A diverse proof of OFDM channel estimation comparing CP-sequences and training-sequences methods under LS frame

This article presents a diverse and primary proof of one indifferent but subtle conclusion of OFDM channel estimation problem, that is, in frequency domain performance of CP-based channel estimation method can hardly surpass the conventional ones such as training-sequence-based methods. We get the conclusion and first give detailed proof that under LS principle when directly transform cyclic prefix (CP) into frequency domain as CP-sequences, we can always find those training-sequences which have better performance than the CP-sequences method. Specifically, we first calculate MSE of Least-Square (LS) principle. Then, according to MSE calculated we give our central proof using DFT analysis and multitudes of inequality relations. At last, we also give simulation that ensures the correctness of our proofs and give new suggestions of this topic concerned.