Variable partial-update NLMS algorithms with data-selective updating

We note that some existing algorithms are based on the normalized least-mean square(NLMS)algorithm and aim to reduce the computational complexity of NLMS all inherited from the solution of the same optimization problem,but with different constraints.A new constraint is analyzed to substitute an extra searching technique in the set-membership partial-update NLMS algorithm(SM-PU-NLMS)which aims to get a variable number of updating coefficients for a further reduction of computational complexity.We get a closed form expression of the new constraint without extra searching technique to generate a novel set-membership variable-partial-update NLMS(SM-VPU-NLMS)algorithm.Note that the SM-VPU-NLMS algorithm obtains a faster convergence and a smaller mean-squared error(MSE)than the existing SM-PU-NLMS.It is pointed out that the closed form expression can also be applied to the conventional variable-step-size partial-update NLMS(VSS-PU-NLMS)algorithm.The novel variable-step-size variable-partial-update NLMS(VSS-VPU-NLMS)algorithm is also verified to get a further computational complexity reduction.Simulation results verify that our analysis is reasonable and effective.