Peak Sidelobe Research Articles

WCA-Based Low-PSLL and Wide-Nulling Beampattern Synthesis for Radar Applications

There are many unavoidable array errors in practical scenarios, which would drastically increase the sidelobe level (SLL) and distort the performance of radar systems accordingly. In this paper, an effective beampattern synthesis approach is proposed to realize a low peak sidelobe level (PSLL) and wide-nulling in the presence of array errors, thus improving the consequent performance of the radar. In particular, the covariance matrix of the sidelobe region (CMSR) is incorporated into the optimization. Considering the randomness of array errors, the statistical mean method is adopted to obtain a more accurate calculation of the CMSR in the presence of array errors based on a Monte Carlo trial. To efficiently and effectively solve the optimization problem, an advanced metaheuristic algorithm, i.e., the water cycle algorithm (WCA), is adopted when seeking the corresponding optimal weight vectors. Numerical results are provided and discussed to demonstrate the effectiveness of the proposed approach including the results based on a wideband linearly spaced magneto-electric (ME) dipole array.

Ensemble Learning-Based Multi-Cues Fusion Object Tracking in Complex Surveillance Environment.

The vast majority of currently available kernelized correlation filter (KCF)-based trackers simply make use of a single object feature to define the object of interest. It is impossible to avoid tracking instability while working with a wide variety of complex videos. In this piece of research, an ensemble learning-based multi-cues fusion object tracking method is offered as a potential solution to the issue at hand. Using ensemble learning to train multiple kernelized correlation filters with different features in order to obtain the optimal tracking parameters is the primary concept behind the improved KCF-based tracking algorithm. After that, the peak side lobe ratio and the response consistency of two adjacent frames are used to obtain the fusion weight. In addition, an adaptive weighted fusion technique is applied in order to combine the response findings in order to finish the location estimation; finally, the tracking confidence is applied in order to update the tracking model in order to prevent model deterioration. In order to increase the adaptability of the revised algorithm to size-change, a Bayesian estimate model based on scale pyramid has been presented. This model is able to determine the optimal scale of the object, which is the goal of this endeavor. The tracking results of a number of different benchmark movies demonstrate that the algorithm that we have suggested is able to effectively eliminate the effects of interference elements, and that its overall performance is superior to that of the comparison algorithms.

Advanced Marine Predator Algorithm for Circular Antenna Array Pattern Synthesis.

The pattern synthesis of antenna arrays is a substantial factor that can enhance the effectiveness and validity of a wireless communication system. This work proposes an advanced marine predator algorithm (AMPA) to synthesize the beam patterns of a non-uniform circular antenna array (CAA). The AMPA utilizes an adaptive velocity update mechanism with a chaotic sequence parameter to improve the exploration and exploitation capability of the algorithm. The MPA structure is simplified and upgraded to overcome being stuck in the local optimum. The AMPA is employed for the joint optimization of amplitude current and inter-element spacing to suppress the peak sidelobe level (SLL) of 8-element, 10-element, 12-element, and 18-element CAAs, taking into consideration the mutual coupling effects. The results show that it attains better performances in relation to SLL suppression and convergence rate, in comparison with some other algorithms for the optimization case.

Enhancement of three-dimensional image visualization under photon-starved conditions.

In this paper, we propose enhancement of three-dimensional (3D) image visualization under photon-starved conditions using preprocessing such as contrast-limited adaptive histogram equalization (CLAHE) and histogram matching. In conventional imaging techniques, photon-counting integral imaging can be utilized for 3D visualization. However, due to a lack of photons, it is challenging to enhance the visual quality of 3D images under severely photon-starved conditions. To improve the visual quality and accuracy of 3D images under these conditions, in this paper, we apply CLAHE and histogram matching to a scene before photon-counting integral imaging is used. To prove the feasibility of our proposed method, we implement the optical experiment and show the performance metric such as peak sidelobe ratio.

Deep null fixing on optimal compromise among sum and difference patterns of thinned arrays through the Schelkunoff unit circle representation

Difference far-field patterns represent a way for pin-pointing a target in both azimuth and elevation, extremely useful in radar applications. At the present work, an innovative method for synthesizing good compromise solutions among sum and difference patterns providing low complexity of the antenna feeding network for uniform thinned arrays is addressed. This procedure uses a hybrid version of the Simulated Annealing algorithm (hybrid SA) to optimize a cost function of radiation characteristics for both sum and difference patterns as peak directivity and side lobe level (SLL) while fixing deep nulls. In this framework, examples of half-wavelength spaced linear arrays from 40 to 120 elements were analyzed, as well as an extension to planar arrays by means of separable distributions was developed. The performance of the method is analyzed with different examples and its potential outlined, showing the ability of fixing deep nulls in both sum and difference patterns which share the same uniform excitation relative amplitudes.

Synthesis of Thinned Planar Arrays Using 0-1 Integer Linear Programming Method

This paper proposes a fast optimization method for synthesizing thinned planar antenna arrays. A 0-1 integer linear programming (ILP) model was proposed for the antenna array optimization. This model mainly aims to minimize the peak sidelobe level (PSLL) and consider the design requirements of narrow beamwidth and high directivity, finally obtaining the optimal distribution of the turned “ON” element positions in the aperture. Several cases of planar array designs with different aperture sizes and scan angles were provided in the paper and compared with other popular algorithms. Numerical results showed that the new method can effectively optimize the thinned planar arrays, including large-scale arrays, while significantly reducing the computational cost and time.

A Sidelobe Suppression Method for Circular Ground-Based SAR 3D Imaging Based on Sparse Optimization of Radial Phase-Center Distribution

Circular ground-based SAR (GBSAR) is a new 3D imaging GBSAR with the potential of acquiring high-quality 3D SAR images and 3D deformation. However, its donut-shaped spectrum and short radius of antenna rotation cause high sidelobes on 3D curved surfaces, resulting in 3D SAR images with poor quality. The multi-phase-center circular GBSAR with full array can effectively suppress sidelobes by filling the donut-shaped spectrum to be the equivalent solid spectrum, but it requires a larger number of phase centers, increasing system cost and engineering difficulties. In this paper, a sidelobe suppression method for circular GBSAR 3D imaging based on sparse optimization of radial phase-center distribution is proposed to suppress high sidelobes at low cost. By deriving the point spread function (PSF) of multi-phase-center circular GBSAR and taking the peak sidelobe level (PSL) and integrated sidelobe level (ISL) of the derived PSF as multi-objective functions, we solve the multi-objective optimization problem to optimize the sparse distribution of radial phase centers. The advantage of the proposed method is that the solved optimal radial phase-center distribution can effectively suppress the 3D sidelobes of circular GBSAR with a limited number of phase centers. Finally, the sidelobe suppression effect of the proposed method is verified via 3D imaging simulations.

Synthesis of uniform amplitude sparse linear dipole arrays with multiple shaped‐beam patterns by sharing element rotations and positions

In this article, a novel method of synthesizing sparse linear dipole arrays with multiple shaped-beam patterns is proposed by finding a set of common element rotations and positions along with individual excitation phases. Compared with most shaped multiple-pattern synthesis methods using nonuniform amplitude excitations, the proposed method adopts the uniform amplitude excitation and exploits the element rotation as a supplementary degree of array freedom. Such a method enables each amplifier to work at its optimal level and avoids the usage of unequal power dividers for the array feeding network, thus reducing the cost, space, and weight of the radiation system. The shaped multiple-pattern synthesis problem with multiple constraints including the peak sidelobe level, cross-polarization level, minimum element spacing, and array length is formulated and optimized by particle swarm optimization. Two examples for synthesizing sparse linear dipole arrays with multiple shaped-beam patterns are conducted to validate the effectiveness and superiority of the proposed method. Synthesis results show that the proposed method can save antenna elements and avoid the usage of unequal power dividers for test cases. Moreover, the full-wave simulations are also conducted in these two examples.

On the Performance of Mobile Cellular-Connected Drones Under Practical Antenna Configurations

Providing seamless connectivity to unmanned aerial vehicle user equipment (UAV-UE) is very challenging due to the encountered line-of-sight interference and reduced gains of down-tilted base station (BS) antennas. For instance, as the altitude of UAV-UEs increases, their cell association and handover procedure become driven by the side-lobes of the BS antennas. In this paper, the performance of cellular-connected UAV-UEs is studied under 3D practical antenna configurations. Two scenarios are studied: scenarios with static, hovering UAV-UEs and scenarios with mobile UAV-UEs. For both scenarios, the UAV-UE coverage probability is characterized as a function of the system parameters. The effects of the number of antenna elements on the UAV-UE coverage probability and handover rate are then investigated. Moreover, a lower bound on the handover probability is derived as a function of the number of antenna elements and the UAV-UE mobility speed. Results reveal that the UAV-UE coverage probability under a practical antenna pattern is lower than that under a simple antenna model. Moreover, vertically-mobile UAV-UEs are susceptible to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">altitude handover</i> due to consecutive crossings of the nulls and peaks of the antenna side-lobes. The effect of altitude handover is also shown to be effectively mitigated by serving UAV-UEs cooperatively from multiple ground BSs.

An analytical study of spatial resolution enhancement for a dual-frequency acoustic beamformer

In this paper, we address an acoustic directed-self-assembly (DSA) problem for aiming to pattern particles based on creating an appropriate acoustic field by the fine adjustment of transducer operating parameters. The proposed idea is to incorporate the DSA problem with multi-frequency beamforming techniques. First, the boundary element method (BEM) is implemented for the direct modeling of the proposed DSA problem. Then, it is integrated with the concept of dual-frequency beamforming. In this study, the influence of changing excitation frequency is investigated on the spatial resolution enhancement of the pressure field. Also, the optimal frequency difference is calculated theoretically to produce two adjacent pressure traps with maximum separability and, therefore, maximum spatial resolution in a two-frequency acoustic beamformer without any restriction on the chamber shape. The performance of the proposed Dual-Frequency Beamforming (DFB) method is evaluated by simulations based on the finite element method (FEM) and compared with conventional Delay-And-Sum (DAS), Eigen Vector-Based (EigVec-based), and Bessel Beam techniques. Several evaluation metrics such as Full Width at Half Maximum (FWHM), Peak Side-lobe Level (PSL), Contrast Ratio (CR), Positioning Accuracy (PA), and processing time are considered for comparisons. Simulation results indicate the superiority of the proposed DFB method over the mentioned methods in separability and focusing precision when the two pressure traps are close to each other.

A Novel Method for Maximum Directivity Synthesis of Irregular Phased Arrays

A novel and effective method for the design of maximum directivity irregular phased arrays is proposed in this article. By decomposing the radiation pattern of irregular arrays (IAs) into the product of subarray pattern and subarray array factor, the principal factor for the reduction of directivity and the appearance of high sidelobes is analyzed. Aimed at maximizing directivity of IAs, a binary quadratic optimization problem (BQOP) is established for the design of subarray tiling configuration, where the directivities at considered scanning angles satisfying given peak sidelobes level (SLL) is maximized. To consider the directivities at all the scanning angles within given scan ranges, a concept of “generalized directivity” is introduced and defined. Meanwhile, it is known that high directivity usually enables to suppress high SLL to a great extent. Therefore, the BQOP is reduced to a simplified binary quadratic problem (SBQP) for the maximization of the “generalized directivity” without the high-dimensional constraint on SLL. The associated complex excitations at subarray level are solved using convex optimization after the subarray tiling configuration is determined. By comparing to the reported state-of-the-art methods, several representative numerical examples are implemented to assess the effectiveness of the proposed method.

Fourier Transform of SAR Data Cube and 3-D Range Migration Algorithm

To develop a 3-D imaging synthetic aperture radar(SAR) algorithm, a theoretical expression for a Fourier transform of data cube is required. In this article, we introduce a function representing the Fourier transform of 3-D SAR data cube. The function is derived using the method of stationary phase and similar to the one used for 2-D data matrix. For verification and evaluation, a 3-D range migration algorithm using this function for bulk compression is examined. The simulation results based on the parameters of an experimental terahertz indoor SAR testbed show that the algorithm can well focus the 3-D image and, hence, verify the derived function. The image quality assessments such as spatial resolutions and peak sidelobe ratio are used to further evaluate the function and the algorithm. The measured results are compared with the ones provided by a backprojection algorithm.

A Low Sidelobe Deceptive Jamming Suppression Beamforming Method With a Frequency Diverse Array

The deceptive jamming technique can threaten a synthetic aperture radar (SAR) imaging system by repeatedly transmitting copied radar signals back to the radar. A conventional phased array can generate only an angle-dependent beam and cannot distinguish the jammer from other targets. Instead, a frequency diverse array (FDA) can offer a range-angle-dependent beampattern by introducing small frequency offsets to array elements, which can be adopted to distinguish signals from different range cells. Thus, considering that the position of the jammer is unknown, it is necessary to suppress the range peak sidelobe as much as possible. To lower this value, this communication proposes a weighted FDA to achieve the optimal solution at the expense of raising other range sidelobes.

On the design of linear sparse arrays with beampattern shift invariant properties

We investigate the design of linear sparse arrays and multiple-input multiple-output (MIMO) linear sparse arrays with beampattern shift invariant property (BSIP) and determine the necessary and sufficient conditions needed to achieve BSIP. Moreover, we show how to theoretically calculate the precise peak sidelobe level (PSL) values of their array beampatterns. We also establish the relationship between the number of antennas and the beampattern of a linear sparse array with BSIP. Furthermore, built on our theoretical analysis, we devise computationally efficient cyclic algorithms to design linear sparse arrays with BSIP and their MIMO counterparts by minimizing the PSL values of their beampatterns. In addition, we introduce a design method to avoid angle ambiguities even when the pointing direction of the linear array beampattern is the extreme case of 90∘ or -90∘. Numerical examples are provided to support our theoretical analysis and demonstrate that our proposed algorithms can be used to obtain linear sparse arrays with 3-dB main beam widths narrower while simultaneously PSL values lower than those of the existing arrays.

Frequency‐domain multireceiver synthetic aperture sonar imagery with Chebyshev polynomials

Based on Chebyshev polynomials, the two-way slant range is first approximated by the fourth-order polynomial approximation. With the series reversion method, the point target reference spectrum (PTRS) which is further used for the development of imaging algorithm in this letter is obtained. The presented method processes the echoed signal corresponding to each transmitter/receiver pair. And then a high-resolution synthetic aperture sonar (SAS) image is obtained by coherently superposing all coarse-resolution images. Comparing the peak sidelobe ratio (PSLR) and integration sidelobe ratio (ISLR), the performance of the presented method is superior to that of the traditional method. Simulations are further validated by the presented method.

Peak Sidelobe Level and Peak Crosscorrelation of Golay–Rudin–Shapiro Sequences

Sequences with low aperiodic autocorrelation and crosscorrelation are used in communications and remote sensing. Golay and Shapiro independently devised a recursive construction that produces families of complementary pairs of binary sequences. In the simplest case, the construction produces the Rudin–Shapiro sequences, and in general it produces what we call Golay–Rudin–Shapiro sequences. Calculations by Littlewood show that the Rudin–Shapiro sequences have low mean square autocorrelation. A sequence’s peak sidelobe level is its largest magnitude of autocorrelation over all nonzero shifts. Høholdt, Jensen, and Justesen showed that there is some undetermined positive constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> such that the peak sidelobe level of a Rudin–Shapiro sequence of length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{n}$ </tex-math></inline-formula> is bounded above by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(1.842626\ldots)^{n}$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.842626\ldots $ </tex-math></inline-formula> is the positive real root of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X^{4}-3 X-6$ </tex-math></inline-formula> . We show that the peak sidelobe level is bounded above by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5(1.658967\ldots)^{n-4}$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.658967\ldots $ </tex-math></inline-formula> is the real root of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X^{3}+X^{2}-2 X-4$ </tex-math></inline-formula> . Any exponential bound with lower base will fail to be true for almost all <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> , and any bound with the same base but a lower constant prefactor will fail to be true for at least one <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> . We provide a similar bound on the peak crosscorrelation (largest magnitude of crosscorrelation over all shifts) between the sequences in each Rudin–Shapiro pair. The methods that we use generalize to all families of complementary pairs produced by the Golay–Rudin–Shapiro recursion, for which we obtain bounds on the peak sidelobe level and peak crosscorrelation with the same exponential growth rate as we obtain for the original Rudin–Shapiro sequences.

Shaped-Beam Pattern Synthesis With Sidelobe Level Minimization via Nonuniformly-Spaced Sub-Array

This article deals with the low-sidelobe shaped-beam pattern synthesis (SBPS) problem using two nonuniformly spaced subarray configurations, including amplitude and amplitude–phase subarray configurations. An optimization model is proposed for the SBPS problem to minimize the peak sidelobe level by jointly optimizing the subarray configuration and element excitations/positions. A typical advantage of the proposed model is to reduce the system control points while maintaining the benign array performance. However, the formulated problem is a mixed-integer nonconvex one, which makes it challenging. Besides, this problem cannot be directly solved due to the existence of coupling optimization variables. Thus, a set of auxiliary variables is introduced to move the coupling optimization variables into equality constraints. These equality constraints are converted into quadratic penalty forms and are added to the objective function. Then, an efficient iterative algorithm is proposed using the penalty-based optimization method, which solves the original problem by iteratively solving a series of subproblems based on the inexact block coordinate descent technique. Numerical examples with different beam patterns are performed to verify the effectiveness of the proposed algorithm.

Синтез разреженной линейной антенной решетки с сохранением ширины главного лепестка и минимальным пиковым уровнем боковых лепестков при помощи генетического алгоритма

This paper proposes a genetic algorithm as an instrument for antenna array thinning. The algorithm with a deliberately chosen fitness function allows synthesizing thinned linear antenna arrays with low sidelobe level while maintaining the half-power beamwidth of a full linear array. Based on results from existing papers in this field and known approaches to antenna array thinning, a classification of thinning types is introduced. The optimal thinning type for a linear thinned antenna array is determined on the basis of a maximum attainable sidelobe level. The variation of main direction pattern characteristics, such as peak sidelobe level and half-power beamwidth, with respect to a thinning coefficient, are discussed for a number of amplitude tapers.

Design Analysis of Array of Dipole Transmitters for Wireless Power Transfer

Considered in this work are the radiation aspects of a radio-frequency wireless power transfer system. Using the halfwave dipole as a candidate of choice, the current distribution on the antenna is first evaluated and presented using the versatile electromagnetic numerical Method of Moment technique (MoM). Using the current distribution obtained from the kernel of integration, the radiation fields for the single dipole element was obtained. Also, the analysis is extended to uniformly space linear antenna arrays using broadside and ordinary endfire arrays as candidates of interest. The simulation results for the broadside and endfire arrays were presented for 5, 6, 7, 10, 20 and 30 array elements at 0.3, 0.4 and 0.5 inter-element spacing. The peak directivity of broadside array occurs at 30 elements, 0.5λ spacing, and exceeds endfire array peak directivity by 11.27%. In addition to the advantage of an improved directivity achieved by the 7-element broadside array, an improved peak sidelobe level (PSLL) with the lowest PSLL for 7, 20, and 30 elements broadside array occurring at -12.0534 dB, -12.4298 dB, -12.6642 dB, -13.2246 dB, and -13.2747 dB respectively.

Doppler Shift Tolerance of Typical Pseudorandom Binary Sequences in PMCW Radar.

In the context of all-digital radar systems, phase-modulated continuous wave (PMCW) based on pseudorandom binary sequences (PRBSs) appears to be a prominent candidate modulation scheme for applications such as autonomous driving. Among the reasons for its candidacy are its simplified transmitter architecture and lower linearity requirements (e.g., compared to orthogonal-frequency division multiplexing radars), as well as its high velocity unambiguity and multiple-input multiple-output operation capability, all of which are characteristic of digital radars. For appropriate operation of a PMCW radar, choosing a PRBS whose periodic autocorrelation function (PACF) has low sidelobes and high robustness to Doppler shifts is paramount. In this sense, this article performs an analysis of Doppler shift tolerance of the PACFs of typically adopted PRBSs in PMCW radar systems supported by simulation and measurement results. To accurately measure the Doppler-shift-induced degradation of PACFs, peak power loss ratio (PPLR), peak sidelobe level ratio (PSLR), and integrated-sidelobe level ratio (ISLR) were used as metrics. Furthermore, to account for effects on targets whose ranges are not multiples of the range resolution, oversampled PACFs are analyzed.