Solving Ellipsoid-Constrained Integer Least Squares Problems

A new method is proposed to solve an ellipsoid-constrained integer least squares (EILS) problem arising in communications. In this method, the LLL reduction, which is cast as a QRZ factorization of a matrix, is used to transform the original EILS problem to a reduced EILS problem, and then a search algorithm is proposed to solve the reduced EILS problem. Simulation results indicate the new method can be much more computationally efficient than the existing method. The method is extended to solve a more general EILS problem.