Wideband Linear Frequency Modulation Research Articles

Studies on High-Resolution Airborne Synthetic Aperture Radar Image Formation with Pseudo-Random Agility of Interpulse Waveform Parameters

By means of alteration of the transmitted linear frequency modulation (LFM) signal waveform parameters, such as pulse width or chirp rate, initial phase, pulse repetition interval (PRI), and chirp rate polarity at every position of synthetic apertures, the pseudo-random agility technology of interpulse waveform parameters in airborne Synthetic Aperture Radar (SAR) actively increases the complexity and uncertainty of radar waveforms. This technology confuses jamming interception receivers, thus improving its anti-interference ability for active coherent jamming, which is one of the main research interests of airborne SAR technology. But the pseudo-random agility technology for interpulse waveform parameters faces certain challenges of large computation and complex system design, which need to be further studied and solved. To address these issues, a processing scheme of high-resolution SAR image formation which is appropriate for agile interpulse waveform parameters is proposed in this paper. This method can deal with multiple agile parameters, not only single ones as in most existing literature. Its computation load is nearly comparable to that of traditional SAR image formation with constant waveform parameters. The high-resolution SAR imaging results obtained by processing SAR raw data with agile interpulse waveform parameters demonstrate the effectiveness of the proposed method. In addition, real SAR images with resolutions of 0.5 m and 0.15 m, which are rarely found in the public literature, are shown under the circumstance of randomly changing the transmitted wideband LFM signal pulse parameters one by one.

Calibration of Wideband LFM Radars Based on Sliding Window Algorithm

This paper addresses the challenges of wideband signal beamforming in radar systems and proposes a new calibration method. Due to operating conditions, the frequency-dependent characteristics of the system can be changed, and the amplitude, phase, and time delay error can be generated. The proposed method is based on the concept of the sliding window algorithm for linear frequency modulated (LFM) signals. To calibrate the frequency-dependent errors from the transceiver and the time delay error from the true time delay elements, the proposed method utilizes the characteristic of the LFM signal. The LFM signal changes its frequency linearly with time, and the frequency domain characteristics of the hardware are presented in time. Therefore, by applying a matched filter to a part of the LFM signal, the frequency-dependent characteristics can be monitored and calibrated. The proposed method is compared with the conventional matched filter-based calibration results and verified by simulation results and beampatterns. Since the proposed method utilizes LFM signal as the calibration tone, the proposed method can be applied to any beamforming systems, not limited to LFM radars.

Spatial deception suppression for wideband linear frequency modulation signals based on fractional Fourier transform with robust adaptive beamforming

Wideband linear frequency modulation (LFM) signal is popular for target detection and imaging in wideband array radar systems. In this paper, a novel and robust adaptive wideband digital beamforming (DBF) algorithm is proposed for suppressing the deception jamming of wideband LFM signals. Firstly, wideband LFM echoes are treated as narrowband signals using fractional Fourier transform (FrFT) with a specific order. Secondly, a robust and adaptive narrowband DBF method based on steering vector estimation, covariance matrix reconstruction, and low-pass filtering are applied to suppress deception jamming. Finally, the inverse FrFT is performed to transform the processing results back to the time-domain wideband signals. Compared with the conventional time- and frequency-domain wideband beamformers, the proposed algorithm significantly reduces the amount of calculation and computational complexity. The simulation results indicate that the proposed algorithm can effectively suppress deception jamming, and its interference suppression capability is approximately like that of an optimal beamformer. Furthermore, the validity and effectiveness of the proposed algorithm are verified with the experimental data in a microwave anechoic chamber.

Photonic-Assisted Wideband Frequency Down-Converter With Leakage Cancellation and Image Rejection for FMCW Radar Receiver

Frequency modulated continuous wave (FMCW) radars with de-chirping receivers can achieve high resolution and real-time microwave imaging. However, the inherent leakage interference from transmitter to receiver and image interference from image frequencies will degrade sensitivity and dynamic range of the receiving system. In this paper, a novel photonic-assisted down-converter based on a dual-polarization binary phase-shift keying (DP-BPSK) modulator, which can achieve leakage cancellation and image rejection concurrently for wideband linear frequency modulated (LFM) signals, is proposed and demonstrated. Both theoretical analysis and simulation verification are performed. Considering this scheme in the application of a radar receiver, the leakage signal, signal of interest, and image signal are emulated as wideband LFM signals with 2GHz bandwidth centered at 20, 21, 19GHz. The simulation results show an excellent leakage cancellation depth and image rejection depth of 54dB and 53.5dB respectively. The proposed scheme can be applied in an FMCW radar receiver so as to optimize the detection performance.

A Method Against Interrupted Sampling Repeater Jamming Based on Genetic Algorithm and Compressed Sensing Reconstruction

By analyzing the discontinuous character in time domain, a jamming suppression method is propose to counter Interrupted sampling reperter jamming(ISRJ, which is an effective coherent jamming to wide-band linear frequency modulation signal. The discontinuous character of ISRJ and the instantaneous frequency change rule after stretch is firstly analyzed. Secondly, by controlling the adjustment parameters, the generalized S transform is utilized to obtain the time-frequency grayscale image of received signal. Then, the grayscale image can be segmented by using genetic algorithm to construct a time-domain filter, and the time-domain filter can be used to extract the echo band without jamming signal. Finally, the extracted signal is used as compressed data to construct a compressed sensing minimization model, and the compressed sampling matching pursuit algorithm is used to reconstruct the target echo signal. Simulation shows that this method has good jamming suppression performance.

Analytical Model and Real-Time Calculation of Target Echo Signals on Wideband LFM Radar

In wideband radar system testing and performance evaluation, target echo simulation should simultaneously meet real-time and high-precision requirements. In this paper, we focus on the wideband linear frequency modulated (LFM) radar signal, derive the echo signal time-domain analytical expression based on the multiscattering center model and propose a high-precision real-time echo simulation calculation method. Regarding the low model reliability and poor versatility problems in the current wideband radar target calculation, the analytical model proposed here truly reflects the inner-pulse modulation characteristics of the radar transmit signal and the wideband electromagnetic scattering characteristics of the target. Current wideband radar target signal calculation accuracy and real-time performance are also difficult to balance. Considering this problem, the wideband radar target echo analytical model proposed in this paper avoids the large amount of calculations required for the full numerical calculation and effectively improves the calculation accuracy and real-time performance of wideband radar target echo signal calculations without reducing calculation accuracy. The real-time calculation method involves elaborate amplitude-phase control. Simulation analysis and experimental verification confirmed the reliability and validity of these results. These research results have important theoretical significance and practical application value in the field of hardware-in-the-loop simulation.

Processing Continuous Active Sonar Transmissions to Achieve an Arbitrarily Fast Update Rate With Full Instantaneous Bandwidth

A processing technique for continuous active sonar (CAS) that uses linear frequency modulation (LFM) waveforms is presented. LFM CAS employs wideband long-duration LFMs with 100% transmit duty cycle. The received signals are typically processed in sub-bands by forming a sequence of matched-filter replicas that correspond to consecutive segments of the full waveform; this increases the update rate of the sonar at the cost of decreased performance in each sub-band due to the decrease in processing bandwidth and duration (energy). The algorithm presented in this article achieves fast updates by forming a sequence of unique matched-filter replicas through a number of circular shifts to the transmitted LFM, resulting in processing across the frequency jump between pings. This approach allows increased processing duration and bandwidth (up to the full duration/bandwidth of the LFM) at the cost of reduced independence between updates. The circular-shift algorithm is mainly considered in the limit where the full duration and bandwidth of the waveform are exploited to provide partially independent detection and ranging opportunities. The update rate can be arbitrarily chosen independent of processing duration. The algorithm is validated with sonar data from the LCAS15 sea trial.

Fractional Fourier transform based underwater multi-targets direction-of-arrival estimation using wideband linear chirps

In underwater applications, linear chirp signal with linearly instantaneous frequency over the signal bandwidth also known as a linear frequency modulated (LFM) signal is often used in active sonar to realize direction of arrival (DOA) estimation of targets. For this kind of wideband signal, traditional array signal processing method firstly transforms the time domain signal into frequency domain using fast Fourier transform (FFT) and then does beamforming for each sub-band. Different from FFT based signal processing method, this paper uses fractional Fourier transform (FRFT) for preprocessing of wideband LFM signals. By FRFT preprocessing, the wideband LFM signals are transformed into narrowband signals in the fractional Fourier domain, avoiding the influence of cross-interference terms. This paper compares the performance of FRFT based DOA estimation using conventional beamforming (CBF), minimum variance distortionless response (MVDR) and robust Capon beamforming (RCB) respectively. Then the revised RCB (RRCB) algorithm is proposed to solve the DOA estimation problem with a small number of snapshots. Simulations are carried out for single target and multi-targets DOA estimation using FFT based and FRFT based array signal processing method respectively. Simulation results show that FRFT based array signal processing method can achieve much narrower main lobe and higher main-to-side lobe ratio in low signal-to–noise ratio conditions. Besides, it can realize accurate DOA estimation of two adjacent targets while FFT based array signal processing method fails.

Determination of Fast-Moving Objects’ Speed and Range with Linear Frequency Modulation Continuous Wave Radar Using Autocorrelation Scheme

Introduction. A hardware basis of modern Advanced Driver Assistance Systems (ADAS) consists of millimeterrange radars, characterized by a relatively short range (meters – tens of meters). At the same time, improving of traffic safety requires to increase the range at least to several hundred meters. The one way to achieve such values is to increase wavelength of a probing signal, to use the centimeter range of wavelengths, for example. The paper represents a detailed description of main steps of signal processing algorithm in the model of the ADAS low-power centimeter range radar, which provides fast-moving objects speed and range definition.Aim. Development of an algorithm for estimating the range and the speed of targets by an autocorrelation radar with a wide-band continuous linear frequency modulation (linear FM) signal in order to increase the rate of the ADAS system estimates formation.Materials and methods. The proposed algorithm is based on the methods of primary and secondary digital processing of radar signals. The model of a centimeter-range autocorrelation radar with a broadband continuous linear FM probing signal was used for practical researches. MATLAB software was used to process the received signal samples.Results. The algorithm has been developed to determine the speed and the range of fast-moving objects in conditions when their movement during the evaluation interval significantly exceeds the radar range resolution. The use of simplified Kalman filtering for inter-period secondary signal processing allowed to increase significantly the stability of the algorithm. In a full-scale experiment using the low-power radar model with continuous radiation of the centimeter range, it was shown that a stable assessment of a real car speed and range was provided at a distance of at least about one kilometer.Conclusion. The results of the field experiment make it possible to draw conclusions that the proposed algorithm is highly robust even in the absence of inter-period secondary processing. Its usage allows one to improve the stability of the algorithm without considerable additional computational costs. It is possible because near-linear dynamics of the observation object and of the radar carrier makes it sufficient to use a simplified implementation of Kalman filter in the form α-β-algorithm.

Fast algorithm for 3D wideband LFM source localisation based on time delay under a uniform circular array

Traditional localisation technologies for wideband linear frequency modulation (LFM) source are always confined to the far-field situation and suffer from high computational cost for dealing with multiple sub-narrowband components. In this study, by performing temporal delay-and-correlation to wideband LFM signals, a fast and closed-form algorithm based on phase differences is proposed for three-dimensional (3D) source localisation (azimuth angle, elevation angle, and range) under a uniform circular array. First, the cross-correlation of the array outputs with their temporally delayed version is calculated to develop a new single-frequency signal model. Then, the phase differences of adjacent sensors’ transformed outputs are exploited to construct indefinite equations. After that, the least-square method is employed to estimate the source's 3D parameters simultaneously. Moreover, theoretical analysis and numerical examples show the aperture restriction in avoiding ambiguity can be relaxed under the new signal model. Finally, simulations demonstrate the effectiveness and advantages of the proposed algorithm.

An improved multiplication modulation deception jamming method for countering ISAR

This paper proposes a dechirping multiplication modulation jamming method for countering ISAR. The wideband linear frequency modulation (LFM) signal is converted into a single-tune signal after the dechirping and extraction process. We use the high resolution range profile (HRRP) of the target as the template and it is performed a fast Fourier transform to generate the modulation signal. Then the radar signal is multiplied by the modulation signal pulse by pulse to derive the baseband jamming signal. At last the jamming signal is conducted Chirp transform to derive the jamming signal in wideband formation. In contrast to the conventional convolution method, the proposed algorithm not only reduces the hardware complexity and computation load, but also exhibits a simply and flexible structure which can be implemented in FPGA. Both the simulation result and the measured data illuminate the validity of the proposed method.

DOA estimation of LFM sources based on time-frequency interferometer in UCA

Based on the time-frequency (t-f) interferometer of the uniform circular array (UCA), a new direction of arrival (DOA) estimation algorithm of multiple linear frequency modulation (LFM) sources is proposed. Firstly, the cross smoothed pseudo Wigner-Ville distribution (SPWVD) of the elements’ output is calculated and the single source t-f points are selected by using a “noise threshold” procedure and cluster based algorithm. Then, by selecting different groups of sensor pairs, the proposed algorithm can solve the phase ambiguity of the t-f points by using a focusing based algorithm. And a lookup table based ambiguity resolution algorithm is also presented to reduce the computational complexity. The simulation results illustrate that the proposed t-f interferometer can be applied to multiple wideband LFM sources and it also can improve the DOA estimation precision compared with the traditional phase interferometer and sub-band interferometer. Especially in the low signal to noise ratio (SNR) and limited snapshots situations, the estimation root mean square errors (RMSEs) of the proposed algorithm are also within 3°.

Robust wideband beamforming method for linear frequency modulation signals based on digital dechirp processing

This study presents a robust digital beamforming (DBF) method for wideband digital array radar, which uses linear frequency modulation (LFM) waveforms. Firstly, received signals are digitally dechirped, followed by narrowband filtering and decimation. Then the authors generate time-variant factors to compensate phase perturbations induced by the dechirp processing. It is proved that the wideband LFM signals can be treated as narrowband signals after compensation. Finally, a robust adaptive narrowband DBF method based on uncertain set constraints and interference-plus-noise matrix reconstruction is applied to suppress the interferences. The proposed method is computationally efficient and feasible for real-time applications. It behaves robustly in the presence of direction of arrival estimation errors across a wide range of signal-to-noise ratios. Simulations demonstrate the effectiveness and feasibility of the proposed method.

Off-Grid DOA Estimation for Wideband LFM Signals in FRFT Domain Using the Sensor Arrays

For the direction-of-arrival (DOA) estimators based on sparse signal representation, the feasibility and precision are greatly restricted by the inherent limitation of the predefined spatial discrete grids. In this paper, based on the high aggregation characteristic of wideband linear frequency modulation signals, we derive the modified fractional domain sparse model (MFDSM) in DOA estimation and propose a novel off-grid DOA estimation method via alternating descent iteration (OGDEADI). The simulation results show that our proposed MFDSM-OGDEADI method has enhanced estimation accuracy and better angular resolution in terms of signal-to-noise ratio, angle difference, grid size, and angle bias, and it also has the advantage of being less sensitive to the grid size.

Sub-Nyquist Sampling and Parameters Estimation of Wideband LFM Signals Based on FRFT

Last years, most sub-Nyquist sampling and parameters estimation methods for linear frequency modulated (LFM) signals are based on compressed sensing (CS) theory. However, nearly all CS reconstruction algorithms are with high computational complexity and difficult to be implemented in hardware. In this paper, a novel framework of sub-Nyquist sampling and low-complexity parameters estimation for LFM signals is proposed. The incoherent sampling in CS theory is introduced into the construction of sub-Nyquist sampling system, but no CS reconstruction algorithm is employed in the estimation of parameters. Based on the energy aggregation of LFM signals in the proper fractional Fourier transform (FRFT) domain, the chirp rate and center frequency can be estimated by linear operations. Accordingly, the proposed estimation method is easily realized compared with existing estimation methods based on CS. Simulation results verify its effectiveness and accuracy.

Photonics-based coherent wideband linear frequency modulation pulsed signal generation.

A photonics-based scheme is proposed to generate wideband linear frequency modulation pulses with broadly tunable carrier frequencies for coherent radars. The approach integrates the concept of the microwave-photonic multiplication and coherent beating to enable reconfiguration of the bandwidth and carrier frequency of the generated pulses. The phase fluctuation between two beating arms is suppressed by a stabilization technique based on an optical phase-locked loop to maintain the pulse-to-pulse phase coherence. Further, we also demonstrate a coherent radar system, including the generation, wireless transmission and detection of the radar echo signal in the Ka-band. The coherent integration of several echo signals is achieved. About 8dB of signal-to-noise ratio improvement is obtained with every ten-fold of integration times. The range resolution of the radar system is ∼3.75 cm, which is close to the theoretical prediction.

Radar wideband digital beamforming based on time delay and phase compensation

ABSTRACTIn conventional phased array radars, analogue time delay devices and phase shifters have been used for wideband beamforming. These methods suffer from insertion losses, gain mismatches and delay variations, and they occupy a large chip area. To solve these problems, a compact architecture of digital array antennas based on subarrays was considered. In this study, the receiving beam patterns of wideband linear frequency modulation (LFM) signals were constructed by applying analogue stretch processing via mixing with delayed reference signals at the subarray level. Subsequently, narrowband digital time delaying and phase compensation of the tone signals were implemented with reduced arithmetic complexity. Due to the differences in amplitudes, phases and time delays between channels, severe performance degradation of the beam patterns occurred without corrections. To achieve good beamforming performance, array calibration was performed in each channel to adjust the amplitude, frequency and phase of the tone signal. Using a field-programmable gate array, wideband LFM signals and finite impulse response filters with continuously adjustable time delays were implemented in a polyphase structure. Simulations and experiments verified the feasibility and effectiveness of the proposed digital beamformer.

Dual-Band LFM Signal Generation by Optical Frequency Quadrupling and Polarization Multiplexing

A photonic approach to generating dual-band linear frequency modulation (LFM) signal is proposed based on optical frequency quadrupling and polarization multiplexing. This is achieved by using an integrated polarization multiplexing dual-parallel Mach-Zehnder modulator to perform frequency quadrupling in two orthogonal polarizations independently. After optical-to-electrical conversion, two LFM signals in different frequency bands can be generated simultaneously. The proposed scheme has a very simple and compact structure. Thanks to the frequency quadrupling technique, high-frequency, and wideband LFM signals can be generated with low speed electrical devices. The central frequency, bandwidth, and temporal duration of the generated LFM signals can be easily adjusted. In the experiment, the generation of dual-band LFM signals in K-band and Ka-band (centered at 20 and 30 GHz, respectively) is demonstrated. Tunability of the central frequency, bandwidth, and time duration is also verified. The proposed signal generator is a promising candidate in dual-band multi-function radar applications.

Implementation of wideband digital transmitting beamformer based on LFM waveforms

A wideband digital transmitting beamformer based on linear frequency modulation (LFM) signals is presented in this study. The wideband beamformer is realised as a combination of direct digital synthesisers and fractional delay (FD) filters in polyphase structure. By using coordinate rotation digital computer algorithm, high intermediate frequency wideband LFM signal is generated and phase compensation for beamforming is accomplished in field programmable gate array. The impact of different number of quantisation bits on signal generation is analysed. The results of waveform generation and FD filter design are given. At last, the transmitting beam pattern is simulated.

DOA estimation for wideband LFM signals with a few snapshots

The wideband linear frequency modulation (LFM) signals are widely used in information systems. The conventional direction-of arrival (DOA) estimation algorithms of LFM signals rely on a large number of snapshots, some of which are not reliable in numerous practical applications such as underwater array processing. To solve the above problem, we present a modified sparse iterative covariance (MSPICE)-based estimation method in fractional Fourier transform (FrFT) domain to estimate the DOA of wideband LFM signals. First, we extend the original SPICE algorithm in FrFT domain with a specific transform order for wideband LFM signals. Then, we utilize the energy centrobaric modification method to make the original SPICE more accurate without adding more computational complexity. The simulation results demonstrate the effectiveness of the proposed method.