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Underwater acoustic channels often have to face the interference of impulsive noise, which is usually modeled by α-stable distribution in simulation experiments. To solve the problem of underwater acoustic channel estimation under impulsive noise, this paper proposes a convex combination–variable-step-size least mean p-norm algorithm. The algorithm incorporates a convex combination into the variable-step-size least mean p-norm algorithm and uses the convex combination of different convergence domains provided by changing the parameters of the Gaussian function to further improve the effect after convergence. The simulation results of channel estimation show that the convex combination–variable-step-size least mean p-norm algorithm provides a more stable, robust, and universal solution than the variable-step-size least mean p-norm algorithm. [ABSTRACT FROM AUTHOR]