Carrier Frequency Offset Tracking Research Articles

Bayesian Learning-Assisted Joint Frequency Tracking and Channel Estimation for OFDM Systems

Orthogonal frequency division multiplexing (OFDM) is very sensitive to the carrier frequency offset (CFO). The CFO estimation precision heavily makes impacts on the OFDM performance. In this paper, a new Bayesian learning-assisted joint CFO tracking and channel impulse response estimation is proposed. The proposed algorithm is modified from a Bayesian learning-assisted estimation (BLAE) algorithm in the literature. The BLAE is expectation-maximization (EM)-based and displays the estimator mean square error (MSE) lower than the Cramer-Rao bound (CRB) when the CFO value is near zero. However, its MSE value may increase quickly as the CFO value goes away from zero. Hence, the CFO estimator of the BLAE is replaced to solve the problem.

An Efficient Carrier Frequency Offset Tracking for OFDMA Systems Using Normalized Least-Mean-Square Algorithm

In orthogonal frequency-division multiple access (OFDMA), carrier frequency offset (CFO) destroys the orthogonality between subcarriers due to Doppler effect of the channel and also causes inter-carrier interference (ICI) as well as multiple access interference (MAI). In this paper, CFO tracking algorithm for OFDMA system is presented to overcome the effect of ICI as well as MAI. The proposed algorithm employs normalized least-mean-square (NLMS) algorithm which tracks the residual carrier frequency offset in OFDMA system. The proposed NLMS-based tracking algorithm uses average of all residual carrier frequency offset (RCFO) for improving the mean square error (MSE) performance. The proposed NLMS-based frequency tracking along with frequency offset compensator improves the error performance by reducing the effect of ICI and MAI. Simulation results indicate that the proposed algorithm achieves better tracking performance in the presence of frequency offset. From the results, it is observed that the MSE of the proposed estimator is improved about 3.8 dB at SNR = 20 dB with the frequency offset.

The PS-BCJR Algorithm for Joint Frequency Synchronization and Data Decoding in TCM systems

This study proposes a per-survivor based BCJR algorthm for joint frequency synchronization and data decoding in trellis coded modulation (TCM) systems. The proposed algorithm uses two probing signals and a carrier frequency offset (CFO) tracker to calculate the modified gamma factor involved in the BCJR algorithm. To track the CFO, a state-time process recursively updates the CFO tracker using the soft-information provided by the modified gamma factor. The state-time process consists of a state-process and a time-process. The state-process takes advantage of the state-diversity in the TCM signals to choose the most probable CFO update corresponding to the state with the maximal modified gamma factor. Based on this CFO value, and in conjunction with the tentatively selected probing signals, the succeeding time-process can iteratively track the CFO using the trellis structure of the TCM signals. This study also develops a least-square-linear-fitting (LSLF) approach based on the CFO trace to dynamically adjust the step-size for the CFO tracker. Computer simulations show that unlike the conventional augmented a posteriori probability (A2P2) method having a small CFO tracking range, the proposed approach can handle a significantly larger CFO because of its ML-based CFO estimate. In addition, the proposed LSLF step-size determination ensures the PS-BCJR a higher accuracy in CFO estimation than the A2P2.

Multiple carrier frequency offsets tracking in co‐operative space‐frequency block‐coded orthogonal frequency division multiplexing systems

This study addresses the problem of carrier frequency offset (CFO) tracking in co-operative space-frequency block-coded orthogonal frequency division multiplexing (OFDM) systems with multiple CFOs. Considering that the inserted pilot tones are decayed by data subcarriers in the presence of multiple CFOs, a novel recursive residual CFO tracking (R-RCFOTr) algorithm is proposed. This method first removes CFO-induced inter-carrier interference from data subcarriers, and then updates the residual CFO (RCFO) estimation of each OFDM block recursively. When used in conjunction with a multiple CFOs estimator, the proposed R-RCFOTr can effectively mitigate the impacts from the multiple RCFOs with affordable complexity. Finally, simulation results are provided to validate the effectiveness of our proposed R-RCFOTr algorithm, which has performance close to that of perfect CFO estimation at moderate and high signal-to-noise ratio, and significantly outperforms conventional CFO tracking algorithm for large CFOs.

Carrier frequency offset tracking for constant modulus signalling-based orthogonal frequency division multiplexing systems

This study presents a blind carrier frequency offset (CFO) tracking algorithm for orthogonal frequency division multiplexing systems with constant modulus signalling. Both single-input single-output and multiple-input multiple-output (MIMO) systems are considered. Based on the assumption that the channel frequency response (CFR) has been estimated by training symbols and keeps constant over one frame duration, we discover that the CFO can be estimated via minimising the power difference between the received signals and the CFR. The polynomial rooting method is exploited to derive a low complexity solution. The expectation and mean-square error of the proposed method are derived mathematically. Besides, the effect of channel estimation error on the performance of CFO tracking is addressed and it is shown that the proposed algorithm is robust to this error. At last, this blind scheme can be applied to a MIMO system with the aid of space time block codes.

Turbo Processing for Joint Channel Estimation, Synchronization, and Decoding in Coded MIMO-OFDM Systems

This paper proposes a turbo joint channel estimation, synchronization, and decoding scheme for coded multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. The effects of carrier frequency offset (CFO), sampling frequency offset (SFO), and channel impulse responses (CIRs) on the received samples are analyzed and explored to develop the turbo decoding process and vector recursive least squares (RLSs) algorithm for joint CIR, CFO, and SFO tracking. For burst transmission, with initial estimates derived from the preamble, the proposed scheme can operate without the need of pilot tones during the data segment. Simulation results show that the proposed turbo joint channel estimation, synchronization, and decoding scheme offers fast convergence and low mean squared error (MSE) performance over quasistatic Rayleigh multipath fading channels. The proposed scheme can be used in a coded MIMO-OFDM transceiver in the presence of multipath fading, carrier frequency offset, and sampling frequency offset to provide a bit error rate (BER) performance comparable to that in an ideal case of perfect synchronization and channel estimation over a wide range of SFO values.

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.

A pilot-based fast algorithm for joint estimation of frequency offset and channel in OFDM

Efficient estimations of the carrier frequency offset (CFO) and channel are vital to orthogonal frequency division multiplexing (OFDM). In this paper, a new fast algorithm is proposed for estimating the CFO based on the pilot structure in [M. Morelli, U. Mengali, An improved frequency offset estimator for OFDM applications, IEEE Commun. Lett. 3(3) (1999) 75–77; H.K. Song, Y.H. You, J.H. Paik, Y.S. Cho, Frequency-offset synchronization and channel estimation for OFDM-based transmission, IEEE Commun. Lett. 4(3) (2000) 95–97]. The new method first identifies a coarse estimation of the CFO and then refines it by a least square (LS) method. It always gives a more accurate estimation than the multi-stage method in [H.K. Song, Y.H. You, J.H. Paik, Y.S. Cho, Frequency-offset synchronization and channel estimation for OFDM-based transmission, IEEE Commun. Lett. 4(3) (2000) 95–97] and is better than the method in [M. Morelli, U. Mengali, An improved frequency offset estimator for OFDM applications, IEEE Commun. Lett. 3(3) (1999) 75–77] at low SNR. It only slightly worse than the maximum likelihood estimator at high SNR. Furthermore, the proposed method can be used for CFO tracking. Also, in this paper, channel estimation by using the same pilot block is considered. The best values for the non-null subcarriers are found to optimize the channel estimation and peak to average power ratio (PAPR) simultaneously. Simulations demonstrate that the proposed methods are effective.

A time-frequency decision-feedback loop for carrier frequency offset tracking in OFDM systems

Acquisition and tracking are two crucial stages necessary to the carrier frequency synchronization in orthogonal frequency division multiplexing (OFDM) systems. In this letter, by employing the rotation property of OFDM data subcarriers, a simple time-frequency decision-feedback loop without the use of pilot subcarriers is proposed for the fine carrier frequency offset (CFO) tracking. Specifically, with proper loop parameters, a residual CFO less than 10% of the subcarrier spacing may be well tracked for quarternary phase-shift keying (QPSK) modulation in the presence of noise, while for systems using QPSK, 16-QAM, and 64-QAM modulation schemes, the bit-error rate (BER) performance very close to that of an offset-free system may be achieved in both additive white Gaussian noise (AWGN) and frequency selective fading channels. Moreover, a hardware implementation in a practical OFDM system is fulfilled which verifies the effectiveness of the proposed scheme.