Linear Frequency Modulation Signal Research Articles

Inverse Synthetic Aperture Radar Imaging of Space Targets Using Wideband Pseudo-Noise Signals with Low Peak-to-Average Power Ratio

With the number of new satellites increasing dramatically, comprehensive space surveillance is becoming increasingly important. Therefore, high-resolution inverse synthetic aperture radar (ISAR) imaging of satellites can provide an in-situ assessment of the satellites. This paper demonstrates that pseudo-noise signals can also be used for satellite imaging, in addition to classical linear frequency-modulated chirp signals. Pseudo-noise transmission signals offer the advantage of very low cross-correlation values. This, for instance, enables the possibility of a system with multiple channels transmitting instantaneously. Furthermore, it can significantly reduce signal interference with other systems operating in the same frequency spectrum, which is of particular interest for high-bandwidth, high-power systems such as satellite imaging radars. A new routine has been introduced to generate a wideband pseudo-noise signal with a peak-to-average power ratio (PAPR) similar to that of a chirp signal. This is essential for applications where the transmit signal power budget is sharply limited by the high-power amplifier. The paper presents both theoretical descriptions and analysis of the generated pseudo-noise signal as well as the results of an imaging measurement of a real space target using the introduced pseudo-noise signals.

Noise Immunity of Binary Chirp Signals

The results of a study of the noise immunity of receiving signals with linear frequency modulation in telecommunication information transmission systems are considered. Analytical expressions for the synthesis of binary signals by linear frequency modulation with control parameters are obtained. The dependence of the structure of linear frequency modulation signals on the shaping parameters has been studied. The optimization problem of finding the maximum value of the Euclidean distance for linear frequency modulation signals of a binary structure has been solved by modeling. Differences have been established in the noise immunity of receiving linear frequency modulation signals in relation to the binary structures of opposite and orthogonal signals. Diagrams of time and spectral fragments of linear frequency modulation signals are presented, explaining the essence of the research results. Graphs are presented for comparative assessment of the noise immunity of receiving binary signals of various structures in terms of the bit error probability as a function of the signal-to-noise ratio in the channel. The essence of correlation processing of signals with a large base is revealed.

A Low-Cost Wideband Digital Array Antenna Based on Stretch Processing Technique

Wideband digital phased array radar offers the advantages of high range resolution, which improves the recognition ability for multiple targets, group targets, and high-speed targets. Traditional wideband phased arrays use true time delay to compensate for aperture fill time; however, the cost increases significantly. In this paper, a wideband elemental digital array architecture based on the stretch processing method is proposed. By utilizing the time-domain and frequency-domain translation equivalence of the LFM (Linear Frequency Modulation) signal waveform, the equivalent aperture fill time is compensated for through frequency shift and phase shift after stretch processing. Compared to traditional wideband digital arrays, this method can dramatically reduce the required sampling rate and lower the requirements on antenna hardware, thereby reducing the manufacturing cost of system. A comprehensive analysis of the signal processing process and stretch processing method is provided. And an antenna array prototype is developed to verify the T/R channel compensation and wideband beamforming. Measured results show that the antenna is capable of ±60° scanning in azimuth plane and ±40° scanning in elevation plane, with a bandwidth of 500 MHz in S-band. The results demonstrate excellent wideband beam performance and accurate lobe scanning, which confirms the validity of the proposed wideband architecture for stretch processing, frequency shift, and phase shift. This method can be widely applied to the low-cost design and wideband performance improvement of wideband digital array radar.

Reconfigurable multi-channel microwave photonic receiver for a multi-band signal based on cascaded microring resonator banks

What we believe to be a novel reconfigurable multi-channel microwave photonic (MWP) receiver for multi-band RF signal is demonstrated for the first time, to the best of our knowledge. A reconfigurable MWP signal processing chip based on two cascaded microring filter banks is employed in the proposed receiver, which slices the multi-band RF input into several narrow band signals and selects optical frequency comb lines for frequency converting of each channel. Due to the significant reconfigurability of the signal processing chip, the proposed receiver can flexibly choose the output frequency band of each channel, and thus different frequency components of the multi-band RF input can be down converted to the intermediate frequency (IF) band for receiving or converted to other frequency band for forwarding. A multi-band RF signal composed of a linear frequency modulation (LFM) signal with 2 GHz bandwidth and a quad-phase shift keyed (QPSK) signal with 100 Mbit/s rate is experimentally received and reconstructed by the proposed receiver, where the reconstructed LFM component exhibits a signal to noise ratio (SNR) of 10.2 dB, and the reconstructed QPSK component reaches a high SNR of 26.1 dB and a great error vector magnitude (EVM) of 11.73%. On the other hand, the QPSK component of the multi-band RF signal centered at 13.5 GHz is successfully converted to 3.1 GHz.

Accurate TDOA estimation using matching cumulative estimator for LFM signal with small samples

This paper introduces two matching cumulative estimators designed for achieving gridless time difference of arrival (TDOA) estimation for linear frequency modulated (LFM) signals with limited samples. A designed matching basis function, customized to the source signal waveform, is employed to calculate with the received data. Time delay matching is then utilized to formulate a monotonic objective function related to the estimated TDOA, enabling gridless estimation. To enhance robustness, especially in scenarios characterized by small samples and low signal to noise ratios (SNRs), a nonlinear cumulative transformation, comprised of a series of strongly convex operations, is incorporated to mitigate the impact of noise on the peak calculation of the objective function. Simulation results validate the efficacy of the two proposed TDOA estimators, particularly under challenging conditions involving small samples and low SNRs.

The Synchrosqueezed Method and Its Theory-Analysis-Based Novel Short-Time Fractional Fourier Transform for Chirp Signals

Time–frequency analysis is an important tool used for the processing and interpretation of non-stationary signals, such as seismic data and remote sensing data. In this paper, based on the novel short-time fractional Fourier transform (STFRFT), a new modified STFRFT is first proposed which can also generalize the properties of the modified short-time Fourier transform (STFT). Then, in the modified STFRFT domain, we derive the instantaneous frequency estimator for the chirp signal and present a new type of synchrosqueezing STFRFT (FRSST). The proposed FRSST presents many results similar to those of the synchrosqueezing STFT (FSST), and it extends the harmonic signal to a chirp signal that offers attractive new features. Furthermore, we provide a detailed analysis of the signal reconstruction, theories, and some properties of the proposed FRSST. Several experiments are conducted, and all of the results illustrate that the proposed FRSST is more effective than the FSST. Finally, based on the linear amplitude modulation and frequency modulation signal, we present a derivation for analyzing the limitations of the FRSST.

Novel motion parameter estimation and coherent integration algorithm for high maneuvering target with jerk motion

The high maneuvering target with jerk motion detection suffers from range migration (RM) and Doppler frequency migration (DFM). In this paper, the fourth order polynomial signal model is used to model the radar echo signal, and a novel high maneuvering target detection method is proposed. The RM is eliminated with Keystone transform (KT) and acceleration searching, and then the aligned echoes are extracted. With two defined symmetric autocorrelation functions (SAF) and the scaled Fourier transform, the third and fourth order motion parameters are estimated. Based on the estimated high order motion parameters, the fourth order polynomial phase signal is turned into linear frequency modulated (LFM) signal. To estimate the chirp rate of the LFM signal, a fast implementation method of second order Wigner Ville Distribution (SoWVD), named frequency domain SoWVD (FDSoWVD) is proposed. Based on the triple estimated motion parameters, the DFM is compensated and then the coherent integration can be achieved by fast Fourier transform, followed which the detection process is performed. Compared with other representative algorithms, the proposed method achieves a good balance between the computation complexity and detection ability. The effectiveness of the proposed method is verified by experiment with synthetic and raw data.

Modeling of harmonics of amplitude and nonlinear frequency-modulated signals

In vibroseismic data, nonlinear signal distortions called harmonics are usually present. The previously proposed method of separating the signal and its harmonics makes it possible to improve the quality of the initial data, as well as to obtain additional information about the geological structure of the earth interior. One of the limitations of the proposed methodology is its initial development for linear frequency-modulated signals. A new method of prediction of harmonics that allows non-linear frequency modulation as well as amplitude variation is proposed.

Photonic Approach to Multi-band Dual-chirp Microwave Waveform Generation with Quadruple Bandwidth

We propose a scheme for generating a microwave waveform with dual-band, dual-chirp, linearly chirped characteristics and quadruple chirp bandwidth. In this scheme, we employ two cascaded Mach-Zehnder modulators (MZMs), with each modulated by a microwave signal and a linearly frequency modulated (LFM) signal. This modulation technique extends the LFM signal to multiple frequency bands and enhances its bandwidth. By properly adjusting the microwave signal's frequency and the LFM's carrier frequency, we can intelligently combine the up-chirp and down-chirp signals obtained after heterodyne beating in the photodetector (PD). This combination results in the creation of multi-band dual-chirp signals with quadruple chirp bandwidth. Our simulation demonstrates the simultaneous generation of dual-chirp microwave waveforms in the X, Ka, U, and V bands, with central frequency-bandwidth ranges of 10GHz-4GHz, 30GHz-4GHz, 50GHz-4GHz, and 70GHz-4GHz respectively. These dual-chirp signals possess a bandwidth four times that of the driving chirp signal, leading to a Time Bandwidth Product (TBWP) four times greater than that of the driving chirp signal. Consequently, the proposed scheme has the potential to significantly improve range Doppler resolution in modern radar systems. Additionally, the high-frequency and large-bandwidth dual-band dual-chirp LFM signals generated by this approach are anticipated to enhance range resolution and detection range in multitarget radar systems.

Doppler and Channel Estimation Using Superimposed Linear Frequency Modulation Preamble Signal for Underwater Acoustic Communication

Due to the relative motion between transmitters and receivers and the multipath characteristic of wideband underwater acoustic channels, Doppler and channel estimations are of great significance for an underwater acoustic (UWA) communication system. In this paper, a preamble signal based on superimposed linear frequency modulation (LFM) signals is first designed. Based on the designed preamble signal, a real-time Doppler factor estimation algorithm is proposed. The relative correlation peak shift of two LFM signals in the designed preamble signal is utilized to estimate the Doppler factor. Moreover, an enhanced channel estimation algorithm, the correlation-peak-search-based improved orthogonal matching pursuit (CPS-IOMP) algorithm, is also proposed. In the CPS-IOMP algorithm, the excellent autocorrelation characteristic of the designed preamble signal is used to estimate the channel sparsity and multipath delays, which are utilized to construct the simplified dictionary matrix. The simulation and sea trial data analysis results validated the designed preamble, the proposed Doppler estimation algorithm, and the channel estimation algorithm. The performance of the proposed Doppler factor estimation is better than that of the block estimation algorithm. Compared with the original OMP algorithm with known channel sparsity, the proposed CPS-IOMP algorithm achieves a similar estimation accuracy with a smaller computational complexity, as well as requiring no prior knowledge about the channel sparsity.

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.

Sine Approximation-Based Comparison Method for Determining the Phase–Frequency Characteristic of Analog-to-Digital Converters

The analog-to-digital converters (ADCs) have been widely used in the applications of such as precision metrology, motion control, position and pose estimation, whose phase-frequency characteristic usually brings in an inevitable influence. In order to ensure the performance of these applications, the phase-frequency characteristic of ADCs has to be definitely determined before they are used. In this study, a new sine approximation-based comparison measurement method is presented, which accurately deter- mines this characteristic by utilizing the linear frequency modulation signal with high carrier frequency and narrow bandwidth instead of the sinusoidal signal. Experimental results demonstrate that the presented method is able to obtain the satisfactory accuracy for the phase-frequency characteristic of general ADCs and promote the improve- ment of their applications.

Fast 3D positioning based on a simplified THz photonic stereo ISAR system.

In this work, a THz stereo inverse synthetic aperture radar scheme based on photonics is proposed, and proof-of-concept experimentally demonstrated, achieving high resolution and fast three-dimensional (3D) positioning of multiple targets. An optical frequency comb and a uni-traveling carrier photodiode are employed to photonically generate a linear frequency-modulation signal at 300-320GHz. By two incoherent measurements at different angles with one pair of antennas, 3D positioning of plane reflectors over a distance of 0.6m is successfully accomplished, achieving a resolution of 7.5mm for both range and azimuth dimensions, and a maximum experimental height error of 4mm.

Improved Lv’s Distribution for Noisy Multicomponent LFM Signals Analysis

This paper presents the improved Lv’s distribution (ImLVD) for noisy multicomponent linear frequency-modulated (LFM) signals analysis, which is of significant importance in radar signal processing. Two goals of this paper are (i) to overcome drawbacks of the Lv’s distribution (LVD), and (ii) to study mechanisms of the constant delay introduction. Theoretical comparisons in cross-term suppression, resolution, peak-to-sidelobe level, anti-noise performance and implementation are performed for the maximum likelihood (ML) method, Wigner–Hough transform (WHT), LVD, parameterized centroid frequency–chirp rate distribution (PCFCRD) and ImLVD. Based on theoretical comparisons and illustrative examples, superiorities of the ImLVD are demonstrated and several unclear mechanisms of the introduced constant delay are interpreted. Finally, three numerical examples are given to illustrate that, because of the high cross-term suppression, resolution, peak-to-sidelobe level and anti-noise performance without the non-uniform integration variable, the ImLVD is more suitable for noisy multicomponent LFM signals analysis.

Studies on High-Resolution Airborne Synthetic Aperture Radar Image Formation with Pseudo-Random Agility of Interpulse Waveform Parameters

By means of alteration of the transmitted linear frequency modulation (LFM) signal waveform parameters, such as pulse width or chirp rate, initial phase, pulse repetition interval (PRI), and chirp rate polarity at every position of synthetic apertures, the pseudo-random agility technology of interpulse waveform parameters in airborne Synthetic Aperture Radar (SAR) actively increases the complexity and uncertainty of radar waveforms. This technology confuses jamming interception receivers, thus improving its anti-interference ability for active coherent jamming, which is one of the main research interests of airborne SAR technology. But the pseudo-random agility technology for interpulse waveform parameters faces certain challenges of large computation and complex system design, which need to be further studied and solved. To address these issues, a processing scheme of high-resolution SAR image formation which is appropriate for agile interpulse waveform parameters is proposed in this paper. This method can deal with multiple agile parameters, not only single ones as in most existing literature. Its computation load is nearly comparable to that of traditional SAR image formation with constant waveform parameters. The high-resolution SAR imaging results obtained by processing SAR raw data with agile interpulse waveform parameters demonstrate the effectiveness of the proposed method. In addition, real SAR images with resolutions of 0.5 m and 0.15 m, which are rarely found in the public literature, are shown under the circumstance of randomly changing the transmitted wideband LFM signal pulse parameters one by one.

Wigner-Ville distribution and ambiguity function of QPFT signals

The quadratic phase Fourier transform(QPFT) has received my attention in recent years because of its applications in signal processing. At the same time the applications of Wigner-Ville distribution (WVD) and ambiguity function (AF) in signal analysis and image processing can not be excluded. In this paper we investigated the Wigner-Ville Distribution (WVD) and ambiguity function (AF) associated with quadratic phase Fourier transform (WVD-QPFT/AF-QPFT). Firstly, we propose the definition of the WVD-QPFT, and then several important properties of newly defined WVD-QPFT, such as nonlinearity, boundedness, reconstruction formula, orthogonality relation and Plancherel formula are derived. Secondly, we propose the definition of the AF-QPFT, and its with classical AF, then several important properties of newly defined AF-QPFT, such as non-linearity, the reconstruction formula, the time-delay marginal property, the quadratic-phase marginal property and orthogonal relation are studied. Further, a novel quadratic convolution operator and a related correlation operator for WVD-QPFT are proposed. Based on the proposed operators, the corresponding generalized convolution, correlation theorems are studied. Finally, a novel algorithm for the detection of linear frequency-modulated(LFM) signal is presented by using the proposed WVD-QPFT and AF-QPFT.

Adaptive bias control of optical IQ modulator with low LFM dither and strong fluctuation resistance.

An innovative approach has been proposed for adaptive bias control in optical IQ modulators. In contrast to traditional approaches that utilize sine dither, this method employs a linear frequency modulated (LFM) signal as the dither, associated with the fractional Fourier Transform (FrFT) to extract the bias point drift. The LFM signal, after undergoing FrFT, transforms into a compressed signal (CS) with energy concentration in the fractional domain. Utilizing this signal for bias point monitoring, the proposed method demonstrates robust bias control even in the presence of substantial interferences, as substantiated by comprehensive simulations and experimental investigations. Remarkably, in a 20-Gbaud 16QAM signal transmission, the proposed approach achieves stable control of the bias point for over 4 hours, even in the presence of voltage fluctuations, while effectively reducing the dither amplitude by half. Furthermore, it maintains a low bit error rate (BER) below 10-5 even under intentional external interference.

Chirp Rate Estimation of LFM Signals Based on Second-Order Synchrosqueezing Transform

For the problem of low time-frequency aggregation of the short-time Fourier transform (STFT), which causes the parameter estimation performance degradation of linear frequency modulation (LFM) signals at low signal-to-noise ratio (SNR), second-order synchrosqueezing transform (SSST) is proposed based on the square of STFT amplitude. The time-frequency resolution and energy aggregation are improved by means of squeezing and reassigning the time-frequency spectrum. Meanwhile, in order to decrease the calculation of classical parameter estimation methods, the Hough transform is used for rough estimation, and then the fractional Fourier transform (FRFT) is used for accuracy estimation based on the Renyi entropy. The simulation result shows that higher estimation accuracy is obtained at low SNR, and it has better robustness.

High-purity linearly frequency-modulated signal generation based on the integrated semiconductor laser subject to the dynamical optoelectrical feedback.

A novel photonic method of linearly frequency-modulated (LFM) signal generation with high purity based on the monolithically integrated semiconductor laser (MISL) subject to the dynamical optoelectrical feedback is proposed and demonstrated in this paper. In this approach, the MISL is firstly operated in period-one state. By introducing the dynamical optoelectrical feedback to modulate the MISL, the generated LFM signals would be constantly optimized as long as the delay of the feedback loop is matched with the repetition period of the LFM signal. In this system, no additional high-speed external modulator, high-frequency electrical LFM oscillator are required, highly simplifying the framework and reducing the power consumption. In the current proof-of-concept experiment, one LFM signal with the bandwidth as large as 5.6 GHz is generated and the corresponding frequency comb contrast can be drastically improved by 51 dB. Furthermore, the effect of the delay mismatch is also discussed in this paper.

OFDM-MIMO radar assisted dual-function radar communication system using index modulation

Dual-function radar communication (DFRC) system exploits a hardware platform to achieve both radar and communication functions. Compared to utilizing separate radar and communication systems, DFRC has better performance in spectrum utilization. In this paper, assisted by orthogonal frequency division multiplexing-multiple input multiple output (OFDM-MIMO) radar, we propose a DFRC system architecture combining generalized space shift keying (GSSK) modulation and subcarrier index modulation (SIM) techniques. In this scheme, linear frequency modulation (LFM) signal is explored as the transmission waveform of OFDM-MIMO radar to complete the radar function. Furthermore, the proposed scheme combines GSSK and SIM to carry the communication information to the antenna index and subcarrier index to complete the communication function. Based on this architecture, a novel low complexity frequency detection communication demodulation algorithm is proposed, and the achievable rate communication performance of the system is analyzed. Numerical and simulation results verify the feasibility and effectiveness of the proposed system.