In this paper, we investigate the quality of a weighted leastsquare (WLS) parameter estimation method based on binary observations when only a finite number of samples are available. An upper bound of the number of samples that are necessary for identifying system with a given accuracy is theoretically derived. The accuracy is defined in the sense of correlation coefficient between the system parameters and our estimated system parameters. Furthermore, we compare theoretical results with simulations in order to study the validity of the results practically.