We propose a new pilot structure for inter-carrier interference (ICI) estimation and compensation in order to improve the performance of the forthcoming Digital Video Broadcasting-Next Generation Handheld (DVB-NGH) standard in mobile environments. Although classical pilot patterns and channel estimation techniques achieve good performance in fixed reception, their design can be improved for high-mobilty receivers, where the effects of ICI become more severe. For such scenarios, we propose to approximate the ICI and channel parameters using a basis expansion model (BEM). The proposed channel estimation model is assessed with new pilot designs and in combination with an ICI mitigation algorithm, showing the effectiveness of this technique by removing the error floor experienced with the ideal channel knowledge case with large Doppler frequencies.