Doppler Shift Estimation Research Articles

Doppler Stretch and Delay Statistical Performance Comparison for Wideband and Narrowband Signal Model

Narrowband approximation of Doppler effect by a frequency shift is inappropriate for some problems of radiolocation, hydro acoustics or passive location. In this case it is necessary to use Doppler stretch (time-scaling) as a signal parameter. Statistical performance of joint Doppler stretch and delay for arbitrary spectral width signal without narrowband approximations is derived in this paper.Narrowband and wideband parameters relations are investigated for triangle impulse with linear spectral modulation. Besides, Fisher Information Matrices (FIM) differences are analyzed. In the narrowband limit consideration of results in well-known FIM of Doppler shift and delay estimation are proposed. Another feature of wideband FIM is reference time dependence on time delay variance. Transition from Doppler stretch to Doppler frequency shift considering narrowband limitations results in translation invariant FIM.The article shows that reference time variance of delay estimation is related to estimated parameter modification and velocity influence on delay. Also, estimation variances in narrowband signal model differ from wideband parameter variances by magnitude of spectrum width to central frequency ratio.

Enhanced Dynamic Range Power Independent Doppler Frequency Estimation System

A Doppler shift estimation system with relatively high dynamic range is conceived and demonstrated. The scheme is based on dual mixing the modulated radar echo and frequency to voltage mapping. Hence, it needs no radio frequency auxiliary part. This makes the system capable of becoming integrated into any photonic radar, which would positively affect the cost and size of such system. Since the mixing procedure is all-optical, the system is able to identify the Doppler frequency of a radar echo with carrier frequency as high as 40 GHz independent of its amplitude. The system dynamic range can be as high as 42 dB at 10-GHz radar carrier with an acceptable error of 5%. This dynamic range was achieved using lock-in amplification technique.

Multitarget Joint Delay and Doppler-Shift Estimation in Bistatic Passive Radar

We study the problem of jointly estimating the delays and Doppler shifts of multiple targets in a bistatic passive radar system when the unknown signal from the illuminator of opportunity (IO) is modeled as a correlated stochastic process. We treat all the delays and Doppler shifts as continuous-valued parameters to avoid straddle loss due to discretization. A computationally efficient method based on the expectation maximization (EM) algorithm is proposed, which breaks up the complex multidimensional maximum likelihood estimation problem into several separate optimization problems, one optimization per target. The algorithm provides estimates of all the targets’ delays and Doppler shifts along with the estimate of the IO signal and each target's component signal in the surveillance channel. The Cramer–Rao lower bound (CRLB) is also derived. Simulation results are presented, where we compare the proposed algorithm with the conventional cross-correlation (CC) estimator, modified CC (MCC) estimator, EM with successive interference cancellation (EM-SIC) estimator, and CRLB. It is shown that when the targets are well separated on the delay-Doppler shift plane, the proposed method outperforms all the estimators. Moreover, when the targets are close in this plane, the CC and EM-SIC estimators fails to distinguish the targets, whereas the proposed method successfully estimates the delays and Doppler shifts and outperforms the MCC in this case as well. Finally as the signal-to-noise ratio increases, the performance of the proposed method approaches that of the CRLB.

Low‐complexity methods for joint delay and Doppler estimation of unknown wideband signals

A joint time delay and Doppler shift estimation of unknown wideband signals is studied in the sense that the variation of time delay over time and the migration of Doppler shift over signal frequency cannot be neglected. By partitioning the received signals into short time segments, a novel wideband signal model is proposed. Based on this model, the maximum likelihood estimate (MLE) of the time delay at the starting point of observation and the Doppler shift at the signal carrier frequency is derived. With well compensation of the migrations of these parameters, the MLE derived could achieve higher estimation accuracy. To lower the computational complexity, a fast estimation algorithm based on the Keystone transform is also presented. After correcting the migrations through the Keystone transform, successive one-dimensional Fourier transform, instead of two-dimensional grids search, is used to achieve coherent processing of the received signals. The Cramer-Rao lower bound analysis for wideband cases is presented and the computational complexity of the proposed algorithms is analysed. Simulation results demonstrate the superiority of the proposed methods for wideband cases.

Joint Estimation of Frequency Offset and Doppler Shift in High Mobility Environments Based on Orthogonal Angle Domain Subspace Projection

Conventional frequency preshift technology cannot distinguish between the large Doppler shift and the frequency offset aroused by crystal oscillator, which significantly hinders the system performance improvement in high mobility environments when the frequency offset is present. In this paper, a joint frequency offset and Doppler shift estimation algorithm in high mobility environment based on orthogonal angle domain subspace projection is proposed, which can track the fast time-varying Doppler shift and separate the Doppler shift from the frequency offset. First, an orthogonal angle domain subspace projection algorithm is proposed to project the Doppler spread caused by high mobility into equivalent Doppler shifts in each orthogonal subspace. Second, it utilizes equivalent Doppler shift of all orthogonal subspaces to jointly estimate the maximal Doppler shift and frequency offset. Finally, the estimates are used to compensate the frequency error in the received signal. Moreover, the maximum Doppler shift estimation, together with the projection vectors and the received power on each orthogonal subspace, is fed back and exploited in the subsequent transmitted signal. Simulation results show that the proposed method can estimate the two parameters accurately and eliminate almost all the errors on the Doppler rapidly changing area when SNR is up to 15 dB. Compared with the conventional receiver with automatic frequency control, the receiver with our proposed method achieves better system performance even on the Doppler rapidly changing area.

Evaluation and improvement of LCR-DSR channel parameter estimator in mobile communications

Evaluation and improvement of LCR-DSR channel parameter estimator in mobile communicationsThis paper presents a comprehensive investigation on the optimization of a joint estimator employing the double sampling rate (DSR) technique, in which the Doppler shift estimation based on the level crossing rate (LCR) has been evaluated analytically in terms of the mean square error (MSE). Subsequently, the relationship between the MSE and the channel sampling interval is presented for optimization. Finally, the optimal channel sampling interval is obtained as well as an improved performance of the signal-to-noise ratio (SNR) and Doppler shift estimation. Sufficient simulations demonstrate a good performance for the proposed algorithm.

Cramer-Rao bounds for the joint delay-Doppler estimation of compressive sampling pulse-Doppler radar

Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling (CS) pulse-Doppler (CSPD) radar are developed with different analog-to-information conversion (AIC) systems. However, a unified metric is absent to evaluate their parameter estimation performance. Towards this end, this paper derives the deterministic Cramer-Rao bound (CRB) for the joint delay-Doppler estimation of CSPD radar to quantitatively analyze the estimate performance. Theoretical results reveal that the CRBs of both time-delays and Doppler shifts are inversely proportional to the received target signal-to-noise ratio (SNR), the number of transmitted pulses and the sampling rate of AIC systems. The main difference is that the CRB of Doppler shifts also lies on the coherent processing interval. Numerical experiments validate these theoretical results. They also show that the structure of the AIC systems has weak influence on the CRBs, which implies that the AIC structures can be flexibly selected for the implementation of CSPD radar.

ICI Mitigation by Estimation of Double Carrier Frequency Offsets in High-Speed-Railway Communication Systems for Smart Cities

The urbanization and the fourth industrial revolution lead to the explosion of smart cities. One of the most prior problems to solve in digital cities is transportation infrastructures and high speed railway (HSR) is an effective solution. In communication aspect of HSR, the passenger's demand and transportation management networks require high-speed data services with reliable connections. Orthogonal frequency division multiplexing (OFDM) is a modulation method in the advanced communication systems to provide broadband communications services. OFDM is substantial against inter-symbol-interference due to long symbol duration, but it is very sensitive to doppler effect that happens when the speed of the train is getting much faster. In addition, inter-carrier interference (ICI) caused by high doppler frequency shift has a severe impact on OFDM in case of high channel variations. In this paper, we propose an ICI mitigation method by utilizing the estimation and pre-compensation of high doppler shifts in HSR communication systems for smart cities. The estimate of the doppler shift is based on a preamble frame of data in communication link between EnodeB and user equipment. The simulation results show that the performance of system has been improved using the proposed model.

Estimation of Delay and Doppler shift of Weighted OFDM of Radar Targets

Estimation of Delay and Doppler shift of Weighted OFDM of Radar Targets

A general and yet efficient scheme for sub-Nyquist radar processing

We study the target parameter estimation for sub-Nyquist pulse-Doppler radar. Several past works have addressed this problem but either have low estimation accuracy for off-grid targets, take large computation load, or lack versatility for analog-to-information conversion (AIC) systems. To overcome these difficulties, we present a general and efficient estimation scheme. The scheme first formulates a general model in the sense that it is applicable to all AICs regardless of whether the targets are on or off the grids. The estimation of Doppler shifts and delays is performed sequentially, in which the Doppler estimation is formulated into a spatial spectrum estimation problem and the delay estimation is decomposed into a series of compressive parameter estimation problems with each corresponding to an estimated Doppler shift. By the sequential and decomposed processing, the computational complexity is substantially reduced, and by the parametric estimation techniques, the high accurate estimation is obtained. Theoretical analyses and numerical experiments show the effectiveness and the correctness of the proposed scheme.

Accurate joint estimation of Doppler shift and SNR in mobile communications with high vehicle speed

The signal-to-noise ratio (SNR) and Doppler shift significantly affect vehicular communication. Therefore, we investigate the biases of an iterative Doppler shift estimator by addressing the approximation of the autocorrelation function (ACF), and then explicitly view the estimation errors occurring at high vehicle speeds. Accordingly, a refined process by exploiting the interpolation operation is proposed to reduce the estimation bias at high moving speeds. Subsequently, an SNR estimator is presented by utilizing the bias variation in different iterations, where the estimates of the Doppler shift in the first and final rounds of iterations are combined to construct a bias ratio, and this ratio is then employed to derive an SNR estimator. Computer simulations have shown that our proposed algorithm achieves accurate estimates for both the SNR and Doppler shift in wide ranges of working SNRs and mobile speeds, i.e., at a simulated velocity approaching 300 km/h.

Radio Environment Map-Aided Doppler Shift Estimation in LTE Railway

Due to the high mobility of high-speed trains (HSTs), Doppler shift estimation has been a big challenge for HSTs. In this paper, we consider an orthogonal frequency-division multiplexing (OFDM) system based on the long-term evolution (LTE) railway standard and design the novel Doppler shift estimation algorithm. By exploiting features of HSTs, i.e., regular and repetitive routes and timetables, resulting in a predictable Doppler shift curve, a radio environment map (REM) including the Doppler shift information can be constructed via field tests. Based on REM, a maximum a posteriori estimator (MAPE) is proposed to provide an accurate estimation of Doppler shift. It uses the estimation from REM (REME) as a priori knowledge and exploits the cyclic prefix (CP) structure of OFDM to provide a maximum a posteriori estimation. The Cramer–Rao lower bounds (CRLBs) are derived. The performance of MAPE is evaluated via simulations and compared to that of REME, the classical CP-based estimator, and other existing methods. It is shown that MAPE significantly outperforms the existing methods in terms of both estimation mean square error (MSE) and bit error rate.

A Robust Algorithm for Estimation and Compensation of Doppler Shift in Underwater Acoustic OFDM Communication Systems

A Robust Algorithm for Estimation and Compensation of Doppler Shift in Underwater Acoustic OFDM Communication Systems

Performance Analysis of Global Navigation Satellite System Signal Acquisition Aided by Different Grade Inertial Navigation System under Highly Dynamic Conditions

Under the high dynamic conditions, Global Navigation Satellite System (GNSS) signals produce great Doppler frequency shifts, which hinders the fast acquisition of signals. Inertial Navigation System (INS)-aided acquisition can improve the acquisition performance, whereas the accuracy of Doppler shift and code phase estimation are mainly determined by the INS precision. The relation between the INS accuracy and Doppler shift estimation error has been derived, while the relation between the INS accuracy and code phase estimation error has not been deduced. In this paper, in order to theoretically analyze the effects of INS errors on the performance of Doppler shift and code phase estimations, the connections between them are re-deduced. Moreover, the curves of the corresponding relations are given for the first time. Then, in order to have a better verification of the INS-aided acquisition, a high dynamic scenario is designed. Furthermore, by using the deduced mathematical relation, the effects of different grade INS on the GNSS (including Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS)) signal acquisition are analyzed. Experimental results demonstrate that the INS-aided acquisition can reduce the search range of local frequency and code phase, and achieve fast acquisition. According to the experimental results, a suitable INS can be chosen for the deeply coupled integration.

Joint Delay and Doppler Shift Estimation for Multiple Targets Using Exponential Ambiguity Function

The estimation of delay and Doppler shift parameters in the presence of multiple targets in radar applications are addressed in this study. The construction of a new ambiguity function, namely, exponential ambiguity function, is proposed by introducing an exponent $p$ into the traditional ambiguity function. Some important properties of the exponential ambiguity function are derived. Then the joint delay and Doppler shift estimation algorithm is proposed based on the combination of the exponential ambiguity function and wavelet denoising method. The performance of the proposed estimation algorithm is theoretically analyzed, verified via Monte Carlo simulation, and compared with the performance of the traditional ambiguity function. Simulation results and theoretical performance analysis show that the proposed estimation algorithm outperforms the existing methods for closely located targets.

Low Complexity Residual Doppler Shift Estimation for Underwater Acoustic Multicarrier Communication

We propose two computationally efficient residual Doppler shift estimation methods for underwater acoustic multicarrier communication. The first method is based on computing the phase of the root of a low order polynomial. The second method is a closed-form least squares estimate given the unwrapped phases of the minimal eigenvector of a small data matrix. The complexities of both estimates are significantly lower compared to the methods commonly used in underwater acoustic multicarrier communication, which result in nonlinear least squares estimators and thus require a fine grid search in the frequency domain. Numerical simulations show that the mean square errors of the proposed methods have similar performance as the common estimation techniques, achieve the Cramer–Rao lower bounds at low noise levels, and agree with their theoretically derived variances. Pool experiments and sea trial results further demonstrate that the suggested estimates yield similar results as the common nonlinear least squares estimates but at a lower complexity.

Comparison of Adaptive Spectral Estimation for Vehicle Speed Measurement with Radar Sensors.

Vehicle speed-over-ground (SoG) radar offers significant advantages over conventional speed measurement systems. Radar sensors enable contactless speed measurement, which is free from wheel slip. One of the key issues in SoG radar is the development of the Doppler shift estimation algorithm. In this paper, we compared two algorithms to estimate a mean Doppler frequency accurately. The first is the center-of-mass algorithm, which based on spectrum center-of-mass estimation with a bandwidth-limiting technique. The second is the cross-correlation algorithm, which is based on a cross-correlation technique by cross-correlating Doppler spectrum with a theoretical Gaussian curve. Analysis shows that both algorithms are computationally efficient and suitable for real-time SoG systems. Our extensive simulated and experimental results show both methods achieved low estimation error between 0.5% and 1.5% for flat road conditions. In terms of reliability, the cross-correlation method shows good performance under low Signal-to-Noise Ratio (SNR) while the center-of-mass method failed in this condition.

Mobile ultrasonic transducer positioning

For positioning a moving ultrasonic transmitter, most of the existing ultrasonic positioning systems require the use of a bank of correlators to estimate the Doppler shift associated with its movement which require high computational complexity. In this paper, for positioning a moving transmitter, a computationally efficient a Doppler shift estimation and compensation technique is proposed. As the proposed approach has the ability to measure the Doppler shift directly from the received signal, it does not require to use a bank of correlators to estimate the Doppler shift associated with its movement of the transmitter.

Wind profiling for a coherent wind Doppler lidar by an auto-adaptive background subtraction approach.

Auto-adaptive background subtraction (AABS) is proposed as a denoising method for data processing of the coherent Doppler lidar (CDL). The method is proposed specifically for a low-signal-to-noise-ratio regime, in which the drifting power spectral density of CDL data occurs. Unlike the periodogram maximum (PM) and adaptive iteratively reweighted penalized least squares (airPLS), the proposed method presents reliable peaks and is thus advantageous in identifying peak locations. According to the analysis results of simulated and actually measured data, the proposed method outperforms the airPLS method and the PM algorithm in the furthest detectable range. The proposed method improves the detection range approximately up to 16.7% and 40% when compared to the airPLS method and the PM method, respectively. It also has smaller mean wind velocity and standard error values than the airPLS and PM methods. The AABS approach improves the quality of Doppler shift estimates and can be applied to obtain the whole wind profiling by the CDL.

Efficient estimation and compensation of Doppler shift for multicarrier signals in underwater acoustic communications

Orthogonal frequency division multiplexed (OFDM) carriers are well studied in literature for their ability to tolerate multipath effects in the presence of ambient noise in an underwater acoustic (UWA) channel. However UWA Doppler destroys the orthogonality of subcarriers, resulting in severely degraded Signal to Noise ratio (SNR). To mitigate this effect, we present a novel method for Doppler estimation and compensation over this channel. This method involves transmitting a training preamble of up to three OFDM symbols. Doppler estimation is carried out based on a sliding window correlation over an OFDM symbol period between the received and local copy of time samples. After rejecting spurious peaks, the correlation values are normalized and existence of Doppler detected when the correlation value exceeds a set threshold. The Doppler shift is then estimated post FFT. Specifically the phase angle of received pilot samples is averaged over three OFDM symbols. This estimated shift is used to compensate the ...