Stepped Frequency Waveform Research Articles

Coherent stepped-frequency waveform generation based on recirculating microwave photonic frequency conversion.

We propose a novel method for generating coherent and wideband stepped-frequency waveforms using recirculating microwave photonic frequency conversion (MWP-FC). By injecting a narrowband signal into an MWP-FC loop utilizing a dual-parallel Mach-Zehnder modulator (DPMZM), the signal frequency is continuously converted to produce a stepped-frequency waveform with a wide bandwidth. Within the MWP-FC loop, photo-electric conversion is achieved based on self-mixing detection, where the optical phase noise can be suppressed, guaranteeing stability and coherence of the generated signal. In a proof-of-concept experiment, a stepped-frequency signal with a frequency interval of 2 GHz and a bandwidth of about 16 GHz and a stepped-frequency chirp signal with a frequency interval of 3 GHz and a bandwidth of about 15 GHz are generated. In addition, coherence of the generated signals is verified by coherent integration and de-chirping.

A New Method for Moving-Target HRRP via Double Step Frequency Verified by Simulation

The stepped-frequency (SF) waveform is highly sensitive to the target motion, which induces range shift and echo spread in a high-range-resolution profile (HRRP). This paper proposes a method based on a cross-transmitted double-stepped frequency (DSF) waveform and the phase-cancellation technique. The proposed method obtains the stationary HRRP of the moving targets according to the inverse discrete Fourier transform (IDFT) and complex multiplication. The results also show that the proposed method eliminates the generated false peaks from the existing methods. As a result, the obtained signal-to-noise ratio (SNR) of the HRRP using the proposed method is improved. Due to the cross-transmitted DSF waveform application, the proposed method adapts to higher speed targets. The analysis and simulation results validate the effectiveness of the proposed approach.

Contactless Monitoring Technique for Live Shielded Cable via Stepped-Frequency Waveform Reflectometry and Inductive Coupler

Low-voltage shielded cables serve critical roles in controlling and measuring advanced power systems to ensure their reliability and safety. As a consequence, it is important to monitor the cables. However, conventional monitoring techniques for nonoperating power systems are limited regarding safety issues that eventually affect the reliability of a power system and result in economic losses. In this article, a contactless signal communication approach via an inductive coupler is applied to stepped-frequency waveform reflectometry to monitor operating power systems. Additionally, a long short-term memory (LSTM)-based neural network model is adapted to compensate for the nonlinear distortion in signals yielded by couplers. Compared to conventional approaches, LSTM has advantages, as it can restore the nonlinearities of couplers because it can respond to various nonlinear factors, such as the dimension of the coupler, the length of the cable, or the position of the signal application. The proposed reflectometry system for monitoring live shielded cables is tested on 75-m 2-core shielded cables with two cases of fault simulations, and the efficacy of the proposed technique in real fields is also verified.

MIMO Radar Sparse Recovery Imaging with Wideband Interference Prediction

Multiple-input multiple-output (MIMO) radar three-dimensional (3D) imaging is widely applied in military and civil fields. However, MIMO is easily affected by wideband interference (WBI). To solve this problem, in this study, we propose a sparse recovery imaging method with WBI prediction based on the predictive recurrent neural network (PredRNN) and the tensor-based smooth L0 (TSL0) algorithm. Firstly, we extract the time-frequency (TF) feature of the historical measured WBI via the short-time Fourier transform (STFT) operation. In this way, we can use PredRNN to exploit the spatiotemporal correlation of the WBI in the TF domain to predict the TF feature of the WBI in the future. Then, we adaptively design the random sparse stepped frequency waveform by selecting non-overlapped frequencies with the WBI according to the predicted WBI TF feature. Finally, we apply the TSL0 algorithm to reconstruct the 3D high-resolution target image from the sparse signal cube. Simulation results show the high performance and robustness of the proposed imaging method in the presence of different WBIs.

Open-Loop Distributed Beamforming Using Wireless Phase and Frequency Synchronization

Coordinating the operations of separate wireless systems at the wavelength level can lead to significant improvements in wireless capabilities. We address a fundamental challenge in distributed radio frequency system cooperation—inter-node phase alignment—which must be accomplished wirelessly and is particularly challenging when the nodes are in relative motion. We present a solution to this problem that is based on a novel technique combining high-accuracy ranging and frequency transfer. We demonstrate the system in the first fully wireless open-loop coherent distributed beamforming experiment. Inter-node range estimation to support phase alignment was performed using a two-tone stepped frequency waveform (TTSFW) with a single pulse, while a two-tone waveform was used for frequency synchronization. The approach was implemented on a two-node dynamic system using Ettus X310 software-defined radios (SDRs), with coherent beamforming at 1.5 GHz.

Stepped Frequency Waveform Optimization for Formation Targets Detection

Formation targets have the characteristics of close distance, RCS difference and strong motion correlation. Radar should have enough resolution and anti-jamming ability to detect formation targets in the complex electromagnetic environment. The stepped frequency signal can be synthesized into a large bandwidth signal, so as to improve the range resolution and enhance the recognition performance of formation targets. In order to detect small targets next to large targets in formation targets, the signal needs to have low sidelobe characteristics. In this letter, we propose an optimized stepped frequency signal that can be synthesized into a large bandwidth with low autocorrelation sidelobes and a stopband to against narrowband interference. The proposed method can well detect small targets next to large target in formation, and has a certain narrowband anti-jamming ability. The simulation experiment results verify the advantages of the proposed waveform.

Detection and Characterization of Multiple Discontinuities in Cables with Time-Domain Reflectometry and Convolutional Neural Networks.

In this paper, a convolutional neural network for the detection and characterization of impedance discontinuity points in cables is presented. The neural network analyzes time-domain reflectometry signals and produces a set of estimated discontinuity points, each of them characterized by a class describing the type of discontinuity, a position, and a value quantifying the entity of the impedance discontinuity. The neural network was trained using a great number of simulated signals, obtained with a transmission line simulator. The transmission line model used in simulations was calibrated using data obtained from stepped-frequency waveform reflectometry measurements, following a novel procedure presented in the paper. After the training process, the neural network model was tested on both simulated signals and measured signals, and its detection and accuracy performances were assessed. In experimental tests, where the discontinuity points were capacitive faults, the proposed method was able to correctly identify 100% of the discontinuity points, and to estimate their position and entity with a root-mean-squared error of 13 cm and 14 pF, respectively.

Design and Processing Method for Doppler-Tolerant Stepped-Frequency Waveform Using Staggered PRF

Stepped-frequency waveform may be used to synthesize a wideband signal with several narrow-band pulses and achieve a high-resolution range profile without increasing the instantaneous bandwidth. Nevertheless, the conventional stepped-frequency waveform is Doppler sensitive, which greatly limits its application to moving targets. For this reason, this paper proposes a waveform design method using a staggered pulse repetition frequency to improve the Doppler tolerance effectively. First, a generalized echo model of the stepped-frequency waveform is constructed in order to analyze the Doppler sensitivity. Then, waveform design is carried out in the stepped-frequency waveform by using a staggered pulse repetition frequency so as to eliminate the high-order phase component that is caused by the target’s velocity. Further, the waveform design method is extended to the sparse stepped-frequency waveform, and we also propose corresponding methods for high-resolution range profile synthesis and motion compensation. Finally, experiments with electromagnetic data verify the high Doppler tolerance of the proposed waveform.

A sensing matrix optimization method for sparse random stepped-frequency signal based on autocorrelation function

Based on the theory of sensing matrix optimization and the characteristics of step frequency waveform, this paper proposes a sensing matrix optimization method for sparse random step frequency signal based on autocorrelation function. Firstly, on the basis of constructing sparse reconstruction model, the internal relationship between the waveform parameters of sparse random step frequency signal and the construction mode of sensing matrix is given. Secondly, the relationship between the mutual coherence matrix and the autocorrelation function matrix of signal is analyzed, and the conclusion that under specific conditions, these two matrices are the same. Therefore, the optimal design of sensing matrix is transformed into the optimal design of sparse random stepped frequency signal based on autocorrelation function. Finally, a sparse waveform design method based on the joint constraint of the maximum and average sidelobes of the autocorrelation function is proposed. Simulation experiments verify the relationship between the mutual coherence matrix and the autocorrelation function matrix of signal, and through waveform design, the sensing matrix optimization and the improving performance of signal sparse recovery are realized.

4D Automotive Radar Sensing for Autonomous Vehicles: A Sparsity-Oriented Approach

We propose a high-resolution imaging radar system to enable high-fidelity four-dimensional (4D) sensing for autonomous driving, i.e., range, Doppler, azimuth, and elevation, through a joint sparsity design in frequency spectrum and array configurations. To accommodate a high number of automotive radars operating at the same frequency band while avoiding mutual interference, random sparse step-frequency waveform (RSSFW) is proposed to synthesize a large effective bandwidth to achieve high range resolution profiles. To mitigate high range sidelobes in RSSFW radars, optimal weights are designed to minimize the peak sidelobe level such that targets with a relatively small radar cross section are detectable without introducing high probability of false alarm. We extend the RSSFW concept to multi-input multi-output (MIMO) radar by applying phase codes along slow time to synthesize a two-dimensional (2D) sparse array with hundreds of virtual array elements to enable high-resolution direction finding in both azimuth and elevation. The 2D sparse array acts as a sub-Nyquist sampler of the corresponding uniform rectangular array (URA) with half-wavelength interelement spacing, and the corresponding URA response is recovered by completing a low-rank block Hankel matrix. Consequently, the high sidelobes in the azimuth and elevation spectra are greatly suppressed so that weak targets can be reliably detected. The proposed imaging radar provides point clouds with a resolution comparable to LiDAR but with a much lower cost. Numerical simulations are conducted to demonstrate the performance of the proposed 4D imaging radar system with joint sparsity in frequency spectrum and antenna arrays.

Jamming Efficiency Analysis Based on the Range Profile of Target With Chaff

Chaff cloud is widely used in target covering. In this paper, a jamming performance estimation strategy is presented for the elliptical and cubic chaff clouds. The range profiles of the composite models of the plane with the chaff cloud are experimentally accessed in an anechoic chamber using a stepped-frequency waveform measurement system. Then, dimensions, characteristic length, and distributing entropy of the equivalent scattering centers of the plane and the jammer are extracted from the measured range profiles, respectively. Based on these features, support vector machines, naive Bayesian classification, and decision tree classification methods are employed to determine the recognition rate of the target under the chaff jamming, and then determine the jamming efficiency of the two kinds of chaff clouds. Results show that two types of chaff clouds are able to reduce the target recognition rate. Besides, when the radar uses the Euclidean distance and decision tree classification methods to complete the recognition task, a good jamming efficiency can be achieved by releasing the elliptical or the cubic chaff cloud. Meanwhile, a low level of jamming performance outcomes using the support vector machines classification method. It is also found that the chaff cloud released from the side of the plane achieves a better jamming performance compared with the other releasing locations. Finally, the influence of environmental noise on the recognition rate of the plane is studied. Estimating results show that the recognition rates decrease with the increasing of the power level of the noise. When the transmitting power level of the noise reaches 1.2 times the reflected power level of the target, it is quite hard to estimate the jamming performance of two kinds of chaff clouds.

Stepped Frequency Pulse Compression With Noncoherent Radar Using Deep Learning

A deep neural network (DNN) is used for achieving subpulse resolution in noncoherent stepped frequency waveform radar. The tradeoff between high resolution and long range in radar systems is often addressed using pulse compression, allowing both long pulses and high resolution by increasing the pulse bandwidth. This typically requires a coherent radar. In this article we present a deep learning-based solution for achieving subpulse resolution with a noncoherent radar. Our results for such a system are comparable to an equivalent coherent system for signal-to-noise ratios (SNRs) greater than 10 dB. All results are based on simulated data.

Front-Wall Clutter Removal in Through-the-Wall Radar Based on Weighted Nuclear Norm Minimization

The front-wall clutter removal in the case of the through-the-wall radar (TWR) system is studied in this work. To remove the wall clutter, its low-rank property is utilized, and at the same time, the sparse property of the target returns is exploited to perform target reconstruction. To account for the unparalleled setting of the antenna and the wall, a weighted nuclear norm minimization (WNNM) is employed, and the resulting problem is solved in an alternating manner. In addition, different transmitted waveform signals, including monofrequency and stepped-frequency waveforms, are used to demonstrate their effects on the clutter suppression performances. The experimental results show that the proposed WNNM with stepped-frequency waveform outperforms other approaches.

High-Accuracy Multinode Ranging For Coherent Distributed Antenna Arrays

The design and experimental implementation of a waveform for high-accuracy internode ranging in a coherent distributed antenna array is presented. Based on a spectrally sparse high-accuracy ranging waveform, the presented multifrequency waveform enables high-accuracy ranging between multiple nodes in an array simultaneously, without interference. The waveform is based on a unique time–frequency duplexing approach combining a stepped-frequency waveform with different step cycles per node pair. The waveform also inherently includes beneficial disambiguation properties. The ambiguity function of the waveform is derived, and theoretical bounds on the ranging accuracy are obtained. Measurements were conducted in software-defined radio-based nodes in a three-element distributed array, demonstrating high-accuracy unambiguous ranging between two slave nodes and one master node.

Algorithms for Locating and Characterizing Cable Faults via Stepped-Frequency Waveform Reflectometry

The paper presents algorithms to realize effectively and accurately the stepped-frequency waveform reflectometry (SFWR), i.e. the reflectometric technique based on the use of sinusoidal bursts. This technique is useful for monitoring the health status of connection cables, but has many other applications, like other reflectometric techniques. The paper outlines the theory of SFWR, highlighting the problems associated to the transient components in the reflected signals; presents a method to minimize the effect of the transients, estimating the frequency response function (FRF) of interest with very low systematic error; shows how to use the FRF to locate and characterize faults in cables; evaluates accurately, using simulated cables with exactly known characteristics, the errors associated to the proposed methods. Overall, the paper demonstrates how the SFWR technique can be effectively used for testing cables, and in general determine, via reflectometry, parameters of interest of transmission lines.

High-Accuracy Localization Using IEEE 802.11 WiFi Legacy Preamble

We explore the use of synchronization bits from a standard 802.11 preamble for high-accuracy localization. The multi-tone short training field present in 802.11 standards that use a Legacy preamble is investigated in comparison to a common remote sensing waveform known as the stepped frequency waveform that shares similar waveform characteristics to the preamble. We present the 802.11 standard and the connection to the stepped frequency waveform, derive the theoretical lower bound on the short training field, present a comparison of simulated results, and present experimental wireless measurements demonstrating ranging accuracies on the order of 1.9 mm.

Interference Mitigation in Automotive Radars Using Pseudo-Random Cyclic Orthogonal Sequences.

The number of small sophisticated wireless sensors which share the electromagnetic spectrum is expected to grow rapidly over the next decade and interference between these sensors is anticipated to become a major challenge. In this paper we study the interference mechanisms in one such sensor, automotive radars, where our results are directly applicable to a range of other sensor situations. In particular, we study the impact of radar waveform design and the associated receiver processing on the statistics of radar–radar interference and its effects on sensing performance. We propose a novel interference mitigation approach based on pseudo-random cyclic orthogonal sequences (PRCOS), which enable sensors to rapidly learn the interference environment and avoid using frequency overlapping waveforms, which in turn results in a significant interference mitigation with analytically tractable statistical characterization. The performance of our new approach is benchmarked against the popular random stepped frequency waveform sequences (RSFWS), where both simulation and analytic results show considerable interference reduction. Furthermore, we perform experimental measurements on commercially available automotive radars to verify the proposed model and framework.

Sparse Frequency Waveform Optimization for High-Resolution ISAR Imaging

The stepped-frequency waveform is usually used to synthesize a wideband signal in the radar imaging system. To reduce the amount of data and coherent pulse intervals (CPIs), as well as to improve antijamming abilities, the sparse stepped frequency is employed in the area of inverse synthetic aperture radar (ISAR) imaging. Nevertheless, the traditional sparse stepped linear frequency modulation waveform (SSLFMW) has a shortage of high grating lobes caused by missing frequency bands, resulting in a degradation of the ISAR imaging quality. Many methods have been proposed to reduce the effect of grating lobes by echo signal processing. However, the method of grating lobe reduction is rarely studied from the aspect of waveform optimization. In this article, a novel SSLFMW with the low grating lobes in the ISAR imaging system is proposed. By deriving the autocorrelation function (ACF), the relation between grating lobes and waveform parameters, including stepped-frequency and phase-coded elements, is established. An optimization method based on alternate iteration is designed to optimize waveform parameters and reduce grating lobes. Based on this optimized SSLFMW, we establish an ISAR imaging framework with the compressive sensing (CS) theory. Finally, the experiments are designed to show that the optimized SSLFMW has lower grating lobes. Both simulated and real measured data are used to prove that the optimized waveform has a better performance in the high-resolution range profile (HRRP) synthesis and ISAR imaging compared with the traditional SSLFMW.

Insulation Characteristics and Fault Analysis of HTS Cable via Stepped Frequency Waveform Reflectometry

The characteristics of the HTS cable including conductivity, permittivity, and insulation characteristics vary depending on the conditions of temperature and pressure during operations. We propose a diagnostic method that estimates the propagation constant of the HTS cable and detect the location and the degree of the fault using stepped frequency waveform reflectometry. The performance of proposed method is verified by the HTS cable experiment regarding the propagation constant estimation and the fault detection. The results of HTS cable cooled by the liquid nitrogen are also compared with the results at the room temperature to analyze the insulation characteristics change according to the state. The proposed method is expected to be further applied to monitor the condition of HTS cable system regarding temperature and pressure.

Phase Compensation and Image Autofocusing for Randomized Stepped Frequency ISAR

Randomized stepped frequency (RSF) waveforms are attractive for inverse synthetic aperture radar (ISAR) imaging due to their synthetic-bandwidth system architecture and outstanding electronic counter-countermeasure characteristics. However, the extra complexities of the RSF radar's frequency oscillator and the target echo model make phase compensation and image autofocusing more complicated. In this paper, we introduce a novel method for the phase compensation and image autofocusing of RSF-ISAR. The new method consists of the following two stages: the first is a parametric coarse compensation for target radial motion, and the second is a non-parametric fine compensation for motion residuals and radar system imperfection. Two target models, a naive target consisting of unit point scatterers and a Yak-42 target obtained from field experiments, are used for numerical analysis, which shows the effectiveness and superiority of the proposed method.