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Millimeter-wave (mmW)/Terahertz (THz) wideband communication employing alarge-scale antenna array is a promising technique of the sixth-generation (6G)wireless network for realizing massive machine-type communications (mMTC). Toreduce the access latency and the signaling overhead, we design a grant-freerandom access scheme based on joint active device detection and channelestimation (JADCE) for mmW/THz wideband massive access. In particular, byexploiting the simultaneously sparse and low-rank structure of mmW/THz channelswith spreads in the delay-angular domain, we propose two multi-rank aware JADCEalgorithms via applying the quotient geometry of product of complex rank-$L$matrices with the number of clusters $L$. It is proved that the proposedalgorithms require a smaller number of measurements than the currently knownbounds on measurements of conventional simultaneously sparse and low-rankrecovery algorithms. Statistical analysis also shows that the proposedalgorithms can linearly converge to the ground truth with low computationalcomplexity. Finally, extensive simulation results confirm the superiority ofthe proposed algorithms in terms of the accuracy of both activity detection andchannel estimation.

Exploiting Simultaneous Low-Rank and Sparsity in Delay-Angular Domain for Millimeter-Wave/Terahertz Wideband Massive Access