A new derivation of least-squares-fitting principle for OFDM channel estimation

Many channel estimation and data detection algorithms of the orthogonal frequency division multiplexing (OFDM) system have been proposed. Some of these algorithms are based on the principle of linear minimum mean-square error (LMMSE) estimation, which is theoretically optimal. There are also some algorithms developed based on the least-squares-fitting (LSF) principle, which finds a regression polynomial to fit a block of tentative channel estimates in the least-squares sense. The LSF principle is a non-statistical approach, while the LMMSE algorithm is statistical and it needs to known or estimate the channel statistics like correlation matrices and signal-to-noise ratio (SNR). This letter proposes a novel viewpoint of the LSF principle. We show that the non-statistical LSF principle can be derived alternatively from the statistical LMMSE principle by eigenvector approximation. This constructs a link between these two principles. The mean-square estimation error (MSEE) analysis shows that there are common terms in the MSEE expressions of these two principles. This further validates the constructed link. Based on the derived link and MSEE analysis, we also give some characteristics and discussions of the LSF principle.