An Adaptive Compact Kernel TFD Analysis Based on Parameters Pre-estimation for the Multi-component Non-stationary LFM Signals

Referring to the coherent wideband linear frequency modulation (LFM) signals, direction of arrival (DOA) estimation based on fractional Fourier transform (FRFT) is proposed. In this method, the observed signals are first transformed to fractional Fourier (FRF) domain, using the superior time-frequency localization, time-variant direction matrix is changed into time-invariant one. By dint of the forward/backward (FB) spatial smoothing techniques, the corresponding correlation matrix is constructed. Then the DOA of multicomponent coherent wideband LFM signals can be estimated by the traditional MUSIC algorithm simultaneously. Simulation verifies the effectiveness of the novel method.

Background: For the traditional Fourier Transform (FT), it cannot effectively detect the frequency of non-stationary signals with time. Analyzing the local characteristics of time-varying signal by using FT is hard to achieve. Therefore, many time-frequency analysis methods which can meet different needs have been proposed on the basis of the traditional Fourier transform, like the Short Time Fourier Transform (STFT), the widely used Continuous Wavelet Transform (CWT), Wigner-Ville Distribution (WVD) and so on. However, the best time and frequency resolution cannot be achieved at the same time due to the uncertainty criterion. Methods: From the point of view of optimizing time-frequency performance, a new Generalized S Transform (GST) window function optimization method is proposed by combining time frequency aggregation with an improved genetic algorithm in this paper. Results: In the noiseless condition, the Linear Frequency Modulation (LFM), Nonlinear Frequency Modulation (NLFM) and binary Frequency Shift Keying (2FSK) signals are simulated. The simulation results prove that the method can improve the time-frequency concentration and decreasing Rényi entropy effectively. Compared with other four traditional time-frequency analysis methods, the improved GST has more advantages. Conclusion: In this paper, a new method of optimizing the window function in GST based on improved GA is proposed in this paper. Experiments on LFM, NLFM and 2FSK signals show that the proposed method not only has the advantages of high resolution, but also determines the optimal parameters via the time frequency focusing criterion and the Rényi entropy. Compared with the other four kinds of time-frequency analysis methods, the optimized GST based on improved GA in this paper has the best time-frequency focusing.

This paper describes the challenges of detection and parameter estimation priori unknown multi-component radar signals with linear frequency modulation (LFM) in intense noise and complex jamming conditions. A method including two stages is proposed: The first stage is to detect signals, or in other words, estimate the chirp rate, and second is to estimate the pulse width of signals. The proposed approach is firstly examined by identifying the LFM signals in the environment of intense noise and mixing that noise with the continuous wave (CW) signal in MATLAB. An experiment with real-time LFM signals confirms that the method is able to detect and estimate the parameters of multi-component LFM signals in intense noise or in combining CW signal and that noise with a signal-to-noise ratio (SNR) greater than -18dB and -12dB, respectively.

Signal integration, as an effective method of detecting weak target, is widely used in areas of radar, sonar, etc. In previous studies of long-time coherent integration, researchers usually established a multi-pulse echo model with linear frequency modulation (LFM) signal due to its good compression performance and large Doppler tolerance. Then, perfect analytical formula can be deduced to compensate for range migration and Doppler spread, which is helpful in analyzing the mechanism of long-time coherent integration in depth. However, besides LFM, a wide variety of signal waveforms are also used in modern sonar and underwater guidance system to meet the requirements for diverse applications. For instance, continuous wave (CW) pulse is often used in signal detection, high resolution direction of arrival (DOA) estimation, and velocity estimation, while large time-bandwidth product waveforms such as modulated signal, coded signal, and pseudo-random signal are utilized for special tasks like anti-interference detection, channel matching, and active concealed detection. Therefore, the formulas and corresponding instructive conclusions deduced by LFM have no generality when other sonar waveforms are used in pulse integration. In this paper, we focus on long-time coherent integration for arbitrary signal reflected by underwater target moving with a uniform velocity and propose a motion-compensated coherent integration method for arbitrary complex envelop signal. A kind of general ambiguity function (GAF) for transmitted signal is defined to present a unified expression based on GAF for the output of the matched filter. The operation not only helps us to describe and calculate the pulse compression form of the arbitrary complex envelop by using a general mathematical model, but also provides information about the range migration and Doppler frequency shift of the multi-pulse echo, which is needed in pulse range alignment and FFT integration. For the matched filter output expressed by the GAF, Keystone transform is utilized to correct the complex envelop of the multi-pulse echo and eliminate the range walk. Then, Doppler frequency shift is compensated for by performing FFT transform, and the long-time coherent integration for arbitrary complex envelop is realized. To verify the correctness of the proposed method, we carry out the computer simulation on both signal integration and detection performance by using four sonar waveforms, i.e., CW signal, LFM signal, m-sequence phase-coded signal, and Costas frequency hop coded signal. The simulation results show that the proposed motion-compensated coherent integration method is applicable to arbitrary complex envelop signal. We also design an anechoic water tank experiment scheme which can successfully obtain the multi-pulse echoes of constant moving target. The motion-compensated coherent integration of the experimental data of the above-mentioned four waveforms further validates the effectiveness of the proposed method.

We propose a photonics-assisted equivalent frequency sampling (EFS) method to analyze the instantaneous frequency of broadband linearly frequency modulated (LFM) microwave signals. The proposed EFS method is implemented by a photonic scanning receiver, which is operated with a frequency scanning rate slightly different from the repetition rate of the LFM signals. Compared with the broadband LFM signal analysis based on temporal sampling, the proposed method avoids the use of high-speed analog to digital converters, and the instantaneous frequency acquisition realized by frequency-to-time mapping is also simplified since real-time Fourier transformation is not required. Feasibility of the proposed method is verified through an experiment, in which frequency analysis of Kα-band LFM signals with a bandwidth up to 3 GHz is demonstrated with a moderate sampling rate of 100 MSa/s. The proposed method is highly demanded for analyzing the instantaneous frequency of broadband LFM signals used in radar and electronic warfare systems.

A linear frequency modulation (LFM) signal and its corresponding de-chirp operation are one of the basic methods for wideband radar signal processing, which can reduce the burden of the radar system sampling rate and is more suitable for large-bandwidth signal processing. More importantly, most existing methods against interrupted sampling repeater jamming (ISRJ) are based on time–frequency (TF) or frequency domain analysis of the de-chirped signal. However, the above anti-ISRJ methods cannot be directly applied to multiple-input multiple-output (MIMO) radar with multiple beams, because the angular waveform (AW) in mainlobe directions does not possess the TF properties of the LFM signal. Consequently, this work focuses on the co-optimization of transmit beampattern and AW similarity in wideband MIMO radar systems. Different from the existing works, which only concern the space–frequency pattern of the transmit waveform, we recast the transmit beampattern and AW expressions for wideband MIMO radar in a more compact form. Based on the compact expressions, a co-optimization model of the transmit beampattern and AWs is formulated where the similarity constraint is added to force the AW to share the TF properties of the LFM signal. An algorithm based on the alternating direction method of multipliers (ADMM) framework is proposed to address the aforementioned problem. Numerical simulations show that the optimized waveform can form the desired transmit beampattern and its AWs have similar TF properties and de-chirp results to the LFM signal.

A novel in-band OSNR monitoring technique based on fractional Fourier transform of LFM signal

This paper considers the localization of an emitter with an unknown linear frequency modulation (LFM) signal in the passive radar systems based on the direct position determination (DPD) method. To improve the localization accuracy, a novel strategy, wherein the position of the emitter and the unknown transmitted signal are jointly estimated, is proposed. As a result, a six-dimensional estimation problem is formulated, which is, however, computationally intractable for any general application scenario. By combining the DPD algorithm with short time Fourier transform (STFT), a fast and practical suboptimal algorithm, i.e., DPD-STFT, is also designed here to achieve the joint estimation for the emitter position and the unknown parameters of the LFM signal. Simulation results show that the localization performance of the DPD-STFT method is much better than the existing DPD algorithms which do not estimate the transmitted signal.

Because of the high frequency and large bandwidth of the transmitted signal of inverse synthetic aperture Ladar (ISAL), effect as dispersion in range profile exists when imaging uncooperative targets, which leads to the distortion on one-dimensional range profile. The echo model of ISAL is established for uncooperative target. Research shows that, for uniform motion target and uniformly accelerated target, ISAL signals after optical heterodyne processing can be considered as multi-component linear frequency modulation (LFM) signals with the same chirp rate. An ISAL motion compensation method based on fractional Fourier transform (FRFT) is proposed here. Simulation results demonstrate the validity of this method. (5 pages)

Real-world phenomena that can be formulated as signals are often affected by a number of factors and appear as multi-component modes. To understand and process such phenomena, “divide-and-conquer” is probably the most common strategy to address the problem. In other words, the captured signal is decomposed into signal components for each individual component to be processed. Unfortunately, for signals that are superimposition of non-stationary amplitude-frequency modulated (AM-FM) components, the “divide-and-conquer” strategy is bound to fail, since there is no way to be sure that the decomposed components take on the AM-FM formulations which are necessary for the extraction of their instantaneous frequencies (IFs) and amplitudes (IAs). In this paper, we propose an adaptive signal separation operation (ASSO) for effective and accurate separation of a single-channel blind-source multi-component signal, via introducing a time-varying parameter that adapts locally to IFs and using linear chirp (linear frequency modulation) signals to approximate components at each time instant. We derive more accurate component recovery formulae based on the linear chirp signal local approximation. In addition, a recovery scheme, together with a ridge detection method, is also proposed to extract the signal components one by one, and the time-varying parameter is updated for each component. The proposed method is suitable for engineering implementation, being capable of separating complicated signals into their components or sub-signals and reconstructing the signal trend directly. Numerical experiments on synthetic and real-world signals are presented to demonstrate our improvement over the previous attempts.

A novel algorithm based on Discrete-Improved-Radon-Fourier-Ambiguity-Transform (DIRFAT) is proposed for linear frequency modulated (LFM) signal detection and parameter estimation in this paper. By the proposed algorithm, the components can be coherently integrated into distinct peaks on DIRFAT plane, and their parameters can be estimated simultaneously. The proposed algorithm consists of three stages. Firstly, eliminate the linear chirp rate of the every component on discrete ambiguity function (DAF) plane by axis rotation (AR). Afterward, compensate the phase item caused by AR. Otherwise, the energy of the components may spread. Finally, coherently integrate the components and realize components detection. Compared with several existing algorithms, DIRFAT algorithm has better parameter estimation accuracy. Both simulations and real data processing demonstrate that DIRFAT algorithm can detect and analyze Multi-component LFM signals effectively without the affection of the cross-terms.

Chirplet transform (CT) is effective in characterization of instantaneous frequency (IF) for monocomponent linear-frequency-modulated signal. However, the CT is not suitable to analyze multicomponent signal with nonlinear-frequency-modulated component. In this paper, a time-frequency fusion technique based on polynomial CT (PCT) (TFPCT) is proposed to characterize the time-frequency structure of such signals. The TFPCT relies on the fact that the PCT is able to concentrate the energy closely along the IF of the monocomponent signal in time-frequency distribution (TFD). For multicomponent signal, the TFPCT first estimates the proper coefficients with respect to individual component and, second, produces a series of the TFD using the PCT. Each TFD has better energy concentration along the IF of one component. Then, in order to reduce the interference of unwanted component and preserve the component of interest, each TFD is filtered and grouped as an image. At last, the TFPCT combines these TFDs to be an eventual fused TFD, which has the energy concentrating closely along the IF of all components. Comparison with several conventional TFD methods on both numerical multicomponent signal and bat echolocation signal validates the potential and the effectiveness of the proposed method.

We focus on the problem of compressive sampling of Linear Frequency Modulation(LFM) signal via Matching Pursuit. We designed an adaptive matching pursuit algorithm through dynamic dictionary optimization. Results from the sparse property of LFM under Chirplet Basis, we use Chirplet atom to generate dictionary. Then by feeding the information of signal back into dictionary generating process, the grid error can be reduced significantly. It also allows us to get better parameter estimation results and lower signal sampling rate. We demonstrate computing performance on a LFM signal sampling example.

The Renyi Entropy (ER) of a time-frequency distribution (TFD) has been used for estimating the signal information content and the TFD complexity in the time-frequency (TF) plane. In this paper we provide an experimental comparison of the performance of ER obtained from Wigner-Ville distribution (WVD), Spectrogram (SP), Choi-William Distribution (CWD), Born-Jordan Distribution (BJD) and Modified B Distribution (MBD). The performances are tested on two component Gabor logon and LFM signals with the goal of illustrating the effects on ER obtained from different TFDs when signalpsilas TF parameters varies. The presented analysis shows that high-resolution TFDs, such as the MBD, result into consistent ER measures.

Polynomial Wigner Ville distribution (PWVD) is considered as a tool for recognition of signals with an unknown frequency modulation law. This time-frequency distribution (TF) with multi-linear kernel is an optimal form for signals with a polynomial frequency modulation law. Instantaneous frequency (IF) is the important property of non-stationary signals, i.e. signals whose spectral contents vary with time. Then the recognition of unknown signals can be formulated as the problem of estimation of its instantaneous frequency. The studies of estimation of IF for noiseless signals can be found in literature. The noise embedded in a signal has large influence on time-frequency distribution and can change the true value of the IF. Time-frequency distribution strongly depends on the kind of noise. In this paper signals embedded in additive gaussian and impulse noise have been considered. Estimation of the instantaneous fiequency in impulsive noise background is different than in gaussian noise and requires robust forms of time-frequency distributions. In this paper the application of the robust form of the Wigner-Ville distribution (WVD_r) and the robust form of the polynomial Wigner-Ville distribution (PWVD_r) for IF estimation is presented. Maxima of these distributions are assumed as the estimates of true values of IF. The theoretical background of WVD_r and PWVD_r distributions is introduced and several numerical experiments of IF estimation are presented.