A set membership NLMS algorithm for colored noise environment [adaptive filter applications]

The performance of an adaptive filter is restricted by the statistical behavior of the additive noise. The aim of this paper is to improve the convergence speed and steady state error of the set-membership normalized least mean square (SM-NLMS) algorithm in a colored noise environment. The noise is assumed to follow an auto-regressive (AR) model with bounded excitation uncorrelated samples. Without information about the noise parameters, the traditional SM-NLMS algorithm results in an unsatisfactory performance. A new simple SM algorithm is introduced to estimate the channel and the noise parameters simultaneously. The proposed algorithm efficiently exploits the redundant information of the noise to combat the noise. Theoretical results and simulations illustrate that the proposed algorithm has remarkable performance improvement over the NLMS and the traditional SM-NLMS algorithms. This proposed is successfully applied to a decision-directed algorithm for a QPSK communication scheme over an ISI channel with heavily colored noise environment.