Main Lobe Width Research Articles

Fast Convergence Method for Scaling Window Sidelobe Magnitude

Windows such as Dolph-Chebyshev window and Kaiser window are adjustable, whereas windows such as Hamming window and Blackman window are traditionally not adjustable. In [1], a technique for trading off main lobe width against sidelobe magnitude for any arbitrary window, including the traditionally non-adjustable windows, was presented. However, the method in [1] requires a large number of iterations if the specification is very tight. Developed based on a new perspective on the window adjustment principle, a new method to achieve the same adjustment capability as in [1], but at a very much fewer iterations is presented in this letter. Our new method is particular useful if the specification is very tight.

A Method for Scaling Window Sidelobe Magnitude

Many types of windows have been designed in the past decades for various applications. Each window type has its own specific characteristics. In this letter, we present a general technique for trading off main lobe width against sidelobe magnitude for any arbitrary window while keeping the number of sidelobe peaks and their relative magnitudes unchanged although their exact locations and magnitudes are changed.

Decimetre Level Range Resolution for Beidou B3I Signal-Based Passive SAR Imaging—Proof-of-Concept Experimental Demonstrations

The construction of the Beidou B3 satellite system, a new-generation global navigation satellite system, has been completed worldwide, however the respective implementation studies remain in the start-up stage. Accordingly, studies of passive Beidou B3I signal-based synthetic aperture radar (Beidou B3I-SAR) are very meaningful in terms of promoting the rapid development of the Beidou technique. This paper proposes methods for Beidou B3I SAR imaging of decimetre level range resolution. To separate aliased reflected B3I signals at range domain, we presented cascaded secondary order differentiation operator (Diff2) and cascaded Teager-Kaiser (TK) operator, applied them to the regions where exists range compressed pulses, respectively. Thereafter to eliminate the obvious side-lobes which brought by the proposed operators and with the values less than zero, zero thresholding scheme is employed. To obtain the final range compressed signals with decimetre range resolution, phase recovery component is performed to the respective zero thresholded pulses. To validate the proposed methods, both proof of concept simulation and the experiment with field Beidou B3I signal raw data are carried out for comparison. The results show that indeed main-lobe width of range compressed pulse can reach the level 0.4 m. This reveals that decimetre level range resolution can be achieved for Beidou B3I-SAR on the basis of proposed methods, in contrast to the current best result of meters level in passive GNSS-based SAR related studies. Meanwhile, in a comparison of the proposed methods on the basis of cascaded Diff2 operator and cascaded TK operator, the later is outer-performed, since the respective brought interference level in background region is less.

Robust Acoustic Imaging Based on Bregman Iteration and Fast Iterative Shrinkage-Thresholding Algorithm.

The acoustic imaging (AI) technique could map the position and the strength of the sound source via the signal processing of the microphone array. Conventional methods, including far-field beamforming (BF) and near-field acoustic holography (NAH), are limited to the frequency range of measured objects. A method called Bregman iteration based acoustic imaging (BI-AI) is proposed to enhance the performance of the two-dimensional acoustic imaging in the far-field and near-field measurements. For the large-scale norm problem, Bregman iteration (BI) acquires the sparse solution; the fast iterative shrinkage-thresholding algorithm (FISTA) solves each sub-problem. The interpolating wavelet method extracts the information about sources and refines the computational grid to underpin BI-AI in the low-frequency range. The capabilities of the proposed method were validated by the comparison between some tried-and-tested methods processing simulated and experimental data. The results showed that BI-AI separates the coherent sources well in the low-frequency range compared with wideband acoustical holography (WBH); BI-AI estimates better strength and reduces the width of main lobe compared with generalized inverse beamforming (-GIB).

Optimization of two-stage NLFM signal using Heuristic approach

Background/Objectives: The design of appropriate Non-Linear Frequency Modulation (NLFM) signals continues to be the focus of research in radar pulse compression theory for sidelobe reduction. This study focuses on a heuristic design and optimization algorithm to optimize the side lobe values of the NLFM signal designed using two-piece wise linear frequency modulation (LFM) functions. Methods: 1) Heuristic search identifies the optimum B1, T1, and B2, T2, which yield the lowest sidelobe value of the designed function.2) Compute all the side lobe values of the designed NLFM signal using an algorithm developed in Python scripting language. To plot a complete contour map for all the calculated side lobe values, which helps identify the associated variations in the range of side lobe values. Finally, optimize the side lobe values keeping the main lobe width and time-bandwidth (BT) product unchanged by designing a dynamic optimization algorithm. Findings: The algorithm developed considered all side lobe levels after the main lobe for optimization. The focus is mainly on the peak sidelobe ratio (PSLR) value without affecting the other parameters. The results demonstrate that the achieved side lobes exhibit their desired levels. Novelty: The method is useful in all types of hardware associated with weather radar applications to military solutions. The technique can be extended to other multistage signals consisting of piecewise linear Segments. Keywords: Contour; LFM; NLFM; optimization; PSLR

A Study of Comb Beam Transmission on Phased Array Weather Radars

The comb beam transmission (TX) approach, which forms a power antenna radiation pattern with multiple mainlobes, was studied for application to phased array weather radars. Combining the use of comb TX and a digital beamforming receiver enables a weather radar to observe multiple directions simultaneously. Numerical simulations show that the two-way antenna radiation patterns formed by comb TXs have properties comparable to conventional weather radar observation: almost the same mainlobe widths are achieved, and with reference to the mainlobe peak, the maximum sidelobe level is less than −37 dB, and the sidelobe level reaches −60 dB at an angle of 13.77°. These properties are superior to the wide TXs that are normally utilized by phased array weather radars. A simulation that applied the comb TX approach to a current C-band weather radar showed that the volume scan time can be reduced from almost 500 s to 1 min.

An improved smooth-windowed Wigner-Ville distribution analysis for voltage variation signal

This paper outlines research conducted using bilinear time-frequency distribution (TFD), a smooth-windowed wigner-ville distribution (SWWVD) used to represent time-varying signals in time-frequency representation (TFR). Good time and frequency resolutions offer superiority in SWWVD to analyze voltage variation signals that consist of variations in magnitude. The separable kernel parameters are estimated from the signal in order to get an accurate TFR. The TFR for various kernel parameters is compared by a set of performance measures. The evaluation shows that different kernel settings are required for different signal parameters. Verification of the TFD that operated at optimal kernel parameters is then conducted. SWWVD exhibits a good performance of TFR which gives high peak-to-side lobe ratio (PSLR) and signal-to-cross-terms ratio (SCR) accompanied by low main-lobe width (MLW) and absolute percentage error (APE). This proved that the technique is appropriate for voltage variation signal analysis and it essential for development in an advanced embedded system.

An Improved Gravity Search Algorithm and Its Application in Planar Array Synthesis

An improved gravity search algorithm, adaptive gravity search algorithm (AGSA), is proposed to solve the problem that the gravity neutralization caused by the cumulative effect of particle inertia mass at the end of iteration, which will affect the optimization performance. An adaptive decay factor is designed, which can produce different gravitation values at different iteration stages of the algorithm and accelerate the mining ability of the algorithm at the later iteration stage. In order to enhance the memory ability of the algorithm, the influence of elite particles is added to the realization of the speed to expand the exploration ability. The improved algorithm is used to optimize uniform concentric ring array, the main lobe width optimized by the AGSA is 6.7°narrower and the side lobe level is 5.1 dB and 1.8 dB lower than the algorithm in the literature. It is clear that the pattern obtained by AGSA meets the desired pattern very well. Moreover, when the number of iterations is 2 000, the fitness value of the improved algorithm is increased by 30%. It can be seen that AGSA outperforms the algorithm in the literature in evolutionary speed and accuracy. Sparse concentric ring array also has the same optimization results. The effectiveness of the proposed improved algorithm in solving the array pattern synthesis is proved.

Frequency Diverse Array Beampattern Synthesis With Taylor Windowed Frequency Offsets

Frequency diverse array (FDA) is capable of generating a range-angle-dependent beampattern via adjusting the frequency offset across array elements. The classical linear FDA generates an S-shaped beampattern due to the range-angle-dependent coupling. In order to remove the coupling, and obtain a well-focused dot-shaped beampattern, several FDA frameworks are proposed via adjusting frequency offsets. It seems that the window based tapering frequency offsets are able to form a single maximum with a satisfactory mainbeam sharpness. However, most window-based FDA schemes are focused on classical fixed windows. In this letter, an FDA framework with Taylor windowed frequency offsets is first proposed. Considering that adjustable tapering windows allow adjustments by parameter manipulation, the optimized parameters of the window function are determined. The FDA beamforming results with all kinds of frequency offsets are measured, and compared. Numerical results validate the superiority of proposed FDA in terms of mainlobe width, and sidelobe level.

A Method of Improving the Correlation Properties of OFDM Chirp Waveform Diversity

In this letter, an orthogonal frequency-division multiplexing (OFDM) chirp waveform diversity design scheme is proposed to achieve better correlation properties. First, the subchirp duration and bandwidth are optimized simultaneously to increase the degree of freedom in waveform diversity. Second, an optimization procedure is proposed based on the idea of Gram-Schmidt orthogonalization. To reduce the problem complexity, the design problem is separated into several subproblems. Each subproblem corresponds to designing an OFDM chirp composite waveform and is optimized by the Pareto optimization framework. Simulation results show that the proposed method outperforms the conventional methods in terms of both autocorrelation peak sidelobe level (APSL) and cross correlation peak level (CPL) under the circumstance of the same mainlobe width.

A simple approach to nonstationary source waveform estimation in seismic records

A simple and practical method for source-waveform estimation from reflection seismic records is implemented by iterative identification of locally strongest reflections. Instead of conventional hypotheses about statistical properties of the whole records, the method is based on a general observation that stronger reflection peaks occur relatively sparsely and that smaller peaks adjacent to them are mutually incoherent. Tests with real well logs suggest that the subsurface often possesses such sparseness. Based on this property, the source waveform is obtained from seismic records by optimizing a combination of its practically important properties, such as the main-lobe width, side-lobe amplitudes, and phase character. Similarly, other types of optimization criteria can be used. The approach is stable with respect to noise and parameter variations and allows estimating the source waveforms without well-log control. By including inverse [Formula: see text]-filtering, time-variant amplitude scaling, and/or band-pass filtering, the approach allows correcting for reflection amplitude variations, nonstationarity due to seismic attenuation and dispersion, and also for coherent noise consisting in possible amplitude variations and phase shifts of the low- or high-frequency components of the records. By using the estimated source waveform, time-dependent waveforms and nonstationary wavelet matrices can be predicted at any reflection time. The method is illustrated by synthetic examples of logs with von Kármán distributions of velocity fluctuations and real well logs from an oil reservoir. In the synthetics, the spectral character and shape of the main lobe of the source waveform are reproduced well in all cases, and the phase character of the source is partly recovered when the subsurface reflectivity is dominated by reflections that are relatively sparse and strong compared to the adjacent reflectivity. In cases in which the phase of the source signal is unknown, the obtained waveforms are characterized by simple shapes with low-amplitude side lobes. Such waveforms are suitable for many applications from well ties and numerical modeling to deconvolution and [Formula: see text]-compensation.

Application of the adaptive array reduction method for offset acoustic source localisation

Acoustic beamforming arrays are typically designed assuming that the noise source of interest is aligned with the geometric centre of the array or near it, and with some prior knowledge of the frequency range of interest. This method of array design works well and provides sufficient performance provided that the source of interest is located at or near the centre of the investigated region, known as a scanning grid. If a source is recorded at some distance away from the scanning grid centre, its representation within a beamforming source map can be distorted, the Main Lobe Width (MLW) can be enlarged and the remainder of the source map may possess significant sidelobes. The magnitude of the Maximum Sidelobe Level (MSL) often increases as the source is moved away from the scanning grid centre, which can be problematic when the relative alignment between the array centre and the source cannot be altered. By using an array design that is fixed within a testing facility, the region in which optimal MSL and MLW performance can be obtained is limited. By using a recently published technique known as the Adaptive Array Reduction Method (AARM), these issues can be overcome provided that some information regarding the source location and the frequency range of interest is known prior. An array can be designed for a specific source location and frequency, thus significantly improving the MSL, MLW and lobe-distortion, relative to an array locked in a fixed position. In this paper, the AARM is experimentally verified, revealing excellent agreement with simulated source maps. Furthermore, the AARM is used to design arrays based on a centred and non-centred source and their numerical and experimental performances are compared against some logarithmic spiral and randomised pattern arrays, clearly revealing significantly improved source image maps for acoustic sources located away from the scanning grid centre.

Superresolution technology based on a heterodyne detection system

Diffractive superresolution elements (DSEs) placed on a pupil plane can generate a diffractive main lobe whose width is smaller than that of an Airy disk, allowing for the realization of superresolution technology based on pupil filtering. However, the energy of the main lobe decreases dramatically with the decreasing of main lobe width, namely, the implementation of this superresolution technology is at the cost of effective signal power. This restricts greatly the development of this technology. In order to solve this problem, this study suggests the use of a heterodyne detection system (HDS) with this technology. The resolution characteristics of the HDS are analyzed through theoretical deduction. According to research results, HDS has the same longitudinal resolution and twice as high transverse resolution as a direct detection system (DDS). More significantly, the theoretical analyses show that HDS can increase detection sensitivity significantly compared with DDS. Hence, the proposed method makes it possible to detect extremely faint signals using this superresolution technology. In addition, because HDS lowers the requirements on main lobe energy due to its high sensitivity, the design of DSE can achieve a smaller width of main lobe, which can further improve the resolution of the superresolution technology based on pupil filtering.

Accurate Frequency Estimation by Using Three-Point Interpolated Discrete Fourier Transform Based on Rectangular Window

Windowed interpolated discrete Fourier transform (DFT) has been well-studied to deal with the spectral leakage and picket fence effects in frequency estimation. When the number of acquired sine-wave cycles is small, the long-range spectral leakage of the negative frequency is the main cause of low accuracy. In this article, a novel frequency estimator using three-point interpolated DFT based on rectangular window is proposed. The spectral superposition of positive and negative frequencies is adopted in the proposed interpolation algorithm to remove both short- and long-range spectral leakage. The influence of white noise on frequency estimation can be reduced because the adopted rectangular window has the narrowest mainlobe width or the smallest equivalent noise bandwidth among all windows. Simulation and experimental results confirm that the proposed method outperforms existing windowed interpolated DFT algorithms.

Optimised staggered grid finite difference operators based on the combined window function

ABSTRACT The staggered grid finite difference (SGFD) method has been widely utilised in seismic forward modelling. The accuracy of forward modelling results has a great influence on the results of subsequent seismic imaging and seismic inversion. Numerical dispersion is one of the inherent problems in the SGFD method. To suppress dispersion, we here introduce the truncated window function method, which can get optimised finite difference operators after truncating spatial convolution series of the pseudo-spectral method. The empirical criteria of window functions are the main lobe width that should be as narrow as possible and the side lobe attenuation should be as large as possible. According to these criteria, we propose the combined window function method based on the Gaussian window and Hanning window. The result of the amplitude spectrum response shows that the new combined window has narrower main lobe and greater side lobe attenuation, which results in higher accuracy in numerical simulations with SGFD operators. Numerical tests also illustrate the effectiveness of this new method.

Bandwidth optimization and side-lobe levels reduction in PC radar using Legendre orthogonal polynomials

Time-bandwidth product (TBP), peak side-lobe level (PSL), integrated side-lobe level (ISL), and relative main-lobe width are considered important performance parameters in pulse compression (PC) radar for the selection of transmitting waveforms. In radar system, linear frequency modulated (LFM) waveforms are popular for transmission. LFM waveforms suffer from the range side-lobes problem which affects accurate detection of the target. This paper describes a new transmitting waveform based on Legendre orthogonal polynomial (LOP) for bandwidth optimization and side-lobe levels reduction in PC radar. PC provides the benefits of long duration pulse for better range resolution and detection. Different order LOPs are examined with varying optimizing parameter (γ), and the polynomial giving optimum performance is chosen. Further, different windowing methods are added in cascade to decrease the side-lobes but with the limitation of wider relative main-lobe width. Simulation results indicate that the proposed LOP gives better side-lobe reduction than LFM and Chebyshev chaotic sequences.

Improved high‐precision approach based on deconvolution in MIMO sonar imagery

Multiple-input multiple-output (MIMO) sonar enables high-resolution imaging, which is extremely useful in underwater acoustic high-precision imagery. However, the first peak sidelobe levels and beamwidth performance degrade significantly when conventional tapering is applied due to the non-uniformity of the spanned virtual linear array, which prevents MIMO sonar from obtaining high-precision images with high resolution and high definition. Therefore, an improved high-precision approach in MIMO sonar imagery is proposed based on deconvolution to realise sidelobe suppression and to narrow the mainlobe width. The relationship between the target's beam power function and the pattern of the actual transmitting–receiving arrays is derived first, and design criteria are presented for MIMO sonar arrays to enhance the resolution. Subsequently, according to the orthogonality of the transmitting signals, the echo is separated by matched filtering, and then joint beamforming is employed to attain the beam data. Finally, the focused images are processed by deconvolution to enhance the clarity of the image and simultaneously obtain higher resolution. Numerical simulations and lake experiments are presented to demonstrate that high-precision images in MIMO sonar are achieved utilising the proposed approach, which also involves a lower computation load.

Achromatic reflected metalens for highly directional and long-distance acoustic probing

Simultaneous temporal and spatial focusing of a pulse is of significance for detection and imaging. Here, an achromatic reflected metalens is designed using hybrid resonance and anti-resonance. The theoretical result demonstrates that the anti-resonance provides an extra degree of freedom to control local phases of reflected waves, yielding an achromatic lens of thickness equal to one half of central wavelength. To overcome the shortcoming of traditional approach to design lenses (neglecting the intercell coupling), a boundary integral method is proposed to alleviate the focus deviation over a broadband. The achromatic feature of designed lens is then verified in the frequency range from 2800 to 5600 Hz by an experiment. Owing to a very weak frequency dependence of focal point and a high reflected focusing efficiency over a broadband, a highly directional and long-distance acoustic probing scheme (the mainlobe width about 80) is proposed with the aid of achromatic reflected metalens and being confirmed by another experiment, where a signal processing method using triple sensors separated by a subwavelength interval is adopted to eliminate the interferences between incident waves and reflected waves. Our result may find its application in a long-distance underwater acoustic probing.

Implementation of MOIDS Algorithm for Optimal Parameter Selection of SFPT for Modern Radars

Modern radars require signals of the large frequency range to attain relatively greater range resolution. Frequency stepping is the technique to convert the narrowband signal, i.e., a train of pulses into a wideband signal to achieve high accuracy in range resolution measurements. Due to the cause of constant step in frequency of successive pulses, grating lobes appeared when the period of pulse multiplied by step in frequency exceeds unity as is needed in modern radars. Hence to achieve the best resolution, grating lobes height, sidelobes level, and mainlobe width have to be minimum. In this paper an attempt has been made to diminish grating lobes, minimize sidelobes and reduce mainlobe width using MOIDSA to find the parameters of Stepped Frequency Pulse Train (SFPT) mechanism. The compromise between various lobes is obtained by using three dimensional Pareto fronts for different ranges of SFPT parameters.

Frequency Invariant Beamforming for a Small-Sized Bi-Cone Acoustic Vector-Sensor Array.

In this work, we design a small-sized bi-cone acoustic vector-sensor array (BCAVSA) and propose a frequency invariant beamforming method for the BCAVSA, inspired by the Ormia ochracea’s coupling ears and harmonic nesting. First, we design a BCAVSA using several sets of cylindrical acoustic vector-sensor arrays (AVSAs), which are used as a guide to construct the constant beamwidth beamformer. Due to the mechanical coupling system of the Ormia ochracea’s two ears, the phase and amplitude differences of acoustic signals at the bilateral tympanal membranes are magnified. To obtain a virtual BCAVSA with larger interelement distances, we then extend the coupling magnified system into the BCAVSA by deriving the expression of the coupling magnified matrix for the BCAVSA and providing the selecting method of coupled parameters for fitting the underwater signal frequency. Finally, the frequency invariant beamforming method is developed to acquire the constant beamwidth pattern in the three-dimensional plane by deriving several sets of the frequency weighted coefficients for the different cylindrical AVSAs. Simulation results show that this method achieves a narrower mainlobe width compared to the original BCAVSA. This method has lower sidelobes and a narrower mainlobe width compared to the coupling magnified bi-cone pressure sensor array.