Impulsive noise can greatly degrade the performance of long wave communications.This paper proposes the optimal design of the Gaussian-tailed zero memory nonlinearity (GZMNL) function to suppress impulsive noise.The GZMNL function which was proposed for the symmetric -stable (SS) noise is not robust in applications

because of the lack of adaptive parameters.This paper proposes to design the GZMNL parameters adaptively to control the linear range and the tails

so that the GZMNL can be effective for various noise distributions.In the GZMNL design

the efficiency is employed as the objective function which is maximized over the GZMNL parameters.To solve this optimization problem

we develop a derivative-free optimization algorithm which searches the maximum efficacy adaptively.Considering practical applications

we propose two fast algorithms for the GZMNL design in the SS noise

as well as a robust method for the GZMNL design in unknown noise distributions.Simulation results based on the SS noise and real atmospheric noise show that the GZMNL design achieves almost the best nonlinearity in known noise distributions.The GZMNL design is effective and robust for unknown noise distributions.