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 l0 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-Lmax matrices with the maximum number of scattering clusters Lmax. 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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This paper investigates the issue of cooperative activity detection for grant-free random access in the sixthgeneration (6G) cell-free wireless networks with sourced and unsourced paradigms. First, we propose a cooperative framework for solving the problem of device activity detection in sourced random access. In particular, multiple access points (APs) cooperatively detect the device activity via exchanging low-dimensional intermediate information with their neighbors. This is enabled by the proposed covariance-based algorithm via exploiting both the sparsity-promoting and similarity-promoting terms of the device state vectors among neighboring APs. A decentralized approximate separating approach is introduced based on the forward-backward splitting strategy for addressing the formulated problem. Then, the proposed activity detection algorithm is adopted as a decoder of cooperative unsourced random access, where the multiple APs cooperatively detect the list of transmitted messages regardless of the identity of the transmitting devices. Finally, we provide sufficient conditions on the step sizes that ensure the convergence of the proposed algorithm in the sense of Bregman divergence. Simulation results show that the proposed algorithm is efficient for addressing both sourced and unsourced massive random access problems, while requires a shorter signature sequence and accommodates a significantly larger number of active devices with a reasonable antenna array size, compared with the state-of-art algorithms.