Linear Frequency Modulation Waveform Research Articles

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.

Robust wide-range chirp rate measurement based on a flexible photonic fractional Fourier transformer.

We propose a photonic-assisted approach to measure the chirp rate of a linear frequency modulation waveform (LFMW) with a long duration, based on tunable photonic fractional Fourier transform (FrFT). Since the FrFT order can be continuously tuned by varying the frequency shift in an optical frequency-shifting loop (FSL), a specific FrFT order leads the fundamental frequency component arising in the output electrical spectrum to reach its maximum value, after the photonic-to-electrical conversion. Based on the designated FrFT order and the corresponding fundamental frequency in the output electrical spectrum, the chirp rate measurement over a wide range can be accessed, even the signal-to-noise ratio (SNR) of the input LFMW is substantially low. Simulation results indicate that the chirp rate of a 0.16-ms LFMW over a frequency range from 20 GHz to 26 GHz can be precisely characterized, with a relative measurement error of less than 0.13%, under the SNR condition of 0 dB. Moreover, an unambiguous chirp-rate measurement within the range of -5200 MHz/µs to 550 MHz/µs can be achieved. Hence, the proposed chirp rate measurement is featured with broadband operation, robust noise tolerance, low-frequency detection, and long-duration LFMW characterization.

High-performance linear frequency-modulated signal generation based on optically injected semiconductor laser with dual-loop optoelectronic feedback

<sec>Linear frequency-modulated (LFM) waveforms have numerous applications in high-resolution radar detection, high-speed wireless communication, and high precision measurement. The generation of LFM microwave signals based on conventional electronic technologies is limited in their center frequency and bandwidth, which are usually less than a few gigahertz. Fortunately, the inherently large bandwidth offered by photonic technology is very hopeful of breaking through the electronic bottleneck. A variety of photonics-based approaches to generating the LFM waveforms have been reported, including the frequency-to-time mapping method and the external modulation method. However, these solutions suffer poor tunability or expensive RF sources. In recent years, the LFM waveform generation based on optically injected semiconductor lasers (OISLs) has attracted increasing attention. By introducing a low-speed electrical signal to control the period-one (P1) dynamics of an OISL, the LFM waveforms with a large bandwidth are generated. Nonetheless, the generated microwave signal has poor spectral purity, which restricts its many practical applications.</sec><sec>In this work, a high-performance microwave LFM waveform generation scheme based on an OISL with dual-loop optoelectronic feedback is proposed and demonstrated experimentally. In this scheme, the optical injection strength of an OISL is controlled first by a triangular-like voltage signal to generate LFM waveforms with a large bandwidth. Then, the quality of the generated LFM signal is comprehensively improved by introducing a delay-matched dual-loop optoelectronic feedback structure. Based on the Fourier domain mode locking principle (FDML) and the self-injection locking technique, both a short-delay optoelectronic feedback loop and a long-delay optoelectronic feedback loop are introduced to simultaneously improve the spectral purity and phase stability of the generated LFM signals. In the proof-of-concept experiment, by analyzing the spectral quality and phase deviation of the generated LFM signal, a comb contrast of 40 dB, a comb linewidth of 1 kHz, and a phase deviation ∆<i>φ</i> of less than π/3 are simultaneously obtained. In addition, the parameters such as bandwidth and center frequency of the generated LFM signal generated can be flexibly tuned, and an LFM signal with a large bandwidth up to 8 GHz (18–26 GHz) is generated in the experiment. The proposed scheme features a simple and compact structure, high spectral quality and flexible tuning, thus may find applications in broadband radar and high-speed communication systems.</sec>

Parametric NLFM Waveform for Spaceborne Synthetic Aperture Radar

The non-linear frequency modulation (NLFM) waveform can shape the power spectrum such that its autocorrelation output exhibits very low sidelobes without loss of signal-to-noise ratio (SNR), compared with the linear frequency modulation (LFM) waveform. However, the NLFM waveform has attained little acceptance in spaceborne SAR system due to its distinct disadvantages, e.g., greater system complexity and limited development of the NLFM generation devices. In this paper, we report a parametric piecewise linear (PWL) model for the generation of the general NLFM waveform. Through this model, a novel generation approach, which can significantly reduce the signal computing resources on board, is proposed. Nevertheless, the existed advanced NLFM waveforms, which possess a lower sidelobe under fixed main lobe, suffer from severe performance degradation with this parametric model. To this end, an empirically advanced NLFM waveform is further proposed. This proposed waveform not only allows for a low computing complexity generation by a modified parametric PWL model, but also its performance degradation is dramatically reduced. Finally, detailed simulation experiments are performed to verify the excellent performance of the proposed NLFM waveform.

Ultrahigh-factor frequency multiplication based on optical sideband injection locking for broadband linear frequency modulated microwave generation

In this paper, we propose and demonstrate a novel photonics-enabled frequency multiplication system with an ultrahigh multiplication factor (MF) for broadband linear frequency modulated (LFM) microwave generation. A pair of distributed feedback (DFB) lasers are injection-locked to two optical sidebands with different orders, which are excited by a narrow-band LFM waveform with a frequency range of 2∼3 GHz. Frequency-multiplied LFM waveforms are generated by beating the two DFB outputs. Thanks to the injection locking, the frequency-multiplied signals have excellent spurious suppression and linearity. The measured spurious suppression ratio exceeds 21.4 dB and the linearity is better than 1 × 10−5. The MF reconfigurability and the central frequency tunability are also demonstrated. A series of 20-fold frequency-multiplied LFM waveforms with different central frequencies and a 30-fold frequency-multiplied signal with a frequency range from 16 GHz to 46 GHz are generated. Moreover, a feedback setup is employed to stabilize the waveform phase against environmental interferences. The measured standard deviation of the remaining phase jitter is around 5.5 ∘ .

Costas-coded linear frequency modulation waveform generation based on a VCO-controlled Fourier domain mode locking optoelectronic oscillator.

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.

Experimental Results of Underwater Acoustic Communication with Nonlinear Frequency Modulation Waveform.

In this paper, we propose underwater acoustic (UWA) communications using a generalized sinusoidal frequency modulation (GSFM) waveform, which has a distinct ambiguity function (AF) and correlation function characteristic. For these reasons, it is more robust in multipath channels than the conventional chirp spread spectrum (CSS) with a linear frequency modulation (LFM) waveform. Four types of GSFM waveforms that are orthogonal to each other are applied for each symbol in the proposed method. To evaluate the performance of the proposed method, we compared the performances of the proposed method and conventional method by conducting diverse experiments: simulations, lake trials and sea trials. In the simulation results, the proposed method shows better performance than the conventional method. The lake trial was conducted with a distance of 300~400 m between the transmitter and receiver. As a result of the experiment, the average bit error rate (BER) of the proposed method is and that of the conventional method is , which shows that the proposed method is superior to the conventional method. The sea trial was conducted at a distance of approximately 20 km between the transmitter and receiver at a depth of 1500 m, and the receiver was composed of 16 vertical line arrays (VLAs) with a hydrophone. The proposed method had a BER of in one channel and was error free in the other.

A performance comparison between m-sequences and linear frequency-modulated sweeps for the estimation of travel-time with a moving source.

This manuscript discusses the utility of maximal period linear binary pseudorandom sequences [also referred to as m-sequences or maximum length sequences (MLSs)] and linear frequency-modulated (LFM) sweeps for the purpose of measuring travel-time in ocean-acoustic experiments involving moving sources. Signal design and waveform response to unknown Doppler (waveform dilation or scale factor) are reviewed. For this two-parameter estimation problem, the well-known wide-band ambiguity function indicates, and moving-source observations corroborate, a significant performance benefit from using MLS over LFM waveforms of similar time duration and bandwidth. The comparison is illustrated with a typical experimental setup of a source suspended aft of the R/V Sally Ride to a depth of∼10 m and towed at∼1 m/s speed. Accounting for constant source motion, the root mean square travel-time variability over a 30 min observation interval is 53 μs (MLS) and 141 μs (LFM). For these high signal-to-noise ratio channel impulse response data, LFM arrival-time fluctuations mostly appear random while MLS results exhibit structure believed to be consistent with source (i.e., towed transducer) dynamics. We conclude with a discussion on signal coherence with integration times up to 11 MLS waveform periods corresponding to ∼27 s.

Design of Optimized Coded LFM Waveform for Spectrum Shared Radar System.

To meet the increasing demands for remote sensing, a number of radar systems using Linear Frequency Modulation (LFM) waveforms have been deployed, causing the problem of depleting frequency resources. To address this problem, several researchers have proposed the Spectrum Shared Radar System (SSRS) in which multiple radars share the same frequency band to transmit and receive their own signals. To mitigate the interferences caused by the signal transmission by other radars, SSRS employs orthogonal waveforms that inherit the orthogonality of the waveforms from orthogonal codes. However, the inherited orthogonality of the codes is significantly reduced when incorporating LFM waveforms with the codes. To solve this problem, in this paper, we propose a novel but simple scheme for generating a set of optimized coded LFM waveforms via new optimization framework. In the optimization framework, we minimize the weighted sum of autocorrelation sidelobe peaks () and cross-correlation peaks () of the coded LFM waveforms to maximize the orthogonality of the waveforms. Through computer simulations, we show that the waveforms generated by the proposed scheme outperform the waveforms created by previous proposals in terms of and .

Detection of LFM Radar Signals and Chirp Rate Estimation Based on Time-Frequency Rate Distribution.

Linear frequency-modulated (LFM) signals are the most significant example of waveform used in low probability of intercept (LPI) radars, synthetic aperture radars and modern communication systems. Thus, interception and parameter estimation of the signals is one of the challenges in Electronic Support (ES) systems. The methods, which are widely used to accomplish this task are mainly based on transformations from time to time-frequency domain, which concentrate the energy of signals along an instantaneous frequency (IF) line. The most popular examples of such transforms are the short time Fourier transform (STFT) and Wigner-Ville distribution (WVD). However, for LFM waveforms, methods that concentrate signal energy along a line in the time-frequency rate domain may allow to obtain better detection and estimation performance. This type of transformation can be obtained using the cubic phase (CP) function (CPF). In the paper, the detection of LFM waveform and its chirp rate (CR) parameter estimation based on the extended forms of the standard CPF is proposed. The CPF was originally introduced for instantaneous frequency rate (IFR) estimation for quadratic frequency modulated (QFM) signals i.e., cubic phase signals. Summation or multiplication operations on time cross-sections of the CPF allow to formulate the extended forms of the CPF. Based on these forms, detection test statistics and the estimation procedure of LFM signal parameters have been proposed. The widely known estimation methods assure satisfying accuracy for high SNR levels, but for low SNRs the reliable estimation is a challenge. The proposed approach based on joint analysis of detection and estimation characteristics allows to increase the reliability of chirp rate estimates for low SNRs. The results of Monte-Carlo simulation investigations on LFM signal detection and chirp rate estimation evaluated by the mean squared error (MSE) obtained by the proposed methods with comparisons to the Cramer-Rao lower bound (CRLB) are presented.

Underwater acoustic communication using nonlinear frequency modulation waveform with low side-lobe characteristics

In fluctuating underwater acoustic (UWA) communication, reducing the interference caused by multi-path propagation is important to get better performance. For this reason, Chirp Spread Spectrum (CSS), which has insensitive Doppler effect and having effective bandwidth, using Linear Frequency Modulation (LFM) waveform was used in UWA communication before. But LFM waveform has high auto-correlation function sidelobes it becomes interference and gets worse performance in reverberation environment. This presentation proposes an UWA communication using Generalized Sinusoidal Frequency Modulation (GSFM) waveform which is generalized form of sinusoidal FM. GSFM waveform usually attains much higher spectral efficiency and lower peak-to-average power ratio than LFM while maintaining same bandwidth and pulse duration. GSFM waveform has various types and we use two GSFM pulses that is a Forward type in time-frequency domain and a time reversing type of Forward type in this presentation. Each type represents binary values '0' and '1', respectively. Each of pulses occupy same band of frequency and each of GSFM pulses have nearly orthogonality. Simulation results in various underwater channel environments with noise will be presented. A Bellhop-based underwater channel model is used for simulation. The proposed method will be analyzed compared to the conventional CSS method with LFM waveform.

Enhanced Noise Tolerance Levels for Digital Receiver using Non-Linear Frequency Modulation

One of the critical issues concerning the industries of aerospace and Defence is the accuracy and precision levels of the possible range resolution. And equally important is the detection of the signal in the presence of noisy environments. Signal-to-Noise ratio is one such measure that ensures enhancement of target detection in tough environments. Besides this, high range resolution is also essential for the digital receiver to identify closely spaced multiple targets. The projected digital receiver design primarily highlights the possibility of pulse compression techniques combined with linear frequency modulation and non-linear frequency modulation waveforms for refining the range resolution of targets compared to their counterpsrts, the traditional waveforms. The range resolution and detection enhancement using the advanced signal processing techniques in the presence of noisy environments have been presented with evidence from the simulations accomplished in MATLAB. The ability of the pulse compression waveform to perform in the presence of noise has been tested. Further, this paper presents the minimum signal to noise ratio of the received echo signal for achieving the required range resolution with MATLAB simulations. The paper also includes further plan of work to make this design more robust as an adaptable receiver for industrial applications.

A waveform design method for frequency diverse array systems based on diversity linear chirp waveforms

AbstractA frequency diverse array (FDA) radar has attracted wide attention, due to its capability to provide a range-angle dependent beampattern and to scan the spatial without phase shifters or rotating arrays. However, FDA systems will suffer from low echo signal energy or high sidelobe peaks when detecting targets by beamforming based on existing receivers. To reduce the sidelobe peak of detection results while increasing the echo signal energy, in this paper, we propose an FDA radar system based on diversity linear frequency modulation waveforms. Correspondingly, we propose a receiver architecture with a time-variant beamforming chain. The proposed system retains the ability of the FDA system to automatically spatial beam scanning, owing to the frequency increment across elements. By increasing the pulse duration of transmitted signals, we enhance the echo signal energy. By applying the artificial bee colony algorithm to design the bandwidth of each chirp signal, the proposed system reduces the sidelobe level of detection results while increasing pulse width. Numerical simulation results are presented to demonstrate the effectiveness of the proposed system.

Joint Frequency and PRF Agility Waveform Optimization for High-Resolution ISAR Imaging

Traditional radar waveforms are easily intercepted and interfered with by enemy’s reconnaissance system with the time–frequency periodic pattern recognition. Frequency and pulse repetition frequency (PRF) agility is an effective approach to decrease interception probability and increase anti-jamming capabilities. On the other hand, the agility brings about high sidelobes and the difficulty of parameter estimation using the range-Doppler signal processing. In this article, an optimization and high-resolution imaging algorithm for sparse stepped linear frequency modulation waveform (SSLFMW) with frequency and PRF agility is developed. The range and Doppler 2-D autocorrelation function of the agile waveform is investigated to pave a way to find an optimization strategy for frequency and PRF to suppress range and Doppler sidelobes. Relied on the pulse trains of low Doppler sidelobes, we propose a method of cognitive transmitting and motion retrieval based on the maximum likelihood principle to eliminate the frequency and range coupling in velocity estimation. The 2-D sparse reconstruction with conjugate gradient solver is proposed to efficiently reconstruct the high-resolution range-Doppler image with the frequency and PRF agility waveform. Both simulated and real-measured data sets are used to verify the improved performance of the proposal.

An improved time reversal mirror based on standard linear frequency modulation waveform

Time reversal mirror (TRM) technology is the adaptive focusing method evolved from the phase conjugate method in optics. Conventional incentive method in TRM technology is a narrow pulse signal with a high bandwidth. In this paper, the autocorrelation property of the TRM was proved from the time-reversal symmetry of the wave equation. The linear frequency modulation (LFM) signal is adopted as the exciting signal in the TRM, which gives the dual autocorrelation function waveform, including the exciting signal and transport channel response. Theoretical results show that the peak value of the transducer array’s focusing signal is determined by the pulse width of the LFM signal and the number of array elements. In addition, the adaptive filtering deconvolution method is used to precisely regulate the input signal to ensure that the final detecting signal is the expected LFM waveform, which eliminates the effect of the transport channel and enhances matched filtering effects. The results hold great theoretical significances for the development of TRM technology in ultrasonic detection.

Downlink Synchronization for OTFS-Based Cellular Systems in High Doppler Environments

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.

Space-Time Coding Technique for Coherent Frequency Diverse Array

Coherent frequency diverse array (FDA) radar is able to cover all directions with a stable gain by transmitting a single frequency-shifted waveform. However, it is revealed in this work that the range resolution scales linearly with the number of elements, which is limited by the fixed element number. By leveraging the relationship between the beam direction and the signal frequency, we link the sub-bands of the emitted signal to angular sectors. Based on the fact, a novel transmit diversity technique, referred to as two-dimensional (2-D) space-time coding (STC), is proposed to improve the range resolution. For a specific observation direction, the frequency band of each pulse is shifted by STC to synthesize a full bandwidth after the pulse accumulation. Furthermore, the piecewise LFM (linear frequency modulation) waveform design can be combined with the STC technique to synthesize the transmit beampattern flexibly without range resolution degradation for each pulse. Compared with the state-of-the-art technologies, the proposed STC technique has superiorities in range resolution improvement, ultra-low range sidelobe level, interference suppression, and beampattern design capability. In addition, multi-dimensional ambiguity functions are derived to assess the performance in range-angle-Doppler domain, including the range and angle resolutions, the sidelobe level (SLL) and the angular coverage. To satisfy practical demands, the general receive processing procedures are also designed. The proposed method and corresponding theoretical analysis are verified by extensive numerical results.

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.