Geometric Machine Learning Over Riemannian Manifolds for Wireless Link Scheduling

Shelim, Rashed; Ibrahim, Ahmed S.

doi:10.1109/access.2022.3153324

Cited by 8 publications

(2 citation statements)

References 29 publications

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“…Recently, the geometric perspectives of codebook design utilizing SPD characteristics of correlated channels have been considered in [30], [31]. Riemennian geometry has found application in wireless communication, such as wireless link scheduling in device-to-device networks [32]- [34].…”

Section: A Riemannian Manifolds and Hpd Geometrymentioning

confidence: 99%

Covariance Shaping Over Riemannian Manifolds for Massive MIMO Communication

Sadique,

Nasim,

Ibrahim

2023

IEEE Access

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Acquiring accurate instantaneous channel state information (CSI) is a challenging aspect of massive multi-input multi-output (MIMO) communication. Utilizing statistical information, such as channel covariance matrix, to design statistical beamforming vectors is robust when compared to instantaneous CSI. In this paper, we propose a novel MIMO covariance shaping scheme over Riemannian manifolds. It serves as an effective statistical beamforming solution to a number of close proximity user equipment (UE) that are undergoing substantial channel correlation. Proposed algorithm exploits the Hermitian positive definite nature of covariance matrices lying over Riemannian manifold. We introduce Wasserstein distance function as a Riemannian metric to measure distances between channel covariance matrices. Furthermore, K-means clustering technique is utilized to effectively identify the optimal shape of effective optimal covariance matrices. Our findings suggest that maximizing the geodesic distance between covariance matrices ultimately leads to a corresponding increase in the network throughput, as determined by the beamforming vector used to shape the covariance matrices. Simulation results validate that the proposed solution converges faster than Euclidean-based state-of-the-art, while maintaining the same computational complexity. Finally, the sum rate performance asymptotically achieves full capacity for two-UE case and more than 96% of the upper bound exhaustive search benchmark for multi-UE scenario.

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Section: A Riemannian Manifolds and Hpd Geometrymentioning

confidence: 99%

Covariance Shaping Over Riemannian Manifolds for Massive MIMO Communication

Sadique,

Nasim,

Ibrahim

2023

IEEE Access

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“…Riemannian geometry [22] has been recently considered in designing beamforming vectors [23], [24] and in other wireless problems such as link scheduling [25], [26]. In addition, non-Euclidean methods have been utilized in codebook design such as non-conic Riemannian manifolds (i.e, unitary, fixed rank) as in [27], and [28].…”

Section: Introductionmentioning

confidence: 99%

Millimeter Wave Beamforming Codebook Design via Learning Channel Covariance Matrices Over Riemannian Manifolds

Nasim

Ibrahim

2022

IEEE Access

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Covariance matrices of spatially-correlated wireless channels in millimeter wave (mmWave) vehicular networks can be employed to design environment-aware beamforming codebooks. Such covariance matrices can be represented over non-Euclidean (i.e., curved surfaces) manifolds, thanks to their symmetric positive definite (SPD) structures. In this paper, we propose three learning models for channel covariance estimation over Riemannian manifolds. First, we propose an unsupervised Riemannian K-means clustering approach, where Log-Euclidean metric (LEM) is utilized as a distance metric among channel covariance matrices over the Riemannian manifold. Second, we propose a Riemannian Competitive Learning (RCL) model, which is an online clustering solution that is intended to reduce the learning time of the offline K-means models. Third, we apply a Riemannian Dictionary Learning (RDL) model that leverages the sparsity properties of mmWave channels, while estimating their channel covariance matrices. Simulation results show that the proposed Riemannian K-means, online RCL and RDL models can achieve 41%, 30% and 44% higher data rate, respectively, than their Euclidean-based counterparts. Furthermore, they require few training samples and hence fast construction of codebook design in dynamic environments, which leads to low latency communication.

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