  In massive multiple-input multiple-output (MIMO) systems, the downlink
transmission performance heavily relies on accurate channel state information
(CSI). Constrained by the transmitted power, user equipment always transmits
sounding reference signals (SRSs) to the base station through frequency
hopping, which will be leveraged to estimate uplink CSI and subsequently
predict downlink CSI. This paper aims to investigate joint channel estimation
and prediction (JCEP) for massive MIMO with frequency hopping sounding (FHS).
Specifically, we present a multiple-subband (MS) delay-angle-Doppler (DAD)
domain channel model with off-grid basis to tackle the energy leakage problem.
Furthermore, we formulate the JCEP problem with FHS as a multiple measurement
vector (MMV) problem, facilitating the sharing of common CSI across different
subbands. To solve this problem, we propose an efficient Off-Grid-MS hybrid
message passing (HMP) algorithm under the constrained Bethe free energy (BFE)
framework. Aiming to address the lack of prior CSI in practical scenarios, the
proposed algorithm can adaptively learn the hyper-parameters of the channel by
minimizing the corresponding terms in the BFE expression. To alleviate the
complexity of channel hyper-parameter learning, we leverage the approximations
of the off-grid matrices to simplify the off-grid hyper-parameter estimation.
Numerical results illustrate that the proposed algorithm can effectively
mitigate the energy leakage issue and exploit the common CSI across different
subbands, acquiring more accurate CSI compared to state-of-the-art
counterparts.
