modulation. We first
introduce the concept of triple beams (TBs) in the space-frequency-time (SFT)
domain and establish a TB based channel model using sampled triple steering
vectors. With the established channel model, we then investigate the optimal
channel estimation and pilot design for pilot segments. Specifically, we find
the conditions that allow pilot reuse among multiple user terminals (UTs),
which significantly reduces pilot overhead and increases the number of UTs that
can be served. Moreover, we propose a channel prediction method for data
segments based on the estimated TB domain channel. To reduce the complexity, we
formulate the channel estimation as a statistical inference problem and then
obtain the channel by the proposed constrained Bethe free energy minimization
(CBFEM) based channel estimation algorithm, which can be implemented with low
complexity by exploiting the structure of the TB matrix together with the chirp
z-transform (CZT). Simulation results demonstrate the superior performance of
the proposed channel acquisition approach.
