  6G operators may use millimeter wave (mmWave) and sub-terahertz (sub-THz)
bands to meet the ever-increasing demand for wireless access. Sub-THz
communication comes with many existing challenges of mmWave communication and
adds new challenges associated with the wider bandwidths, more antennas, and
harsher propagations. Notably, the frequency- and spatial-wideband
(dual-wideband) effects are significant at sub-THz. This paper presents a
compressed training framework to estimate the time-varying sub-THz MIMO-OFDM
channels. A set of frequency-dependent array response matrices are constructed,
enabling channel recovery from multiple observations across subcarriers via
multiple measurement vectors (MMV). Using the temporal correlation, MMV least
squares (LS) is designed to estimate the channel based on the previous beam
support, and MMV compressed sensing (CS) is applied to the residual signal. We
refer to this as the MMV-LS-CS framework. Two-stage (TS) and MMV FISTA-based
(M-FISTA) algorithms are proposed for the MMV-LS-CS framework. Leveraging the
spreading loss structure, a channel refinement algorithm is proposed to
estimate the path coefficients and time delays of the dominant paths. To reduce
the computational complexity and enhance the beam resolution, a sequential
search method using hierarchical codebooks is developed. Numerical results
demonstrate the improved channel estimation accuracy of MMV-LS-CS over
state-of-the-art techniques.
