Spectral curvature approximation speeds up MIMO network power control
Spectral-NFP: Certified Low-Rank Curvature Majorization for Accelerating WMMSE
Information Theory
Summary
In wireless networks with many antennas, adjusting the power of signals to maximize overall data rates is computationally hard using traditional methods. The authors propose a new approach called Spectral-NFP that smartly simplifies complex matrix calculations by keeping only the most important parts, allowing for faster updates with minimal loss in accuracy. Their method can achieve nearly the same performance as the exact approach but in a fraction of the time, especially for large antenna arrays. This makes managing wireless communication more efficient without sacrificing much quality.
What this means in practice
- •For wireless network engineers: Accelerate power allocation computations in multicell MIMO systems to support high data rates with large antenna arrays more efficiently.
- •For signal processing developers: Implement faster transmit signal optimization steps by reducing complexity while retaining essential curvature information in optimization.
Authors
Jianhang Zhu, Tsung-Hui Chang, Kaiming Shen
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.