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25 pages, 3014 KiB

Open AccessArticle

Beamforming Design for STAR-RIS-Assisted NOMA with Binary and Coupled Phase-Shifts

by Yongfei Liu, Yuhuan Wang and Weizhang Xu

Entropy 2025, 27(2), 210; https://doi.org/10.3390/e27020210 - 17 Feb 2025

Cited by 1 | Viewed by 961

This paper investigates the joint optimization of active and passive beamforming in simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted non-orthogonal multiple access (NOMA) systems, with the aim of maximizing system throughput and improving overall performance. To achieve this goal, we propose an iterative and efficient algorithmic framework. For active beamforming optimization, the fractional programming (FP) method is employed to reformulate the non-convex optimization problem into a convex problem, making it more tractable. Additionally, Nesterov’s extrapolation technique is introduced to enhance the convergence rate and reduce computational overhead. For the phase optimization of the STAR-RIS, a binary phase design method is proposed, which reformulates the binary phase optimization problem as a segmentation problem on the unit circle. This approach enables a closed form solution that can be derived in linear time. Simulation results demonstrate that the proposed algorithmic framework outperforms existing benchmark algorithms in terms of both system throughput and computational efficiency, verifying its effectiveness and practicality in STAR-RIS-assisted NOMA systems. Full article

(This article belongs to the Special Issue Entropy and Time–Frequency Signal Processing)

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12 pages, 1594 KiB

Open AccessArticle

An Accelerated Symmetric Nonnegative Matrix Factorization Algorithm Using Extrapolation

by Peitao Wang, Zhaoshui He, Jun Lu, Beihai Tan, YuLei Bai, Ji Tan, Taiheng Liu and Zhijie Lin

Symmetry 2020, 12(7), 1187; https://doi.org/10.3390/sym12071187 - 17 Jul 2020

Cited by 2 | Viewed by 2808

Abstract

Symmetric nonnegative matrix factorization (SNMF) approximates a symmetric nonnegative matrix by the product of a nonnegative low-rank matrix and its transpose. SNMF has been successfully used in many real-world applications such as clustering. In this paper, we propose an accelerated variant of the multiplicative update (MU) algorithm of He et al. designed to solve the SNMF problem. The accelerated algorithm is derived by using the extrapolation scheme of Nesterov and a restart strategy. The extrapolation scheme plays a leading role in accelerating the MU algorithm of He et al. and the restart strategy ensures that the objective function of SNMF is monotonically decreasing. We apply the accelerated algorithm to clustering problems and symmetric nonnegative tensor factorization (SNTF). The experiment results on both synthetic and real-world data show that it is more than four times faster than the MU algorithm of He et al. and performs favorably compared to recent state-of-the-art algorithms. Full article

(This article belongs to the Special Issue Advances in Symmetric Tensor Decomposition Methods)

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