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Rethinking Maximum Flow Problem and Beamforming Design through Brain-inspired Geometric Lens

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Document pages: 6 pages

Abstract: Increasing data rate in wireless networks can be accomplished through atwo-pronged approach, which are 1) increasing the network flow rate throughparallel independent routes and 2) increasing the user s link rate throughbeamforming codebook adaptation. Mobile relays are utilized to enable achievingthese goals given their flexible positioning. First at the network level, wemodel regularized Laplacian matrices, which are symmetric positive definite(SPD) ones representing relay-dependent network graphs, as points overRiemannian manifolds. Inspired by the geometric classification of differenttasks in the brain network, Riemannian metrics, such as Log-Euclidean metric(LEM), are utilized to choose relay positions that result in maximum LEM.Simulation results show that the proposed LEM-based relay positioning algorithmenables parallel routes and achieves maximum network flow rate, as opposed toother metrics (e.g., algebraic connectivity).Second at the link level, we design unique relay-dependent beamformingcodebooks aimed to increase data rate over the spatially-correlated fadingchannels between a given relay and its neighboring users. To do so, we proposea geometric machine learning approach, which utilizes support vector machine(SVM) model to learn an SPD variant of the user s channel over Riemannianmanifolds. Consequently, LEM-based Riemannian metric is utilized forclassification of different channels, and a matched beamforming codebook isconstructed accordingly. Simulation results show that the proposedgeometric-based learning model achieves the maximum link rate after a shorttraining period.

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