5G wireless standards require a much lower latency than what current wireless systems can guarantee. The main challenge to fulfill this requirement is the capability to support short packet transmission, in contrast to most of the current standards which use a long data packet structure. In this paper, we propose an efficient receiver technique that exploits information obtained during the data transmission period to improve the reception quality of the short packet transmission. Two key ingredients of the proposed method are 1) estimation of the receiver filter using the received samples in the data transmission period, not in the interference training period, and 2) soft decision- directed channel estimation that uses the data symbols for re-estimation of the channels. Numerical results confirm the effectiveness of the proposed receiver algorithms.