Solving Box-Constrained Integer Least Squares Problems

A box-constrained integer least squares problem (BILS) arises from several wireless communications applications. Solving a BILS problem usually has two stages: reduction (or preprocessing) and search. This paper presents a reduction algorithm and a search algorithm. Unlike the typical reduction algorithms, which use only the information of the lattice generator matrix, the new reduction algorithm also uses the information of the given input vector and the box constraint and is very effective for search. The new search algorithm overcomes some shortcomings of the existing search algorithms and gives some other improvement. Simulation results indicate the combination of the new reduction algorithm and the new search algorithm can be much more efficient than the existing algorithms, in particular when the least squares residual is large.