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We analyze the effects of pilot-assisted channel estimation on achievable data rates (lower bound on information capacity) over a frequency flat time-varying channel. Under a block-fading channel model, the effects of the estimation error are evaluated in the case of the estimates being available at the receiver only (open loop) and in the case when the estimates are fed back to the transmitter allowing water pouring transmitter optimization (closed loop). Using a characterization of the effective noise due to estimation error, we analyze the achievable rates as a function of the power allocated to the pilot, the channel coherence time, the background noise level, as well as the number of transmit and receive antennas. The analysis presented here can be used to optimally allocate pilot power for various system and channel operating conditions, and to also determine the effectiveness of closed loop feedback.