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

翻译：使用大型天线阵列的宽频通信(mmW)/Terahertz(Thz)是第六代(6G)无线网络实现大规模机器型通信(MMTC)的一个很有希望的技术。为减少接入时间和信号管理,我们设计了一个基于联合主动装置探测和频道估计(JADCE)的无赠款随机访问机制,用于毫米W/Thz宽带大规模访问。特别是利用毫米W/Thz频道同时稀少和低级别结构,其分布在延迟角域,我们提议采用两种多层次了解JADCE算法,即应用复杂等级-L$基质产品和组数的商数几何测量法,以美元为单位。事实证明,拟议的算法需要比目前已知的常规稀疏和低级恢复算法测量范围要少一些。统计分析还表明,拟议的算法可以以低的计算复杂度直线向地面归。最后,广泛的模拟结果证实了拟议算法在测测算活动和频道的精确度方面都具有优势。