Piecewise Linear Frequency Modulated Research Articles

Magneto-acousto-electrical tomography using nonlinearly frequency-modulated ultrasound.

Objective. In this study, nonlinearly frequency-modulated (NLFM) ultrasound was applied to magneto-acousto-electrical tomography (MAET) to increase the dynamic range of detection.Approach. Generation of NLFM signals using window function method-based on the principle of stationary phase-and piecewise linear frequency modulation method-based on the genetic algorithm-was discussed. The MAET experiment systems using spike, linearly frequency-modulated (LFM), or NLFM pulse stimulation were constructed, and three groups of MAET experiments on saline agar phantom samples were carried out to verify the performance-respectively the sensitivity, the dynamic range, and the longitudinal resolution of detection-of MAET using NLFM ultrasound in comparison to that using LFM ultrasound. Based on the above experiments, a pork sample was imaged by ultrasound imaging method, spike MAET method, LFM MAET method, and NLFM MAET method, to compare the imaging accuracy.Main results. The experiment results showed that, through sacrificing very little main-lobe width of pulse compression or equivalently the longitudinal resolution, the MAET using NLFM ultrasound achieved higher signal-to-interference ratio (and therefore higher detection sensitivity), lower side-lobe levels of pulse compression (and therefore larger dynamic range of detection), and large anti-interference capability, compared to the MAET using LFM ultrasound.Significance. The applicability of the MAET using NLFM ultrasound was proved in circumferences where sensitivity and dynamic range of detection were mostly important and slightly lower longitudinal resolution of detection was acceptable. The study furthered the scheme of using coded ultrasound excitation toward the clinical application of MAET.

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.

Performance Analysis of NLFM Signals with Doppler Effect and Background Noise

This paper focuses on the study of effect of background noise and Doppler Effect on various Nonlinear Frequency Modulation (NLFM) waveforms designed using two stage piece-wise and three stage piece-wise linear and non linear functions. The background noise investigated is Additive White Gaussian Noise (AWGN). Simulations are carried out for different target speeds ranging from 100 to 5000km/hour to study Doppler Effect. The simulations are carried out using Matlab software. Among the waveforms designed, the NLFM function designed using two piece-wise Linear Frequency Modulation (LFM) is observed to be Doppler tolerant and also not affected by noise, as the SNR changes from -20 to 20 dB the peak side-lobe level (PSL) of this signal is around -34.84 dB.

Convolutional Windows for Side Lobe Reduction

A lot of applications in radar systems necessitate low range side-lobe performance which is achieved by pulse compression processing. Linear Frequency Modulation (LFM) signal is mainly used chirp signal for this processing. The paramount drawback in LFM is the first side-lobe level of -13dB at the receiver side. In this paper, LFM signal is modified by using simple two-stage piece wise linear frequency modulation (PWLFM) functions. The autocorrelation function of this PWLFM signal exhibited low peak sidelobe level ratio (PSLR) value compared to its counterpart LFM signal. An attempt is made to further reduce the side lobe values by using novel Convolutional windows. The simulation results confirm a significant side lobe reduction by the LFM signal designed using PWLFM functions when a more flexible Power of Cosine window function is applied compared to all other window functions.

Research of Mobile Underwater Acoustic Communication of M-Ary Combining FDM and Piecewise-LFM

Aiming at the countering doppler shift, a mobile underwater acoustic communication scheme of M-ary via FDM-PLFM is proposed. The cross-correlation between piecewise linear frequency modulation(PLFM) and traditional LFM signal is analyzed based on the cross-correlation function. Combining with frequency division multiplexing(FDM), the spectrum utilization of traditional underwater acoustic LFM communication scheme is improved. With the underwater acoustic LFM communication scheme, the new scheme does not require the doppler frequency shift compensation at the low doppler shift. The simulation results show that the present scheme has lower bit error rate than that for the traditional underwater acoustic M-ary LFM communication method under higher data rate conditions.

Transmit beampattern design for coherent FDA by piecewise LFM waveform

In transmit beampattern design, it is desirable to maximize the power around locations of interest. Multiple-input multiple-output (MIMO) radar transmits orthogonal waveforms, which is hardly achievable in practical applications. Moreover, the constant modulus constraint and the computational burden limit the system performance. In this paper, we propose an effective piecewise linear frequency modulation (PLFM) waveform for coherent frequency diverse array (FDA) radar to synthesize the desired transmit beampattern. By deriving the relationship between the beam direction and the transmit signal frequency, we find that different sub-band of transmitted signal corresponds to different angular sector. With the relationship between frequency band and mainlobe of beampattern, the beampattern synthesis is transformed into the design of waveform spectrum which is realized by designing the PLFM waveform in this paper. Compared with the state-of-the-art technique, the proposed PLFM waveform in coherent FDA enjoys the advantage of the constant modulus, low sidelobe level and reduced computation complexity. In addition, the multi-dimensional ambiguity function and the transmit beampattern response are derived to examine the properties. Numerical results are presented to validate the effectiveness of the proposed method.

Refining the ambiguity domain characteristics of non-stationary signals for improved time–frequency analysis: Test case of multidirectional and multicomponent piecewise LFM and HFM signals

This paper aims at providing a more accurate description of the ambiguity domain characteristics of a piecewise multicomponent non-stationary signals with focus on piece-wise linear frequency modulated (LFM) (PW-LFM) signal and a mixed LFM and hyperbolic FM (HFM). The main motivation comes from the observed PW-LFM nature of several real life signals. It is essential that the characteristics of these types of signals be taken into account for the design of high resolution Time–Frequency Distributions (TFDs) and therefore to improve the application and interpretation of time–frequency signal analysis and processing. In this paper the ambiguity function (AF) of a general PW-LFM signal is derived exactly and then analyzed to deduce important properties. The precise location and behavior of both auto-terms and cross-terms of a general piecewise LFM signal can be deduced from its AF. Numerical simulations using different types of test signals confirm the analytical derivations. An extension of the PW-LFM test signal is also presented by using HFM signals. For such signals, the exact analytical expression of auto-terms is given as well as the expression of cross-terms between HFM and LFM. The results obtained can be used in future studies to design more advanced quadratic time–frequency distributions (QTFDs) that exhibit improved properties in terms of resolution and accuracy.

Detection of low-velocity and floating small targets in sea clutter via income-reference particle filters

In this paper, an adaptive composite generalized likelihood ratio test (GLRT) detector using the forward-backward income-reference particle filter (FB-IRPF) for signal estimation is proposed to detect low-velocity and floating small targets in high-resolution sea clutter. In integration duration of the order of seconds, target returns with nonlinear Doppler modulation and amplitude slow fluctuation are parameterized by a piecewise linear frequency modulated (PW-LFM) model equipped by a two-dimensional dynamic system of unknown statistics. Correspondingly, temporal nonstationary sea clutter time series is modelled into a piecewise spherical invariant random vector (PW-SIRV) sequences. By introducing the optimal test statistic at each piece as the user-defined cost and embedding it into the route of the forward-backward cost-reference particle filter (FB-CRPF), the FB-IRPF is developed to estimate the state sequence of a PW-LFM signal and to integrate its income at all the pieces. Using the integrated income as the test statistic, the adaptive composite GLRT is derived. It is compared with the fractal-based detector and tri-feature-based detector in a recognized sea clutter dataset for small target detection. The results show that the proposed detector attains better overall detection performance and is complementary with the tri-feature-based detector to some extent.

An Improved Design of High-Resolution Quadratic Time–Frequency Distributions for the Analysis of Nonstationary Multicomponent Signals Using Directional Compact Kernels

This paper presents a new advanced methodology for designing high resolution time–frequency distributions (TFDs) of multicomponent nonstationary signals that can be approximated using piece-wise linear frequency modulated (PW-LFM) signals. Most previous kernel design methods assumed that signals auto-terms are mostly centered around the origin of the $(\nu,\tau)$ ambiguity domain while signal cross-terms are mostly away from the origin. This study uses a multicomponent test signal for which each component is modeled as a PW-LFM signal; it finds that the above assumption is a very rough approximation of the location of the auto-terms energy and cross-terms energy in the ambiguity domain and it is only valid for signals that are well separated in the $(t,f)$ domain. A refined investigation led to improved specifications for separating cross-terms from auto-terms in the $(\nu,\tau)$ ambiguity domain. The resulting approach first represents the signal in the ambiguity domain, and then applies a multidirectional signal dependent compact kernel that accounts for the direction of the auto-terms energy. The resulting multidirectional distribution (MDD) approach proves to be more effective than classical methods like extended modified B distribution, S-method, or compact kernel distribution in terms of auto-terms resolution and cross-terms suppression. Results on simulated and real data validate the improved performance of the MDD, showing up to 8% gain as compared to more standard state-of-the-art TFDs.

Good code sets from complementary pairs via symmetrical/antisymmetrical chips

Golay complementary code pairs have the advantage of being biphase codes, available at a variety of lengths, with exact sidelobe cancellation. However, they require transmission at two frequencies or channels. At the receiver, the two codes require reception in their own matched filters. The two matched filter outputs are then added, resulting in complete sidelobe cancellation. However, frequency- or channel-selective fading could result in inexact sidelobe cancellation. This paper introduces a new code constructed from the complementary code pair (A, B) by concatenating them with a gap in between, using one frequency band or one channel. The autocorrelation of this code contains a zero-sidelobe region on either side of the mainlobe and an adjacent region of small cross-correlation sidelobes. This is achieved by having the chips used for A and B satisfy the following two conditions: The two chips are symmetrical/antisymmetrical mirror images of each other and the cross-correlation between them is small-i.e., they are quasiorthogonal in the convolution sense. The symmetry/antisymmetry property results in the zero-sidelobe region, while the quasiorthogonality makes the adjacent region of cross-correlation sidelobes small. Linear frequency-modulated (LFM) and piecewise LFM chips satisfy both the symmetry/ antisymmetry and quasiorthogonality conditions. The symmetry/antisymmetry property is shown to be invariant under frequency-selective fading; therefore, sidelobe cancellation is also fading invariant. Any good code set that satisfies the symmetry/antisymmetry condition could be used as chips with the same Golay complementary code pair to generate a good code set with a zero-sidelobe region and an adjacent region of small cross-correlation sidelobes. Such sets are generated by varying the slope of the LFM and piecewise LFM chips.

Piecewise LFM waveform for MIMO radar

To separate the received signals in a multiple-input multiple-output (MIMO) radar, the transmitted signals should be orthogonal or have a low cross-correlation level. Some other properties, such as low autocorrelation sidelobes, high range resolution, and good Doppler tolerance are also desired. However, they are difficult to achieve simultaneously. In general, an improved criterion is at the cost of another degraded one. In this paper, we propose a piecewise linear frequency modulation (PLFM) waveform for the MIMO radar. The transmitted signals are pulse trains, including diversified subpulses, which are divided into three segments with controllable durations and bandwidths. The duration sequence of the second segment is obtained by the genetic algorithm to optimize the cross correlation. Theoretical analyses and numerical results are presented to illustrate the properties of the proposed PLFM waveform. Compared with the polyphase coding and the discrete frequency coding waveforms, the PLFM waveform has a lower cross-correlation level and higher degrees of freedom. The relationship of the bandwidths among different segments can be used to adjust the sidelobe peak and the main lobe width of the autocorrelation function.

Newborn EEG Seizure Detection Using Time-Frequency Matched Filtering

Abstract Background: The analysis of Electroencephalography (EEG) signals acquired from epileptic babies shows that seizures can be modeled as piecewise linear frequency modulated (LFM) signals. This fact motivated the use of time-frequency matched filters (TFMFs) for seizure detection in newborn EEG. A TFMF is characterized by a unique test statistic, which is found based on the time-frequency (TF) correlation between the signal under analysis and a template. The test statistic is compared with a threshold to determine the presence or absence of the template in the signal under analysis. Objectives: We present two seizure detection algorithms based on the general class of TFMFs and an improved algorithm in the ambiguity domain and evaluate their performance using real EEG signals. Methods: The method includes the following stages: Based on TF analysis of newborn EEG, we create a template set containing M piecewise LFM signals with L pieces and slopes. We define test statistics based on the TF correlation...

Novel analytic technique for obtaining the spectrum associated with piecewise-linear frequency modulation

Novel analytic technique for obtaining the spectrum associated with piecewise-linear frequency modulation

Novel analytic technique for obtaining the spectrum associated with piecewiselinear frequency modulation

A new analytic method is presented for determining the frequency spectra associated with frequency-modulated waves. A piecewise-linear approximation to the modulation is used, the spectra being calculated for each piece. The sum of these spectra gives the total spectrum for the modulated signal.

Novel analytic technique for obtaining the spectrum associated with piecewise-linear frequency modulation

Novel analytic technique for obtaining the spectrum associated with piecewise-linear frequency modulation