Parameter Optimization of Generalized S Transform Based on Improved Genetic Algorithm

The mostly applicable radar signal is pulse signal with linear frequency modulation (LFM). The main feature such signal is time-bandwidth product (so called base) which is calculated as product of pulse duration and signal bandwidth. Theoretical peak to sidelobe level is achievable with time-bandwidth product value grater than 100. For time-bandwidth product smaller then 100 (i.e. short pulse duration or narrow deviation of FM modulation) peak-to-sidelobe level (PSL) and pulse compression coefficient are significantly reduced. Non-linear frequency modulated (NLFM) radar signal for small time-bandwidth product features better PSL and pulse compression coefficient. The NLFM signal synthesis algorithm and simulation results are presented in the paper. LFM and NLFM signals with small time-bandwidth product are compared and results are discussed in aspect of radar resolution improvement.

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.

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.

Microwave interferometer is one of the devices for measuring the movement travel– –varying or time-varying velocity of projectile in bore. Microwave interferometer first obtains the Doppler echo signal including the motion information of the projectile in bore, then the velocity is measured based on instantaneous frequency estimation (IFE) of the processed and transformed signal. The parametric time-frequency analysis method can make spectral energy of nonlinear frequency modulation (FM) signal concentrate at some range in the new transform domain. As the motion echo signal of projectile in bore (MSPB) is a nonlinear FM signal, it could be described by polynomial chirplet, one of polynomial FM signal modes, which is used to construct transform kernel for the signal. In this paper, Polynomial chirplet transform (PCT) method is proposed to analyze the simulation and experiment echo signals of projectile in bore. The estimation error and Renyi entropy are used to measure quantify of the time-frequency distribution. Compared with short-time Fourier transform (STFT) method and Wigner-Ville distribution (WVD) method, our results show that the PCT method has most powerful anti-interference performance and highest accuracy of instantaneous frequency estimation for the simulation signal, and lowest Renyi entropy of the instantaneous frequency estimation for the experiment signal. In general, the PCT method has powerful anti-interference performance and high time-frequency concentration and accuracy of instantaneous frequency estimation for the motion echo signal of projectile in bore.

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.

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.

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.

In synthetic aperture radar (SAR) imaging, geometric resolution, sidelobe level (SLL) and signal-to-noise ratio (SNR) are the most important parameters for measuring the SAR image quality. The staring spotlight mode continuously transmits signals to a fixed area by steering the azimuth beam to acquire azimuth high geometric resolution, and its two-dimensional (2D) impulse response with the low SLL is usually obtained from the 2D weighted power spectral density (PSD) by the selected weighting window function. However, this results in the SNR reduction due to 2D amplitude window weighting. In this paper, the staring spotlight SAR with nonlinear frequency modulation (NLFM) signal and azimuth non-uniform sampling (ANUS) is proposed to obtain high geometric resolution SAR images with the low SLL and almost without any SNR reduction. The NLFM signal obtains non-equal interval frequency sampling points under uniform time sampling by adjusting the instantaneous chirp rate. Its corresponding PSD is similar to the weighting window function, and its pulse compression result without amplitude window weighting has low sidelobes. To obtain a similar Doppler frequency distribution for low sidelobe imaging in azimuth, the received SAR echoes are designed to be non-uniformly sampled in azimuth, in which the sampling sequence is dense in middle and sparse in both ends, and azimuth compression result with window weighting would also have low sidelobes. According to the echo model of the proposed imaging mode, both the back projection algorithm (BPA) and range migration algorithm (RMA) are modified and presented to handle the raw data of the proposed imaging mode. Both imaging results on simulated targets and experimental real SAR data processing results of a ground-based radar validate the proposed low sidelobe imaging mode.

Linear Frequency Modulation (LFM) is a pulse compression method which is largely implemented in the radar applications. The high peak sidelobe is its main problem instead of its superiority on the simplicity and Doppler tolerance characteristics. The curve-shaped Nonlinear Frequency Modulation (NLFM) has been developed for overcoming this lack and prior investigation showed that this method provide lower sidelobe suppression than LFM. For obtaining the overall performance to be compared with LFM method, this research will investigate the curve-shaped NLFM in the case of Doppler effects and high level background noise. The Doppler effects considered in this research consist of two including center frequency shift and time dilation. Then, the background noise investigated is Gaussian distributed noise with signal to noise ratio (SNR) levels in range 0dB to −20dB. According to the simulation results, in the Doppler shift case, the curve-shaped NLFM is more sensitive than LFM as other NLFM drawbacks. However, this method is better than LFM in the time dilation scenario. Then, this pulse compression also has better detectability than LFM in the certain case of high level background noise condition.

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.

For the analysis of multi-component non-stationary linear frequency modulation (LFM) signals based on the high-resolution time-frequency distribution (TFD), an adaptive compact kernel-based TFD (ACKD) is presented in this paper. In the proposed ACKD, the signal is firstly represented in the ambiguity domain and then convolved with an optimal signal-dependent adaptive compact kernel. This kernel is designed based on the pre-estimation parameters which is related with the energy distribution directions and lengths of the auto-terms in the ambiguity domain. The Boashash-Sucic normalized instantaneous resolution performance measure method is used to evaluate and make comparisons. Simulation results are displayed to justify the feasibility and validity of the proposed method. In all presented cases, compared with the Wigner-Ville distribution (WVD) and the classical CKD, the proposed ACKD shows a significant performance improvement in terms of the cross-interferences rejection and energy concentration of component signals around their respective instantaneous frequency (IF).

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.

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.