Yingning Peng

Radon-Fourier Transform for Radar Target Detection, I: Generalized Doppler Filter Bank

Based on the coupling relationship among radial velocity, range walk, and Doppler frequency of the moving targets echoes, a novel method is proposed, i.e., Radon-Fourier transform (RFT), to realize the long-time coherent integration for radar target detection. The RFT realizes the echoes spatial-temporal decoupling via joint searching along range and velocity directions, as well as the successive coherent integration via the Doppler filter bank. Besides, four equivalent RFTs are obtained with respect to the different searching parameters. Furthermore, a generalized form of RFT, i.e., generalized Radon-Fourier transform (GRFT), is also defined for target detection with arbitrary parameterized motion. Due to the similarity between the RFT and the well-known moving target detection (MTD) method, this paper provides detailed comparisons between them on five aspects, i.e., coherent integration time, filter bank structure, blind speed response, detection performance, and computational complexity. It is shown that MTD is actually a special case of RFT and RFT is a kind of generalized Doppler filter bank processing for targets with across range unit (ARU) range walk. Finally, numerical experiments are provided to demonstrate the equivalence among four kinds of RFTs. Also, it is shown that the RFT may obtain the coherent integration gain in the different noisy background and the targets blind speed effect may be effectively suppressed. In the meantime, both the weak target detection performance and the radar coverage of high-speed targets may be significantly improved via RFT without change of the radar hardware system.

MIMO Radar Waveform Design in Colored Noise Based on Information Theory

In this paper, we consider multiple input multiple output (MIMO) radar waveform design in colored noise. Two information theoretic measures are used as criterions for optimal waveform design under transmitted power constraint. The first one is by maximizing the mutual information between target impulse response and target echoes; the second one is by maximizing the relative entropy between two hypotheses: in the first hypothesis we assume the target is not present in the echoes while in the second hypothesis we assume the target exists in the echoes. We derive optimal solutions for both cases. Interestingly, both optimal solutions require that transmitted waveform should “match” with the target and noise. However, the optimal solutions of the two problems lead to different power allocation strategies.

Radar Maneuvering Target Motion Estimation Based on Generalized Radon-Fourier Transform

The slant range of a radar maneuvering target is usually modeled as a multivariate function in terms of its illumination time and multiple motion parameters. This multivariate range function includes the modulations on both the envelope and the phase of an echo of the coherent radar target and provides the foundation for radar target motion estimation. In this paper, the maximum likelihood estimators (MLE) are derived for motion estimation of a maneuvering target based on joint envelope and phase measurement, phase-only measurement and envelope-only measurement in case of high signal-to-noise ratio (SNR), respectively. It is shown that the proposed MLEs are to search the maximums of the outputs of the proposed generalized Radon-Fourier transform (GRFT), generalized Radon transform (GRT) and generalized Fourier transform (GFT), respectively. Furthermore, by approximating the slant range function by a high-order polynomial, the inherent accuracy limitations, i.e., the Cramer-Rao low bounds (CRLB), and some analysis are given for high order motion parameter estimations in different scenarios. Finally, some numerical experimental results are provided to demonstrate the effectiveness of the proposed methods.

Orthogonal complex filter banks and wavelets: some properties and design

Previous wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases offer a number of potential advantageous properties. For example, it has been suggested that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property, then it must exhibit linear phase as well. In this paper, we prove that a linear-phase complex orthogonal wavelet does not exist. We study the implications of symmetry and linear phase for both complex and real-valued orthogonal wavelet bases. As a byproduct, we propose a method to obtain a complex orthogonal wavelet basis having the symmetry property and approximately linear phase. The numerical analysis of the phase response of various complex and real Daubechies wavelets is given. Both real and complex-symmetric orthogonal wavelet can only have symmetric amplitude spectra. It is often desired to have asymmetric amplitude spectra for processing general complex signals. Therefore, we propose a method to design general complex orthogonal perfect reconstruct filter banks (PRFBs) by a parameterization scheme. Design examples are given. It is shown that the amplitude spectra of the general complex conjugate quadrature filters (CQFs) can be asymmetric with respect the zero frequency. This method can be used to choose optimal complex orthogonal wavelet basis for processing complex signals such as in radar and sonar.

Doppler Keystone Transform: An Approach Suitable for Parallel Implementation of SAR Moving Target Imaging

In this letter, a synthetic aperture radar (SAR) data reformatting approach named Doppler keystone transform (DKT) is proposed to correct the range migration of a moving target. By using the DKT, the SAR imaging program, i.e., the 2-D matched filtering, can be transformed into separate 1-D operations along range or azimuth direction, and therefore, the DKT is suitable for the parallel implementation of SAR imaging of the moving target. Our simulations show that by combining the DKT and the Doppler phase compensation methods, the moving target can be well imaged in high signal-clutter-ratio case.

Radon-Fourier Transform for Radar Target Detection (III): Optimality and Fast Implementations

As a generalized Doppler filter bank processing, Radon-Fourier transform (RFT) has recently been proposed for long-time coherent integration detection of radar moving targets. The likelihood ratio test (LRT) detector is derived here for rectilinearly moving targets. It is found that the proposed LRT detector has the identical form as the existing RFT detector, which means that the RFT detector is an optimal detector for rectilinearly moving targets under the white Gaussian noise background. For the fast implementations of the RFT detector, instead of the joint 2-D trajectory searching and coherent integration in pulse-range domain, the 1-D fast Fourier transform (FFT)-based frequency bin RFT (FBRFT) method is proposed in the pulse-range frequency domain without loss of integration performance. Moreover, at the cost of a controllable performance loss, a suboptimal approach called subband RFT (SBRFT) is also proposed to reduce the storage memory. It is shown that not only the long-time coherent integration gain can be obtained via the proposed SBRFT, but also the computational complexity and memory cost can be reduced to the level of the conventional Doppler filter banks processing, e.g., moving target detection (MTD). Some numerical experiments are also provided to demonstrate the effectiveness of the proposed methods.

Location and Imaging of Moving Targets using Nonuniform Linear Antenna Array SAR

By using a linear antenna array, velocity synthetic aperture radar (VSAR) can detect, focus, and locate slowly moving targets well. However, it may mis-locate fast moving targets in the azimuth (cross-range) direction. In this correspondence, we propose a synthetic aperture radar (SAR) with a nonuniform linear antenna array and give a design of the antenna arrangement. It is shown that our proposed nonuniform linear antenna array SAR (NULA-SAR) can locate both slowly and fast moving targets correctly. An integrated NULA-SAR algorithm for moving target imaging is also presented, and it is verified by some simulations.

A Velocity Estimation Algorithm of Moving Targets using Single Antenna SAR

A new algorithm is proposed for velocity estimation of moving targets in single antenna synthetic aperture radar (SAR). Based on the fact that different velocity vectors cause different geometrical figures of the two-dimensional (2-D) signature in the range-Doppler (RD) domain, this algorithm estimates the azimuth and range velocities by a 2-D search such that the range cell migration correction (RCMC) and the second range compression (SRC) are correctly performed. It is shown that, using the proposed algorithm, the Doppler ambiguity problem can be avoided and satisfactory accurate velocity estimation can be obtained in high signal-to-clutter ratio (SCR) scenarios.

Ground Moving Target Signal Analysis in Complex Image Domain for Multichannel SAR

For along-track multichannel synthetic aperture radar, this paper proposes a novel ground moving target signal model in the high-resolution complex image domain. Based on the range-Doppler imaging of static scene, the 2-D complex response of an isolated rectilinearly moving target is derived via the stationary phase principle (SPP) approximations. It is shown that moving targets in complex domain can be divided into three types according to the 2-D motion distribution and the SPP approximation conditions. Different from the known peaklike response of a static target, different amplitude and phase modulations will appear for different types of moving targets. Moreover, a single target can be split into two targets in the image when its Doppler spectrum spreads over two ambiguous Doppler zones. All types of targets will have the same Doppler interferometric effect along multichannel images, which is decided by the targets ambiguous Doppler frequency. Furthermore, with the proposed signal model, the complex image properties can be completely described and analyzed. Finally, some numerical experiments are also provided to demonstrate the effectiveness of the proposed signal model and analysis.

Bistatic Linear Antenna Array SAR for Moving Target Detection, Location, and Imaging With Two Passive Airborne Radars

In this paper, we propose a bistatic linear array synthetic aperture radar (BLA-SAR) system for moving target detection, location, and imaging. In the BLA-SAR system, a geostationary satellite is used as a transmitter, and two airborne linear array radars are used as passive receivers, where the transmitted waveforms from the geostationary satellite may have two different carrier frequencies, two linear array antennas on two different airplanes may be equipped with different spacings, or two airplanes may fly with two different velocities. It is shown that, using the BLA-SAR, not only the stationary clutter can be suppressed but also locations of both slow and fast moving targets can be accurately estimated. Furthermore, an effective BLA-SAR algorithm of moving target imaging is also proposed. Lastly, some numerical experiments are given to demonstrate the effectiveness of the BLA-SAR