Scattered Pilots and Virtual Carriers Based Frequency Offset Tracking for OFDM Systems: Algorithms, Identifiability, and Performance Analysis

In this paper, we propose a novel carrier frequency offset (CFO) tracking algorithm for orthogonal frequency division multiplexing (OFDM) systems by exploiting scattered pilot carriers and virtual carriers embedded in the existing OFDM standards. Assuming that the channel remains constant during two consecutive OFDM blocks and perfect timing, a CFO tracking algorithm is proposed using the limited number of pilot carriers in each OFDM block. Identifiability of this pilot based algorithm is fully discussed under the noise free environment, and a constellation rotation strategy is proposed to eliminate the c-ambiguity for arbitrary constellations. A weighted algorithm is then proposed by considering both scattered pilots and virtual carriers. We find that, the pilots increase the performance accuracy of the algorithm, while the virtual carriers reduce the chance of CFO outlier. Therefore, the proposed tracking algorithm is able to achieve full range CFO estimation, can be used before channel estimation, and could provide improved performance compared to existing algorithms. The asymptotic mean square error (MSE) of the proposed algorithm is derived and simulation results agree with the theoretical analysis

Carrier Frequency Offset Estimation for OFDM Systems using Repetitive Patterns

This paper deals with Carrier Frequency Offset (CFO) estimation for OFDM systems using repetitive patterns in the training symbol. A theoretical comparison based on Cramer Rao Bounds (CRB) for two kinds of CFO estimation methods has been presented in this paper. Through the comparison, it is shown that the performance of CFO estimation can be improved by exploiting the repetition property and the exact training symbol rather than exploiting the repetition property only. The selection of Q (number of repetition patterns) is discussed for both situations as well. Moreover, for exploiting the repetition and the exact training symbol, a new numerical procedure for the Maximum-Likelihood (ML) estimation is designed in this paper to save computational complexity. Analysis and numerical result are also given, demonstrating the conclusions in this paper

A robust timing and frequency synchronization for OFDM systems

Abstract—A robust symbol-timing and carrier-frequency synchronization scheme applicable to orthogonal frequency-division-multiplexing systems is presented. The proposed method is based on a training symbol specifically designed to have a steep rolloff timing metric. The proposed timing metric also provides a robust sync detection capability. Both time domain training and frequency domain (FD) training are investigated. For FD training, maintaining a low peak-to-average power ratio of the training symbol was taken into consideration. The channel estimation scheme based on the designed training symbol was also incorporated in the system in order to give both fine-timing and frequency-offset estimates. For fine frequency estimation, two approaches are presented. The first one is based on the suppression of the interference introduced in the frequency estimation process by the training symbol pattern in the context of multipath dispersive channels. The second one is based on the maximum likelihood principle and does not suffer from any interference. A new performance measure is introduced for timing estimation, which is based on the plot of signal to timing-error-induced average interference power ratio against the timing estimate shift. A simple approach for finding the optimal setting of the timing estimator is presented. Finally, the sync detection, timing estimation, frequency estimation, and bit-error-rate performance of the proposed method are presented in a multipath Rayleigh fading channel. Index Terms—Frequency-offset estimation, orthogonal frequency-division multiplexing (OFDM), symbol-timing estimation, synchronization, training symbol. I