One-sided Precoder Designs on Manifolds for Interference Alignment

TL;DR

This paper introduces manifold-based precoder design algorithms for interference alignment in multi-user channels, achieving maximum degrees of freedom with improved convergence and system capacity.

Contribution

It develops novel steepest descent algorithms on Stiefel and Grassmann manifolds for interference alignment, reducing complexity and overhead compared to traditional methods.

Findings

Algorithms outperform previous methods in convergence speed.

Achieve higher system capacity.

Attain maximum degrees of freedom.

Abstract

Interference alignment (IA) is a technique recently shown to achieve the maximum degrees of freedom (DoF) of $K$-user interference channel. In this paper, we focus on the precoder designs on manifolds for IA. By restricting the optimization only at the transmitters' side, it will alleviate the overhead induced by alternation between the forward and reverse links significantly. Firstly a classical steepest descent (SD) algorithm in multi-dimensional complex space is proposed to achieve feasible IA. Then we reform the optimization problem on Stiefel manifold, and propose a novel SD algorithm based on this manifold with lower dimensions. Moreover, aiming at further reducing the complexity, Grassmann manifold is introduced to derive corresponding algorithm for reaching the perfect IA. Numerical simulations show that the proposed algorithms on manifolds have better convergence performance and higher system capacity than previous methods, also achieve the maximum DoF.