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We propose a relax-and-round approach combined with a greedy search strategyfor performing complex lattice basis reduction. Taking an optimizationperspective, we introduce a relaxed version of the problem that, while stillnonconvex, has an easily identifiable family of solutions. We construct asubset of such solutions by performing a greedy search and applying aprojection operator (element-wise rounding) to enforce the original constraint.We show that, for lattice basis reduction, such a family of solutions to therelaxed problem is the set of unitary matrices multiplied by a real, positiveconstant and propose a search strategy based on modifying the complexeigenvalues. We apply our algorithm to lattice-reduction aided multiple-inputmultiple-output (MIMO) detection and show a considerable performance gaincompared to state of the art algorithms. We perform a complexity analysis toshow that the proposed algorithm has polynomial complexity.

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