Grant-Free Access in Multi-Cell Massive MIMO through Learning Cooperative Activity Detection over Riemannian Manifolds

Grant-free (GF) or random access is a key enabler for low-latency massive machine-type communications (mMTC), where devices are sporadically active and transmit small amounts of data. Massive multiple-input multiple-output (mMIMO) technology can enable users’ activity detection for such random access, due to its inherent spatial diversity. One approach employs the sample covariance matrices of received signals to estimate the activity detection. Such covariance-based schemes utilize sub-optimal search algorithms (e.g., coordinate-wise gradient descent) to find solutions for the non-convex maximum likelihood (ML) estimation problem of user activity detection. Covariance matrices are symmetric positive definite (SPD) ones and hence they can be represented over Riemannian manifolds (i.e., curved surfaces). Consequently, users can be represented over such non-Euclidean manifold using a combination of the sufficient-statistic sample covariance matrices and user-dependent pilot sequences. Such unique user’s modeling over Riemannian manifolds paves the road to use geometric-based solutions for activity detection. Specifically in this paper, we propose to utilize geometric k-means clustering to divide users of multi-cell massive MIMO system into two distinct groups, namely, active and inactive ones. Geodesic distances among users’ representations over Riemannian manifold are measured using log-determinant Bregman divergence. Simulation results show that the proposed method reduces probability of miss detection compared to Euclidean-based state-of-the-arts. Finally, the proposed method requires less complexity than Euclidean ones.