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In this paper we study the effects of practical pilot- assisted channel state estimation on the achievable information theoretic data rates (uplink and downlink) in a multiple antenna multiuser TDD system. Specifically, we consider a wireless system with multiple antennas at the base station and a number of mobile terminals each with a single antenna. We analyze the performance of uplink multiuser detection and downlink transmitter optimization that are based on linear spatial filtering. Using a discrete version of the continuously time-varying wireless channel we analyze how a lower bound on the achievable data rates depends on (1) the arrangement of pilot symbols (preamble or postamble); (2) the duration of the uplink and downlink transmissions; and (3) the percentage power allocated to the pilot. Furthermore, we also present the effects of the terminal speeds on the achievable data rates, thereby providing prescriptions for the practical design of the pilot. Specifically, our results point to an uplink postamble with flexible percentage (about 20 - 25 %) pilot power allocation, and transmission durations tailored for specific ranges of terminal speeds.