An Improved Feedforward Frequency Offset Estimator

In this correspondence, we propose a new feedforward frequency offset or single frequency estimator which is based on a single weighted sample correlation with lag k, computed from N noisy observations. The new estimator is a simple generalization of the unweighted Lank-Reed-Pollon (LRP) estimator introduced in [G. W. Lank, I. S. Reed, and G. E. Pollon, ";A Semicoherent Detection and Doppler Estimation Statistic,"; IEEE Transactions on Aerospace and Electronic Systems, vol. 9, no. 2, pp. 151-165, March 1973]. It is shown that by relaxing the requirement for frequency estimation range, an estimator with improved accuracy and lower threshold may be designed. In particular, the estimator is able to provide a 20 log₁₀(k) dB threshold reduction. When N is an integer multiple of k, closed-form expressions are derived for the weighting coefficients and also for the minimum variance. Analytical and simulation results are presented which assess and demonstrate the estimator performance.