Peak Sidelobe Research Articles

Cognitive waveform design with desired spectrum-autocorrelation properties

This paper proposes a novel cognitive waveform design methodology aimed at shaping a specified spectrum and achieving good autocorrelation properties in terms of the spectrum band notch and local autocorrelation peak sidelobe level (A-PSL). To this end, the Pareto optimization framework is introduced that minimizes the lp-norm of multi-objective functions both encompassing the stopband energy and local A-PSL. In addition, along with energy and peak-to-average power ratio constraints to ensure hardware compatibility, the out-of-band (OOB) spectrum energy and the rest autocorrelation sidelobe level are restricted to resist the OOB strong interference (also prevent spectrum leakage) and enhance multiple target detectability, respectively. To tackle the resultant nonconvex nonsmooth (in general NP-hard) design problem, an iterative majorization minimization proximal method of multipliers (MM-PMM) algorithm is developed along with each iteration involving multiple subproblems which are solved through a majorization method or closed-form solutions. In particular, resorting to Wiener-Khintchine theorem, the developed algorithm is efficiently implemented via the fast fourier transform and element-wise arithmetic. Extensive numerical examples highlight that the synthesized waveform shares the desired spectrum-autocorrelation properties and is capable of enhancing the weak target detection and anti-jamming performance in comparison with some counterparts.

Highly Directive Array Pattern Synthesis in Different phi Planes of a Large CCRAA Using Array Thinning Technique

This paper presents a pattern synthesis method of a sizeable concentric circular ring array (CCRAA) of isotropic antennas using Evolutionary Algorithms. In this method, the array is thinned using the optimum set of binary excitations to achieve the desired highly directive pencil beam patterns with lower peak side lobe level(SLL). The half-power beam width and first null beam width is kept constant to obtain such highly directive beam patterns with lower peak SLL. This pattern is not synthesized to a particular azimuth plane rather in four different ' planes from entire azimuth planes. The isotropic elements are uniformly spaced in the concentric ring. The achieved set of optimum amplitudes are constructed with either 1 or 0 using Differential Evolutionary Algorithm(DE), Genetic Algorithm (GA), and Particle Swarm Optimization Algorithm (PSO). These excitations show the state of the elements. The elements are in “ON” state or in “OFF” state depending upon the excitation ‘1’ or ‘0’. It is also helpful to reduce the complexity of the feed networks. The excitations are also verified in the whole range (0o <phi<360o) of ' planes by selecting four phi planes arbitrarily. The outcomes established the superiority of GA and DE over PSO and also the effectiveness of the proposed method.

On Microstrip Array Antenna with Enhanced Bandwidth and Gain Using Modified Ant Lion Optimization for X-Band Applications

This article furnishes the design and analysis of three concentric circular array antennas (CCAAs) of point sources and a linear microstrip patch array antenna (LMPAA) employing a newly developed hybrid optimization algorithm, the modified ant lion optimization (MALO). The optimum CCAAs employing MALO offer better radiation patterns in terms of the reduction in peak side lobe level, null depths, first null beam width, and directivity considering the same apertures, compared to some other popular optimization algorithms available in the literature. In the other hand, the LMPAA with optimized rectangular ring shaped slots in its ground plane using MALO enhances its bandwidth (BW), gain, and directivity. A prototype of the proposed LMPAA is fabricated, which offers measured values of BW, gain, directivity, and radiation efficiency of 907.1 MHz, 10.26 dBi, 12.19 dB, and 84.16%, respectively. The LMPAA is compared with some previously available designs in the literature to highlight its significance and hence to validate the process of employing optimization algorithms in design and analysis of real antennas.

Radiation Pattern Nulling in Phased Array Antennas Using Superior Discrete Fourier Transform and Dolph‐Tschebyscheff Based Synthesis Techniques

AbstractThis study proposes an improved method for sector nulling in the radiation pattern of rectangular phased array antennas using two different synthesis techniques; an orthogonal Discrete Fourier transform and a quasi‐orthogonal Dolph‐Tschebyscheff based technique. In traditional synthesis techniques, broad elemental beams serve as local field basis functions (FBFs) in an array. Instead, the proposed methods produce low sidelobe narrow beams as FBFs. A set of these FBFs can effectively constitute the array's radiation pattern in a confined angular region. By properly weighting these FBFs, sector pattern nulls in a designated angular range are synthesized without severely distorting the patterns outside this area. The FBFs' optimal weights can be efficiently calculated using a nonlinear minimum least squares error technique, which is later transformed into the array's elemental excitation coefficients. Along with faster convergence, this technique allows control over peak sidelobe level, null depth, and width, making it suitable for GPS anti‐jamming, 5G communications, and other applications requiring interference suppression.

Unequally Spaced Antenna Array Synthesis Using Accelerating Gaussian Mutated Cat Swarm Optimization

Low peak sidelobe level (PSLL) and antenna arrays with high directivity are needed nowadays for reliable wireless communication systems. Controlling the PSLL is a major issue in designing effective antenna array systems. In this paper, a nature inspired technique, namely accelerating Gaussian mutated cat swarm optimization (AGMCSO) that attributes global search abilities, is proposed to control PSLL in the radiation pattern. In AGM-SCO, Gaussian mutation with an acceleration parameter is used in the position-updated equation, which allows the algorithm to search in a systematic way to prevent premature convergence and to enhance the speed of convergence. Experiments concerning several benchmark multimodal problems have been conducted and the obtained results illustrate that AGMCSO shows excellent performance concerning evolutionary speed and accuracy. To validate the overall efficacy of the algorithm, a sensitivity analysis was performed for different AGMCSO parameters. AGMCSO was researched on numerous linear, unequally spaced antenna arrays and the results show that in terms of generating low PSLL with a narrow first null beamwidth (FNBW), AGMCSO outperforms conventional algorithms.

An Efficient Recursive Multibeam Pattern Subtraction (MPS) Beamformer for Planar Antenna Arrays Optimization

In this paper, a new beamforming technique for planar two-dimensional arrays is proposed for optimizing the sidelobe levels (SLLs) by using recursive multibeam pattern subtraction (MPS) technique. The proposed MPS beamformer is demonstrated and its convergence to lower SLL values is investigated and controlled. The performance analysis has shown that the proposed MPS beamformer can effectively reduce the SLL down to less than −50 dB relative to the mainlobe level utilizing the major sidelobes information in the radiation pattern. In addition, the proposed MPS beamformer can be applied to any planar array geometry such as rounded corners rectangular arrays provided that the original array pattern contains sidelobe peaks. The comparison with recent related techniques has shown that the proposed beamformer provides faster convergence time. On the other hand, the proposed technique provides lower sidelobe levels which cannot be achieved by efficient tapering windows for planar two-dimensional arrays. Finally, the scanning performance of the proposed MPS beamformer is demonstrated and the simulation results show solid and consistent SLL levels over the whole angular range from the broadside to endfire directions of the array.

Design and Analysis of Multi-Mode Distributed Array with Hybrid Optimization Method

In this paper, we presented an improved hybrid optimization method to construct distributed array with two identical sub-arrays, which is mainly applied on airplanes as the front-end of communication and detection system. According to different demands on array’s gain and operating distances, the proposed method presents a scheme of implementation of two operate modes by optimizing elements’ positions and excitations. Two sub-arrays are able to work together to realize high gain when the object is quite far away, and one sub-array is able to work alone when the object is relatively close. This method is presented based on Particle Swarm Optimization (PSO) method and convex method, accomplishing that peak sidelobe level (PSLL) of whole array is lowered under -10 dB, and PSLLs of sub-arrays are lowered under -20 dB by supplementing some auxiliary units and re-optimizing array’s excitation distribution. In the procedure of optimization, the hybrid method is designed catering to multiple constraints according to the requirements of practical application. A specific example for synthesizing reconfigurable distributed array is provided and the sensitivity of obtained performance affected by interference of optimized results is discussed.

Analysis of Planar Random Arrays With Stochastic Geometry Tools

The performance of 2-D random arrays is analyzed using the distance distributions of an isotropic homogeneous binomial point process. The array factor is expressed as the superposition of the patterns of equal-amplitude isotropic elements uniformly randomly distributed in a disk area. The distribution of the distance to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> th nearest element from the center of the disk is utilized in the summation, providing a novel representation of the array factor in terms of ordered distances. Furthermore, an alternative distribution is examined by setting a constraint to the distance of the farthest element from the origin. The mean range of the elements in the disk and a numerical calculation of the mean interelement distance is provided. The statistical average and the variance of the array factor as well as the average power pattern are derived and compared to previous results. The 3 dB beamwidth, directivity, nulls, and sidelobe peaks are discussed in terms of the number of elements and the array density. Simulation results for various random arrays and comparison of ensemble-averaged parameters with those of deterministic and sparse arrays from the literature are provided. The results are applicable to collaborative beamforming for distributed wireless ad hoc networks.

Photonic Millimeter-Wave Joint Radar Communication System Using Spectrum-Spreading Phase-Coding

A novel millimeter-Wave (mm-Wave) joint radar and communication (JRC) system based on photonic spectrum-spreading phase-coding is proposed. The key to the proposed system is the convergence of photonic microwave phase-coding and spectrum-spreading multiplexing techniques. Phase-coding enables the generation of wideband mm-Wave JRC signal, leading to both high range resolution (&#x003C; 3.5 cm) for radar detection and high capacity (&#x003E;1 Gb/s) for wireless communication. The spectrum-spreading multiplexing orthogonalizes the radar signal and communication data, highly reducing mutual interferences. In addition, the spectrum-spreading multiplexing is able to improve both peak sidelobe ratio (PSR) for radar and anti-jamming/anti-noise performance for communication. In the proof-of-concept experiments, a JRC phase-coding signal at 35 GHz is generated. For a 5-Gb/s coding rate, the signal-to-noise ratio (SNR) margin is improved by around 13.8 dB for wireless communication below the pre-forward error correction (FEC) limit, while the PSR reaches &#x007E;12 dB for radar. Moreover, the impact of spreading gain on the communication capacity has been discussed, revealing that an optimized spreading gain should be set to balance the radar and communication performances.

Transmit-Receive Beamforming for Distributed Phased-MIMO Radar System

Distributed phased Multiple-Input Multiple-Output (phased-MIMO) radar system consisting of separated subarrays possesses a high angle resolution but with sharing high sidelobes. This paper therefore focuses on the design of a virtual low-sidelobe beampattern in distributed phased-MIMO radar. An iterative framework with respect to subarray layout and receive weighting coefficients is proposed to minimize beampattern Peak Sidelobe Level (PSL) accounting for practical position constraints as well as the mainlobe level restriction. In each iteration, an efficient cyclic optimization algorithm based on the Coordinate Descent (CD) framework is developed to seek for the subarray layout through splitting high dimensional layout optimization problem into multiple one-dimensional optimization problems, and the SemiDefinite Relaxation (SDR) technique and rank one approximation are explored to design weighting coefficients. Numerical simulations are provided to assess the performance of the proposed algorithms in term of the achieved beampattern under different constraints and parameter settings.

Hybrid Coded Excitation of the Torsional Guided Wave Mode T(0,1) for Oil and Gas Pipeline Inspection

Ultrasonic guided wave testing is an essential technique in non-destructive testing for structural integrity of oil and gas pipelines. This technique, based on the pulse-echo method, is often used for the long-range detection of pipelines at any location. However, guided waves suffer from high attenuation when they propagate in attenuative material structures and multiple wave modes due to the excitation, which reduces the power of echo signals and induces corruption caused by coherent noise. In this paper, a developed hybrid coded excitation method that uses the convolution of a Barker code and Golay code pair is proposed and applied for an ultrasonic guided wave testing system to excite the torsional guided wave mode T(0,1) in a steel pipe. The proposed method combines the advantages of these two coding methods and increases the flexibility of code lengths. The performance is evaluated by signal to noise ratio and peak sidelobe level of the processed signal. Both theoretical simulations and experiments have investigated using the proposed codes composed of Barker codes and Golay code pairs of different lengths and combinations. The experimental results show the significant improvement of the signal to noise ratio and the peak sidelobe level due to the proposed hybrid code usage for the excitation of guided waves. The values are further improved to around 32 dB and around −24 dB, respectively. Overall, the proposed hybrid coded method for improving the echo SNR can benefit from guided wave testing to reduce coherent and random noise levels and many other potential applications.

Sidelobe Control for Bistatic SAR Imaging

This letter presents coherent and incoherent nonlinear apodization methods for bistatic synthetic aperture radar (SAR) imaging. The methods are developed on the principle of nonlinear apodization for monostatic SAR imaging and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\omega \,\,-\,\,k$ </tex-math></inline-formula> relationship representing the bistatic region of support. This relationship plays an important role in designing 2-D windows for the apodization methods. The simulation results show that the presented apodization methods work efficiently with bistatic SAR imaging. In the experiment with a coherent dual apodization (CDA) method presented in this letter, the sidelobe attenuates very fast, and the peak sidelobe is reduced about 16 dB, while the resolutions in azimuth and range are maintained.

Waveform and Filter Joint Design Method for Pulse Compression Sidelobe Reduction

A joint waveform and filter design method is developed for suppressing radar pulse compression sidelobe level in this article. The problem is formulated as the minimization of the integrated sidelobe level (ISL) under the constraint of waveform constant modular and filter energy. To control the loss-in-processing gain (LPG), an additional function is introduced to constrain the peak level based on penalty function method. The joint design algorithm is then derived based on the alternating minimization and majorization minimization (MM) schemes. The computation complexity is analyzed and the convergence analysis verifies that the algorithm can converge to a critical point. Specifically, the proposed method is extended to the waveform and filter design for suppressing the peak sidelobe level (PSL). Numerical simulations are carried out to analyze the key parameters, which demonstrate the feasibility of the proposed method. Simulation results show that the ISL and PSL can be significantly reduced with small LPG. Moreover, the proposed method exhibits faster running speed than the existing one and it thus can be applied to longer sequence designs.

Optimal Mismatched Filter Design by Combining Convex Optimization With Circular Algorithm

Mismatched filters (MMF) have been intensively explored for linear-frequency modulation (LFM) waveform sidelobe reduction. Unlike other design strategies, the use of convex optimization (CO) techniques is able to find the optimal design. However, existing studies for CO-based MMF design have focused on minimizing peak sidelobe level (PSL), which might not take the mainlobe widening sacrifice into account. To address this issue, this paper proposes a weighted CO model targeting a flexible tradeoff between sidelobe suppression and mainlobe widening. Moreover, to better control the optimization problem via the presented CO model, the cyclic algorithm (CA) is employed to determine upper limits on mainlobe width. Consequently, the proposed tradeoff MMF design by combining CA with CO would be feasible to meet the requirements of different target detection scenarios. Comprehensive simulations have been carried out to demonstrate the effectiveness of our presented MMF design.

Joint Optimization of Sparse FDAs for Time Invariant Transmit Beampattern Synthesis

Beampattern synthesis of frequency diverse arrays (FDAs) has recently raised increased attention attributed to their range-dependent beampattern. The transmit beampattern of uniform FDA appears <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S$</tex-math></inline-formula> -shaped, which implies coupling in the range-angle domain and thus causing unwanted energy leakage into the area of non-interest. In this work, we propose a joint optimization of sparse FDAs to synthesize a decoupled transmit beampattern from the perspective of spatial-frequency virtual array. Specifically, both spatial and spectral configuration of FDAs are optimized via joint antenna-frequency selection. In order to solve the resultant NP-hard combinatorial optimization problem, we propose an iterative reweighting strategy to transform the original problem into a convex optimization. Further, we proceed to synthesize a time-invariant decoupled beampattern by designing a time-varying unit frequency step. Comparative simulations are provided to manifest the superior performance of the proposed FDA in the metric of normalized peak sidelobe level (NPSLL) of transmit beampatterns.

Novel Method for Designing Waveform With Good Correlation Properties Based on High-Order Norm Unified Representation

This study exploits high-order p-norm to uniformly represent the peak sidelobe level (PSL) and integrated sidelobe level (ISL) commonly used in waveform optimization, and presents a unified optimization objective function by considering the requirement that waveforms have good correlation properties in radar and communication systems. A novel and efficient waveform optimization algorithm is then proposed, which tackles the waveform and waveform set optimization of the PSL, the weighted sidelobe level, the ISL, and the weighted ISL. Applying the unified optimization objective function, the iteration factors are dynamically adjusted based on the quasi-Newton algorithm; in addition, the objective function is optimized with the gradient descent search algorithm and includes the optimization of autocorrelation and cross-correlation. Because certain application scenarios involve the Doppler sensitivity of waveforms, the problem is converted to cross-correlation optimization via channel division of Doppler frequency, and waveform with anti-Doppler sensitivity can be obtained. Multiple numerical simulations illustrate the positive performance of the proposed method. Furthermore, compared with certain traditional algorithms, the waveforms designed by this algorithm demonstrate improved correlation properties.

Joint Transmitting Subarray Partition and Beamforming for Active Jamming Suppression in Phased‐MIMO Radar

AbstractAs the tradeoff between conventional phased‐array and multiple‐input multiple‐output (MIMO) radars, phased‐MIMO radar has been studied in recent years, which can simultaneously obtain coherent processing gain and waveform diversity gain. In this paper, in order to effectively suppress the jamming signal and improve the target detection performance of radar system, a joint transmitting subarray partition and beamforming method in phased‐MIMO radar is proposed. To be specific, at the transmitter, the transmitting array of radar system is partitioned into a certain number of non‐overlapped subarrays, and the subarray structure of transmitting array and the corresponding beamformer weight vectors are simultaneously optimized by constructing the optimization model of maximizing the signal‐to‐noise ratio of the whole received echoes under certain constraint conditions, so as to effectively maximize the power utilization of radar transmitter, reduce the peak sidelobe level of transmit beampattern and improve the radar anti‐jamming performance. Moreover, the adaptive beamforming technique is applied to suppress the jamming signal entering the receiver, so that the transmitting and receiving adaptive degrees of freedom are jointly utilized to enhance the anti‐jamming capability of radar system. Simulation results demonstrate the validity of the proposed method.

Mutual Coupling and Channel Imbalance Calibration of Colocated MIMO Radars

The Multiple-Input Multiple-Output (MIMO) radar combines the signals from multiple transmit and receive elements separately to form a virtual array. Consequently, system imperfections in the MIMO radar caused by channel imbalance and mutual coupling are repeatedly present in the virtual array, affecting the beamforming performance. In this paper, the beam pattern deviations caused by these imperfections are described mathematically in relation to a single point target. Furthermore, a nonparametric calibration technique to estimate and compensate for these effects at different angles is presented by exploiting that the same imperfections are present multiple times in the virtual array. The proposed calibration method is applied to measurements with an 8 <inline-formula> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 8 colocated X-band MIMO radar, and the peak sidelobe level (PSL) and the integrated sidelobe level (ISL) are used as performance parameters. The calibration technique is found to improve both the PSL and the ISL by approximately 15 dB within the whole field-of-view (FOV) for antennas that are not minimum scatterers. For angles above &#x00B1;30&#x00B0; from the antenna boresight, the performance of the proposed calibration method is found to surpass other calibration methods. This is advantageous for MIMO radars as they typically cover a wide FOV.

Definition of Tomographic SAR Configurations for Forest Structure Applications at L-Band

Synthetic aperture radar tomography (TomoSAR) at lower frequencies allows the reconstruction of the 3-D radar reflectivity of volume scatterers allowing access to their physical 3-D structure by means of multiangular SAR acquisitions. The performance of the reconstruction critically depends on the number and (spatial) distribution of the tomographic acquisitions (tracks). This dependence is addressed in this letter with respect to forest applications (volume scatters) at L-band. The letter discusses the optimum definition of tomographic configurations based on the peak sidelobe level (PSL) of the point spread function (PSF). For demonstration, a tomographic data set consisting of 15 acquisitions acquired by the DLR’s F-SAR system at L-band over the Traunstein test site in Germany is used, complemented by airborne LiDAR measurements. Three different reconstruction algorithms (Fourier beamforming, Capon beamforming, and compressive sensing) are implemented and compared to each other for scenarios with a reduced number of acquisitions. Although the limitation of the specific forest, the results show the potential of using the PSL of the PSF to define tomographic configurations optimized for forest structure applications.

A 2-D Frequency-Domain Imaging Algorithm for Ground-Based SFCW-ArcSAR

Arc-synthetic aperture radar (ArcSAR) can observe the surrounding ground objects at 360°, with the advantages of a wide imaging range and constant azimuth angular resolution. In this article, based on the stepped frequency continuous wave (SFCW), fourth-order Taylor expansion, and the series-inversion method, the accurate phase expression of the 2-D spectrum is derived, and then, the 2-D frequency-domain imaging algorithm (2-D-FDA) for ArcSAR is realized. In the simulation part, the imaging results of 2-D-FDA are compared with the backprojection algorithm (BPA) and Liao’s method, which is the reference for 2-D-FDA. The simulation results show that the 2-D-FDA is more applicable to process the data obtained from the antenna with the beamwidth larger than 70°. The SFCW-ArcSAR system consists of a vector network analyzer (VNA), a rotating platform, two antennas, and a control computer. Then, the system is used for the outdoor experiment. The experimental results of the corner reflector show that the point target analysis of 2-D-FDA is consistent with those of the BPA and theory. Under the system parameters in this article, the measured azimuth angular resolution is 0.0177 radian, the peak sidelobe ratio (PSLR) in the range direction is −12.46 dB, and the range resolution is 0.48 m on the ground-range plane. The imaging results of the real scenario processed by BPA and 2-D-FDA are consistent, and the ArcSAR image agrees with the optical image of the experimental scene. The effectiveness and correctness of the 2-D-FDA are verified by simulation and experiment.