  Millimeter-wave/Terahertz (mmW/THz) communications have shown great potential
for wideband massive access in next-generation cellular internet of things
(IoT) networks. To decrease the length of pilot sequences and the computational
complexity in wideband massive access, this paper proposes a novel joint
activity detection and channel estimation (JADCE) algorithm. Specifically,
after formulating JADCE as a problem of recovering a simultaneously
sparse-group and low rank matrix according to the characteristics of mmW/THz
channel, we prove that jointly imposing $l_1$ norm and low rank on such a
matrix can achieve a robust recovery under sufficient conditions, and verify
that the number of measurements derived for the mmW/THz wideband massive access
system is significantly smaller than currently known measurements bound derived
for the conventional simultaneously sparse and low-rank recovery. Furthermore,
we propose a multi-rank aware method by exploiting the quotient geometry of
product of complex rank-$L$ matrices with the number of scattering clusters
$L$. Theoretical analysis and simulation results confirm the superiority of the
proposed algorithm in terms of computational complexity, detection error rate,
and channel estimation accuracy.
