Scalable and Convergent Generalized Power Iteration Precoding for Massive MIMO Systems

TL;DR

This paper introduces a scalable, efficient generalized power iteration precoding method for massive MIMO systems that maintains high spectral efficiency with reduced computational complexity, suitable for large-scale deployments.

Contribution

It develops a low-dimensional, robust precoding framework leveraging subspace properties and matrix inversion simplifications, with proven convergence guarantees for massive MIMO systems.

Findings

Achieves higher spectral efficiency than existing linear precoders.

Reduces computational complexity significantly for large antenna arrays.

Demonstrates robust performance under imperfect channel state information.

Abstract

In massive multiple-input multiple-output (MIMO) systems, achieving high spectral efficiency (SE) often requires advanced precoding algorithms whose complexity scales rapidly with the number of antennas, limiting practical deployment. In this paper, we develop a scalable and computationally efficient generalized power iteration precoding (GPIP) framework for massive MIMO systems under both perfect and imperfect channel state information at the transmitter (CSIT). By exploiting the low-dimensional subspace property of optimal precoders, we reformulate the high-dimensional beamforming problem into a lower-dimensional weight optimization that scales with the number of users rather than antennas. We further extend this framework to the imperfect CSIT scenario by showing that stationary solutions reside in a combined subspace spanned by the estimated channel and error covariance matrices, enabling a robust design via low-rank approximation. To reduce computational cost, we leverage the Sherman-Morrison formula to simplify matrix inversions. Moreover, interpreting the GPIP update as a projected preconditioned gradient ascent method, we establish convergence guarantees and develop a stable and monotonic algorithm using a backtracking line search. Numerical results demonstrate that the proposed methods achieve the highest SE performance compared to state-of-the-art linear precoders with significantly reduced complexity and convergence, highlighting their suitability for large-scale MIMO systems.