A new family of adaptive gradient lattice algorithms based on LMK criterion

The authors extend the idea of minimizing error in the mean fourth, mean sixth, etc. sense to the lattice structure, and they develop a family of LMK (least mean K) adaptive gradient lattice algorithms. This family of algorithms is a generalization of the conventional LMS (least mean squares) adaptive gradient lattice algorithm for which K=1. The convergence behavior of the LMK gradient lattice algorithms is analyzed by deriving approximate expressions for the output mean square error of the adaptive lattice filter and the mean and covariance functions of its coefficients. A computer simulation has been performed to confirm the theoretical analysis results presented here. It is demonstrated that the convergence speed of the proposed algorithm is insensitive to the eigenvalue spread of the input signal and that algorithms with K >1 will outperform the LMS lattice algorithm for certain noise statistics cases