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There has been a considerable interest in determining the limits to communications over multipath fading channels. However, most studies have assumed that the channel is perfectly known at the receiver. In this paper, the random coding error exponent for flat fading channels with realistic channel state information (CSI) is studied. It is assumed that the CSI is obtained via some practical technique which utilizes a linear estimation scheme. Two commonly used techniques for channel estimation are considered in this paper, namely pilot tone extraction and pilot symbol transmission. The degradation in the achievable performance due to partial CSI is assessed and comparison of the different channel estimation methods is made. The focus of this paper is on the Jake's mobile Rayleigh flat fading model. Although Jake's model does not have a Markov property, such as that found in the commonly used exponential correlation model, which is usually attractive from the mathematical tractability point of view, Jake's model has a physical basis. Also, this model is considered herein from the standpoint of the random coding exponent. The results in this paper shed light on the amount of degradation in the achievable performance that is expected when the receiver has partial CSI. Finally, the sensitivity of the loss in achievable performance for the various channel estimation techniques with respect to channel parameters, such as Doppler spread and signal-to-noise ratio (SNR), is studied.