Carrier Frequency Offset Estimation Research Articles

Data Detection With CFO Uncertainty and Nonlinearity for mmWave MIMO-OFDM Systems

The nonlinear distortions attributed by radio frequency power amplifiers (PAs) are inevitable in millimeter-wave (mmWave) systems due to the high frequency and large bandwidth. This nonlinearity induces multiplicative distortion and intercarrier interference in mmWave multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing systems, which in collusion with a frequency-selective channel and a carrier frequency offset (CFO) brings great challenges to signal detection. Furthermore, the nonlinearity destroys orthogonality of the training pilots and degrades the estimation accuracy of the channel gains and the CFO. Also, the target posterior distribution for data detection becomes analytically intractable due to the nonlinearity. In this article, we present an importance-sampling-based framework for estimating the CFO in the presence of PA impairment, which utilizes few pilots and initializes the channel estimator. We propose a particle-filter-based iterative algorithm for data detection, where the intractable posterior distribution is approximated by weighted random measures. Furthermore, a sequential-maximum-likelihood-based semiblind channel estimator in the presence of nonlinearity is proposed. Performances of the estimator and the detector are evaluated by means of normalized mean square error, mean square error, and bit error rate. To validate the efficacy of the channel and the CFO estimator, the Cramer–Rao bound (CRB) and the weighted Bayesian CRB are derived, respectively.

Joint CFO and highly frequency selective channel estimation in FBMC/OQAM systems

Filter Bank-based Multicarrier with Offset Quadrature Amplitude Modulation (FBMC/OQAM) has been considered as an alternative waveform to the conventional Cyclic Prefix (CP)-based Orthogonal Frequency Division Multiplexing (OFDM). Despite the adoption of variants of the latter in 5G NR, FBMC/OQAM is still at the top of the promising multicarrier modulation waveforms for future generation communication systems. Although it enjoys a number of unique advantages over CP-OFDM, most importantly maximum spectral efficiency and good time-frequency localization, it is also sensitive to Carrier Frequency Offset (CFO), which can cause inter-carrier interference that degrades system performance if left uncompensated. Besides, the presence of CFO prevents accurate channel estimation. In this paper, our goal is to propose joint estimators for the channel impulse response (CIR) and CFO via an approximate Maximum Likelihood (ML) approach. No simplifying assumption is made about the channel delay spread so our results also apply to highly frequency selective channels. One of the novelties is that the estimation procedure is aided by so choosing the pilots as to result in zero intrinsic interference in the absence of impairments. Moreover, to reduce the complexity of CFO estimation, a lighter implementation, based on the truncation of the Taylor series expansion of the exponential term containing the CFO, is proposed. Simulation results demonstrate the superiority of the proposed estimators over existing methods, in terms of both mean squared estimation errors and bit error rate.

Joint CFO and channel estimation using pilot aided interpolation for high performance MIMO-OFDM

ABSTRACT Multiple Input Multiple Output (MIMO) system with orthogonal frequency division multiplexing (OFDM) is a promising physical layer candidate for the current and future wireless standards. MIMO increases system throughput while OFDM maximizes spectrum efficiency. To reduce the impacts of frequency selective fading and increase the capacity, MIMO requires precise channel state information (CSI). The presence of carrier frequency offset (CFO) introduces intercarrier interference (ICI) among the subcarriers which degrades the system performance. MIMO channel estimation is done under the assumption of perfect frequency synchronisation between the transmitter and receiver, or zero CFO. However, such an assumption is incorrect for time-varying and frequency-selective wireless channels, and the presence of CFO has an impact on channel estimation accuracy. In the existing methods, CFO and channel estimations are carried out independently using separate training sequences which reduces the spectral efficiency. As a result, the pilot aided interpolation approach is proposed in this paper for the joint estimate and compensation of CFO and channel effects using the same set of pilot tones. Theresults show that the proposed method offers precise CFO and channel estimation which improves the bit error rate performance and carrier to interference power ratio (CIR) of MIMO-OFDM system.

Low-Complexity CFO Estimator for Spectrally Efficient Frequency Division Multiplexing System

In this paper, pilot-based carrier frequency offset (CFO) estimation for spectrally efficient frequency division multiplexing (SEFDM) system is focused in the downlink. Firstly, the designed objective function for CFO estimation is proved to fit parabolic curve approximately. Then, a low-complexity CFO estimator is proposed by computing only four trials. Moreover, the Cramer Rao bound (CRB) of CFO estimation for SEFDM is derived. Considering the non-orthogonality of SEFDM, the novel pilot sequence is proposed for SEFDM via minimizing the derived CRB. Under the effects of timing offset and multi-path, simulation results demonstrate that the proposed pilot sequence for SEFDM outperforms traditional sequences.

Novel Phase and CFO Estimation DSP for Photonics-Based Sub-Thz Communication

Sub-terahertz (THz)-band communication system has drawn much attention as a promising technology to provide future-proof high data rate services. In a photonics-based sub-THz communication system, the generation of THz wave using free running lasers enables us to make a simple, cost effective and frequency tunable implementation. On the other hand, commercially available lasers have relatively broader linewidth and a large carrier frequency offset (CFO). To mitigate the performance degradations due to phase noise and CFO, a carrier recovery digital signal processing (DSP) algorithm is studied for a sub-THz transmission system. We propose a novel phase estimation algorithm to avoid cyclic slips while minimizing phase estimation error to improve BER performance. Our proposed phase recovery DSP algorithm is demonstrated in a 16-quadrature amplitude modulation (QAM) in a 0.3 THz band photonics-based transmission system. Experimental results show that the measured BER are improved from 8.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> to 3.6×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> in a 120 Gb/s 16-QAM transmission using the proposed algorithm. A wide range of CFO estimation is also supported for a sub-THz wireless transmission system using off-the-shelf lasers. Recovery of a CFO between −5 GHz and 5 GHz was also successfully demonstrated.

Design of a Blind Estimation Technique of Carrier Frequency Offset for a Universal-Filtered Multi-Carrier System Over Rayleigh Fading

This letter proposes a blind and simple estimation technique of carrier frequency offset (CFO) for a universal-filtered multi-carrier (UFMC) system under specified carrier assignment. The estimation design is divided into a fractional part and an integer part. In particular, by utilizing the characteristic of auto-correlation functions, the proposed scheme only needs a single UFMC symbol and a few complex multiplications to achieve fractional CFO estimation. Furthermore, the integer CFO is selected from the admissible candidates that minimize the frequency response of the frequency-compensated signal corresponding to the specified null subcarriers. The proposed CFO estimation does not require the aid of pilot symbols, and is easy to implement. Its achievable performance is quantified by our derived closed-form expression of the mean-square error of the proposed fractional CFO estimation. The computer simulation results verify the effectiveness and reliability of the proposed approach that does not require an exhaustive frequency search method.

Blind CFO Estimation in a UFMC System Aided With Virtual Carriers

This letter studies the design of blind estimation technique for carrier frequency offset (CFO) in a universal filtered multicarrier (UFMC) system. We first propose a preliminary scheme, and then further devise a series of improved approaches used in the novel two-stage solution, including stages of initial and residual CFO estimation. For Stage 1, we devise two useful estimation algorithms, respectively. Especially, the latter approach using the frequency-domain received signal avoids intensive computation of the cost function. For Stage 2, we derive a closed-form formula used in the iterations to estimate the residual CFO. It can be shown that the proposed schemes not only provide a performance comparable to that of the non-blind least square-based scheme, but also enjoy much lower computational complexity compared with the conventional exhaustive search approach. The conducted computer simulation results verify the superior performance of the blind CFO estimation for UFMC.

A Low-Complexity LoRa Synchronization Algorithm Robust to Sampling Time Offsets

LoRaWAN is nowadays one of the most popular protocols for low-power Internet of Things communications. Although its physical layer, namely LoRa, has been thoroughly studied in the literature, aspects related to the synchronization of LoRa receivers have received little attention so far. The estimation and correction of carrier frequency and sampling time offsets (STOs) are, however, crucial to attain the low sensitivity levels offered by the LoRa spread-spectrum modulation. The goal of this article is to build a low-complexity, yet efficient synchronization algorithm capable of correcting both offsets. To this end, a complete analytical model of a LoRa signal corrupted by these offsets is first derived. Using this model, we propose a new estimator for the STO. We also show that the estimations of the carrier frequency and the STOs cannot be performed independently. Therefore, to avoid a complex joint estimation of both offsets, an iterative low-complexity synchronization algorithm is proposed. To reach a packet error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> , performance evaluations show that the proposed receiver requires only 1 or 2 dB higher signal-to-noise ratio than a theoretical perfectly synchronized receiver, while incurring a very low computational overhead.

A novel orthogonal frequency division multiplexing with index modulation waveform with carrier frequency offset resistance and low peak‐to‐average power ratio

SummaryIn this paper, we propose a novel orthogonal frequency division multiplexing (OFDM) scheme with high carrier frequency offset (CFO) resistance and low peak‐to‐average power ratio (PAPR). In this scheme, we consider a hybrid model with two subblock types, namely, pilot subblocks and standard subblocks. In pilot subblocks, active subcarriers are utilized for PAPR reduction while inactive carriers generated by the index modulation (IM) are utilized for the coarse CFO estimation. For standard subblocks, we consider unique subcarrier activation patterns (SAPs) with high‐diversity IM to enhance the bit error performance of the overall system. Additionally, the inactive data tones in standard subblocks are utilized for fine CFO estimation, which enhances the CFO estimation quite significantly. Furthermore, in this paper, we show that proposed hybrid OFDM‐IM (H‐OFDM‐IM) scheme can outperform conventional OFDM‐IM and classical OFDM both in CFO estimation and PAPR reduction without requiring transmission of any side information. Finally, we show both mathematically and through computer simulations that proposed H‐OFDM‐IM can achieve a satisfactory bit error rate (BER) performance under high CFO scenarios.

Comparison of SPS and FA methods for Blind Carrier Frequency Offset Estimation in OFDM systems

In orthogonal frequency-division multiplexing (OFDM) systems, synchronization issues are of great importance since synchronization errors might destroy the orthogonality among all subcarriers and, therefore, introduce intercarrier interference (ICI) and intersymbol interference (ISI). Several schemes of frequency offset estimation in OFDM systems have been investigated. This paper compares performance and computational complexity of Smoothing Power Spectrum (SPS) and Frequency Analysis (FA) methods for blind carrier frequency offset (CFO) estimation in OFDM systems.

Low-Complexity Joint CFO and Channel Estimation for RIS-Aided OFDM Systems

Accurate channel estimation is essential for achieving the performance gains offered by reconfigurable intelligent surface (RIS)-aided wireless communications. A variety of channel estimation methods have been proposed for such systems; however, none of the existing methods takes into account the effect of synchronization errors such as carrier frequency offset (CFO). In general, CFO can significantly degrade the channel estimation performance of orthogonal frequency division multiplexing (OFDM) systems. Motivated by this, we investigate the effect of CFO on channel estimation for RIS-aided OFDM systems. Furthermore, we propose a joint CFO and channel impulse response (CIR) estimation method for these systems. Simulation results demonstrate the effectiveness of our proposed method, and also demonstrate that the use of time-domain rather than frequency-domain estimation in this context results in an improvement in the mean-squared error (MSE) performance of channel estimation as well as in a significantly lower overall computational complexity.

Design and Testbed Implementation of Multiuser CFOs Estimation for MIMO SC-FDMA System

In this paper, we propose and implement blind multiuser carrier frequency offsets (CFOs) estimation for multi-input multi-output (MIMO) single carrier frequency division multiple access (SC-FDMA) uplink system using orthogonal propagator method (OPM) over a noisy frequency-selective channel. The performance of typical OPM is limited at low signal-to-noise ratio (SNR) due to its noise-free signal model. The additive white Gaussian noise mainly impacts the diagonal elements of the data covariance matrix (DCM) of the received signal. First, the proposed fractional CFOs estimator minimizes the noise effect by reconstructing the denoised diagonal elements of the DCM for the received signal through cubic Hermite interpolation. Therefore, we use modified OPM to estimate multiple CFOs for MIMO SC-FDMA systems. Second, we have used an iterative method based on the first-order Taylor series approximation of the CFO vector to avoid peak ambiguity and reduce the number of iterations required in the grid search. The mean square error of the proposed CFO estimator considerably improves compared with the existing methods at a low SNR regime. The bit error rate performance of the proposed method for MIMO SC-FDMA is also compared with the existing methods. Finally, the proposed estimator is validated by implementing it on radio frequency hardware testbed over an indoor propagation environment.

A Semi-Blind Multiuser SIMO GFDM System in the Presence of CFOs and IQ Imbalances

In this paper, we investigate an open topic of a multiuser single-input-multiple-output (SIMO) generalized frequency division multiplexing (GFDM) system in the presence of carrier frequency offsets (CFOs) and in-phase/quadrature-phase (IQ) imbalances. A low-complexity semi-blind joint estimation scheme of multiple channels, CFOs and IQ imbalances is proposed. By utilizing the subspace approach, CFOs and channels corresponding to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$U$ </tex-math></inline-formula> users are first separated into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$U$ </tex-math></inline-formula> groups. For each individual user, CFO is extracted by minimizing the smallest eigenvalue whose corresponding eigenvector is utilized to estimate channel blindly. The IQ imbalance parameters are estimated jointly with channel ambiguities by very few subcarriers. The proposed scheme is feasible for a wider range of receive antennas number and has no constraints on the assignment scheme of subsymbols and subcarriers, modulation type, cyclic prefix length and the number of subsymbols per GFDM symbol. Simulation results show that the proposed scheme significantly outperforms the existing methods in terms of bit error rate, outage probability, mean-square-errors of CFO estimation, channel and IQ imbalance estimation, while at much higher spectral efficiency and lower computational complexity. The Cramér-Rao lower bound is derived to verify the effectiveness of the proposed scheme, which is shown to be close to simulation results.

Estimasi Carrier Ferquency Offset menggunakan Timing Metric pada Sinyal OFDM

OFDM is one of technology that can be utilized in a variety of telecommunication systems that being widely developed today, for application in LAN, WLAN, 3G, 4G, or 5G. One of the problem faced by the OFDM technology that its sensitivity to Carrier Frequency Offset (CFO) and the lack of synchronization in the OFDM signal. This research aims to design the synchronization that estimates Carrier Frequency Offset (CFO) to obtain synchronization of OFDM signal, where the error of the estimated Carrier Frequency Offset can be obtained, minimized and better than previous studies. The CFO estimation method in this research is using the training symbol on the OFDM symbol and utilize the statistical characteristics of the timing metric. This researchs result shows the Mean Square Error (MSE) of estimated Carrier Frequency Offset to Carrier Frequency Offset input, with range MSE 9.43 x 10-3 at 0 dB SNR input and MSE 1.687 x 10-5 at 30 dB SNR input. If Signal to Noise Ratio is greater, then the value of the mean square error (MSE) will be smaller. The position of the timing metric for timing estimation also affects to CFO estimation. CFO estimation accuracy will be maximized when using maximum timing metric.

Low-Complexity Channel and Carrier Frequency Offset Estimation for Burst-Mode CPM Using Optimized Training Waveforms

We present algorithms of the channel and carrier frequency offset (CFO) estimation for burst-mode continuous phase modulation (CPM) transmission with optimized training waveforms, which are obtained through minimizing the Cramer-Rao bound (CRB). Wirtinger calculus, which provides a framework for complex-valued signal processing, is used to simplify the derivations of CRBs and maximum likelihood estimation. Unlike linear modulation, the training waveform is optimized not only with respect to the modulated training sequence but also the sampling delay and sampling rate due to the continuous phase of CPM waveforms. In order to reduce the computation complexity of the optimization, we derive a closed-form expression for efficient computation of the objective function. The numerical results demonstrate the significant performance improvement of the optimized waveforms compared to the training sequences of previous works. Based on that, we propose two schemes for CFO estimation. The first scheme is a suboptimal maximum likelihood estimation of the CFO and it achieves a better trade-off between the estimation accuracy and complexity compared to optimal maximum likelihood estimation. The second scheme is based on the channel estimation, which leads to much lower implementation complexity than the other estimators. Finally, the measured bit error rate reveals the considerable gain of the estimation algorithm with the optimized training waveform.

Combining IST-Based CFO Compensation and Neural Network-Based Demodulation for Eigenvalue-Modulated Signal

Eigenvalue-based communication technologies using inverse scattering transform (IST) have gained attention as a new transmission strategy in optical fiber communications. In recent years, several studies on artificial neural network (ANN)-based equalization and demodulation schemes for eigenvalue-modulated signal have been conducted to enhance the receiver sensitivity. However, in the case of a presence of a carrier frequency offset (CFO) at receiver, the effects of the CFO on ANN receiver of eigenvalue-modulated signal is yet to be reported. In this study, we numerically and experimentally investigated the generalization performances of eigenvalue domain ANN-based demodulator on CFO. Furthermore, we propose to combine an ANN-based demodulator with a CFO compensation method based on IST and a relation between frequency and eigenvalue shifts. The proposed method, based on an appropriate soliton pulse, achieves a high CFO estimation accuracy of submegahertz order even if the CFO reaches <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 2.5 GHz under the noiseless condition. In the presence of noise and a large CFO of 2.5 GHz, the method attains a CFO estimation accuracy below 60 MHz for OSNR = 10 dB with a low pilot pulse rate, such as 0.064%. We show the simulation results obtained after applying the proposed CFO compensation to the ANN demodulator, which is valid for 2.5 GHz CFO and long-haul transmission over 5000 km. Experiments performed in this study demonstrate successful demodulation of an eigenvalue-modulated signal with OSNR penalty <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&lt; $</tex-math></inline-formula> 1 dB in the presence of CFO within 1 GHz at 2.5 Gb/s.

Improved time and frequency synchronization for dual‐polarization OFDM systems

This article presents techniques for improved estimation of symbol timing offset (STO) and carrier frequency offset (CFO) for dual-polarization (DP) orthogonal frequency division multiplex (DP-OFDM) systems. Recently, quaternion multiple-input multiple-output OFDM has been proposed for high spectral efficiency communication systems, which can flexibly explore different types of diversities such as space, time, frequency, and polarization. This article focuses on synchronization techniques for DP-OFDM systems using a cyclic prefix, where the application of quaternion algebra leads to new improved estimators. Simulations performed for DP system methods show faster reduction of STO estimator variance with a double-slope line in the log-variance line versus signal-to-noise ratio (SNR) plot compared with single-polarization (SP) counterparts, and simulations for CFO estimates show a 3-dB gain of DP over SP estimates for same SNR values defined, respectively, for quaternion-valued or complex-valued signals. Cramer–Rao bounds for STO and CFO are derived for the synchronization methods, correlating with the observed gains of DP over SP OFDM systems.

Estimation of carrier frequency offset and channel state information of generalize frequency division multiplexing systems by using a Zadoff–Chu sequence

This study presents a computationally efficient algorithm for joint carrier frequency offset (CFO) and channel estimation for generalized frequency division multiplexing (GFDM) systems. The proposed algorithm employs a Zadoff–Chu (ZC) sequence as a training sequence spreading in the frequency domain for all subsymbols of the GFDM pilot symbol. The proposed algorithm first estimates the phase rotation factor in the pilot symbol and then coherently combines all subsymbols according to this estimate. The CFO is then estimated from the root of the cost function constructed using the ZC sequence. Finally, the channel estimate is obtained through maximum likelihood estimation and the use of CFO-compensated signals. Compared with conventional approaches, in addition to demonstrating improved estimation accuracy, the proposed algorithm is more computationally efficient because of the use of the ZC sequence. Computer simulations confirm the feasibility of the proposed algorithm.

MIMO-OFDM Joint Radar-Communications: Is ICI Friend or Foe?

Intercarrier interference (ICI) poses a significant challenge for OFDM joint radar-communications (JRC) systems in high-mobility scenarios. In this paper, we propose a novel ICI-aware sensing algorithm for MIMO-OFDM JRC systems to detect the presence of multiple targets and estimate their delay-Doppler-angle parameters. First, leveraging the observation that spatial covariance matrix is independent of target delays and Dopplers, we perform angle estimation via the MUSIC algorithm. For each estimated angle, we next formulate the radar delay-Doppler estimation as a joint carrier frequency offset (CFO) and channel estimation problem via an APES (amplitude and phase estimation) spatial filtering approach by transforming the delay-Doppler parameterized radar channel into an unstructured form. To account for the presence of multiple targets at a given angle, we devise an iterative interference cancellation based orthogonal matching pursuit (OMP) procedure, where at each iteration the generalized likelihood ratio test (GLRT) detector is employed to form decision statistics, providing as by-products the maximum likelihood estimates (MLEs) of radar channels and CFOs. In the final step, target detection is performed in delay-Doppler domain using target-specific, ICI-decontaminated channel estimates over time and frequency, where CFO estimates are utilized to resolve Doppler ambiguities, thereby turning ICI from foe to friend. The proposed algorithm can further exploit the ICI effect to introduce an additional dimension (namely, CFO) for target resolvability, which enables resolving targets located at the same delay-Doppler-angle cell. Simulation results illustrate the ICI exploitation capability of the proposed approach and showcase its superior detection and estimation performance in high-mobility scenarios over conventional methods.

MSE analysis for the finite order joint frequency tracking and channel estimation in OFDM systems

ABSTRACT The technique of orthogonal frequency division multiplexing is very sensitive to the carrier frequency offset (CFO). The requirement for high estimation accuracy when we acquire the CFO value is demanding. An efficient high-order approximation algorithm for jointly estimating the CFO and the channel impulse response (CIR) has been presented in the literature. From their simulation results, it is found that the estimator mean-square error (MSE) values are very close to the Cramer-Rao bound values, indicating that the highest estimation accuracy is achieved. However, no theoretical analysis is provided to confirm this assertion. In this article, we derive the theoretical formulas for the CFO MSE and the average CIR MSE for the estimators. It is found that the theoretical MSE for a joint CFO and CIR estimation problem approximates the Cramer-Rao bound when the signal-to-noise ratio (SNR) is high and the generalized CAZA sequence is used as the preamble. From our simulations, the theoretical results still hold true even for an SNR as low as 5 dB. Consequently, the range of SNR for which the theoretical analysis is valid is quite large.