Compared with channel estimation method based on explicit training sequences, bandwidth is saved for those methods using superimposed training sequences, while it is wasted when Cyclic Prefix (CP) is added. In previous work of McLernon, the Mean Square Error (MSE) performance of Data-Dependent Superimposed Training (DDST) without CP for Single-Input Single-Output (SISO) system was analyzed under the assumption that the data-dependent sequence matrix was a circulant matrix and not interfered by others. In fact, for the system without CP, the data-dependent sequence matrix is not circulant any more and will be interfered. This paper derives the exact expression of MSE for the system without CP and also gives its extension to Multiple-Input Multiple-Output (MIMO) system without CP.