The Diagonal Reduction Algorithm Using Fast Givens

Recently, a new lattice basis reduction notion, called diagonal reduction, was proposed for lattice-reduction-aided detection (LRAD) of multiinput multioutput (MIMO) systems. In this paper, we improve the efficiency of the diagonal reduction algorithm by employing the fast Givens transformations. The technique of the fast Givens is applicable to a family of LLL-type lattice reduction methods to improve efficiency. Also, in this paper, we investigate dual diagonal reduction and derive an upper bound of the proximity factors for a family of dual reduction aided successive interference cancelation (SIC) decoding. Our upper bound not only extends an existing bound for dual LLL reduction to a family of dual reduction methods, but also improves the existing bound.