Step-adaptive approximate least squares

Recently, we proposed approximate least squares (ALS), a low complexity approach to solve the linear least squares problem. In this work we present the step-adaptive linear least squares (SALS) algorithm, an extension of the ALS approach that significantly reduces its approximation error. We theoretically motivate the extension of the algorithm, and introduce a low complexity implementation scheme. Our performance simulations exhibit that SALS features a practically negligible error compared to the exact LS solution that is achieved with only a marginal complexity increase compared to ALS. This performance gain is achieved with about the same low computational complexity as the original ALS approach.