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

TL;DR

This paper introduces novel algorithms for joint device activity detection and channel estimation in mmW/THz wideband massive access, exploiting the channels' simultaneous low-rank and sparsity structure to improve efficiency and accuracy.

Contribution

It proposes two multi-rank aware algorithms based on quotient geometry, requiring fewer measurements and offering linear convergence for mmW/THz channels with delay-angular domain structure.

Findings

Algorithms outperform existing methods in activity detection accuracy.

Reduced measurement requirements compared to traditional sparse and low-rank recovery.

Algorithms converge linearly with low computational complexity.

Abstract

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.