Pilot-Based Simplified ML and Fast Algorithm for Frequency Offset Estimation in OFDMA Uplink

Using a dedicated pilot orthogonal frequency-division multiplexing (OFDM) symbol to estimate the carrier frequency offset (CFO) in the orthogonal frequency-division multiple-access (OFDMA) uplink is considered. Based on the maximum-likelihood principle, a method is derived to estimate the CFOs of all users by optimizing a multidimensional (MD) cost function. To reduce complexity, a specially designed pilot OFDM symbol is proposed to turn the MD optimization problem into independent 1-D optimization problems. It is proven that the CFOs are identifiable by optimizing the 1-D cost functions. Although the 1-D optimization is substantially simpler than the MD optimization, it may still be vulnerable to local minima/maxima and sometimes too complex for wireless applications. A fast algorithm is then derived, which finds the CFOs in closed forms and needs very low computational complexity. General principles and concrete designs for the pilot OFDM symbol are also discussed. Finally, enhanced estimation methods are proposed by using multiple receiving antennas.