Underwater acoustic channels (UWA) are usually sparse, which can be exploited for adaptive equalization to improve the system performance. For the shallow UWA channels, based on the proportional minimum symbol error rate (PMSER) criterion, the adaptive equalization framework requires the sparsity selection. Since the sparsity of the 𝐿 0 norm is stronger than that of the 𝐿 1 , we choose it to achieve better convergence. However, because the 𝐿 0 norm leads to NP-hard problems, it is difficult to find an efficient solution. In order to solve this problem, we choose the Gaussian function to approximate the 𝐿 0 norm. Simulation results show that the proposed scheme obtains better performance than the 𝐿 1 based counterpart.