Nonlinear Frequency Modulation Waveform Research Articles

A novel transmission loss compensation method for radome based on non‐linear frequency modulation waveform design

AbstractThe radome can protect the enclosed antenna from harsh weather and environmental conditions; however, it will cause a non‐negligible effect particularly transmission loss on the wideband signal which has been widely used in electronic systems. For this, a novel transmission loss compensation method for radome based on non‐linear frequency modulation (NLFM) waveform design is proposed. First, the transmission coefficient calculation process is given, Then, the detailed NLFM waveform design method is described in detail. Finally, the simulation experiments are demonstrated to verify the effectiveness of the proposed compensation method. Based on the designed NLFM waveform, the transmission loss can be compensated and a flat frequency response can be obtained, which can achieve excellent performance of pulse compression in the range direction. The proposed NLFM design method has great potential application value in the electronic system.

Constrained radar waveform optimization for a cooperative radar-communication system

The coexistence of radar-sensing and communication systems research has received a surge of interest in recent times to tackle the issue of spectrum inadequacy. Designing an optimized radar waveform for a coexistence scenario has been a challenging task for accomplishing the convergence of radar-sensing and communication functionalities, without degrading the performance at either end. This paper proposes a novel global optimization-based Spatial Branch and Bound (SBnB) approach to optimize the phase coefficients of a Non-Linear Frequency Modulated (NLFM) waveform in a CRCS framework. In addition, the Modified-Power Ratio Constraint-Cramér–Rao Lower Bound (M-PRC-CRLB), a local optimization-based approach is proposed to optimize the phase coefficients of an NLFM waveform. The spectral energy distribution and auto-correlation characteristics of an NLFM waveform are comprehensively investigated for various values of polynomial order (N) and at different threshold Signal-to-Noise-Ratio (SNR) values. To compare the proposed waveform design approaches (M-PRC-CRLB, SBnB) with the existing waveform design approaches namely, Minimum Estimation Error Variance (MEEV) and PRC- CRLB, a Peak-to-Side-Lobe-Ratio (PSLR), and Integrated-Side-Lobe-Ratio (ISLR) are evaluated at various polynomial orders and threshold SNR values. Furthermore, the performance of a CRCS is assessed using the radar estimation rate and communication data rate. The simulation results reveal that the proposed optimized radar waveform design approaches provide improved performance compared to the existing radar waveform design approaches in terms of radar estimation rate. Further, the proposed global optimization-based SBnB approach achieves a comparable performance of the communication data rate. In addition, the proposed approaches accomplish enhanced spectral utilization, controlled side-lobe energy levels, reduced range-domain ambiguities, and a higher information rate in a CRCS.

A 2-D Method Based on Nonlinear Frequency Modulation Waveform and Phase Coding for Range Ambiguity Suppression

Range ambiguity suppression is a key technical challenge for synthetic aperture radar (SAR) systems. Waveform diversity technology is a potential solution due to its low system complexity. In this letter, a 2-D method based on orthogonal nonlinear frequency modulation (NLFM) waveform and azimuth phase coding (APC) for range ambiguity suppression is proposed. This approach not only suppresses range ambiguity energies instead of dispersing them, but also works for multiple consecutive orders of range ambiguity energies. The imaging processing and range ambiguity suppression performance are described in detail. In addition, the range-ambiguity-to-signal radio (RASR) is analyzed, and the simulation results for the point target and distribution scenarios are given to verify the effectiveness and practicality of the proposed scheme.

Research on Ultra-Wideband NLFM Waveform Synthesis and Grating Lobe Suppression.

Ultra-wideband (UWB) nonlinear frequency modulation (NLFM) waveforms have the advantages of low sidelobes and high resolution. By extending the frequency domain wideband synthesis method to the NLFM waveform, the synthetic bandwidth will be limited, and the grating lobe will grow as the number of subpulses increases at a fixed synthetic bandwidth. Aiming for the highly periodic grating lobes caused by equally spaced splicing and small subpulse time-bandwidth products (TxBW), a multisubpulse UWB NLFM waveform synthesis method is proposed in this paper. Random frequency hopping and spectral correction are utilized to disperse the energy of periodic grating lobes and optimize the matched filter of the subpulse, thereby reducing notches and Fresnel ripples in the synthesized spectrum. The results of the hardware-in-the-loop simulation experiment show that the peak sidelobe ratio (PSLR) and the integral sidelobe ratio (ISLR) of the NLFM synthetic wideband waveform (SWW) obtained by 50 subpulses with a bandwidth of 36 MHz are improved by 4.8 dBs and 4.5 dBs, respectively, when compared to the frequency domain wideband synthesis method, and that the grating lobe is suppressed by an average of 10.6 dBs. It also performs well in terms of point target resolution, and it has potential for 2D radar super-resolution imaging.

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.

Nonlinear Frequency-Modulated Waveforms Modeling and Optimization for Radar Applications

Conventional radars commonly use a linear frequency-modulated (LFM) waveform as the transmitted signal. The LFM radar is a simple system, but its impulse-response function produces a −13.25 dB sidelobe, which in turn can make the detection of weak targets difficult by drowning out adjacent weak target information with the sidelobe of a strong target. To overcome this challenge, this paper presents a modeling and optimization method for non-linear frequency-modulated (NLFM) waveforms. Firstly, the time-frequency relationship model of the NLFM signal was combined by using the Legendre polynomial. Next, the signal was optimized by using a bio-inspired method, known as the Firefly algorithm. Finally, the numerical results show that the advantages of the proposed NLFM waveform include high resolution and high sensitivity, as well as ultra-low sidelobes without the loss of the signal-to-noise ratio (SNR). To the authors’ knowledge, this is the first study to use NLFM signals for target-velocity improvement measurements. Importantly, the results show that mitigating the sidelobe of the radar waveform can significantly improve the accuracy of the velocity measurements.

Adaptable Pulse Compression in ϕ-OTDR With Direct Digital Synthesis of Probe Waveforms and Rigorously Defined Nonlinear Chirping

Recent research in Phase-Sensitive Optical Time Doman Reflectometry (ϕ-OTDR) has been focused, among others, on performing spatially resolved measurements with various methods including the use of frequency modulated probes. However, conventional schemes either rely on phase-coded sequences, involve inflexible generation of the probe frequency modulation or mostly employ simple linear frequency modulated (LFM) pulses which suffer from elevated sidelobes introducing degradation in range resolution. In this contribution, we propose and experimentally demonstrate a novel ϕ-OTDR scheme which employs a readily adaptable Direct Digital Synthesis (DDS) of pulses with custom frequency modulation formats and demonstrate advanced optical pulse compression with a nonlinear frequency modulated (NLFM) waveform containing a complex, rigorously defined modulation law optimized for bandwidth-limited synthesis and sidelobe suppression. The proposed method offers high fidelity chirped waveforms, and when employed in resolving a 50-cm event at ∼1.13 km using a 1.2-µs probe pulse, matched filtering with the DDS-generated NLFM waveform results in a significant reduction in range ambiguity owing to autocorrelation sidelobe suppression of ∼20 dB with no averages and windowing functions, for an improvement of ∼16 dB compared to conventional linear chirping. Experimental results also show that the contribution of autocorrelation sidelobes to the power in the compressed backscattering responses around localized events is suppressed by up to ∼18 dB when advanced pulse compression with an optical NLFM pulse is employed.

A Two-Step Optimization Framework for Low Sidelobe NLFM Waveform Using Fourier Series

The nonlinear frequency modulation (NLFM) waveform can achieve low sidelobes without loss of signal-to-noise ratio (SNR) by utilizing a nonlinear time-frequency structure. This letter presents a novel two-step progressive optimization framework for the NLFM waveform using Fourier series by exploiting the advantages of random searches and deterministic modifications. The modified GA is used for the preliminary design of the NLFM waveform, where random searches with waveform diversity and consideration of the signal’s characteristic provide a rapid decrease of sidelobes in early iterations. When the descent speed of the sidelobes slows down, deterministic modifications in the gradient-based tuning are followed to further reduce the sidelobes. In the simulation, the peak-to-sidelobe level ratio (PSLR) is reduced by at least 5 dB with an almost equivalent normalized impulse response width (IRW) under the same time-bandwidth product (TBP) compared with other NLFM waveforms. Finally, the optimized NLFM waveform is implemented on hardware, which verifies its performance.

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.

A Novel Nonlinear Frequency Modulation Waveform With Low Sidelobes Applied to Synthetic Aperture Radar

Synthetic aperture radar (SAR) systems require a favorable waveform for imaging as the radar waveform directly affects the performance of SAR systems, such as image quality and resolution. It is well known that the nonlinear frequency modulation (NLFM) waveform can adjust the time-frequency relation to shape the power spectral density (PSD) and then provide a matched filtering output with lower sidelobes without losing signal-to-noise ratio (SNR). However, it will broaden the main lobe, which means the resolution of the SAR image decreases. Therefore, in this paper, a novel NLFM waveform is proposed. It employs the piecewise linear function (PWL) model to define the instantaneous chirp rate function, and genetic algorithm (GA) is then applied to optimize the waveform. The novel NLFM waveform promises enhanced performance and flexibility due to greater design freedom. Through this method, lower sidelobe is achieved within the same 3-dB main lobe width. Finally, simulation results are presented to verify the practicability of the proposed NLFM waveform.

Low Sidelobe Quasi-Orthogonal NLFM Waveforms With Reciprocating Frequency Modulation

The difficulty in designing quasi-orthogonal radar waveforms is to ensure low levels of autocorrelation sidelobe peak (ASP) and cross-correlation peak (CCP) under a large number of waveforms. This letter proposes a waveform model with reciprocating nonlinear frequency modulation (RNLFM) for the quasi-orthogonal waveform design. The RNLFM waveform both enjoys the low sidelobe characteristics of nonlinear frequency modulation (NLFM) and high degrees of freedom from reciprocating frequency modulation. A greedy optimization framework is presented to decompose the waveform design problem into two optimization problems that minimize ASP and CCP levels, respectively. Simulation results show that the ASP and the CCP levels of the optimized RNLFM waveforms are reduced by 5.5~9.5 dB and 0.2~2.4 dB respectively, compared with other quasi-orthogonal waveforms under the same waveform number.

The photothermal wave field and high-resolution photothermal pulse compression thermography for ceramic/metal composite solids

Pulse compression thermography has been recently developed to increase the signal-to-noise ratio (SNR) and enhance depth resolvability. However, a distinctively high SNR and depth resolvability is usually required for the accurate characterization of the (thin) topcoat thickness and defects of multilayer ceramic/metal composite solids (CMCSs). To this end, based on the Green function approach, a photothermal wave model for three-layer CMCSs consisting of a semitransparent ceramic coating and two-layer opaque metal solids is first derived, where a spatially varied volumetric heat source and an interior interface heat source described as the Dirac delta function are considered. The dependence of the thermal wave behaviors on both the thickness and photothermal properties of the semitransparent coating is investigated using the model. Inspired by high-precision radar target detection, two nonlinear frequency modulation (NLFM) waveforms, whose instantaneous frequency curves are respectively convex and concave quadratic function, are explored. Results indicate the NLFM waveform with the instantaneous frequency curve of concave quadratic function outperforms conventional LFM and Barker waveforms in terms of the SNR and depth resolvability. Finally, we reveal that a proper window function can further significantly improve the pulse compression quality. Our investigation can provide direct guidance for the accurate and reliable non-destructive testing and evaluation of multilayer CMCSs.

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.

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.

Quasi-Orthogonal Waveforms for Ambiguity Suppression in Spaceborne Quad-Pol SAR

This article deals with the synthesis and analysis of quasi-orthogonal nonlinear frequency modulation (NLFM) waveforms to mitigate the impairments of ambiguous returns in quadrature-polarimetric (quad-pol) synthetic aperture radars (SARs). To this end, focusing on signals with a continuous piecewise linear instantaneous frequency, the design of a waveform pair exhibiting both a low cross correlation energy (CCE) and low peak to sidelobe ratios (PSLRs), is considered. To handle the resulting nondeterministic polynomial (NP) hard problem, a coordinate descent (CD) method is employed, where, at each step, the marginal minimization is tackled via a MATLAB optimization toolbox. Hence, transmission/reception schemes jointly capitalizing quasi-orthogonal NLFM waveforms and azimuth phase coding (APC) techniques are proposed to suppress ambiguity interference. Moreover, a systematic framework for the evaluation of the resulting azimuth ambiguity-to-signal ratio (AASR) and range ambiguity-to-signal ratio (RASR) is provided. Finally, detailed simulation experiments based on the LuTan (LT-1) parameters are carried out to verify the practicability and effectiveness of the newly proposed transceiver schemes.

A variable chirp rate stepped frequency linear frequency modulation waveform designed to approximate wideband non-linear radar waveforms

The non-linear frequency modulation (NLFM) waveform is one of the existing waveforms that can be used in high range resolution radar applications. However, a high sampling frequency and consequently an expensive ADC are required. To overcome this drawback while taking advantage of the features of the NLFM waveform, we suggest approximating the wideband NLFM waveform by a piecewise linear waveform and using it in a stepped frequency (SF) framework. Thus, a variable chirp rate SF-LFM waveform is proposed where SF is combined with a train of LFM pulses having different chirp rates, durations, and bandwidths. In this paper, these parameters are derived from a tangent-based NLFM waveform. At the receiver, a generalized version of the time domain (TD) algorithm is proposed to process the received echoes. Our purpose is to obtain the high range resolution profile (HRRP) whose properties are of the same magnitude orders as those obtained using a tangent-based NLFM waveform. These properties are the peak sidelobe ratio, the integrated sidelobe, and the range resolution. Toward this goal, a multi-objective optimization issue is addressed to deduce the parameters of the proposed waveform by using two types of approaches based on evolutionary algorithms. Their relevance is compared. Our analysis and simulations show that the proposed approaches attain the targeted performance goals with a smaller sampling frequency at the receiver.

OFDM Chirp Waveform Design Based on Imitating the Time–Frequency Structure of NLFM for Low Correlation Interference in MIMO Radar

The orthogonal frequency division multiplexing (OFDM) chirp signal has its special merits of high-range resolution by exploiting a full bandwidth as multiple input multiple output (MIMO) radar signal. After simulation, there are some high peaks in the autocorrelation function and cross correlation function of conventional OFDM chirp signals, which may increase the correlation interference and reduce the detection performance of MIMO radar signal. This letter proposes to reduce the autocorrelation sidelobe peak (ASP) of OFDM chirp signal by subsection imitating the nonlinear frequency modulation (NLFM) signal's time-frequency structure. Since a suitable difference should be made between the subchirp rates and subchirp carrier frequencies of each of the two designed OFDM chirp signals for reducing the cross correlation peaks (CP), the imitated NLFM waveforms' design problem is solved by the proposed optimized method. At last, subchirps of the designed signals are coded by a group of optimized codes. The simulation shows the designed OFDM chirp signals have lower ASP and CP than the conventional ones and referenced previous OFDM signals, and their ASP decreases as the number of subchirps increases.

Non-continuous piecewise nonlinear frequency modulation pulse with variable sub-pulse duration in a MIMO SAR radar system

ABSTRACTThis paper proposes an implementation of non-continuous piecewise nonlinear frequency modulation (N-PNLFM) signals in MIMO radar which are composed of a sequence of N-PNLFM subpulses. The N-PNLFM subpulse can be divided into three segments, the first and third segment are composed of linear frequency modulation (LFM) waveforms. The LFM waveforms in each N-PNLFM subpulse will be orthogonal in one sequence of our new N-PNLFM signal. A non-linear frequency modulation (NLFM) waveform is in the central component of each N-PNLFM subpulse, the bandwidths of each NLFM waveforms are distributed randomly. Each subpulse can be controlled by different variable parameters in both auto-correlation and cross-correlation functions. In order to suppress the high sidelobes in the new N-PNLFM signal and increase the diversity of signals, each subpulse duration is also distributed randomly. Our proposed PNLFM signals are optimized by applying a particle swarm optimization (PSO) algorithm. Comparing with other PNLFM signals, numerous simulations illustrate that our implementation achieves better performance.

A Novel NLFM Waveform With Low Sidelobes Based on Modified Chebyshev Window

It is well known that the nonlinear frequency modulation (NLFM) chirp waveform can shape advantageously the power spectrum density (PSD) such that the autocorrelation function exhibits reduced sidelobes as the window function. However, differences between the PSD and window function due to the Gibbs effects caused by the Fresnel integral would lead to deteriorative performance of the NLFM chirp waveform. In particular, the correlation function of NLFM waveform with Chebyshev PSD is seriously inconsistent with the lowest sidelobe level of the Chebyshev window function possesses. To overcome the inconsistency, therefore, in this letter, a novel NLFM waveform with modified Chebyshev window PSD is proposed, which combines the Chebyshev with edge distortion compensation, allowing, in theory, low sidelobe level as Chebyshev window. Using theoretical analysis also confirmed by simulation, this letter shows that the novel NLFM waveform possesses low sidelobes without high computational complexity in design.

Mitigating Range Ambiguities With Advanced Nonlinear Frequency Modulation Waveform

Range ambiguity suppression is a technical challenge for current synthetic aperture radar systems. A potential solution is to orthogonally modulate the transmitting pulses; however, these orthogonal waveforms (e.g., up-down chirp waveforms) actually cannot reduce the cross correlation energy (CCE). Nonlinear frequency modulation (NLFM) waveform can change the time–frequency relationship to adjust the energy distribution within the bandwidth to reduce the CCE. In this letter, a novel orthogonal NLFM waveform optimization framework is proposed. Through this framework, advanced NLFM waveforms with low sidelobe and CCE are constructed. Furthermore, point and distributed scene simulation results are presented to verify the practicability of the proposed waveforms. In addition, the system scheme, waveform design, and range ambiguity suppression performance are detailed.