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.
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