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

Joint Activity Detection and Channel Estimation for mmW/THz Wideband Massive Access