This thesis addresses the problem of the estimation of the time-varying channel in multiuser receiver with space-time block coding (STBC). We have to obtain the accurate channel state information for recovering the symbol of interested user with the transmit diversity gain. For the estimation and tracking of the slowly time-varying channel, we use the adaptive or stochastic-gradient algorithm using the proposed cost function. In this case, the proposed cost function guarantees the faster convergence rate to adapt the time variation of the channel. If we adjust the weighting parameter in the cost function adaptively, we can obtain a better channel tracing capability with no MSE performance degradation. And, for the estimation and tracking of the fast time-varying channel, we use the Kalman filtering method using the first-order Markov channel model. In this case, we propose the estimation method of the process and measurement noise statistics required in the Kalman filtering process. If we obtain the accurate parameters for the noise statistics, a better tacking performance of the fast time-varying channel can be guaranteed. Simulation results show the advantages of the proposed channel estimation methods.