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This work investigates the feasibility of adaptive Tomlinson-Harashima preceding schemes for mobile communication systems. It is assumed the existence of a feedback channel that sends channel status information (CSI) from the receiver to the transmitter. We will consider that CSI consists of channel impulse response predictions obtained with two methods: Kalman filtering and particle filtering. Kalman filtering estimates the channel parameters from training data whose transmission contributes to bandwidth-inefficient communication. However, blind estimation techniques, such as particle filtering, provide higher spectral efficiencies with a small loss in performance.