The asymmetry and fringe inclination of the sawtooth-like waveform observed in the self-mixing signal obtained from a semiconductor laser with optical feedback enable the direction discrimination of line-of-sight motion of external target surfaces. We investigated the effects of linewidth enhancement factor and feedback strength on the asymmetry and the direction of fringe inclination of the signal by numerical simulations. For the first time, we show that direction of the fringe inclination is determined not only by the direction of the target motion but also by the value of the linewidth enhancement factor.