Three new and efficient carrier frequency offset estimators are created for the case of disjoint pilot symbol blocks. The estimators are efficient in both a statistical sense and a computational sense. They are formulated to reduce computational cost for use in real-time applications, such as FPGA (field programmable gate array) devices. A reduced cost maximum likelihood (ML) frequency estimator is described. It is a generalization of the approximate ML estimator for a single block of pilot symbols. A number of recent ML estimation techniques are integrated with the purpose of reducing the computational cost while preserving estimation performance. The estimator incorporates multirate signal processing methods, FFT periodogram searches, and directed periodogram searches. The subsequent relationships between FFT lengths, resampling rates, and search iterations is established. The proposed estimator exhibits very good accuracy, operating range, and a low SNR threshold, and has low cost. A data-aided frequency estimator based on the measurement of phase increments, is also derived. It has extremely low cost, but a high SNR threshold. However, its formulation is such that a careful analysis of the range error problem may be performed. From this analysis certain conclusions are made about proper pilot symbol organization, and these conclusions are applicable to other frequency estimators. The third estimator is a generalization of the autocorrelation frequency estimation technique. The generalizations are needed to account for the spacings between the pilot blocks. A novel iterative approach, incorporating a Kalman filter, is used to improve operating range. It is shown that the autocorrelation frequency estimator exhibits good accuracy while maintaining a useful operating range. Real-time architectures are described for the ML and autocorrelation frequency estimators using disjoint pilot blocks. The computational cost and estimation performance of the proposed estimators are analyzed and it is shown that they give estimation performance near to theoretical limits, while preserving wide operating range. We see that the autocorrelation estimator is appropriate for small numbers of pilot symbols, while the ML estimator is appropriate for large numbers of pilot symbols. The new frequency estimators are the first to be derived (for the case of disjoint blocks of pilot symbols) such that computational cost is kept low, while still achieving high accuracy, a wide operating range, and low SNR thresholds.



College and Department

Ira A. Fulton College of Engineering and Technology; Electrical and Computer Engineering



Date Submitted


Document Type





frequency estimation, wireless receiver, synchronization, FPGA, digital implementation