Analytic Comparison for Channel Response Estimation Based on Time- and Frequency-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. One can also estimate the time-domain (TD) channel impulse response (CIR) by inserting a unit pulse ahead of each OFDM block. However, there is no analytic comparison between the CR estimation based on FD pilot symbols and TD unit pulses. In this paper, we first consider the 1-D blocks of CRs and give the analytic comparison of mean-squares error (MSE) for the CR estimation based on TD and FD pilot signals, respectively. For the linear minimum MSE (LMMSE) algorithm, which attains the minimum MSE for the CR estimation based on FD pilots, we derive an MSE lower bound among all possible distributions of pilot symbols. This MSE lower bound coincides with the MSE attained by the optimal CR estimation based on TD unit pulses, under the condition that both FD and TD pilot signals have the same power. Our analysis also indicates that when the number of FD pilots is smaller than the rank of correlation matrix of CRs, it results in an error floor. We further extend our analysis to 2-D blocks of CRs and show that the MSE formulas for CR estimation based on FD and TD pilot signals share the same forms and that they have close numerical values.