NCV Filter Design for Radar Tracking of Maneuvering Targets with LFM Waveforms

When tracking maneuvering targets with a nearly constant acceleration (NCA) Kalman filter with discrete white noise acceleration (DWNA), the selection of the process noise variance is complicated by the fact that the process noise errors are modeled as white Gaussian, while target maneuvers are deterministic or highly correlated in time. In recent years for nearly constant velocity (NCV) Kalman filters, the deterministic tracking index was introduced and used to develop a relationship between the maximum acceleration of the target and the process noise variance that minimizes the maximum mean squared error (MMSE) in position. A lower bound on the process noise variance was also expressed in terms of the maximum acceleration and deterministic tracking index. In this paper, the design methods for NCV Kalman filters with DWNA are extended to develop design methods for NCA Kalman filters with DWNA tracking maneuvering targets. The effectiveness of the design methods are illustrated via Monte Carlo simulations.

Interrupted sampling repeater jamming (ISRJ) has attracted extensive attention in radar electronic countermeasures due to its low time delay and strong coherence. However, the jamming effectiveness of ISRJ is closely related to waveform characteristics, often failing to produce the desired multi-false target deception effect. To address this issue, an extended ISRJ (EISRJ) method focusing on the construction of a frequency-domain periodic sampling pattern is proposed, which can realize deception jamming effects, similar to ISRJ on linear frequency modulation (LFM) waveforms, for various non-linear frequency modulation (NLFM) waveforms by simply using a non-periodic sampling function. Based on the principle of stationary phase, the intrinsic mechanism behind why ISRJ achieves multi-false-target deception effects on LFM waveforms but fails on NLFM waveforms is revealed from the frequency-domain perspective. Building upon this insight, the EISRJ theory, based on waveform time-frequency modulation correspondence and the design of extended interrupted sampling functions, is established. Implementation analysis indicates that electromagnetic metamaterials have advantages over traditional digital radio frequency memory-based jammers in achieving non periodic interrupted sampling and retransmission, without the need to address transceiver antenna isolation issues. Simulation experiments across multiple parameters and NLFM waveforms further validate the correctness and superiority of the EISRJ.

Efficient forward-looking imaging via synthetic bandwidth azimuth modulation imaging radar for high-speed platform

This paper proposes a downlink synchronization and cell identity (CID) estimation technique for cellular systems based on orthogonal time-frequency space (OTFS). In the proposed technique, each base station (BS) transmits one detection preamble (DP) and two OTFS symbols (pilot and secondary-CID (SCID) signal (SS)). The DP based on a linear frequency-modulated (LFM) waveform, called proposed-LFM (pLFM), carries the primary-CID (PCID) for symbol timing (ST) synchronization, whereas the SS based on the Zadoff-Chu (ZC) sequence mapped in the delay-Doppler domain carries the SCID. The pLFM is obtained by discretizing the LFM waveform, increasing the frequency sweeping parameter beyond the limit of the operational bandwidth, and incorporating the PCID into the LFM waveform. The autocorrelation and cross-correlation functions of the pLFM are analyzed to examine its correlation properties under the influence of a high Doppler shift. To reduce the undesirable correlation properties (side peak and time ambiguity), a receiver processing (RP) scheme is developed for the pLFM. It is found that the pLFM with RP is suitable for the DP design because it can provide an accurate ST in high-mobility scenarios. In addition, the influence of OTFS modulation on the ZC sequence is derived and a low-complexity detection algorithm based on message passing is applied to detect SCID at the user equipment. The simulation results demonstrate that the proposed downlink synchronization and CID estimation techniques are suitable for OTFS-based cellular systems in high-Doppler environments.

This article presents a novel electronic protection (EP) technique against coherent jammer (CJ) or digital radio frequency memory (DRFM) that significantly reduces the false detection rate (FDR). CJs are electronic attack (EA) devices that receive and manipulate radar signals by adding time delay, Doppler shift, and gain before transmitting the signal back to the radar. The intention is clearly to produce false detections in the radar receiver. In this work, we utilize a new matched filter that mitigates emission from the coherent jammer. With the use of linear frequency modulation (LFM) and Frank-coded waveforms, simulations show that the technique reduces the FDR caused by CJs significantly.

Chirp radar uses linear frequency modulated (LFM) waveforms that produce biased measurements of target range due to the range-Doppler coupling in the signal. The range- Doppler coupling of LFM waveform can both improve and worsen the tracking accuracy in a radial coordinate. The system behavior in an unsteady state is essential, for example, when it jumps from one moving object to another (a coordinate jump). Therefore, the transient response of αβ-filter is studied by an impulse response. Moreover, the stability boundaries of αβ-filter with alternating range-Doppler coupling coefficient are evaluated.

Frequency diversity in linear frequency modulated (LFM) waveforms can introduce unintended range shifts among receive radars in a distributed environment. This can make it difficult to predict where interference will occur in those receive radars, particularly when multipath is considered. This paper introduces the concept of interference region in range-frequency space to characterize the interference levels at a receive radar caused by waveforms transmitted from different radars in a distributed architecture. Linear frequency modulated (LFM) stretch-processed waveforms provide wide bandwidth and high range resolution while imposing only modest demands on the digital processing capabilities of a radar system. For this reason they are the waveform family of choice for many current wideband radar systems, including synthetic aperture radar (SAR) systems. However, LFM waveforms do not easily lend themselves to applications that require orthogonality, such as distributed radar architectures. The widespread use of these waveforms and the processing advantages they provide make it worthwhile to examine schemes for their use in a distributed environment. The paper uses interference region analysis to assess the effectiveness of frequency diversity, upchirp-downchirp diversity and chirp slope mismatch using LFM stretch-processed waveforms in a distributed environment.

Pulse compression is a method for achieving most of the benefits of a short pulse while keeping within the practical constraints of the peak power limitation. It is usually a suitable substitute for the short pulse waveform except when a long minimum range might be a problem or when maximum immunity to repeater ECM is desired. Pulse compression radars, in addition to overcoming the peak-power limitations, have an EMC (Electromagnetic Compatibility) advantage in that they can be made more tolerant to mutual interference. This is achieved by allowing each pulse-compression radar that operates within a given band to have its own characteristic modulation and its own particular matched filter.. In this paper, we shall implement (LFM) linear frequency modulation digital pulse compression technique using (FPGA) which has distinct advantages compared to other application specific integrated circuits (ASIC) for the purposes of this work. The FPGA provides flexibility, for example, full reconfiguration in milli-seconds and permits a complete single chip solution.

A novel approach to generating tunable Costas-coded linear frequency modulation waveforms (LFMWs) from an optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. The OEO works under Fourier domain mode locking, where the oscillation modes are selected by using a fast-scanning microwave bandpass filter based on phase-modulation-to-intensity-modulation conversion via stimulated Brillouin scattering. Costas coding is realized by using an open-loop voltage-controlled oscillator (VCO) with a fast tuning speed to generate an agile fast-scanning probe light via electro-optic frequency shift. The bandwidth of the generated Costas-coded LFMWs can be tuned by varying the voltage range of the low-frequency waveform applied to the VCO, and the center frequency can be finely tuned by varying the electro-optic frequency shift of the pump light. In the experiment, Costas-coded LFMWs with a 12-bit Costas code sequence of [9 5 7 12 6 4 1 8 11 10 2 3], a period of 20.39 µs and tunable frequency range are generated. The cross-correlation result with a time delay of 102.5 µs indicates that the generated Costas-coded LFMWs have excellent pulse-to-pulse coherence. In addition, the bad phase noise performance of the open-loop VCO has a negligible influence on the generated Costas-coded LFMWs. Benefited from employing an open-loop VCO with a fast tuning speed and a broad operation bandwidth, this approach has potential in generating agile broadband multi-format radar waveforms with low phase noise and excellent pulse-to-pulse coherence directly from an OEO.

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.

Synthetic aperture radar (SAR) systems are getting more and more applications in both civilian and military remote sensing missions. With the increasing deployment of electronic countermeasures (ECM) on modern battlefields, SAR encounters more and more interference jamming signals. The ECM jamming signals cause the SAR system to receive and process erroneous information which results in severe degradations in the output SAR images and/or formation of phony images of nonexistent targets. As a consequence, development of the electronic counter-countermeasures (ECCM) capability becomes one of the key problems in SAR system design. This paper develops radar signaling strategies and algorithms that enhance the ability of synthetic aperture radar to image targets under conditions of electronic jamming. The concept of SAR using chaotic carrier frequency agility pulses (CCFAP-SAR) is first proposed. Then the imaging procedure for CCFAP-SAR is discussed in detail. The ECCM performance of CCFAP-SAR for both depressive noise jamming and deceptive repeat jamming is analyzed. The impact of the carrier frequency agility range on the image quality of CCFAP-SAR is also studied. Simulation results demonstrate that, with adequate agility range of the carrier frequency, the proposed CCFAP-SAR performs as well as conventional radar with linear frequency modulation (LFM) waveform in image quality and slightly better in anti-noise depressive jamming; while performs very well in anti-deception jamming which cannot be rejected by LFM-SAR.

This paper discusses the implementation of GNU radio-based software defined radio (SDR) for designing a frequency modulated continuous wave (FMCW) radar to detect stationary and moving targets. The use of SDR system in which its components are implemented by means of software is to reduce cost and complexity in the design and implementation. Whilst the signal processing of FMCW radar is carried out using Matlab R® with triangular linear frequency modulation (LFM) waveform to obtain the target distance and the target relative speed for stationary and moving target, respectively. From the result, it is shown that the radar is successfully implemented using GNU radio-based SDR with the capability in distance target detection of 14.79km for a moving target away from the radar with the relative speed of 50m/s.

In this work, we investigate the use of the guard bands of a linear frequency modulated (LFM) radar waveform for communications. For illustration, quaternary phase-shift keying (QPSK) is used. The effect of the LFM waveform on the symbol error rate (SER) is investigated. Conversely, the effect of injecting the QPSK RF carriers on the radar's probability of detection (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> ) is also investigated. To reduce the interference on each other, a spectral distance metric is introduced and its effect on SER and P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> is evaluated. To mitigate the obvious effect or large radar power compared to communications, radar mainlobe notch filtering, parameter estimation and subtraction are used in the communications receiver. In terms of the radar's P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> , the effect of low-power communications due to the use of the guard bands turns out to be minimal.

To solve the problem of missing measurements in highly manoeuvring target tracking, an expected‐mode‐augmentation‐based unscented Kalman filter with missing measurements compensation (EMA‐MMCUKF) is designed based on the variable‐structure multiple model method. In the proposed EMA‐MMCUKF, the random missing measurements are described by the Bernoulli distribution, and the one‐step prediction is used as the compensation. Based on the proposed EMA‐MMCUKF, a Bayesian estimation‐based expected‐mode‐augmentation unscented Kalman filter with missing measurements compensation (BE‐EMA‐MMCUKF) is proposed for adaptive estimation of the sensor measurement reception rate, where the unknown measurement reception rate can be estimated by fully utilising prior information. Simulation results demonstrate that the proposed EMA‐MMCUKF can effectively track the manoeuvring target at different measurement reception rates. Moreover, when the sensor prior information differs significantly from the true measurement reception rate, the proposed BE‐EMA‐MMCUKF can effectively estimate the unknown sensor measurement reception rate and improve the accuracy of manoeuvring target tracking compared with non‐estimation of the sensor measurement reception rate.

Active sonar systems that transmit large time‐bandwidth (TW) product linear frequency‐modulated (LFM) waveforms and receive echoes from targets of unknown speed can suffer considerable correlation losses that cannot be predicted from conventional (narrow‐band) ambiguity function theory. As is well known, the theory can be modified to include the effects of Doppler distortion on large TW‐product signals by correlating the received signal against a reference that is a time‐compressed version of the transmitted signal. In this paper, the effects of multipath (or target highlight structure) and Doppler on the correlation process for rectangular weighted large TW‐product LFM waveforms are examined. When the received echo contains no multipath, the correlator peak output is a maximum for the reference channel that is closest in Doppler to the target. However, in a multipath environment, the correlator output peak does not generally occur at the correct Doppler reference channel. The spreading of the cross‐ambiguity function as a result of Doppler mismatch and multipath is calculated in terms of the delay‐Doppler coordinates and magnitude of the extrema. It is shown that, under multipath conditions, correct estimates of target parameters can be recovered through integration of the correlator output.