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Orthogonal frequency-division multiplexing (OFDM) can be used to support high-data-rate transmissions over time-dispersive fading channels. Many OFDM-based communication systems use packet-based transmission, where channel estimation is needed for the detection of information-carrying symbols. The finite impulse response (FIR) channel model is simple and effective for some simulations of channel estimation for the OFDM-based communication systems over the time-dispersive channels; yet, it is only an approximate channel model that cannot be used in the case of accurate channel estimation. Unfortunately, many researchers have overlooked this issue and have been devising channel-estimation algorithms squarely based on the FIR channel model. While the channel estimation results from these algorithms can be impressive for the FIR channels, the algorithms can hardly be applied in real-world applications. This paper explains in detail the reason the FIR channel model is only an approximate channel model for the OFDM-based communication systems, trying to discourage the inappropriate usage of this model, which can lead to fruitless efforts. This paper also presents a realistic channel model for OFDM-based communication systems, which can be used to realistically access the channel parameter-estimation algorithms.