Carrier Frequency Offset Estimation Research Articles

A Robust Transceiver for Narrow-Band Communications in Presence of Carrier Frequency Offset

We address narrow-band communications in presence of large and time-varying carrier frequency offset (CFO) at the receiver. This is a general assumption which includes the condition due to the Doppler effect where the transmitter and/or receiver are moving with a relative time-varying speed. A robust transceiver system is proposed to dynamically estimate and compensate the CFO. The proposed system is particulary attractive for low data-rate communications (e.g., voice service) where the CFO is significantly larger than the data bandwidth. A two-step carrier recovery scheme is developed with large acquisition range and fast frequency tracking. The proposed method provides accurate CFO estimation with affordable complexity. We also devise a robust frame synchronization scheme to provide accurate timing in presence of CFO. Furthermore, non-coherent detection with soft-decision decoding is employed to provide a low-complexity receiver with acceptable sensitivity. The proposed transceiver design is implemented on FPGA and real-time experiments are conducted on a Xilinx ZC706 evaluation base board along with AD-FMCOMMS3 daughterboard. After validating the experiments compared to the simulation results, the design was optimized for implementation on XC7Z020 and further integrated with the analog front-end on a board with smaller footprint.

Training‐based frequency synchronisation and highly frequency selective channel estimation for OFDM/OQAM systems

This work addresses frequency synchronisation and channel estimation for highly frequency selective orthogonal frequency division multiplexed systems with offset quadrature amplitude modulation. A two-step approach is proposed, wherein a coarse carrier frequency offset (CFO) estimator, which does not require channel knowledge, is designed in the first step by exploiting the correlation between the received and training signals. A time-domain model is derived for the joint estimation of fine CFO (FCFO) and highly frequency selective channel in the second step. In contrast to the frequency domain model in the literature, the derived time-domain model does not require the channel to be frequency flat. Based on the time-domain model, the weighted least squares and minimum mean square error estimators are investigated to jointly estimate the FCFO and frequency selective channel. The Cramer-Rao lower bounds (CRLBs) are derived for the proposed estimators, and are used to evaluate the performance of the joint FCFO and channel estimation in the presence of inter-symbol-interference due to the overlapping of adjacent time-domain orthogonal frequency division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) symbols. Simulation results demonstrate achievability of the CRLB bounds and performance gain of the proposed estimators over the state-of-the-art existing estimators.

A two-stage approach to estimate CFO and channel with one-bit ADCs

In this paper, a two-stage approach is proposed to estimate the carrier frequency offset (CFO) and channel with one-bit analog-to-digital converters (ADCs). Firstly, a simple metric which is only a function of the CFO is proposed, and the CFO is estimated via solving the one-dimensional optimization problem. Secondly, the generalized approximate message passing (GAMP) algorithm combined with expectation maximization (EM) method is utilized to estimate the channel. In order to provide a benchmark of our proposed algorithm in terms of the CFO estimation, the corresponding Cramér-Rao bound (CRB) is derived. Furthermore, substantial numerical results are conducted to demonstrate the effectiveness of the proposed approach when applied to mmWave channel.

Blind digital modulation classification for STBC‐OFDM system in presence of CFO and channels estimation errors

Here, the authors propose a robust blind digital modulation classification (BDMC) algorithm for space time block coding (STBC)-based MIMO-OFDM system in the presence of carrier frequency offset (CFO) and channel estimation errors. Previous papers published on the topic of modulation identification were limited to single-carrier systems operating over frequency-flat channels. The problem of joint channel and CFO estimation in conjunction with blind digital modulation classification for STBC-OFDM in frequency selective channel and in the presence of the impulsive noise has not been addressed before to the best of their knowledge. To cope with performance degradation of BDMC due to CFO and channels errors, they propose joint semi-blind CFO and channels estimation methods. Higher order statistics (HOS), used for feature extraction, are combined with pattern recognition methods to solve the modulation identification problem. The main contribution of their work is the development of estimators, the study of their impacts on the blind classification capability, and the use of simulations to demonstrate the superior performance of the proposed algorithms.

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.

Enhanced Carrier Frequency Offset Estimation Based on Zadoff–Chu Sequences

The carrier frequency offset (CFO) estimation through correlating a received Zadoff–Chu (ZC) sequence with a locally generated one is considered. The effect of the CFO on the correlation outputs is first analyzed. The obtained results justify for the first time the feasibility of estimating the CFO using an absolute value ratio (AVR)-based approach. Moreover, an existing AVR-based technique is re-visited and found to suffer from a sign flip problem, where the estimated CFO has a different sign from the true value, especially under small CFOs and/or low signal-to-noise ratios. An enhanced CFO estimator is thus proposed and shown to be able to effectively mitigate the sign flip issue and offer improved estimation accuracy over the original method.

Frequency offset estimation for nonlinear frequency division multiplexing with discrete spectrum modulation.

Although fruitful studies have been conducted on carrier frequency offset (CFO) estimations in linear coherent optical fiber communication systems, there are few studies on CFO estimations and recoveries in the systems based on the nonlinear Fourier transform (NFT). Although the CFO is originated from the linear frequency domain, it definitely has effects on nonlinear spectra, including the shift of the nonlinear frequency and the phase rotations of the scattering data, which are similar to its effects on linear spectra. This work indicates that it is feasible to estimate frequency offset (FO) by capturing symbol variations in the nonlinear frequency domain (NFD) rather than in the linear frequency domain; the latter was usually exploited in the literature. Based on a thorough investigation of the FO induced behavior that appears in a nonlinear frequency division multiplexing (NFDM) system, we proposed a nonlinear frequency domain estimation method aided by training symbols (TS) using an angle search algorithm after NFT operations at the receiver. The discussions in this paper prove that the proposed method is generally applicable to the NFDM systems regardless of whether using single or multiple eigenvalues. A performance comparison between the NFD method and the conventional method in the linear frequency domain is performed with different modulation formats for both single and multiple eigenvalue NFDM transmission systems. The analysis results show that the proposed method holds the better stability and estimation accuracy in contrast with the linear domain estimation method. The TS overhead can also be deduced dramatically, which implies better transmission efficiency. Therefore, the NFD method is more powerful for eigenvalue NFDM transmission systems, especially for the scenarios where high order modulation formats and multiple eigenvalues are utilized.

CFO/Channel estimation algorithms for space‐time block coded orthogonal frequency division multiplexing wireless relay networks without using cyclic prefix of OFDM

This study presents a simple technique, which is used to estimate both channel state and carrier frequency offset (CFO) in decode-and-forward relay systems, where coded orthogonal frequency division multiplexing is employed without cyclic prefix. On the basis of the least-square criterion, we derive the estimate of CFO and channel with the aids of consecutive blocks of pilot symbols. The initially proposed estimation technique achieves a distinguished performance by using a two-dimensional complete search approach; however, the computation becomes more and more intensive when the search granularity becomes finer and finer. For this reason, we further present an iterative approach as an alternative solution, which provides a performance comparable with that of the complete search method, while greatly reducing the implementation complexity. Besides, we also derive a closed-form expression of the CFO estimate for the considered system, which allows us to avoid the exhaustive search during the estimation processing. Computer simulations have been conducted to verify the efficiency of the proposed schemes.

Time domain synchronous OFDM system for optical fiber communications

A spectrum efficient OFDM scheme named Time Domain Synchronous-OFDM (TDS-OFDM) is introduced into coherent optical transmission system, in which the pseudo noise (PN) sequence is exploited as guard interval to realize frame synchronization, compensate the carrier frequency offset (CFO), and estimate and equalize channel simultaneously. Since there is no pilot signals or training symbols in TDS-OFDM, the proposed scheme can achieve higher spectral efficiency (SE) above 10% improvement comparing with CP-OFDM. The proposed method is implemented and verified in a 28GBaud QPSK OFDM system and a 28GBaud 16QAM OFDM system. It is demonstrated that the proposed scheme shows high CFO estimation accuracy and synchronous accuracy. Under CFO and linewidth of laser source set as 100MHz and 100kHz respectively, BER of QPSK OFDM system is below 3.8e-3 at the optical signal-to-noise ratio (OSNR) of 13dB, and BER of 16QAM OFDM system is below 3.8e-3 at the OSNR of 20dB.

Frequency synchronization for interleaved OFDMA uplink systems

This study presents a novel frequency synchronization scheme for orthogonal frequency division multiple access uplink systems. The proposed approach first estimates the carrier frequency offset (CFO) from the zeros of a backward prediction system. Then, based on the CFO estimates, two types of filters, namely zero-forcing and the linearly constrained minimum variance filters, are developed to suppress multiple access interference (MAI). Computer simulation results show that in addition to having a reduced computational complexity, the proposed algorithm has reliable CFO estimates and possesses at least a 3-dB power gain in MAI suppression over conventional minimum mean square error algorithms for frequency synchronization.

Joint Time and Frequency Synchronization in Halved Phase-Only MIMO

Halved phase-only multiple input multiple output (HPO-MIMO) completes wireless transmission based on $\pi$ -periodic phase measurements, which are directly acquired by phase detectors at the base station. However, existing synchronization algorithms for MIMO can no longer be applied into HPO-MIMO, because they work under complete measurements with both magnitude and phase information but HPO-MIMO loses magnitude information completely. This correspondence paper proposes a joint time and frequency synchronization algorithm for HPO-MIMO, which exploits the repeatability of a pilot preamble. Starting-time and carrier frequency offset (CFO) are jointly estimated under a grid-searching manner. At first, continuous starting-time and CFO estimation are uniformly sampled from their potential value ranges. On all potential starting-time points, the received phase measurements are uniformly sliced according to the repetition structure of the preamble, and then the phase rotations due to CFO are removed based on each potential CFO value. The shifted phase measurements would show strong similarities if CFO is successfully compensated. The similarities among these sliced phase sequences are characterized by a metric named phase sequence distance (PSD). They are summed up as a final PSD, whose minimum value corresponds to the estimated starting time and CFO. Simulation results validate the effectiveness of the synchronization algorithm under different signal-to-noise ratios and lengths of preamble. HPO-MIMO with our synchronization algorithm can even perform similarly as its perfect-synchronized correspondence.

An Approach to Wideband and High Accuracy Microwave Photonic Signal Carrier Recovery Based on Carrier Period Measurement

We propose and experimentally demonstrate an approach to carrier frequency and phase recovery of a microwave photonic signal based on carrier period measurement (CPM). In the approach, a coarse carrier frequency offset (CFO) estimation is first performed, which is realized by measuring the crossing period of the microwave signal with its mean level. Then, an envelope detection method is used to simultaneously estimate the residual CFO and the carrier phase. Through the two steps, wideband and high-accuracy carrier recovery can be realized. The proposed approach is validated by an experiment. Effective carrier recovery of a microwave photonic signal is achieved with a carrier frequency varying from 7 to 37 GHz carrying a 2-Gbaud on–off -keying or quadrature phase shift keying baseband signal. The CFO estimation range is from −21 to +9 GHz, and the CFO estimation errors are less than 0.1 MHz.

Investigation of blind CFO estimation for GFDM system using universal software radio peripheral: theory, simulations and experiments

Generalised frequency division multiplexing (GFDM) utilises a circular pulse shaping mechanism to hinder out-of-band emissions and for achieving low latency. However, fallacious synchronisation of this multicarrier technique would lead to severe inter carrier interference and inter symbol interference. Conventional training sequence-based methods alleviate the effect of time and frequency misalignments by using the concept of data repetition in the pilot preamble, which recedes data efficacy. This study enlightens various aspects in real-time implementation of blind GFDM signal transceiver using oversampling for carrier frequency offset (CFO) correction in indoor environments. It is observed that the phase shift between neighbouring sample points in an oversampled GFDM symbol is constant throughout the symbol duration. This phase shift is found to be unassociated with either subcarrier or subsymbol indices. Using this property, the maximum likelihood estimate of the CFO is deduced and is analysed in various channel environments. The Cramer–Rao lower bound for the oversampling-based GFDM signal model is derived and the authors prove through simulation that the proposed algorithm results in a little error floor. The results obtained in simulations have been validated with real-time test bed built with universal software radio peripheral 2953R as hardware and LabVIEW as software.

Analysis of CFO Estimation for QAM-FBMC Systems Considering Non-Orthogonal Prototype Filters

The carrier frequency offset (CFO) on the orthogonal waveforms such as orthogonal frequency division multiplexing and offset quadrature amplitude modulation filter-bank multi-carrier (QAM-FBMC) has been well studied. However, the impact of the CFO on the QAM-FBMC systems is more complicated because of non-orthogonal prototype filters. The unavoidable interference from the non-orthogonality makes pilot signal design difficult and makes it hard to estimate the CFO accurately. In this paper, we discover the impact of the CFO on QAM-FBMC systems, evaluate the procedures of the basic CFO estimation methods, and analyze the performances of the CFO estimations. For the integer part estimation of CFO, we propose the design of pilot symbol that has a prominent peak at pilot subcarrier location in the up-sampled frequency domain. For the fractional part estimation, we formulate the basic CFO estimation by using two adjacent pilot symbols, and we analyze the mean-squared error performances with linear approximation and Cramer-Rao lower bound. We compare the performance of the CFO estimator and analytic approach in the additive white Gaussian noise and the pedestrian channel and show that the proposed estimator works well in the non-orthogonal QAM-FBMC systems.

Data-Aided Frequency Offset Estimation for CE-OFDM Broadband Satellite Systems

In recent years, the constant-envelope orthogonal frequency-division multiplexing (CE-OFDM) has been considered as a candidate waveform in broadband satellite systems as it has a 0-dB peak-to-average power ratio (PAPR). However, the carrier frequency offset (CFO) estimation scheme for CE-OFDM broadband satellite systems directly affects system performance. In this paper, we analyze the network architecture and the propagation environment of CE-OFDM broadband satellite systems, and we propose a data-aided CFO estimation strategy based on the frequency domain pilot symbols. The Cramer–Rao bound (CRB) of our CFO estimator is given by mathematical analysis, and the effect of the number of pilot symbols on the estimation performance is analyzed. The pilot symbol-based CFO estimator is composed of a phase demodulator and a discrete Fourier transform (DFT) module, and it can obtain a large estimation range under a small pilot overhead. The simulation results show that the CE-OFDM broadband satellite systems can achieve a good bit error rate (BER) performance by using the proposed strategy to estimate and compensate the CFO.

Sparse Bayesian Learning Assisted CFO Estimation Using Nonnegative Laplace Priors

This correspondence paper aims at addressing the estimation of carrier frequency offset (CFO) for the uplink orthogonal frequency-division multiple access systems. Since the CFOs of the signals from different active users are sparsely distributed in the frequency domain, a sparse Bayesian learning (SBL) is tailored to determine the CFO in this paper, ending up with the SBL assisted CFO (SBL-CFO) estimator. In particular, the CFO estimation problem is first formulated as a sparse nonnegative least squares (S-NNLS) problem. Meanwhile, background noise and sampling errors are mitigated utilizing a selection matrix and a whitening filter, respectively. This enables us to exploit the SBL with nonnegative Laplace prior (SBL-NLP) to solve the S-NNLS problem. Furthermore, in order to make the convergence of the SBL-NLP algorithm faster and its estimation more accurate, the hyperprior inherent in the SBL-NLP algorithm is initialized by the traditional SBL with nonnegative Gaussian prior. Simulation results show that our proposed SBL-CFO estimator significantly outperforms the state-of-the-art estimators in terms of estimation accuracy, especially when the CFOs and the number of active users are large.

Frequency Synchronization for OFDM-Based Massive MIMO Systems

Massive multiple input multiple output (MIMO) is a key technology in the fifth-generation wireless networks. However, its performance heavily relies on accurate synchronization. Additionally, synchronization can impose an enormous amount of computational complexity to the system. To deal with this issue, in this paper, we propose a low-complexity frequency synchronization technique with a high accuracy for the uplink of multiuser orthogonal-frequency-division multiplexing-based massive MIMO systems. First, we propose a carrier frequency offset (CFO) estimation whose computational complexity increases only linearly with respect to the number of base station (BS) antennas. Second, we propose a CFO compensation method that is performed after combining the received signals at the BS antennas, and as a result, its computational complexity is independent of the number of BS antennas. As a third contribution, the effect of the CFO estimation error is studied, and it is proven that by applying our proposed CFO compensation technique, the CFO estimation error causes only a constant phase shift. We then propose an algorithm to efficiently calculate and remove the estimation error. Our simulation results testify the efficacy of our proposed synchronization technique. As it is demonstrated, our proposed synchronization technique leads to a bit error rate performance that is very close to the one for a fully synchronous system.

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.

Fast Iterative Semi-Blind Receiver for URLLC in Short-Frame Full-Duplex Systems With CFO

We propose an iterative semi-blind (ISB) receiver structure to enable ultra-reliable low-latency communications in short-frame full-duplex (FD) systems with carrier frequency offset (CFO). To the best of our knowledge, this is the first paper to propose an integral solution to channel estimation and CFO estimation for short-frame FD systems by utilizing a single pilot. By deriving an equivalent system model with the CFO included implicitly, a subspace-based blind channel estimation is proposed at the initial stage, followed by CFO estimation and channel ambiguities elimination. Then, the refinement of channel and the CFO estimates is conducted iteratively. The integer and fractional parts of CFO in the full range are estimated as a whole and in closed-form at each iteration. The proposed ISB receiver significantly outperforms the previous methods in terms of frame error rate, mean square errors of channel estimation and CFO estimation and output signal-to-interference-and-noise ratio, while at a halved spectral overhead. Cramer–Rao lower bounds are derived to verify the effectiveness of the proposed ISB receiver structure. It also demonstrates high-computational efficiency as well as the fast convergence speed.

Multi-Node ML Time and Frequency Synchronization for Distributed MIMO-Relay Beamforming Over Time-Varying Flat-Fading Channels

In this paper, we investigate maximum likelihood (ML) time delay (TD) and carrier frequency offset (CFO) synchronization in multi-node decode-and-forward cooperative relaying systems operating over time-varying channels. This new synchronization scheme is embedded into a distributed multiple input multiple output (MIMO)-relay beamforming transceiver structure to avoid the drawbacks of multidimensional ML estimation at the destination and to minimize the overhead cost. By accounting for a perfect Doppler spread value, the new synchronization solution delivers accurate TD and CFO estimates. For real-world operation, however, this new technique can be jointly implemented with any Doppler spread estimator in a new iterative scheme using a time-constant channel (TCC)-based synchronization method at the initialization step. The resulting TD and CFO estimates along with the channel estimates are then fed into a distributed MIMO-relay beamforming transceiver of $K$ single-antenna nodes, for pre-compensation at each node of the transmitted signals, to ensure constructive maximum ratio combining (MRC) at the destination. Simulation results show significant synchronization accuracy improvement over previous distributed multi-node synchronization techniques assuming TCCs. The latter translates into noticeable gains in terms of useful link-level throughput, more so at higher Doppler or with more relaying nodes.