Blind identification of single input multiple output systems is considered herein. The low-rank structure of the output signal is exploited to blindly identify the channel using a subspace fitting framework. Two approaches based on a minimal linear parameterization of a subspace are presented and analyzed. The asymptotically best consistent estimate is derived for the class of blind subspace-based techniques. The asymptotic estimation error covariance of the subspace estimates is derived, and the corresponding covariance of the statistically optimal estimates provides a lower bound on the estimation error covariance of subspace methods. A two-step procedure involving only linear systems of equations is presented that asymptotically achieves the bound. Simulations and numerical examples are provided to compare the two approaches.