Column Reordering for Box-Constrained Integer Least Squares Problems

The box-constrained integer least squares problem (BILS) arises in MIMO wireless communications applications. Typically a sphere decoding algorithm (a tree search algorithm) is used to solve the problem. In order to make the search algorithm more efficient, the columns of the channel matrix in the BILS problem have to be reordered. To our knowledge, there are currently two algorithms for column reordering that provide the best known results. Both use all available information, but they were derived respectively from geometric and algebraic points of view and look different. In this paper we modify one to make it more computationally efficient and easier to comprehend. Then we prove the modified one and the other actually give the same column reordering in theory. Finally we propose a new mathematically equivalent algorithm, which is more computationally efficient and is still easy to understand.