On the Proximity Factors of Lattice Reduction-Aided Decoding

Lattice reduction-aided decoding (LRAD) features reduced decoding complexity and near-optimum performance in multiinput multioutput communications. In this paper, a quantitative error-rate analysis of LRAD is presented. To this aim, the proximity factors are defined to measure the worst-case losses in decoding distances associated with the decision region relative to infinite lattice decoding (ILD), namely, closest point search in an infinite lattice. Upper bounds on the proximity factors are derived, which are functions of the dimension n of the lattice alone. The study is then extended to the dual-basis reduction. It is found that the bounds for dual basis reduction may be smaller. Reasonably good bounds are derived in many cases. Proximity factors not only imply the same diversity order in fading channels, but also relate the error probabilities of ILD and LRAD.