Carrier Frequency Offset Estimation Algorithm Research Articles

A high‐efficiency frequency synchronization scheme for low Earth orbit satellite communications based on dynamic game theory

SummaryThe rapid development of satellite internet networks has given rise to a new vision for the sixth generation of networking technology. However, the Doppler effect is relatively serious in satellite internet networks because a satellite moves quickly relative to a ground terminal. Therefore, there is an urgent need to study intelligent and dynamic synchronization methods to solve the problem of the rapidly changing Doppler frequency offset. Traditional methods do not consider the impact of spatial changes and typically focus on enhancing the estimation range or accuracy. We analyze various scenarios under phased array beam hopping and establish constraints between the terminal location, satellite ephemeris, subsatellite point track, elevation angle, and carrier frequency offset. We introduce dynamic game theory into frequency synchronization to optimize multiple Doppler estimation performance under rapidly changing channel conditions. We take the combination of carrier frequency offset estimation algorithm strategies at the current moment as the game entity. Simulation results demonstrate that the proposed method can achieve an estimation accuracy of 100 Hz and an estimation range of ±800 kHz. During the onboard test, the probability of achieving complete synchronization (when the synchronization success rate is 1) is 0.65, which is much higher than the 0.15 of the single method.

Adaptive Carrier Frequency Offset Estimation in Interference Environments for OFDMA Uplink Systems

In orthogonal frequency division multiple access (OFDMA) systems, carrier frequency offsets (CFOs) influence the different users. In this paper, we proposed a CFO estimation algorithm with strong interference resistant capability for OFDMA systems. The first part of the proposed algorithm processes the received signals so as to deal with the CFO estimation problem. And the second part of the proposed algorithm is to use the proposed adaptive process to obtain the updated CFO estimation and track the parameters' time‐variations. Simulations demonstrate the effectiveness of this method and show that its performance is to the Cramer‐Rao Bounds (CRB). © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Novel Data-Aided Carrier Frequency Offset Compensation Methods Using Asymmetric-Shape Constellations for Burst-Mode Coherent Reception

This paper introduces a novel data-aided carrier frequency offset (CFO) estimation and compensation method for m-array phase shift keying (m-PSK) signals in burst-mode digital coherent reception. Its key advances are as follows; the use of newly designed training symbols (TS) that exhibit asymmetric distributed constellations after differential decoding and a vector summation based feed-forward CFO estimation algorithm. These offer short response time and strong robustness to training symbols (TS) timing detection error with wide CFO estimation range of ±B/2, where B is signal baudrate. We evaluate the feasibility of the proposal by simulations of and experiments on 12.5-Gbaud SP-QPSK signals that target optical budget enhancement of 25-Gbps/λ-class PONs to realize long-reach and high splitting ratio optical access. The 100-km burst-mode transmission experiments confirm the proposal offers high sensitivity detection of better than −43 dBm with much wider CFO range of above ±10 GHz.

Adaptive Iteration Methods for Blind Carrier Frequency Estimation in Multi‐User OFDMA Systems

Subspace‐based blind carrier frequency offset (CFO) estimation algorithms in orthogonal frequency division multiple access (OFDMA) systems have been developed in the literature. However, the algorithms have some restrictions or require high computational complexity. In this paper, we propose simple iteration schemes to reduce complexity with an adaptive manner and present a time‐variant CFO adaptive estimation method. In the first part of the proposed algorithm, with initial rough estimated CFOs, it employs iterative methods to obtain CFO estimates. And the second part is to use proposed adaptive process to obtain the updated CFO estimation and track the parameters' time‐variations. The simulation results demonstrate the efficacy of the proposed iteration and adaptive schemes and the mean squared errors are near to the Cramer‐Rao bounds. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A novel carrier frequency offset algorithm based on a double Barker code in VDE-TER

The Maritime Very High Frequency (VHF) Data Exchange System (VDES) is a basic method of data exchange in the e-Navigation strategy proposed by the International Maritime Organization (IMO). Regarding the synchronization of the VDE-terrestrial (VDE-TER) communication carrier frequency, using the special structure of the training sequence in a VDE message frame, we propose a novel carrier frequency offset (CFO) estimation algorithm based on the phase difference between the Barker code and its inverse code. We derive the principle model for the Barker code and anti-Barker code algorithm and analyze the frequency offset estimation performance of the proposed algorithm with those of the Fitz, L&R and M&M algorithms. We also present a real-world experiment conducted using a software-defined radio (SDR) platform. The results show that in the VDE-TER channel, the double Barker code (DBC) carrier frequency offset estimation algorithm has good estimation performance and estimations range within the visible range.

Efficient carrier frequency offset estimation algorithm for generalized frequency division multiplexing systems

This paper presents an efficient carrier frequency offset (CFO) estimation algorithm for generalized frequency division multiplexing (GFDM) systems. The proposed algorithm formats the preamble into multiple identical subsymbols, and then decimates the received signal in the time domain to estimate the fractional CFO through array signal processing. After compensating for the fractional CFO, the proposed algorithm uses a low-complexity searching process to estimate the integer CFO in a maximum likelihood. The proposed algorithm presents some distinctive features: (1) it provides the full range of frequency acquisition region (FAR), which was considerably larger than that provided by many existing algorithms whose FAR was limited to one subcarrier spacing; (2) the proposed algorithm can use a single subsymbol to estimate the integer CFO by using the searching process of stepsize 1, significantly reducing its computational complexity; and (3) the decimation of the received signal ensures the proposed algorithm a power gain in fractional CFO estimation, resulting in an improved estimation accuracy compared with conventional algorithms.

Joint low‐complexity equalization and CFO estimation and compensation for UWA‐OFDM communication systems

SummaryFrequency synchronization has a great importance in preserving the performance of the underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) systems. The carrier frequency offset (CFO) estimation can be blind or data‐aided. In this paper, the Zadoff‐Chu (ZC) sequences are used for OFDM synchronization in UWA communications, and they are compared with different data‐aided algorithms. We propose a low‐complexity algorithm for CFO estimation based on ZC sequences. Also, a joint equalization and CFO compensation scheme for UWA‐OFDM communication systems is presented. Simulation results demonstrate that the proposed CFO estimation algorithm allows estimation of the CFO accurately with a simple implementation in comparison with the traditional schemes. Also, the performance of the UWA‐OFDM system can be preserved in the presence of frequency offsets.

Carrier frequency offset estimation for FM and symbiotic FM radio data system hybrid signal

The symbiotic FM radio data system (SRDS) is a radio data system that a specially designed OFDM signal co-lives with FM signal, which enables a significantly higher data rate than existing radio data systems. The cyclic prefix of the OFDM symbol has the same length as the OFDM body, which enables the analytic separation of the co-channel OFDM and FM signal at receiver side, utilizing the fact that the OFDM body and prefix is equal. In this work, we show that the OFDM body and prefix cannot be viewed as equal when there is sufficient carrier frequency offset (CFO). Thus, we propose a two-step CFO estimation algorithm for FM and SRDS hybrid signal. The first step estimates the coarse CFO by exploring the characteristics of the FM signal. Once the coarse CFO is removed, the residual CFO is small enough for FM and OFDM separation. The second step fine estimates CFO from the OFDM-only signal using its repeated PN structure after the separation. Detailed mathematical equations are formulated and simulation results are given. The results show that the proposed algorithm works fine with the simulation setup and has a final residual CFO less than 3.9Hz.

Channel Estimation for Hybrid mmWave MIMO Systems With CFO Uncertainties

Channel estimation at millimeter wave (mmWave) allows designing hybrid precoders and combiners to optimize performance metrics, such as the spectral efficiency. One major source of difficulty when estimating the high-dimensional and large-bandwidth channel, however, is the carrier frequency offset (CFO) that impairs the received signal. Most of the prior work assumes perfect time–frequency synchronization when estimating the channel. However, in practical systems, this assumption does not hold, and joint time–frequency synchronization is an important issue to deal with. In this paper, we propose a multi-stage algorithm for joint CFO and channel estimation. Using a training protocol between a transmitter and a receiver, we estimate first the equivalent low-SNR beamformed channel and the CFO, using the maximum-likelihood (ML) criterion. Thereafter, using these estimates, the high-dimensional multiple-input multiple-output (MIMO) channel is estimated leveraging its angular sparsity. The simulation results show that, using our proposed strategy, small estimation errors and near-optimal values of spectral efficiency can be achieved, without incurring in significant overhead and/or computational complexity.

Message Passing-Based Joint CFO and Channel Estimation in mmWave Systems With One-Bit ADCs

Channel estimation at millimeter wave (mmWave) carrier frequencies is challenging when large antenna arrays are used. Prior work has leveraged the sparse nature of mmWave channels via compressed sensing-based algorithms for channel estimation. Most of these algorithms, though, assume perfect synchronization and are vulnerable to phase errors that arise due to carrier frequency offset and phase noise. Recently, sparsity-aware, non-coherent beamforming algorithms that are robust to phase errors were proposed for narrowband phased array systems with full resolution analog-to-digital converters. Such energy-based algorithms, however, are not robust to heavy quantization at the receiver. In this paper, we develop a joint carrier frequency offset and wideband channel estimation algorithm that is scalable across different hardware architectures. Our method exploits the sparse nature of mmWave channels in the angle-delay domain, in addition to the compressibility of the phase error vector. We formulate the joint estimation as a quantized sparse bilinear optimization problem and then use message passing for recovery. We also give an efficient implementation of a generalized bilinear message passing algorithm for the joint estimation in one-bit receivers. Simulation results show that our method is able to estimate the frequency offset and the channel compressibility, even in the presence of phase noise.

Joint timing and frequency synchronization in coherent optical OFDM systems

In this paper, we review our joint timing and frequency synchronization algorithms in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. We first present a timing estimation method by designing the pattern of the training symbol, whose timing metric has a sharp and clear peak, to ensure accurate timing offset (TO) estimation performance. Then we provide both data-aided (DA) and blind (BL) approaches to estimate the carrier frequency offset (CFO). For the DA algorithm, we utilize the same training symbol structure as the timing estimation does, while for the BL algorithm, we utilize the zero-subcarrier power (ZSP) to achieve full-range CFO estimation. Note that our joint timing and frequency synchronization approaches require only one OFDM symbol, which ensure not only the data transmission efficiency, but also the TO and CFO estimation performance. A modified BL ZSP algorithm is proposed to further improve the CFO estimation performance by taking the power average over a series of OFDM symbols. The effectiveness of the TO estimation algorithm, and both the DA and BL CFO estimation algorithms are verified and demonstrated in both simulations and experiments.

Integer CFO Estimation Algorithm for SFBC-OFDM Systems

In this letter, we propose an integer carrier frequency offset (CFO) estimation algorithm for a space-frequency block code (SFBC) system. The transmission is based on orthogonal frequency division multiplexing modulation, which is particularly sensitive to CFO. The development of the proposed algorithm is based on the correlation properties of the received signals which result from the spatial redundancy of the SFBC system. The proposed algorithm is applicable to any SFBC system in conjunction with any number of transmit and receive antennas. The proposed algorithm has the advantage of working even with the lack of knowledge of the channel state information, while providing a satisfactory computational complexity. Monte Carlo simulations are conducted to assess the probability of failure of the proposed algorithm. Semi-analytical analysis of the bit error rate performance is also introduced to validate the corresponding simulation results.

Blind CFO Estimation in OFDMA Uplink Transmission With General Carrier Assignment Scheme

Carrier frequency offset (CFO) estimation is a challenging issue in uplink orthogonal frequency division multiple access (OFDMA) systems. Most existing blind estimation methods for these systems are derived under certain types of carrier assignment scheme (CAS). In this letter, we propose a new blind CFO estimation algorithm for uplink OFDMA systems with constant modulus constellation. The proposed estimator can estimate CFO under any type of CAS, with only one antenna at the receiver. Moreover, the proposed method can be applied to OFDMA with or without virtual/null subcarriers. Simulation results show that the proposed estimator performs well under arbitrary CAS.

Maximum likelihood carrier frequency offset estimation algorithm with adjustable frequency acquisition region

This study presents a simple yet effective carrier frequency offset (CFO) estimation algorithm for orthogonal frequency division multiplexing (OFDM) systems. At the transmitter, the proposed algorithm uses null subcarriers to render the OFDM signal periodic in the time domain. At the receiver, these periodic time samples become CFO-bearing signals, which can be adopted to develop the maximum likelihood (ML) CFO estimation algorithm accordingly. In addition to providing reliable and efficient CFO estimation, the proposed algorithm has an adjustable acquisition region linearly proportional to the order of the null subcarrier insertion scheme.

Multi-User CFOs Estimation for SC-FDMA System Over Frequency Selective Fading Channels

Frequency synchronization in single-carrier frequency division multiple access (SC-FDMA) uplink system is a challenging task due to the presence of different carrier frequency offsets (CFOs) for different users. In this paper, we propose a blind CFOs estimation algorithm for SC-FDMA uplink system by oversampling method in the presence of frequency selective fading channel. A cost function is derived which minimizes the power of the off-diagonal elements of a signal covariance matrix while estimating the correct CFOs. The off-diagonal elements are nothing but inter-carrier interference and multiple-access interference introduced in the presence of multiple CFOs. A complete mathematical model has been presented for multiple CFOs estimation under multiple access scenarios. The proposed CFOs estimation method does not require channel-state information which results in lower computational complexity. The higher iteration complexity of grid search algorithm has been further reduced by a deterministic approach . We also derive the Cramer–Rao bound for CFO estimation. The simulation results show that the proposed CFOs estimation method outperforms the existing subspace theory-based methods, specifically in the low signal-to-noise ratio region.

Blind Carrier Frequency Offset Estimation for MIMO-OFDM Systems Based on the Banded Structure of Covariance Matrices for Constant Modulus Signals

This paper addresses the problem of blind carrier frequency offset (CFO) estimation for multi-input-multi-output orthogonal frequency division multiplexing systems. Benefiting from the banded structure of the circulant channel matrix from each transmitting antenna to each receiving antenna, the covariance matrices formulated by circular shifts of received signals also possess the banded structure in the absence of CFO for constant modulus signals. Thus, the cost function can be constructed by minimizing the elements outside the band and a closed-form CFO estimation algorithm is proposed. Since the channel length has an effect on the proposed estimator and channels with high delay spreads may deteriorate the estimation performance, an improved version of the proposed algorithm is investigated under the assumption that the channel remains constant within two consecutive OFDM symbols which is often the case. Experimental results demonstrate that the proposed algorithm shows better performance than the conventional CFO estimation schemes in frequency-selective fading channels and the improved version of the proposed algorithm can further optimize the estimation performance under long channel length conditions.

An Efficient Algorithm and Hardware Architecture for Maximum-Likelihood Based Carrier Frequency Offset Estimation in MIMO Systems

Carrier frequency offset (CFO), which is often caused by the mismatch between the local oscillators in transmitter and receiver, limits the performance of multiple-input multiple-output (MIMO) wireless communication systems. This paper presents a maximum-likelihood-based CFO estimation algorithm for MIMO systems and its efficient hardware design. The proposed algorithm can accurately estimate the CFO, especially at high signal-to-noise ratio. Moreover, the Cramer–Rao lower bound of the proposed method is derived as a performance guideline. In terms of hardware implementation, an efficient pipeline architecture is presented in detail, showing that the architecture only occupies minimal hardware resources so that it can be fitted into a small field-programmable gate array. The proposed architecture can be reconfigured according to different pilot lengths, making it flexible to various frame structures.

Joint Estimation of Carrier and Sampling Frequency Offsets in the Uplink of Multiuser OFDM Systems

This paper considers the joint estimation of the carrier frequency offset (CFO) and sampling frequency offset (SFO) in the uplink of multiuser orthogonal frequency division multiplexing systems, where the received signal at the base station is a mixture of all users’ signals and each user is affected by different frequency offsets. Usually, users’ separation is needed to cope with this challenging multi-parameter estimation problem. Conventional methods adopt the zero-forcing criterion, which will lead to noise enhancement. To overcome this problem, a novel joint CFO and SFO estimation algorithm is proposed. We use the QR decomposition to achieve users’ separation, and the successive interference cancellation technique is employed to estimate the frequency offsets of different users. To further improve the estimation accuracy, the minimum variance unbiased estimator is exploited. Numerical results show that the proposed algorithm offers better performance than existing methods in terms of mean squared error and bit error rate .

A joint recovery scheme for carrier frequency offset and carrier phase noise using extended Kalman filter

Abstract A joint carrier recovery scheme for polarization division multiplexing (PDM) coherent optical transmission system is proposed and demonstrated, in which the extended Kalman filter (EKF) is exploited to estimate and equalize the carrier frequency offset (CFO) and carrier phase noise (CPN) simultaneously. The proposed method is implemented and verified in the PDM-QPSK system and the PDM-16QAM system with the comparisons to conventional improved Mth-power (IMP) algorithm for CFO estimation, blind phase search (BPS) algorithm or Viterbi-Viterbi (V-V) algorithm for CPN recovery. It is demonstrated that the proposed scheme shows high CFO estimation accuracy, with absolute mean estimation error below 1.5 MHz. Meanwhile, the proposed method has the CFO tolerance of [±3 GHz] for PDM-QPSK system and [±0.9 GHz] for PDM-16QAM system. Compare with IMP/BPS and IMP/V-V, the proposed scheme can enhance the linewidth symbol duration product from 3 × 10−4 (IMP/BPS) and 2 × 10−4 (IMP/V-V) to 1 × 10−3 for PDM-QPSK, and from 1 × 10−4 (IMP/BPS) to 3 × 10−4 for PDM-16QAM, respectively, at the 1 dB optical signal-to-noise ratio (OSNR) penalty. The proposed Kalman filter also shows a fast convergence with only 100 symbols and much lower computational complexity.

A Novel Data-Aided Joint Timing and Carrier Frequency Offset Estimation Based on Central Symmetry ZC Sequence in OFDM/OQAM Systems

In this paper, a new data-aided joint timing and carrier frequency offset estimation algorithm in OFDM/OQAM system is proposed by utilizing identical central-symmetry ZC sequences before polyphase structure efficient implementation. Based on excellent auto-correlation performance of ZC sequence we derive a timing offset estimator with high accuracy and arbitrary capture range compared with two existed approaches. After the precision timing, a new frequency offset estimator is proposed by two parts, which considered both the identical and central-symmetry properties separately. Computer simulation indicates conspicuous performance improvement in timing offset and frequency offset estimation, especially in a AWGN channel which the proposed method possesses significant advantages while in multipath channel the new estimator can still reveal better performance when selecting the correct weighting factor.