A Fast Least-Squares Solution-Seeker Algorithm for Vector-Perturbation

Finding the least-squares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real or complex numbers is a problem equivalent to finding the closest lattice-point to a given point and is well known that the search is hard. However, in communications applications the given vector is not arbitrary but rather is an unknown lattice-point that has been perturbed by an additive offset vector whose statistical properties are known, making it relatively easier to decode.