Pilot-assisted maximum-likelihood frequency-offset estimation for OFDM systems

For orthogonal frequency-division multiplexing (OFDM) signals that suffer from frequency-selective fading, we derive the maximum-likelihood (ML) pilot-assisted carrier frequency offset (CFO) estimate and show that most proposals based on repetitive pilot symbols did not use the complete set of sufficient statistics. We convert the problem of obtaining the ML solution from searching exhaustively over the entire uncertainty range to that of solving a spectrum polynomial, thereby greatly reducing the computational load. By properly truncating the polynomial, we obtain a closed-form expression for the corresponding zeros so that the root-searching procedure is greatly simplified. The complexity of locating the desired root is further reduced at almost no expense of performance degradation by an alternate algorithm that uses the fact that the solution is related to the root of a special factor of the polynomial. This alternate method is very attractive for its simplicity and excellent performance that, even at low signal-to-noise ratios (SNRs), is very close to the corresponding Crame´r-Rao lower bound. A detailed analysis of the mean-squared error performance is presented and the analysis is validated by simulations.