How many known symbols are required for linear channel estimation in OFDM?

Training sequences for estimation of channel parameters have been well designed under the condition that the number of the unknown channel parameters is not greater than the number of the known symbols. Without the condition, we develop a method to obtain the optimal number of known pilot symbols for pilot-aided linear channel estimation in orthogonal frequency division multiplexing (OFDM). We derive an expression for channel estimation error covariance from which performance measures can be numerically evaluated to obtain the optimal number of pilot symbols. Using capacity lower bound as a performance measure, we demonstrate that for channels with exponential power profiles, it is better to estimate a truncated version of the channel response, which reveals the disadvantage of the existing design based on the condition.