Deterministic blind identification algorithms of single-input and multi-output (SIMO) systems can effectively estimate channel functions and the common source signal at high signal-noise-ratio (SNR) and small available data sample scenarios. However, it is difficult for them to identify systems accurately when the noise level is high. To deal with the noise problem, this paper develops an exact Maximum-Likelihood (EML) model which is different from the two-stage Maximum-Likelihood (TSML) method or the semi-blind ML method in the literature. The EML model derived from the cross relation equation of two channels does not contain the source signal but channel functions and output observations, hence the identification performance is barely affected by the unknown source signal. In addition, an iterative optimization approach based on variable splitting technique and alternating direction method of multipliers (ADMM) is derived to minimize the negative log-likelihood function. Simulations are carried out to verify the effectiveness of the proposed method.