Achieving reliable underwater acoustic (UWA) communications is challenging due to the rapid changes of UWA channels and presence of impulsive noise. The soft decision feedback equalization (SDFE) has attracted much attention due to its capability of tackling the rapid changes of UWA channels. However, the existing SDFE exhibits error floor and even divergence due to the presence of severe impulsive noise. To overcome this problem, an improved SDFE (ISDFE) is proposed, which incorporates impulsive noise detection, clipping level estimation and damping to handle the impulsive noise. As the performance of the ISDFE also depends on the accuracy of channel estimation (CE), we propose a variable kernel width maximum complex correntropy criterion Kalman filter (VKW-MCCC-KF) algorithm to achieve robust and accurate CE under impulsive noise. With the proposed ISDFE and VKW-MCCC-KF, an iterative receiver for single carrier (SC) UWA mobile communication under impulsive noise is proposed, which in