Motion-compensated coherent integration of constant moving target echoes with arbitrary complex envelope

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.

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.

This paper focuses on the wake-up signal detection design for underwater acoustic communication (UAC) terminals. A wake-up signal detection unit can considerably reduce the power consumption of the terminals. Compared with terrestrial wireless counterparts, the wake-up signal detection design for UAC terminals is challenged by the severe underwater acoustic channels, which is characterized as doubly selective fading and low signal-to-noise ratio (SNR). This paper proposes a wake-up signal detection approach called channel-adaptive detection and location-assisted joint decision (ChAD-LaJD), for UAC terminals. ChAD-LaJD applies a group of linear frequency modulation (LFM) signals as a wake-up signal. In order to increase the detection probability while keeping a low false alarm rate, ChAD-LaJD consists of two procedures: channel-adaptive detection (ChAD) and location-assisted joint decision (LaJD). Besides a pre-determined threshold, ChAD procedure defines two special parameters which reflect instantaneous channel states to detect wake-up signals adaptively. LaJD procedure further exploits the location relationships of LFM signals detected by ChAD to achieve a joint decision. The simulations and field experiments are conducted to evaluate the performance of ChAD-LaJD. The results show that ChAD-LaJD outperforms the conventional methods that consider a fixed threshold (FixTh) and/or constant false alarm rate (CFAR).

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.

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.

The sparse representation using time-frequency atoms is a useful analysis method for radar signal processing. Based on Time-Frequency theory, time-frequency atoms can match radar signals and represent it sparsely. Traditional atomic dictionary can only match the linear frequency modulation signal, while a novel time-frequency atomic dictionary proposed in this paper can not only match the linear time-frequency modulation signal properly but also match the non-linear time-frequency relationship appropriately. It is because that the proposed atomic dictionary has a sinusoidal factor which improves the atoms' ability to match and represent the linear and non-linear frequency modulation signals. Compared with traditional atomic dictionaries, the simulation result shows that the novel atomic dictionary can represent radar intra-pulse modulation signals more effectively and sparsely.

In this paper, a method for detecting and estimating the chirp rate and the pulse width of radar signals with linear frequency modulation based on the cross-correlation function under jamming conditions by continuous-wave signals and white noise is investigated. The proposed method includes two stages; the first is used to detect or estimate the chirp rate of the linear frequency modulation signal, and the second one is used to estimate the pulse width of this signal. In the first part of the paper, the accuracy of the method is studied by simulation a linear frequency modulation signal in the MATLAB environment to determine the lowest value of SNR, at which this technique is still able to detect and estimate the parameters of this signal. Based on the simulation results, a real-time signal is used to verify its functionality in the second part of this paper. The experimental results confirm that the proposed method can detect and estimate the parameters of linear frequency modulation signal under jamming conditions by continuous-wave signals and white Gaussian noise at the value of SNR > −7 dB.

This paper analyses the main factors affecting the estimation accuracy of linear frequency modulation (LFM) signal parameters based on fractional Fourier transform (FRFT). By simulation and comparing we can come to the conclusion that the estimation accuracy of initial frequency is improved along with the search interval decreasing while the modulation frequency slope is improved along with the sample points increasing. Based on which we can improve the estimation accuracy of LFM signal parameters according to different cases at the same computational cost. Simulation results verify the correction of the conclusion.

The fractional Fourier transform (FRFT) can transform the linear frequency modulation (LFM) signal into delta function for a proper orders, since the kernel of FRFT has a property of LFM. Using this property, the paper proposes the filter for LFM signal with noise, which avoids cross-term of quadratic distribution due to the linearity of FRFT. The method can reduce noise by optimizing the parameter p in (p, u) plane. The filtering performance is regulated by the correlation coefficient, and evaluated by mean square error (MSE). Computer simulations show that the proposed algorithm can filter the signals well compared to the pseudo Wigner Ville distribution for avoiding the cross-term problem. The statistical analysis of the MSE is also given for different signal to noise ratio, which illustrates the proposed algorithm has a rather good performance.

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 multi-band dual-chirp linearly frequency modulated (LFM) signal-generation scheme with doubled chirp bandwidth and flexible center frequency and band numbers is proposed. In the scheme, the polarization multiplexed multi-tone optical signals with chirped phases are generated via a dual-polarization dual-parallel Mach–Zehnder modulator (DPMZM) cascaded with a polarization modulator. The two polarization multiplexed lightwaves are recombined as two linearly polarized beams by a polarization beam splitter and are detected by a balanced photodiode with a photocurrent that includes the multi-band dual-chirp LFM signal with doubled bandwidth and multiplied central frequencies but does not have a dc component. Since the orders and numbers of the generated optical sidebands are changed by adjusting the bias voltages of a DPMZM, we can obtain the multi-band dual-chirp LFM signal flexibly. Based on simulation, four-band, six-band and two seven-band dual-chirp LFM signals are generated with four groups of bias voltage configurations. For each case, every dual-chirp LFM signal of the generated multi-band dual-chirp LFM signal has a 5-GHz bandwidth and a time-bandwidth product of 512. The auto-correlations and ambiguity function of the generated LFM signal show good performance of pulse compression and range-Doppler resolution.

The fractional Fourier transform (FRFT) has been used to detect and estimate the parameters of linear frequency-modulated continuous-wave (LFMCW) in low probability of intercept radar waveforms. The FRFT, which is optimal for single linear frequency-modulated (LFM) signals, becomes sub-optimal when applied to LFMCW signals because the observed waveform of this type of signal is composed of concatenated LFM pulses. A new signal processing method, called the periodic FRFT (PFRFT), is proposed for the detection of LFMCW signals. First, the discrete PFRFT is studied and the signal processing gain of this transform for LFMCW signals is analyzed. Second, an adaptive threshold detection and estimation algorithm for LFMCW signals is formulated after analysis of the test statistics of the squared modulus of LFMCW signals when using the probability density function in the presence of Gaussian white noise. It is then proved that PFRFT-based estimation is equivalent to maximum likelihood estimation in the detection and estimation of LFMCW signals. Finally, the results of both the theoretical analysis and verification simulations show that the PFRFT significantly outperforms the FRFT for LFMCW signals.

Linear frequency modulation (LFM) signal is widely used in pulse compression radars, whereas faced with the time delay bias caused by Doppler shift of radar echoes, which must be accounted for in some applicative occasions where the linear frequency modulation ratio is very low or Doppler shift is very large. The method of time delay estimation based on cross-ambiguity function (CAF) could solve the problem but need two-dimensional search around the entire time delay and Doppler shift plane, which increases computational complexity heavily and brings great challenge to real-time processing. An effective time delay estimation method is proposed in this paper based on the relationship of time delay and Doppler shift, which can reduce two-dimensional search to one-dimensional search along LFM signal energy line, and diminish the computation complexity greatly with the same performance of parameters estimation. Simulations proved the validity of the method proposed.