Carrier Frequency Offset Estimation Research Articles

Particle Filter Based Nonlinear Data Detection in Presence of CFO for Frequency Selective mmWave MIMO-OFDM Systems

The nonlinear distortions attributed by the radio frequency (RF) power amplifier (PA) and other RF circuits from the enormous bandwidth of millimeter wave (mmWave) and high frequency design limitations of the integrated circuits involved, degrade the performance of the hybrid mmWave multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. This nonlinear distortions in the hybrid mmWave systems cause nonlinear coupling of the hybrid precoder with the data signals. Further, it induces intercarrier interference (ICI) in the OFDM systems, which also involves the interference from the precoders of other subcarriers. These difficulties in collusion with frequency selective channel and carrier frequency offset (CFO) may pose great challenges to the estimation accuracy of these parameters (channel gains and CFO) and signal detection. The nonlinearity causes the target posterior distribution for data detection as non-Gaussian and analytically intractable. In this work, we present a novel pilot assisted maximum likelihood (ML) based framework for estimating the CFO with PA impairment in the time domain by formulating a low dimensional equivalent channel matrix. The low dimensional equivalent channel matrix is composed of hybrid precoders-combiners, high dimensional MIMO channel, and the nonlinearly distorted components from PA. We further propose a group-sparse Bayesian learning (G-SBL) based semi-blind channel estimator in the time domain, which incorporates the CFO and nonlinearity of PA in its estimation process. With the estimated channel, a procedure to obtain the hybrid precoder and combiner matrices for data transmission is developed next. An iterative algorithm based on particle filter (PF) that effectively handles the nonlinear coupling of precoder matrix with data, and ICI is also proposed for data detection. The performance of the algorithms are evaluated on two different channel models: (a) synthetic geometric based mmWave channel (b) realistic mmWave channel for an urban microcell (UMi) environment. To validate the efficacy of the CFO and channel estimator, the Cramer-Rao bound (CRB) and Bayesian CRB (BCRB) are derived respectively.

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.

An Efficient Frame Optimization Scheme for Low Power Wide Area Networks

In order to support low power wide area networks (LPWANs) with a scarce pilot resource, we discuss the data framing and its corresponding optimization problem. In specific, we design a general pilot-symbol-assisted-modulation (G-PSAM) frame based on the standard PSAM (S-PSAM) frame and derive joint data-aided & non-data-aided Cramer-Rao bounds (DA&NDA CRBs) for carrier frequency offset (CFO), phase offset (PO), and time delay estimation, followed by an approximate DA&NDA CRB for the CFO. With the approximate DA&NDA CRB and the well-known control-variate method (CVM), we then provide an efficient G-PSAM frame optimization scheme, which is asymptotically optimal in terms of the mean-squared-error (MSE) performance. Simulation results show the superiority of the optimized G-PSAM frame over the S-PSAM frame for both the short-packet and long-packet transmissions. Meanwhile, we also present an example verification on the joint DA&NDA aided carrier synchronization (i.e., Turbo synchronization).

Maximum likelihood-based adaptive iteration algorithm design for joint CFO and channel estimation in MIMO-OFDM systems

In this paper, we present a joint time-variant carrier frequency offset (CFO) and frequency-selective channel response estimation scheme for multiple input-multiple output-orthogonal frequency-division multiplexing (MIMO-OFDM) systems for mobile users. The signal model of the MIMO-OFDM system is introduced, and the joint estimator is derived according to the maximum likelihood criterion. The proposed algorithm can be separated into three major parts. In the first part of the proposed algorithm, an initial CFO is estimated using derotation, and the result is used to apply a frequency-domain equalizer. In the second part, an iterative method is employed to locate the fine frequency peak for better CFO estimation. An adaptive process is used in the third part of the proposed algorithm to obtain the updated CFO estimation and track parameter time variations, including the time-varying CFOs and time-varying channels. The computational complexity of the proposed algorithm is considerably lower than that of the maximum likelihood-based grid search method. In a simulation, the mean squared error performance of the proposed algorithm was close to the Cramer-Rao lower bound. The simulation results indicate that the proposed novel joint estimation algorithm provides a bit error rate performance close to that in the perfect channel estimation condition. The results also suggest that the proposed method has reliable tracking performance in Jakes’ channel models.

ICA based estimation and compensation of carrier frequency offset for MBOFDM based UWB systems

A carrier frequency offset (CFO) is addressed as a main type of wireless communication system imperfections in this paper. Carrier frequency offset (CFO) severely deteriorates the performance of OFDM receiver. Here an effective time domain CFO estimation and compensation method using symmetric subcarrier allocation (SCA) for multiband orthogonal frequency division multiplexing (MBOFDM) based ultra-wideband system is proposed. A data supported CFO estimation technique, which is robust to a larger offset, is presented as a novel method in compensation of CFO. An effective separation matrix scheme of OFDM signal with CFO is obtained. Subsequently, independent component analysis (ICA) based CFO estimation is stated. On fully exploiting the ECMA-368 preamble symbols, the proposed technique is capable for carrier frequency offset of 100 ppm, and the result is confirmed through simulations.

Spatial‐Frequency Estimation for OFDM System with Coprime Array

Orthogonal frequency division multiplexing (OFDM) is the key technique of the communication system. In this paper, coprime array is designed in OFDM system to obtain joint direction of arrival (DOA) and carrier frequency offset (CFO) estimates. The proposed system can achieve beamforming and adaptive signal processing, reduce the multipath fading, and attain angle diversity. Meanwhile, coprime array has the advantages of extended array aperture, increased degrees of freedom, and reduced mutual coupling effect, which is adaptable in OFDM system. Moreover, this paper proposes a low‐complexity parameter algorithm with superior performance, which first exploits propagator method (PM) as the initialization and then parallel factor (PARAFAC) method is employed for the accurate DOA and CFO estimation. Simulation results verify the effectiveness of the OFDM coprime array system and the proposed low‐complexity multiparameter algorithm.

Maximum a Posteriori Probability (MAP) Joint Fine Frequency Offset and Channel Estimation for MIMO Systems With Channels of Arbitrary Correlation

Carrier frequency offset (CFO) and channel estimation is a classic topic with a large body of prior work using the maximum likelihood (ML) approach together with the Cramer-Rao lower bound (CRLB) analysis. We give the maximum a posteriori probability (MAP) estimation solution, which is particularly useful for tracking. Unlike the ML cases, the corresponding Bayesian CRLB (BCRLB) shows a clear relation with parameters and low complexity algorithms are provided to achieve the BCRLB in almost all SNR range. Among them, the universal algorithm takes a new approach and avoids error floors of the traditional approach. We assume that the time invariant MIMO channel within a packet can have spatial correlation and nonzero mean. The estimation is based on pilot signals. An unexpected result is that the joint MAP estimation is equivalent to an individual MAP estimation of the frequency offset first, again different from the ML results. We provide insight on the pilot/training signal design based on the BCRLB. Unlike past algorithms that trade performance and/or complexity for the accommodation of time varying channels, the MAP solution provides a different route for dealing with time variation. Within a short enough (segment of) packet where the channel and CFO are approximately time invariant, the low complexity algorithm can be employed. Similar to the belief propagation, the estimation of the previous (segment of) packet can serve as the prior knowledge for the next (segment of) packet.

Spread Spectrum Symbol Detection With Blind Interference Suppression in FBMC-SS

Recent works have demonstrated Filter Bank Multicarrier Spread Spectrum (FBMC-SS) to be a robust communication scheme in the presence of high-power interferers. Existing FBMC-SS symbol detector designs based on analysis filter banks (AFB) suggest using an optimal combining scheme to suppress the interferers, necessitating some noise/interference power estimation method. In this paper, we introduce a symbol detector with blind interference suppression by extending a recently developed packet detection method. We then provide an analysis to show that the existing AFB-based symbol detector and the one proposed in this paper are equivalent in typical usage scenarios. A fully-fledged receiver design is proposed utilizing this symbol detector, with specifics presented for estimation of the channel impulse response and carrier frequency offset (CFO). We also outline a method of iterating upon the channel and CFO estimations to improve the quality of both parameters. Moreover, a modification to allow improved performance of the symbol detector at high SNR is provided. Finally, simulated performance results are presented to corroborate these findings and demonstrate the efficiency of this receiver design.

Joint TOA and DOA Estimation With CFO Compensation Using Large-Scale Array

This paper investigates estimation of direction of arrivals (DOAs) and time of arrivals (TOAs) for a multi-user orthogonal frequency-division multiplexing (OFDM) system that is equipped with large-scale arrays and interfered by carrier frequency offsets (CFOs). We propose a novel scheme for joint TOA and DOA estimation with CFO compensation by taking advantages of large-scale receive antenna arrays. The pilot is designed to balance the pilot length and the estimation performance. The proposed CFO estimation scheme is with lower complexity. After analyzing the resolution of joint DOA and TOA estimation, we find a criterion to choose an appropriate smoothing window for the best resolution and provide insights in sub-carrier selection strategy. We also prove that the large-scale array can asymptotically achieve perfect resolution of both TOA and DOA estimation. We reveal the pseudo peak (PP) elimination property of large-scale arrays and exploit it to develop a novel path number estimation algorithm accordingly. Based on our numerical results, the proposed scheme can efficiently eliminate the CFO effect, the optimized smoothing window attains much better performance, and the path number estimation algorithm performs better than the traditional minimum description length (MDL) approach, especially in the low signal-to-noise ratio (SNR) regime.

Iterative Carrier Frequency Offset Estimation with Independent Component Analysis in BLE Systems

Iterative Carrier Frequency Offset Estimation with Independent Component Analysis in BLE Systems

A Carrier Parameter Decoupling Algorithm for High Order APSK Modulation

In satellite communication, carrier parameter estimation usually uses a serial structure, and the accuracy of frequency offset estimation (FOE) will greatly affect the accuracy of phase offset estimation (POE). A new carrier synchronization mode (NCSM) can realize the decoupling of carrier FOE and POE to a certain extent, but this mode is based on multibase phase shift keying (MPSK) modulation analysis, the decoupling performance is poor when uses in amplitude phase shift keying (APSK) modulation, and the decoupling performance of NCSM has a low tolerance of frequency offset. An improved carrier parameter estimation decoupling technique is proposed to solve these problems. The simulation results show that, compared with the original method, under the premise of ensuring the accuracy of carrier parameter estimation, the proposed method is more robust to the modulation mode, the POE has stronger antioffset ability, and the normalized FOE range has been significantly enhanced.

An Optimum Signal Detection Approach to the Joint ML Estimation of Timing Offset, Carrier Frequency and Phase Offset for Coherent Optical OFDM

Coherent orthogonal frequency-division multiplexing (OFDM) is one of the prime digital modulation techniques for present and future generations of wireless and optical communications. Accurate synchronization is the main obstacle to the implementation of a reliable OFDM receiver. We propose here a joint maximum likelihood (ML) estimator for the timing offset (TO), carrier frequency offset (CFO), and carrier phase offset (CPO) for coherent optical OFDM (CO-OFDM) motivated by the theory of ML signal detection. Our approach starts conceptually with the idea of first computing L replicas of the original OFDM spectrum, where L is a power of two and is assumed sufficiently large. This is done by padding (L-1)N zeros to the end of the N received noisy OFDM samples, where N is the number of OFDM subcarriers. By computing the LN-point discrete Fourier transform (DFT) of these LN time samples, we get L replicas of the DFT of the original OFDM spectrum, where each replica corresponds to the DFT for one hypothesized value of the CFO and the set of possible CFO values is {l/L} <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l=0</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L-1</sup> . We select the most probable replica by choosing the one that is at the minimum Euclidean distance from the original OFDM spectrum, which leads to a matched-filtering (MF) operation in the frequency domain in either a blind or a data-aided manner. Building on this MF concept, we then develop a joint ML estimator of the TO and CPO for each hypothesized value of the CFO. The novelty here is that the TO and the CPO are estimated efficiently as the frequency and phase of a complex sinusoid observed in noise, via either a time-domain or a frequency-domain approach. The resulting joint CFO, CPO, and TO estimator is simpler than existing estimators, both conceptually and in implementation. A much simpler sequential approach in which we first decide on the CFO and then perform a joint TO and CPO estimation is also proposed. The performance loss of this sequential approach compared to the optimum joint approach is small at high signal-to-noise ratio (SNR). We obtain the performance of all our estimators via simulations, and show that they perform better when compared with the existing well-known estimators. Finally, we derive the Cramér-Rao lower bounds (CRLB) on the performance of our estimators, and show via simulations that our estimators for high SNR attain these performance lower bounds.

Residual Carrier Frequency Offset Estimation and Compensation for Commodity WiFi

The various offsets existed in the commodity WiFi devices greatly limit the use of ubiquitous WiFi signals for indoor applications. In this paper, we focus on the estimation and compensation of the residual carrier frequency offset (CFO) for the commodity WiFi devices. Specifically, we consider a distorted channel state information (CSI) model by taking into consideration various CSI errors such as packet detection delay (PDD) and CFO. We propose a multiscale sparse recovery algorithm to get rid of the effect of PDD and extract the carrier frequency component out of CSI. Then, we formulate the residual CFO estimation as a spectrum estimation problem and utilize the MUSIC algorithm to estimate the residual CFO. Real experiments and numerical simulations are conducted to evaluate the performance of the proposed method. The experimental results and simulation results show that the residual CFO is time-varying, and compared with existing methods, the proposed method can better estimate and compensate the residual CFO, and thus achieve better results.

Full‐duplex MIMO‐OFDM systems with imperfect estimation of CFO and time‐varying multipath channels

This Letter proposed a maximum-a-posteriori-based, pilot-aided algorithm for iterative estimation of carrier frequency offset (CFO) and time-varying multiple-input multiple-output (MIMO) multipath channel responses in FD orthogonal frequency division multiplexing (OFDM) systems. Empirical results and related benchmark limits show that the proposed algorithm offers reliable system performance having (i) estimation's mean-squared errors close to related Bayesian Cramer Rao bounds, (ii) data-detection's bit-error rates close to the ideal values under the assumption of perfect channel estimation and synchronisation and (iii) high robustness against the time variation of wireless channels in a network with moving nodes.

Blind Fast CFO Estimation and Performance Analysis for OFDM

Estimation of carrier frequency offset (CFO) is a crucial task for orthogonal frequency-division multiplexing (OFDM) systems, and it should be performed with affordable computational complexity for practicality. This paper proposes two blind and fast CFO estimators for OFDM systems based on null subcarriers. Compared with the existing null subcarriers based estimators, the computational complexity is significantly reduced by avoiding an exhaustive grid searching or a high-order polynomial rooting procedure. The mean squared error (MSE) performance of the proposed CFO estimator is also studied in theory. In addition, the Cramer-Rao bound (CRB) of the CFO estimation for OFDM systems with null subcarriers is derived. Numerical results are provided by computer simulation to verify the validity of theoretical performance analysis and demonstrate the superiority of the proposed estimators.

Practical BER-Based Estimation of Residual OFDM CFO by Reducing Noise Margin

The main OFDM drawbacks are Carrier Frequency Offset (CFO) and large Peak-to-Average Power Ratio (PAPR), which both degrade the Bit Error Rate (BER). Specifically, we consider here clipping or any other PAPR reduction method sufficient to prevent the nonlinear high-power amplifier from generating errors. Moreover, in small cells, the signal-to-noise ratio is large, while the small time dispersion allows the OFDM symbol cyclic prefix to prevent intersymbol interference. This retains the CFO to solely determine the BER and vice versa, enabling indirect estimation of CFO-induced phase distortion by simple BER testing. However, a particular problem is measuring very low BER values (generated by alike residual CFO), which could last a long time in order to acquire statistically enough errors. The test time can be drastically reduced if the noise margin is reduced in a controllable way, by adding the interfering signal to each subcarrier at the receiver. This approach is shown to enable efficient and accurate short-term BER (and so CFO phase error) testing.

Joint CFO and Channel Estimation in OFDM Systems Using Sparse Bayesian Learning

In this article, we study the problem of joint carrier frequency offset (CFO) and sparse channel estimation in orthogonal frequency-division multiplexing (OFDM) communication systems, from the perspective of sparse Bayesian learning (SBL) framework. We first consider the problem in the compressed sensing (CS) context and reformulate it as the problem of recovering a sparse vector from the received signal when CFO and noise variance are unknown parameters that should also be estimated. A novel SBL-based scheme has then been designed to iteratively estimate the CFO, channel impulse response (CIR), and variance of the noise jointly, using the expectation-maximization (EM) algorithm. Both theoretical analysis and simulation results confirm that the proposed scheme outperforms the existing methods while requiring a lower computational cost.

Iterative Carrier Frequency Offset Estimation Scheme for Faster-Than-Nyquist Signaling Systems

As a nonorthogonal mode, faster-than-Nyquist (FTN) signaling transmission can effectively improve the spectrum efficiency of a system. However, FTN signaling inevitably causes inter-symbol interference (ISI). The ISI hinders traditional synchronization methods from operating accurately, and this makes the carrier synchronization of FTN systems more complex. To overcome this issue, we propose an iterative carrier frequency offset (CFO) estimation scheme for an FTN signaling system. The proposed CFO estimation scheme consists of two steps: i) a coarse estimation step based on discrete Fourier transform and ii) a fine estimation step based on a golden-section search algorithm. The simulation results show that the mean square error of the proposed scheme is lower than that of the conventional CFO estimation schemes and approaches the Cramer-Rao Bound, which is an optimal estimation performance bound.

A novel timing and frequency offset estimation algorithm for filtered OFDM system

As a critical technology of 5G air interface waveform, filtered orthogonal frequency division multiplexing (F-OFDM) not only inherits the technical advantages of OFDM, but also has outstanding advantages in system flexibility and spectrum efficiency. However, as a multi-carrier technology, it is still extremely sensitive to sample timing offset (STO) and carrier frequency offset (CFO). In this letter, an improved Park frequency domain training sequence (FS-Park) is proposed to complete STO and CFO estimation of F-OFDM system. Firstly, a real-value pseudorandom number (PN) sequence is sent to each subcarrier as training sequence in frequency domain, the corresponding time domain training symbol has a conjugate symmetry structure. Secondly, the training symbol is utilized for timing synchronization, then the fractional frequency offset is estimated based on the cyclic prefix in time domain. Finally, the integer frequency offset is estimated in frequency domain based on the auto-correlation of PN sequence. The simulation results illustrate that the FS-Park algorithm not only has a single pulse timing metric curve and great STO estimation accuracy, but also has better performance of CFO estimation than classical Park algorithm and Liang Xiao’s method.

The Blind Estimation of Carrier Frequency Offset of Non-cooperative Burst Signal

In order to address the challenge of carrier blind synchronization and blind demodulation for non-cooperative burst signals, a modification scheme of carrier frequency offset estimation is proposed in this paper. Due to the existence of carrier frequency offset and phase offset, the received signal constellation is circular. In the absence of prior information, a non-data-aided method is adopted to estimate carrier frequency offset of the received signal. Then the loop processing method is used to compensate and correct the carrier frequency offset and phase offset to complete the carrier recovery. Simulation results show that the proposed method has high accuracy in carrier frequency offset and phase offset correction when the signal to noise ratio is close to or higher than that of demodulation. Moreover, it has wide extension in engineering practice.