A Relax-and-Round Approach to Complex Lattice Basis Reduction

TL;DR

This paper introduces a relax-and-round method with greedy search for complex lattice basis reduction, demonstrating improved MIMO detection performance with polynomial complexity.

Contribution

It presents a novel relax-and-round approach combined with eigenvalue modification for complex lattice basis reduction, advancing the state of the art.

Findings

Significant performance improvement in MIMO detection.

Polynomial complexity of the proposed algorithm.

Effective solution to a nonconvex optimization problem.

Abstract

We propose a relax-and-round approach combined with a greedy search strategy for performing complex lattice basis reduction. Taking an optimization perspective, we introduce a relaxed version of the problem that, while still nonconvex, has an easily identifiable family of solutions. We construct a subset of such solutions by performing a greedy search and applying a projection operator (element-wise rounding) to enforce the original constraint. We show that, for lattice basis reduction, such a family of solutions to the relaxed problem is the set of unitary matrices multiplied by a real, positive constant and propose a search strategy based on modifying the complex eigenvalues. We apply our algorithm to lattice-reduction aided multiple-input multiple-output (MIMO) detection and show a considerable performance gain compared to state of the art algorithms. We perform a complexity analysis to show that the proposed algorithm has polynomial complexity.