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We consider the channel estimation of a time-slotted wireless communication system with a mobile user and a base station, where the base station employs an M-element (M >; 1) antenna array. The uplink single-input multiple-output (SIMO) channel is usually estimated by training sequence within each time slot. To improve the estimation performance, the channel estimate is often refined by projecting it to the corresponding spatial signal subspace. However, this projection will not work when the number of resolvable multipath rays is larger than that of the antenna array elements, which makes the channel matrix full row rank. In this paper, we formulate the channel estimation under the space-time signal model for this full-row-rank case, and propose a new method by space-time signal subspace projection using both training and unknown data sequences. To further improve the accuracy of the channel estimate, the soft information fed back from the decoder can be used. By involving this soft information, we propose another new channel estimation method. This method approximately follows the maximum likelihood (ML) criterion and is therefore referred to as the approximated ML channel estimation. Numerical results show that these methods can be performed separately or jointly to improve the performance of channel estimation by training sequences.