Linear Frequency Modulation Waveform Research Articles

Range and Velocity Resolution of Linear- Frequency-Modulated Signals on Subarray-Mimo Radar

The most important radar system performance is determining the range-velocity of the detected target. This performance is obtained from processing an ambiguity-function (AF) between signals from target reflections and radar radiation signals. Selection of the appropriate waveform transmitted by the radar is a key factor in supporting high resolution radar performance in the AF. There are many waveforms that have been studied in radar systems, especially for multi-antenna radars, i.e., subarray-MIMO (SMIMO) radar which can form phased array (PA) and MIMO radars simultaneously, in the form of linear-frequency-modulated (LFM) signals. In this paper, we examine the use of LFM waveforms combined with SMIMO radar to produce plots of three-dimensional AF as a function of time delay and Doppler shift. The results of the comparison with the Hadamard signal determine the effectiveness of the observed AF performance on parameters such as magnitude, range-velocity resolution, peak sidelobe level ratio, and integrated sidelobe ratio by taking into account the factors of the number of Tx antennas on the PA radar and the number of Tx subarrays on the MIMO radar. The evaluation results of the SMIMO radar configuration (M = 6) with the number of Tx-Rx antenna elements the being 8 provide the best mainlobe magnitude, sidelobe magnitude, range resolution, velocity resolution, PSLR, and ISLR of AF LFM signals compared to conventional radars are 235.2dB, 7.54dB, 37.5m, 75km/s, 29.89dB, and 29.8dB, respectively. Meanwhile, the LFM signal is far superior to the Hadamard signal which has PSLR and ISLR 1.16dB and -3.36dB, respectively.

A Novel DCSK-Based Linear Frequency Modulation Waveform Design for Joint Radar and Communication Systems

A Novel DCSK-Based Linear Frequency Modulation Waveform Design for Joint Radar and Communication Systems

Photonic generation of Barker encoded dual-nonlinear frequency modulated RADAR waveforms

Photonics enables the development of versatile waveform generators with carrier frequency tunability and broad bandwidths, allowing for high-range resolution for modern radar systems. Linear frequency-modulated waveforms are widely employed in various radar applications due to their large time-bandwidth products but are limited in functionality due to high sidelobe levels, resulting in a poor signal-to-noise ratio (SNR). On the other hand, non-linear frequency-modulated waveforms (NLFM) have a faster sweep rate at the edges than at the center, resulting in high SNRs, which can be boosted further through encoding techniques. A photonic approach for generating Barker-encoded dual-NLFM waveforms through a dual-drive Mach Zehnder modulator is proposed with improved range resolution, pulse compression ratio, and peak-to-sidelobe ratio. A theoretical analysis is performed, which is then modeled, and experimentally confirmed. Barker-encoded dual-NLFM waveforms are generated at 6 GHz with 500 MHz chirp bandwidth showing a maximum range resolution of 19.89 cm with PCR of 9803.

Radar-Centric Photonic Terahertz Integrated Sensing and Communication System Based on LFM-PSK Waveform

The radar-centric terahertz integrated sensing and communication (THz-ISAC) is identified as a significant application in future wireless access networks. Up to date, previously reported demonstrations regarding radar sensing performance lack sufficient support in a complex environment with a strong target masking effect. This work tacks this problem by proposing a radar-centric waveform combining linear frequency modulation (LFM) waveform and phase shift keying (PSK). We first derive sensing metrics of the LFM-PSK waveform through theoretical analysis, including range resolution, peak sidelobe ratio (PSLR), and Cramér-Rao lower bound (CRLB). Then a proof-of-concept experiment on a photonics-assisted integrated sensing and communication (ISAC) system operating at 330 with 18 GHz bandwidth is conducted to verify the performance of the proposed LFM-PSK waveform. In the experiment, the proposed waveform can reach a PSLR of up to 20.9 dB and a range resolution of 1.3 cm, simultaneously accommodating a data transmission of 6 Gbit/s. In addition, the effect of embedding symbols on sensing metrics is also discussed, and by comparing the range solution and PSLR with various data rates, around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim$</tex-math> </inline-formula> 6 dB gain in the PSLR without any deterioration of range resolution is observed.

Cognitive Radar Waveform Design Method under the Joint Constraints of Transmit Energy and Spectrum Bandwidth

The water-filling (WF) algorithm is a widely used design strategy in the radar waveform design field to maximize the signal-to-interference-plus-noise ratio (SINR). To address the problem of the poor resolution performance of the waveform caused by the inability to effectively control the bandwidth, a novel waveform-related optimization model is established in this paper. Specifically, a corrected SINR expression is first derived to construct the objective function in our optimization model. Then, equivalent bandwidth and energy constraints are imposed on the waveform to formulate the waveform-related non-convex optimization model. Next, the optimal frequency spectrum is obtained using the Karush–Kuhn–Tucker condition of our non-convex model. Finally, the transmit waveform in the time domain is synthesized under the constant modulus constraint. Different experiments based on simulated and real-measured data are constructed to demonstrate the superior performance of the designed waveform on the SINR and equivalent bandwidth compared to the linear frequency modulated signal and waveform designed by the WF algorithm. In addition, to further evaluate the effectiveness of the proposed algorithm in the application of cognitive radar (CR), a closed-loop radar system design strategy is introduced based on our waveform design method. The experiments under real-measured data confirm the advantages of CR compared to the traditional open-loop radar structure.

Photonic joint radar and communication system using a chirp-polarity coded LFM waveform

A photonic joint radar and communication system using a frequency improved, bandwidth doubled, chirp-polarity coded linear frequency modulation (LFM) waveform is proposed and demonstrated. In the scheme, a dual-polarization modulator is driven by a repetitive LFM waveform and an RF signal to generate different optical sidebands in two orthogonal polarization directions. Then, the orthogonally polarized optical sidebands are filtered and polarization modulated to achieve chirp-polarity coding. The generated signal is employed to simultaneously perform dual functions. Both the radar echo and the communication reception are processed based on optical de-chirping. The approach is demonstrated by simulation. A chirp-polarity coded LFM waveform with central frequency of 24 GHz, bandwidth of 8 GHz, bit rate of 10 Mbit/s is generated and processed for dual functions. The radar range resolution, unambiguous range, and range-Doppler resolution are investigated. The optical demodulation of the communication is verified, and the speed improvement of communication is discussed.

Multiband LFM waveform generation and band-selection using stimulated Brillouinscattering.

Modern radar systems are designed to simultaneously serve multiple applications such as ranging, surveillance, imaging, or warfare, which necessitates operation at multiple carrier frequencies. Linear frequency modulated (LFM) signals are inherently capable of pulse compression leading to enhanced range resolution and good signal-to-noise ratios; therefore, they are widely employed in various radar applications. In this paper, a photonic-based generation scheme for carrier frequency multiplication of LFM waveforms up to a factor of four through a single dual-drive Mach-Zehnder modulator is proposed and experimentally demonstrated. The technique is employed to produce multiband LFM having wide-bandwidth chirps (500MHz, 1GHz) as well as narrow bandwidth chirps (10, 20MHz) that are compatible with the intrinsic linewidth of stimulated Brillouin scattering (SBS). The frequency bands of the narrow bandwidth chirps are further selected through a frequency-agile Brillouin RF filter. The generated tupled chirped waveforms are at continuous multiples of the RF carrier frequency at 2, 4, 6, and 8GHz, respectively, with the first three multiples having 10MHz and the fourth multiple having 20MHz chirp bandwidth. This scheme is also experimentally verified for generating different tupled products and respective filtering through SBS at multiples of 4GHz up to 16GHz, thereby verifying the system's agility and flexibility.

Instantaneous bandwidth expansion of photonic sampling analog-to-digital conversion for linear frequency modulation waveforms based on up-sampling and fractional Fourier transform signal processing.

An approach to expanding the instantaneous bandwidth of a photonic sampling analog-to-digital converter (ADC) for receiving linear frequency modulation waveforms (LFMWs) is proposed and experimentally demonstrated based on up-sampling and filtering in the fractional Fourier domain. Through twice zero interpolation, the equivalent sampling rate is quadrupled, which also quadruples the nominal instantaneous bandwidth of the photonic sampling ADC. In addition, with the assistance of bandpass filtering in the fraction Fourier domain, the image signals and the harmonic distortions generated in the interpolation process are filtered out. As a result, the effective instantaneous bandwidth of the photonic sampling ADC is doubled. In the experiment, the instantaneous bandwidth of a photonic sampling ADC with a sampling rate of 5 GSa/s for receiving LFMWs is increased from 2.5 GHz to 5 GHz by using the proposed method. Input LFMWs within the frequency range of 24-27 GHz and 30-33 GHz, i.e., with an instantaneous bandwidth of 3 GHz, are digitized without frequency-domain aliasing. Besides, the ability of the proposed method to enhance the ranging accuracy in a broadband radar system is demonstrated. This method reduces the hardware complexity of the photonic sampling ADC for receiving broadband LFMWs in radar systems.

Beampattern Synthesis Based on Novel Receive Delay Array for Mainlobe Interference Mitigation

This paper investigates beampattern synthesis methods based on a novel Receive Delay Array (RDA) to mitigate interferences located in the mainlobe of the beampattern. In our system design, the RDA is developed by transmitting a stepped frequency linear frequency modulation waveform and delaying the received echo with a small time offset between adjacent receive antenna elements. In doing so, a range-angle-dependent beampattern is obtained in the joint transmit-receive spatial domain. A two-stage beamforming scheme, including the equivalent data-independent transmit beamforming and dimension-reduced data-dependent receive beamforming, is then proposed to mitigate mainlobe interferences. Furthermore, according to the adaptive array theory, by designing a transmit weight vector dependent of the interference steering vector, two beampattern synthesis algorithms are developed respectively based on the maximum gain and minimum deviation to adjust multiple responses of the transmit beampattern precisely. The mainlobe of the receive beampattern is also broadened with the use of the derivative constraint. By combining the devised transmit and receive weight vectors, a two-dimensional joint transmit-receive beampattern with a flat-top mainlobe and broadened nulls can be formed, where the interferences are mitigated against the direction-of-arrival (DOA) mismatch. Theoretical and practical analysis as well as parametric studies are provided to demonstrate the effectiveness of the proposed beampattern synthesis methods in mitigating mainlobe interferences.

Wireless Picosecond Time Synchronization for Distributed Antenna Arrays

Distributed antenna arrays have been proposed for many applications ranging from space-based observatories to automated vehicles. Achieving good performance in distributed antenna systems requires stringent synchronization at the wavelength and information levels to ensure that the transmitted signals arrive coherently at the target, or scattered and received signals can be appropriately processed via distributed algorithms. In this article, we address the challenge of high-precision time synchronization to align the operations of elements in a distributed antenna array and overcome time-varying bias between platforms primarily due to oscillator drift. We use a spectrally sparse two-tone waveform, which obtains approximately optimal time estimation accuracy, in a two-way time transfer process. We also describe a technique for determining the true time delay using the ambiguous two-tone matched filter output, and we compare the time synchronization precision of the two-tone waveform with the more common linear frequency modulation (LFM) waveform. We experimentally demonstrate wireless time synchronization using a single-pulse 40-MHz two-tone waveform over a 90-cm 5.8-GHz wireless link in a laboratory setting, obtaining a timing precision of 2.26 ps.

Enhanced target detection using a new cognitive sonar waveform design in shallow water

A cognitive waveform design is proposed for use in SONARs (Sound Operated Navigation and Ranging) for detecting targets in undersurface environment. The study adopts a waveform design procedure exploiting prior knowledge gained from environmental reverberations and target signals based on maximizing signal- to- interference-plus- noise ratio (SINR) in the receiver. A genetic algorithm is set forth to work out the optimal specifications in a wideband waveform design. Using initial Linear Frequency Modulated (LFM) waveform as input to the proposed optimization algorithm, an optimal waveform is obtained showing significant improvements in SINR. A number of experiments are conducted to simulate Probability of Detection (POD) versus Signal-to-Reverberation Ratio (SRR) in underwater environments. Analyzing simulation results reveals considerable improvements in target detection task utilizing optimal waveform design compared to initial LFM waveform. Also, in comparison with the initial LFM waveform, it was noticed that there was a substantial reduction in the bandwidth of the optimized design waveform.Our proposed method solves the problem of finding the optimal frequency for designing a cognitive waveform appropriate to the conditions of the environment and the target. We proposed the genetic algorithm method to solve the waveform design problem that maximize the SINR. This paper provides a general methodology for extracting the optimal frequency parameters of the waveform and can be extended to other parameters in cognitive design.

Mainlobe Deceptive Jammer Suppression in SF-RDA Radar: Joint Transmit-Receive Processing

The problem of mainlobe deceptive jammer suppression with a novel stepped frequency (SF)-receive delay array (RDA) radar is addressed in this paper. In our system design, the linear frequency modulation (LFM) waveform with a SF across the antenna elements is transmitted in a uniform linear array, and the received echo is delayed with a time shift between adjacent antenna elements, introducing extra range-dependent degrees-of-freedom (DOFs) in both transmit and receive domains. Consider a typical form of mainlobe jammers, where multiple false targets are generated in the same transmit pulse or same range bin behind the true target after short time modulation. In this respect, the jammers are discriminated from the true target in the joint transmit-receive spatial frequency domain, and suppressed via a data-dependent beamformer based on the minimum variance distortionless response (MVDR) criterion. To further solve the problem of sample selection due to the pseudo-random distribution of the false targets, two kinds of robust beamformers based on the enhanced Capon power spectrum (ECPS) and the eigen-projection elimination (EPE), are developed to reconstruct the jammer-plus-noise covariance matrix and estimate the steering vector of the true target. The performance of the proposed methods in suppression of mainlobe deceptive jammers is evaluated via numerical simulations and compared with the existing systems and robust beamforming methods.

Multiband dual- and cross-LFM waveform generation using a dual-drive Mach–Zehnder​ modulator

Linear frequency modulation (LFM) signals are widely used in modern radar systems owing to their intrinsic pulse compression capability but are restricted due to a limited range-Doppler resolution. On the other hand, dual- or cross-LFM signals have complementary LFM waveforms at the same time instant that reduces the range-Doppler coupling and thus improving range-Doppler resolution. We propose a simple microwave-photonic-based approach to generate multiband dual- and cross-LFM waveforms using only a single dual-drive Mach–Zehnder modulator (DDMZM). A theoretical analysis is carried out, which is modeled and verified through experiments. Dual- and cross-LFM waveforms at a carrier frequency of 6 GHz and 18 GHz with a bandwidth of 2 GHz is generated by controlling the DC and RF bias of the DDMZM. The tunability of the carrier frequency from 3 GHz to 9 GHz is also verified. A range resolution of 6.3 cm for dual- and cross-LFM waveforms, is obtained with a time-bandwidth-product (TBWP) of 20,000. The proposed technique is a promising solution for dual- and cross-LFM waveform generation in two-band multipurpose radar systems.

A Novel Jamming Method against SAR Using Nonlinear Frequency Modulation Waveform with Very High Sidelobes

Synthetic aperture radar (SAR) systems have the capacity for day-and-night and all-weather surveillance, which has become increasingly indispensable for military surveillance and global comprehensive environmental monitoring. With the development of the high-resolution SAR imaging technique, studies on SAR jamming have also received much interest. Traditional jamming methods are based on linear-frequency-modulated (LFM) signals, and this method can achieve high main-lobe jamming gain. However, its sidelobe jamming energy is very low. To solve this issue, a novel nonlinear frequency modulation (NLFM) waveform design method for SAR jamming is proposed in this paper. Compared with LFM waveforms, the designed waveforms have the same main-lobe jamming gain and very high sidelobes, which can significantly improve jamming performance. Moreover, detailed simulation experiments were carried out to verify the effectiveness of the newly proposed jamming scheme.

Photonic Fractional Fourier Transformation Based on Discrete-Frequency Processing

Photonic fractional Fourier transformation (FRFT) based on discrete-frequency processing is proposed to overcome the limitations of processing latency, resolution, and tunability. Typical applications of FRFT, such as de-chirp processing, separation of two linear frequency modulated waveforms (LFMWs) in fractional domain and filtering of a LFMW from a noisy background, are experimentally demonstrated. The operation bandwidth and spectral resolution are 4 GHz and 60 MHz, respectively. Both the phase and amplitude can be measured by the proposal without relying on complex algorithms, while the processing latency is close to the minimum delay required in the FRFT. All optical devices employed in our system shows great potential in integration.

Joint range-velocity estimation with continuous active sonar

Active sonars using linear frequency-modulated (LFM) continuous waveforms are typically processed in sub-bands to facilitate high target range update rates. Target range-rate is then estimated using incoherently processed matched-filter outputs from each sub-band as input to a tracker. Target returns can easily be confused with clutter because sub-band width is typically chosen to avoid decoherence caused by target and/or platform motion. In this paper, we present methods for joint range-velocity estimation which allows for coherent combination of sub-band outputs and accounts for target/platform motion. The approach involves pre-filtering beamformed sub-band outputs using the transmitted LFM waveform, match-filtering each frequency-domain pre-filtered sub-band under a range-velocity hypothesis, and coherently combining the results. A maximum likelihood estimate (MLE) of range-velocity is formed which involves adaptively suppressing clutter and noise using an estimate of sub-band clutter covariance matrices. Simulation results are presented which indicate that joint range-velocity estimation using coherent processing across sub-bands offers a significant improvement over conventional methods and allows for more flexible selection of sub-band processing bandwidth. Moreover, the approach lends itself to handling the case of partial coherence across sub-bands and offers the potential for improved discrimination of slowly moving targets versus clutter discretes. Work supported by ONR.

Bandwidth-enhanced LFM waveform generator based on dynamic control of an optically injected semiconductor laser.

A bandwidth-enhanced linear frequency-modulated (LFM) waveform generation scheme is proposed and demonstrated based on dynamic control of an optically injected semiconductor laser (OISL). The OISL operates at the period-one (P1) oscillation state under proper injection conditions. After photodetection, a tunable microwave signal is obtained with its frequency determined by the optical injection strength and the detuning frequency between the master and slave lasers. For a fixed detuning frequency, an LFM waveform can be generated by introducing an electrical control signal S(t) with a quasi-sawtooth profile to dynamically manipulate the injection strength of the OISL. Then, to overcome the bandwidth limitation by the achievable P1 frequency range under a given detuning frequency, both the injection strength and the detuning frequency are dynamically controlled to achieve a synthesized P1 frequency range, thus generating LFM waveforms with enhanced bandwidths. In our demonstration, LFM waveforms with a synthesized bandwidth of 8 GHz (12-20 GHz) and 24.8 GHz (12.6-37.4 GHz) are generated in the experiment and simulation, respectively.

SAR Signal Formation and Image Reconstruction of a Moving Sea Target

Maritime application of synthetic aperture radar (SAR) technology for sea-target surveillance and imaging is considered in this study. A SAR scenario, including the kinematics of a SAR satellite and a ship moving on the sea, along with the geometry of the target, are analytically described. A linear frequency modulation (LFM) waveform is applied for the target’s illumination. Based on the target’s geometry, SAR and target kinematics and the LFM waveform, a SAR signal model is synthesized. It is proven that the process of signal formation is a transformation of the three-dimensional (3D) image into a two-dimensional (2D) signal, whereas the target’s 2D imaging is an inverse transformation of the 2D signal into the target’s 2D image. SAR signal components, linear Fourier terms and higher-order phase terms are analytically derived and discussed in detail. Moreover, it is proven that SAR image reconstruction is a motion-compensation procedure, i.e., it removes all phases induced by first- and higher-order motion. Based on the SAR signal analysis, an illustrative iterative image-reconstruction algorithm is derived. The quality of the imaging is evaluated by an entropy cost function. Simulation experiments are carried out to verify the correctness of the theoretical statements in respect of SAR signal formation and image reconstruction.

Broadband linear frequency-modulated waveform generation based on optical frequency comb assisted spectrum stitching.

In this paper, we propose and demonstrate a novel spectrum stitching method for broadband linear frequency-modulated waveform (LFMW) generation. An optical frequency comb (OFC) is modulated by a narrowband LFMW whose bandwidth matches the free spectral range of the OFC. Optical injection locking is employed in extracting one broadband frequency sweeping component from the modulated OFC. In this way, seamless spectrum stitching is realized and a broadband LFMW with a multi-fold time-bandwidth product (TBWP) is obtained. Our scheme has a simple structure, which requires only a single OFC, a modulation module and a baseband waveform generator. An LFMW as broad as 20 GHz is generated from a baseband LFMW with 2GHz bandwidth experimentally. The TBWP is 100 times as large as that of the baseband LFMW. Moreover, the power fluctuation and the phase jumps are both eliminated, ensuring an excellent pulse compression performance. Benefiting from the injection locking technique, the linearity reaches 2.0 × 10-6. The central frequency tuning ability of our scheme is also demonstrated.

Ultra-Low Sidelobe Waveforms Design for LPI Radar Based on Joint Complementary Phase-Coding and Optimized Discrete Frequency-Coding

In this paper, in order to reduce the probability of the radar waveform intercepted by the passive detection system, the time-bandwidth product of the radar waveform is increased, and the detection probability of the radar waveform to the target is improved. This paper tackles the holographic RF stealth radar and proposes a joint coding waveform based on the linear frequency modulation (LFM) waveform. Joint coding uses complementary codes to perform phase-coding, and combines the codewords optimized by genetic algorithm in order to perform discrete frequency-coding waveform. The joint coding waveform model is theoretically analyzed, and the ambiguity function, pulse compression and target detection probability of the joint coding waveform are obtained by numerical simulation. In addition, the complexity of the algorithm and the low probability of intercept (LPI) characteristic of the joint coding waveform are analyzed. The results show that the joint coding waveform has an approximate “pushpin” ambiguity function, ultra-low sidelobe characteristics, better RF stealth and target detection performance. Finally, it has good application prospects in the current battlefield environment.