Spectral-NFP: Certified Low-Rank Curvature Majorization for Accelerating WMMSE
Abstract
Weighted sum-rate maximization in multicell multiple-input multiple-output (MIMO) networks is commonly addressed by the weighted minimum mean-square error (WMMSE) algorithm or fractional programming (FP), both of which, after fixing their auxiliary variables, solve a power-constrained quadratic transmit problem that requires costly dense operations for large arrays. Replacing the underlying curvature matrix with a scaled identity can avoid the matrix inverse operation and thereby reduce complexity, but it discards the curvature eigenvalue structure and yields a loose lower bound. We propose Spectral-NFP, which retains selected dominant curvature eigenpairs and uses a scaled identity matrix to bound the curvature on the remaining subspace from above. The retained rank thus traces a continuous path from NFP to the exact WMMSE transmit update. With the surrogate curvature fixed, Spectral-NFP can be interpreted as Euclidean projected-gradient ascent after a linear coordinate transformation, admitting Nesterov-type acceleration. We derive a lower bound on the one-step transmit-objective gain of Spectral-NFP relative to WMMSE, expressed in terms of the curvature eigenvalues. Under an idealized Wishart model, we analyze this bound in both finite dimensions and the large-system limit, obtaining an asymptotic rank-selection rule. Experimental results show that retaining at most 20% of the transmit dimension, and often less than 10%, achieves more than 99% of the WMMSE WSR. In large-array settings, the measured update time is below 20% of that required by WMMSE.
Related
- Improved Gradient Complexity for Quasi-Newton Proximal Extragradient Methods via Certified Curvature Reuse
- A genus-two spectral curve of the Riemann Ξ-function: Real Structure and Certified Arithmetic Separation of Periods
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BibTeX
@misc{zhu2026spectralnfp,
title = {{Spectral-NFP: Certified Low-Rank Curvature Majorization for Accelerating WMMSE}},
author = {Jianhang Zhu and Tsung-Hui Chang and Kaiming Shen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27369},
eprint = {2609.27369},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27369},
}
RIS
TY - UNPB
TI - Spectral-NFP: Certified Low-Rank Curvature Majorization for Accelerating WMMSE
AU - Jianhang Zhu
AU - Tsung-Hui Chang
AU - Kaiming Shen
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27369
UR - https://arxiv.org/abs/2609.27369
AB - Weighted sum-rate maximization in multicell multiple-input multiple-output (MIMO) networks is commonly addressed by the weighted minimum mean-square error (WMMSE) algorithm or fractional programming (FP), both of which, after fixing their auxiliary variables, solve a power-constrained quadratic transmit problem that requires costly dense operations for large arrays. Replacing the underlying curvature matrix with a scaled identity can avoid the matrix inverse operation and thereby reduce complexity, but it discards the curvature eigenvalue structure and yields a loose lower bound. We propose Spectral-NFP, which retains selected dominant curvature eigenpairs and uses a scaled identity matrix to bound the curvature on the remaining subspace from above. The retained rank thus traces a continuous path from NFP to the exact WMMSE transmit update. With the surrogate curvature fixed, Spectral-NFP can be interpreted as Euclidean projected-gradient ascent after a linear coordinate transformation, admitting Nesterov-type acceleration. We derive a lower bound on the one-step transmit-objective gain of Spectral-NFP relative to WMMSE, expressed in terms of the curvature eigenvalues. Under an idealized Wishart model, we analyze this bound in both finite dimensions and the large-system limit, obtaining an asymptotic rank-selection rule. Experimental results show that retaining at most 20% of the transmit dimension, and often less than 10%, achieves more than 99% of the WMMSE WSR. In large-array settings, the measured update time is below 20% of that required by WMMSE.
ER -