Analytical comparison of mean-squares errors for channel response estimation based on frequency- and time-domain pilot signals

For the orthogonal frequency-division multiplexing (OFDM) system, one can estimate the channel responses (CRs) based on frequency-domain (FD) pilot symbols. On the other hand, one can also estimate the time-domain (TD) channel impulse response by inserting a unit pulse ahead of each OFDM block. However, there is no analytical comparison between the CR estimation based on FD pilot symbols and TD unit pulses. In this paper, we give the analytical comparison of the mean-squares errors (MSEs) for the CR estimation based on TD and FD pilot signals. For the CR estimation based on FD pilot symbols, the linear minimum mean-squares error (LMMSE) algorithm is optimal. We derive an MSE lower bound for the LMMSE algorithm among all possible distribution of pilot symbols. This MSE lower bound coincides with the MSE attained by the optimal CR estimation based on TD unit pulses. We also show that with the uniform distribution of pilot symbols, the resulted MSE is very close to the MSE lower bound for the LMMSE algorithm. Our results conclude that the optimal CR estimation based on TD and FD pilot signals attain almost the same MSEs.