Radon-Wigner Transform Research Articles

A Novel GNSS Sweep Interference Detection and Mitigation Method Based on Radon–Wigner Transform

In this paper, a novel Radon-Wigner transform (RWT) based sweep interference detection and mitigation method has been proposed for global navigation satellite system (GNSS) receivers working in the disturbing scenarios. The proposed GNSS sweep interference detection and mitigation method has been tested using real GPS L1-C/A data disturbed by the sweep interference in a controlled test bench experiment. The results have shown that the proposed method can effectively deal with the cross-term problems with the conventional time-frequency (TF) analysis techniques and provide much improved GNSS interference detection performance in comparison to the existed Wigner-Ville distribution (WVD) and Wigner-Hough transform (WHT) approaches; and the characteristic parameters of the GNSS sweep interfering signal can be efficiently estimated according to the peak position of the RWT computed in the parameter space. In order to excite the GNSS sweep interfering signal, the dechirping and notch filtering techniques have been suggested to realize the GNSS anti-interference functionality, providing satisfactory anti-interference performance for GNSS receivers, this has been further verified by the GNSS signal acquisition experiment in the interfering environment.

Timing synchronization based on Radon–Wigner transform of chirp signals for OTFS systems

Accurate timing synchronization is fundamental for the orthogonal time frequency space (OTFS) system to work properly, but the severe Doppler effect makes it a challenging task in high-mobility environments and high carrier frequency systems. To tackle this challenge, we propose a timing synchronization algorithm based on the Radon-Wigner transform (RWT) of chirp signals for OTFS modulation systems in high-mobility environments, which makes full use of the anti-Doppler performance of chirp signals and the energy aggregation characteristics of RWT to achieve accurate timing synchronization in high-Doppler conditions. Firstly, a training sequence consisting of a dual-chirp signal is transformed from the time domain to the delay-Doppler domain and then superimposed on the user data at the transmitter side. Subsequently, the timing synchronization of the OTFS system is implemented by detecting the peak value of the chirp signal after RWT and computing the difference in peak position between the transmitted and received chirp signals. Simulation results demonstrate that the proposed scheme offers a superior performance gain in low signal-to-noise ratio and high-Doppler conditions.

Rayleigh Wave Reconstruction from Ambient Noise Cross-Correlation Function by Radon-Wigner Transform

The ambient noise tomography is a powerful underground-structure-detection method developed in recent years. The key of this technique is to extract Rayleigh-wave signals from cross-correlation functions (CCF). It is important to suppress the noise in Rayleigh wave signals to increase the accuracy of dispersion-curve extraction. In this paper, a Radon-Wigner Transform (RWT) method is used for Rayleigh-wave reconstruction from CCF. We first introduce the principles of RTW, and then use a multi-component synthetic seismic data to show the processing steps of RWT. Finally, we process actual ambient noise CCF with RWT to reconstruct Rayleigh waves. The results of the synthetic and actual data examples indicate that RWT successfully reconstructed the Rayleigh waves from CCF and improved the signal-to-ratio of the signal.

Mixed LFM Signal Estimation Based on Radon-Wigner Transform and Matching Pursuit

Parameter estimation of mixed signals is a key problem in electronic reconnaissance. Based on Radon-Wigner transform (RWT) and Matching Pursuit (MP) algorithm, a parameter estimation method for mixed LFM signals is proposed in this paper. The core of the method is to separate signal components from the mixed signal and estimate their parameters one by one. Firstly, a rough parameter estimation of the strongest signal is obtained by RWT. After that an optimized estimation based on MP algorithm is performed to fine-tune the estimation result. Then, the strongest signal component is reconstructed with the optimized estimation, and it is separated from the mixed signal. Therefore, by iteratively estimating and separating the stronger signal within the residual mixed signal, all of the signal components can be precisely estimated. Experimental results show that the proposed method is able to achieve satisfactory performance on a lower signal-to-noise ratio.

A novel joint timing/frequency synchronization scheme based on Radon–Wigner transform of LFM signals in CO-OFDM systems

A joint timing and frequency synchronization method has been proposed for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system in this paper. The timing offset (TO), integer frequency offset (FO) and the fractional FO can be realized by only one training symbol, which consists of two linear frequency modulation (LFM) signals with opposite chirp rates. By detecting the peak of LFM signals after Radon–Wigner transform (RWT), the TO and the integer FO can be estimated at the same time, moreover, the fractional FO can be acquired correspondingly through the self-correlation characteristic of the same training symbol. Simulation results show that the proposed method can give a more accurate TO estimation than the existing methods, especially at poor OSNR conditions; for the FO estimation, both the fractional and the integer FO can be estimated through the proposed training symbol with no extra overhead, a more accurate estimation and a large FO estimation range of [−5 GHz, 5GHz] can be acquired.

Hybrid SAR/ISAR imaging of ship targets based on parameter estimation

ABSTRACTTypical Synthetic Aperture Radar (SAR) imaging deals with static targets. This means that moving targets appear blurred in SAR images. Difficulties in imaging are especially noticeable for moving ship targets at sea due to sea waves and each targets individual movement characteristics. Presently, there are no satisfactory results for hybrid SAR and Inverse Synthetic Aperture Radar (ISAR) imaging of multiple ship targets. Focussing on this problem, this letter proposes an improved airborne hybrid SAR/ISAR imaging algorithm based on parameter estimation. In this algorithm, Doppler parameters are estimated by using Radon-Wigner transform (RWT) at first. Then, we improve the traditional data extraction method, in which multi-objective problems are solved through data pre-processing and original characteristics of the data are preserved to the maximum extent. Three representative types of the ship data are selected in this letter and we extract them. Finally, effective ISAR motion compensation methods are adopted for the purpose of gaining focus results. The final images verify a strong feasibility of the proposed algorithm and it provides a good idea for moving ship targets imaging.

An Improved Parameter Estimation Algorithm of LFM Signal Based on the Fractional Fourier Transform

Linear Frequency Modulation (LFM) signal is a common signal in the radar system, how to do parameter estimation of LFM signal quickly and accurately is always the research hot spot. The fractional Fourier Transform (FRFT) as an emerging time-frequency analysis method, because of its transform nuclear is chirp matrix decomposition, so especially suitable for LFM signal processing. But it needs to do global search because the modulation frequency is unknown, which lead to a large amount of calculation. This paper proposed an improved parameter estimation algorithm of LFM signal. We made a rough estimation of modulation frequency by the fast Radon Wigner Transform (RWT) firstly, and then the amount of calculation can be reduced because it only needs to do local search for find the optimal fractional order. In addition, we made a comparison among the new method and other two LFM signal parameter estimation algorithms, and got simulation results under different SNRs. Simulation results show that, parameter estimation accuracy is improved by new algorithm compared to other two algorithms under the same calculation.

A Direction of Arrival Estimation Method for Wideband LFM Signals Based on RWT and ESPRIT Algorithm

In this paper, we proposed a new algorithm to estimate the direction of arrival (DOA) for wideband linear frequency modulation (LFM) signals, using Radon-Wigner transform (RWT) and estimation of signal parameter via rotational invariance techniques (ESPRIT). To eliminate the cross-terms, we first utilize the RWT with its excellent time-frequency concentration performance. Then, through peak searching, the number of targets, the initial interference and the frequency modulation slope are estimated. On the this base, the array signals are reconstructed. Finally, we adopt the ESPRIT algorithm to estimate the DOA of the array signals. The simulation results show that the proposed algorithm can estimate the DOA of non-stationary signals with high precision.

Parameter Estimation of LFM Signal Based on Fast Radon-wigner Transform and Fractional Fourier Transform

In the field of radar and communication, Linear Frequency Modulation (LFM) signal is a very important non-stationary signal, parameter estimation of LFM signal is always the research focus. A new LFM signal parameter estimation algorithm based on fast Radon-Wigner Transform (RWT) and fractional Fourier transform (FRFT) is proposed here. It utilizes fast RWT to calculate modulation frequency of LFM signal, and then according to modulation frequency we use FRFT only once to calculate initial frequency. We made a comparison between new method and other two LFM signal parameter estimation algorithms, and got simulation results under different SNRs. Simulation results show that parameter estimation accuracy and anti-noise performance are improved by using new algorithm, which offers potential for engineering application.

Fast Parameters Estimation of LFM Signals via Radon-Wigner Transform

The line integral of Radon-Wigner Transform (RWT) can transform the line in Wigner-Ville distribution into a point in the plane, which can be used to estimate the chirp rate and initial frequency. The calculation is costly because of two-dimensional (2-D) searching in the plane. Therefore, how to improve calculation velocity is the key of RWT method. Multi-resolution fast parameters estimation algorithm for Linear Frequency Modulation (LFM) signals via RWT is offered in this paper. The analysis results indicate that RWT is similar to Radon-ambiguity Transform (RAT) in calculation load. Performance of the parameters estimation is studied based on Residual Expansion Coefficient (REC) and Frequency Deviation Coefficient (FDC). Simulation results show that the algorithm has reached the Cramer-rao Bound (CRB) even on low SNR. The method has prospective benefits of parameters estimation for multi-component LFM signals.

A Parameter Estimation Method for Poly-Phase Coded Signal Based on the Modified Fractional Fourier Transform

To estimate parameters of poly-phase coded radar signals, a modified Fractional Fourier transform (FrFT) is advanced. This algorithm employs Integrated Quadratic Phase function (IQPF) to estimate frequency rate with which the best degree for Frft is computed. Its computational cost is lower than that of Radon-Wigner transform (RWT) and Radon-Ambiguity transform (RAT). When the signal-to-noise ratio (SNR) is -7 dB, Simulations show its parameter estimation performance closes to the Cramer-Rao Lower Bounds (CRLB).

Union Resolution Performance of Frequency Modulation Parameter Based on RWT for LFM Signals

Union resolution performance of FM (frequency modulation) parameter based on Radon-Wigner transform (RWT) for multi-component LFM (linear frequency modulation) signals is studied. Firstly, the RWT output expression is offered, and the independent resolution performances of initial frequency and chirp rate are analyzed. Secondly, the RWT output approximate analytic expression is given based on quadratic Taylor's series expansion, and the contour property is analyzed. Contour can be used to picture the union resolution performance of FM parameter, and 2-D resolution performance is studied based on approximate analytic expression, and the union resolution expression of FM parameter and resolution ellipse are offered. The simulation results validate the union resolution expression, and show that the union resolution can improve the resolution performance of multi-component LFM signals, contrasted with absolute resolution performance. The paper can help the study of LFM parameter estimation and resolution performance.

Lv's Distribution: Principle, Implementation, Properties, and Performance

This paper proposes a novel representation, known as Lv's distribution (LVD), of linear frequency modulated (LFM) signals. It has been well known that a monocomponent LFM signal can be uniquely determined by two important physical quantities, centroid frequency and chirp rate (CFCR). The basic reason for expressing a LFM signal in the CFCR domain is that these two quantities may not be apparent in the time or time-frequency (TF) domain. The goal of the LVD is to naturally and accurately represent a mono- or multicomponent LFM in the CFCR domain. The proposed LVD is simple and only requires a two-dimensional (2-D) Fourier transform of a parametric scaled symmetric instantaneous autocorrelation function. It can be easily implemented by using the complex multiplications and fast Fourier transforms (FFT) based on the scaling principle. The computational complexity, properties, detection performance and representation errors are analyzed for this new distribution. Comparisons with three other popular methods, Radon-Wigner transform (RWT), Radon-Ambiguity transform (RAT), and fractional Fourier transform (FRFT) are performed. With several numerical examples, our distribution is demonstrated to be a CFCR representation that is computed without using any searching operation. The main significance of the LVD is to convert a 1-D LFM into a 2-D single-frequency signal. One of the most important applications of the LVD is to generate a new TF representation, called inverse LVD (ILVD), and a new ambiguity function, called Lv's ambiguity function (LVAF), both of which may break through the tradeoff between resolution and cross terms.

Pulse processing in optical fibers using the temporal Radon-Wigner transform

It is presented the use of the temporal Radon-Wigner transform (RWT), which is the squared modulus of the fractional Fourier transform (FRT) for a varying fractional order p, as a processing tool for pulses with FWHM of ps-tens of ps. For analysis purposes, the complete numerical generation of the RWT with 0 < p < 1 is proposed to select a particular pulse shape related to a determined value of p. To this end, the amplitude and phase of the signal to be processed are obtained using a pulse characterization technique. To synthesize the processed pulse, the selected FRT irradiance is optically produced employing a photonic device that combines phase modulation and dispersive transmission. The practical implementation of this device involves a scaling factor that depends on the modulation and dispersive parameters. It is explored the variation of this factor in order to obtain an enhancement of the particular characteristic sought in the pulse to be synthesized. To illustrate the implementation of the proposed method, numerical simulations of its application to compress signals commonly found in fiber optic transmission systems, are performed. The examples presented consider chirped Gaussian pulses and pulses distorted by group velocity dispersion and self-phase modulation.

Scaled Radon-Wigner Transform Imaging and Scaling of Maneuvering Target

The use of scaled Radon-Wigner transform (RWT) imaging and simultaneous cross-range scaling is proposed for a maneuvering target using a signal model of a rotating target with uniform acceleration. Three steps are needed to realize such a process. First, the rotational parameters are calculated via the weighted linear least squares method after obtaining frequency modulation parameters of signals in multirange cells. Second, rotational parameters are used to compensate for the slow-time signals. Third, inverse synthetic aperture radar imaging of scaled RWT is implemented with cross-range scaling. Parameter substitution changes every component signal from a slanting line to a horizontal line in the time-frequency plane, and the horizontal line integral can be expressed as a cross-range profile. Compared with conventional RWT imaging methods, this algorithm improves calculation speed greatly and provides more stable imaging performance. This method was tested successfully with simulated and experimental radar data.

Optical pulse compression using the temporal Radon–Wigner transform

The temporal Radon–Wigner transform (RWT), which is the squared modulus of the fractional Fourier transform (FRT) for a varying fractional order p, is here employed as a tool for pulse compression applications. To synthesize the compressed pulse, a selected FRT irradiance is optically produced employing a photonic device that combines phase modulation and dispersive transmission. For analysis purposes, the complete numerical generation of the RWT with 0 < p < 1 is proposed to select the value of p required for pulse compression. To this end, the amplitude and phase of the signal to be processed should be known. In order to obtain this information we use a method based on the recording of two different FRT irradiances of the pulse. The amplitude and phase errors of the recovered signal, which are inherent to the recording process, are discussed in connection with the RWT production. Numerical simulations were performed to illustrate the implementation of the proposed method. The technique is applied to compress signals commonly found in fiber optic transmission systems, such as chirped gaussian pulses, pulses distorted by second and third-order dispersion and nonlinear self-modulated pulses.

Periodic pulse train conformation based on the temporal Radon–Wigner transform

By using the Radon–Wigner transform (RWT), we analyze the temporal selfimaging or Talbot effect for producing well-conformed pulse trains with variable repetition rates and duty-cycles. The relationships linking the selfimaging conditions with the fractional orders of the RWT are first obtained for unchirped pulse trains. Then, we extend the analysis to chirped pulse sequences by deriving the conditions to be fulfilled by an equivalent unchirped pulse train producing the same selfimage irradiances. This result becomes relevant for observing well-defined high order fractional selfimaging, which are of interest due to their repetition rate multiplication. Besides, the effect of the finite extension of the pulse train on the selfimage quality is analyzed and a condition is found for relating the required minimum pulse number with the chirp parameter of the pulses.

Linear frequency-modulated signal detection using Radon-ambiguity transform

A novel time-frequency technique for linear frequency modulated (LFM) signal detection is proposed. The design of the proposed detectors is based on the Radon transform of the modulus square or the envelope amplitude of the ambiguity function (AF) of the signal. A practical assumption is made that the chirp rate is the only parameter of interest. Since the AF of LFM signals will pass through the origin of the ambiguity plane, the line integral of the Radon transform is performed over all lines passing through the origin of the ambiguity plane. The proposed detectors yield maxima over chirp rates of the LFM signals. This reduces the two-dimensional (2-D) problem of the conventional Wigner-Ville distribution (WVD) based detection or the Radon-Wigner transform (RWT) based detector to a one-dimensional (1-D) problem and consequently reduces the computation load and keeps the feature of built-in filtering. Related issues such as the finite-length effect, the resolution, and the effect of noise are studied. The result is a tool for LFM detection, as well as the time-varying filtering and adaptive kernel design for multicomponent LFM signals.

Linear signal synthesis using the Radon-Wigner transform

Thresholding the Radon-Wigner transform (RWT) followed by filtered backprojection to the time-frequency plane reduces noise and cross-term power for multicomponent linear-FM signals. Although the RWT is bilinear, it may be calculated as the magnitude-squared of two linear functions. In this paper, we derive a linear synthesis algorithm from the RWT and demonstrate its efficacy.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Radon transformation of time-frequency distributions for analysis of multicomponent signals

The Radon transform of a time-frequency distribution produces local areas of signal concentration that facilitate interpretation of multicomponent signals. The Radon-Wigner transform can be efficiently implemented with dechirping in the time domain, however, only half of the possible projections through the time-frequency plane can be realized because of aliasing. We show here that the frequency dual to dechirping exists, so that all of the time-frequency plane projections can be calculated efficiently. Both time and frequency dechirping are shown to warp the time-frequency plane rather rotating it, producing an angle dependent dilation of the Radon-Wigner projection axis. We derive the discrete-time equations for both time and frequency dechirping, and highlight some practical implementation issues. Discrete dechirping is shown to correspond to line integration through the extended-discrete, rather than the discrete, Wigner-Ville distribution. Computationally, dechirping is O(2N log 2N) instead of O(N/sup 3/) for direct projection, and the computation is dominated by the fast Fourier transform calculation. The noise and cross-term suppression of the Radon-Wigner transform are demonstrated by several examples using dechirping and using direct Radon-Wigner transformation. >