Peak Sidelobe Level Research Articles

Side lobe level reduction of thinned concentric elliptical array antenna in vertical and horizontal plane for a desired peak directivity

AbstractThis study, describes the design problem of a thinned multiple concentric elliptical arrays of uniformly excited isotropic antennas using meta‐heuristic optimization algorithms; Teaching Learning Based Optimization (TLBO), Crow Search Algorithm (CSA) and Moth Flame Optimization (MFO) algorithm. Two simulations are performed here. In simulation 1, the synthesis of the thinned array structure is presented in the vertical plane at a scanning angle 30° and in simulation 2, the synthesis is performed in the horizontal plane. In both cases, our objective is to minimize side lobe level (SLL) to the extent possible and at the same time maximize the peak directivity to a level higher than the desired value. Here, all the optimization algorithms are applied to obtain the optimum number of switched on and off elements in every concentric ellipse that will meet the above objective. A comparative analysis of all three algorithms is performed using peak directivity, SLL and first null beam width (FNBW) as well as statistical parameters such as mean, SD, best cost function value and run time. To assess the enhanced outcome of the proposed optimization design comparison is also made with the results of a fully populated concentric elliptical array antenna (CEAA) for both the cases separately. This paper shows a measure of effectiveness and potential of all the algorithms mentioned above, for designing a thinned concentric elliptical array.

Beampattern Synthesis via the Constrained Subarray Layout Optimization

This article deals with a joint design of subarray layout vector (LV) and weighted coefficient of radiation element (RE) to achieve desired beampattern for a new array architecture. We first present an architecture of thinned array composed of multiple regular subarrays (ACMRS) and establish corresponding subarray layout and beampattern models. Then, we formulate a new optimization problem aiming to minimize the peak sidelobe level (PSL) and the LV norm under the constraints of power beampattern and subarray layout. The resulting problem is quite challenging to solve due to the highly nonconvex discrete LV and double-sided quadratic constraints. In this respect, we formulate the resultant hybrid optimization problem into a new alternating direction method of multipliers (ADMM) form via introducing a series of auxiliary variables, and propose an approximation algorithm based on ADMM. In each iteration of the proposed ADMM, the tractable and small-sized subproblems are globally or locally solved in parallel. Finally, numerical simulations show that the proposed method can obtain a lower PSL beampattern and a thinner (i.e., fewer REs or subarrays) array while satisfying the given constraints. Furthermore, fullwave simulation also shows that it has good reliability in the application of beampattern synthesis for real array.

Multi-objective self-organizing optimization for constrained sparse array synthesis

Abstract Sparse span array is a critical communication technology for detecting microwave signal, yet it is difficult to simultaneously satisfy both reducing antenna elements' number and maintaining maximum side lobe level. Towards this problem, we propose a multi-objective optimization approach for self-organizing limited-area sparse span array, termed MOSSA. Overall, a uniform framework of multi-objective sparse span array is proposed. Specially, two objectives, number of selected antenna and peak side lobe level, are established for exploring the optimal array distribution in the framework. Based on the framework, for the problem of global-optimum array distribution, we propose a multi-objective particle swarm optimization searching pattern and design a MOSSA algorithm; Furthermore, for the problem of flexibly-adjusted self-organizing array structure, we present a multi-objective genetic programming searching pattern and design a MOSSA-gp algorithm. Moreover, a limited-region mode supplements to the framework. Finally, combination decision strategy assists users to screen out suitable solutions under the guidance of fuzzy-range indexes and then select the optimal solution by a triangle-approximating approach based on minimum Manhattan distance. Numerous experiments demonstrate that the proposed MOSSA outperforms other state-of-the-art algorithms in terms of both antenna elements’ number and maximum side lobe level.

Co-Design of Waveform Correlation Matrix and Antenna Positions for MIMO Radar Transmit Beampattern Formation

In this paper, we investigate the problems of co-design of the waveform correlation matrix (WCM) and antenna positions (AP) for multiple-input multiple-output (MIMO) radar transmit beampattern formation. To design beampattern with good behaviors, we propose two co-design methods. In the first method, the co-design problem of WCM and AP is formulated by minimizing the mean square error (MSE) between the designed beampattern and a desired one. The second method optimizes the WCM and AP to control the mainlobe ripples and the peak sidelobe level. Moreover, the lower- and upper-bound constraints are also considered within some predefined regions, for both two optimization problems. The co-design schemes provide an extra degree of freedom (DoF) to enhance the transmit beampattern behaviors but also make optimization problems very difficult to solve. To cope with the resultant optimization problems, a successive convex approximation (SCA) algorithm is devised. Finally, simulation results are presented to demonstrate the superiorities of the co-design schemes over state-of-the-art methods in terms of the beampattern behaviors.

Enhanced Transmit–Receive Beamforming for Frequency Diverse Array

Frequency diverse arrays (FDAs) have a more flexible beamforming ability than phased arrays since they provide degrees of freedom (DOFs) in both range and angle domains by applying a tiny frequency offset across adjacent elements. Nevertheless, the beampattern of an FDA is not only range–angle-dependent but also time variant when only considering the transmit procedure. In this article, an enhanced transmit–receive beamforming approach is proposed to achieve the time-invariant and symmetrical beampattern with only a single maximum value in range–angle space. First, two FDAs with symmetric logarithmically increasing frequency offsets (SLFOs) are proposed to achieve a maximum value at the desired range–angle region while exhibiting sidelobe in the region out of interest. Second, the receive procedure is devised to compensate the time-variant terms with multiple mixers corresponding to different frequencies. To maintain the shape of the mainbeam and simultaneously reduce the peak sidelobe level (PSLL) of the pattern, the optimization problem is constructed into a semidefinite programming problem. Numerical results show that both of the two proposed FDAs exhibit fine focused, symmetrically distributed transmit–receive beampatterns in range and angle domains.

Design of Shared Aperture Radar Arrays With Low Sidelobe Level of the Two-Way Array Factor

A study to reduce the peak sidelobe level (SLL) of a radar two-way array factor is presented. It applies the condition that the first significant sidelobe of the transmitting array is in the same direction as the first null of the receiving array. Moreover, it is supposed that in the two-way array pattern, two consecutive sidelobes near the main beam become equal. Moving one step further, by combining the advantages of taper distribution and the simplicity of the feed network of uniform arrays, a two-weight amplitude distribution for the radar transmit and receive arrays is designed. The resulting peak SLL of the two-way pattern becomes less than −45 dB.

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.

Correlation Processor Based Sidelobe Suppression for Polyphase Codes in Radar Systems

Peak sidelobe level (PSL), integrated sidelobe level (ISL) and signal to noise ratio (SNR) are the main performance indices in pulse compression radar. Pulse compression is useful in providing two contradicting requirements, namely, higher transmitted power required for longer pulse transmission, and smaller range resolution which is a desirable characteristic of smaller pulse transmission. The sidelobe suppression method proposed in this paper is based on the correlation processor that uses the P4 polyphase codes. P4 codes are known for their better Doppler tolerant property. Sidelobes are undesirable as jammers or noise present in sidelobes may interfere with the desired target. The proposed method has been implemented with six different windows namely Hamming, Hanning, Blackman, Nuttall, Blackman–Nuttall, and Blackman–Harris and results show that PSL value of − 275.6 dB and ISL value of − 152.98 dB are achieved without much degradation in SNR value. Ambiguity function is derived for the designed sequence and the results are compared with the Frank, Barker and P4 code in the delay-Doppler plane. Results show that the proposed method provides significant performance improvement compared to existing sidelobe suppression methods.

Synthesis of Sparse Rectangular Planar Arrays with Multiple Constraints Based on Dynamic Parameters Differential Evolution Algorithm

For solving the problem of the synthesis of sparse rectangular planar arrays with multiple constraints, this paper proposes a Dynamic Parameters Differential Evolution (DPDE) based algorithm. Firstly, to improve searching efficiency and accuracy of Differential Evolution (DE), the proposed method introduces dynamically changing strategies to the scaling factor and the crossover probability of the traditional Differential Evolution algorithm. Secondly, a modified matrix mapping method and the redefinition of mapping principles are presented to make up the defects of strong randomness and low accuracy in existing methods. Finally, simulation experiments of antenna arrays are performed to validate the effectiveness of the proposed method, and the results demonstrate that the proposed method performs out the existing methods in the respect of reducing peak sidelobe level of antenna arrays.

An ADS-Based Sparse Optimization Method for Sonar Imaging Sensor Arrays

The Mills Cross sonar sensor array, achieved by the virtual element technology, is one way to build a low-complexity and low-cost imaging system while not decreasing the imaging quality. This type of sensor array is widely investigated and applied in sensor imaging. However, the Mills Cross array still holds some redundancy in sensor spatial sampling, and it means that this sensor array may be further thinned. For this reason, the Almost Different Sets (ADS) method is proposed to further thin the Mills Cross array. First, the original Mills Cross array is divided into several transversal linear arrays and one longitudinal linear array. Secondly, the Peak Side Lobe Level (PSLL) of each virtual linear array is estimated in advance. After the ADS parameters are matched according to the thinned ratio of the expectant array, all linear arrays are thinned in order. In the end, the element locations in the thinned linear array are used to determine which elements are kept or discarded from the original Mills array. Simulations demonstrate that the ADS method can be used to thin the Mills array and to further decrease the complexity of the imaging system while retaining beam performance.

Affine transformation for synthesis of low sidelobe patterns in planar array antennas with a triangular element grid using the IFT method

This study deals with the affine transformation that is used to convert the triangular element grid of a planar phased array antenna into a square one. By means of this kind of transformation, it is possible to apply the iterative Fourier transform (IFT) method to synthesise low sidelobe tapers for array antennas featuring a triangular grid. Combination of the IFT method with an affine transformation allows the synthesis of low sidelobe tapers of which the peak sidelobe level does not vary with changing frequency and/or altering main beam position. The considered affine transformation was already briefly addressed in earlier publications of this author. In this study detailed information is given on its use in combination with the IFT method. Examples to demonstrate the effectiveness of the combination affine transformation and the IFT method for triangular grid array antennas are given. It will be shown that the peak sidelobe levels of the obtained tapers are invariant with frequency and scan angle when all far-field directions of the array factor are involved in the low sidelobe taper synthesis.

A hybrid algorithm of orthogonal perturbation method and convex optimization for beamforming of sparse antenna array

ABSTRACT In order to realize the beamforming and suppress the side lobe of the sparse antenna array, a hybrid sparse antenna array optimization algorithm based on orthogonal perturbation method (OPM) and convex (CVX) optimization is proposed. The algorithm aims at the expected beam response of main lobe and the suppression of peak side lobe level (PSLL). The OPM is used to optimize the array layout, and it can improve the time performance of pattern synthesis with its deterministic numerical characteristic. Because it is a local optimization algorithm, its optimal effect depends on the initial array layout and element excitation coefficient. Therefore, considering that the local optimal solution of the CVX algorithm is the global optimal solution, the CVX algorithm is used to obtain the optimal element excitation coefficient to achieve the expected beam response of the main lobe. The simulation results show that the hybrid algorithm can achieve a good trade-off between the optimization time, beam response, and the suppression of the PSLL.

Enumeration and Generation of $\rm PSL$ Equivalence Classes for Quad-Phase Codes of Odd Length

Quad-phase codes of a given length can be grouped into equivalence classes based on operations preserving autocorrelation peak sidelobe level, or “ ${\rm PSL}$ -preserving operators.” The task of enumerating these equivalence classes is facilitated by establishing a relationship with the problem of enumerating equivalence classes of $2\times N$ binary grids with respect to a pair of binary grid symmetries. We show this connection by a one-to-one mapping between even-length quad-phase codes and $2\times N$ binary grids. When $N$ is even, this mapping allows the known enumeration of $2\times N$ binary grids to be applied to the enumeration of even-length quad-phase code PSL equivalence classes. Furthermore, this equivalence instructs the development of a simpler algorithm for visiting single representatives of quad-phase-code equivalence classes relative to the operations that preserve PSL. Lastly, we conduct exhaustive searches to determine the optimal ${\rm PSL}$ for quad-phase codes of lengths 25 and 26 (for the smaller of these lengths, the search space contains $4^{25}=2^{50}$ , or roughly 1 quadrillion codes). One of the devices used to narrow the search space while achieving an exhaustive search is to seed the search with the equivalence class representatives of length $N=6$ . The optimal ${\rm PSL}$ for length-25 quad-phase codes is determined to be 2, achieved by the codes in a single size-32 equivalence class. For length 26, the optimal ${\rm PSL}$ is found to be $\sqrt{5}$ , achieved by $604\,480$ codes belonging to 9445 equivalence classes of size 64.

Optimization of Sparse Concentric Ring Arrays Based on Multiple Constraints

This letter is concentrated on the peak sidelobe level (PSLL) suppression problem of equal amplitude concentric ring array (CRA), which is constrained by the array aperture, the minimum element spacing, and the number of elements. Taking the minimum PSLL as the optimization objective, the joint optimization strategy of CRA aperture and ring array spacing is adopted to reduce the computational complexity. A quantum genetic algorithm based on hybrid coding is used to optimize the CRA. The proposed method has the advantages of fast searching speed and powerful searching ability. The simulation results demonstrate the superiority of the algorithm.

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.

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.

Sidelobe Level Optimization of Rectangular Microstrip Patch Antenna Array using Binary Coded Genetic Algorithm

In modern world, communication systems requires development of low cost, minimal weight, and low profile antennas which are capable of maintaining high performance over wide range of frequencies. Patch antenna is one such antenna which fulfills the demands of current communication systems. The widely used microstrip patch antennas are rectangular patch antennas. This paper presenting the application of binary coded Genetic Algorithm (BGA) which is applied to the rectangular patch microstrip antenna with uniform linear arrays. The fitness function of GA is maximum reduction in peak side lobe level of the radiation pattern of the antenna with maximum reduction in the side lobe level and also achieved the minimum possible null to null beam width, the resultant radiation patterns for both before GA and after GA of microstrip array are compared. The radiation patterns are presented for 20,50,100 number of elements. All the simulated results are obtained by using MATLAB software.

Broadband Generalized Sidelobe Canceler Beamforming Applied to Ultrasonic Imaging

A broadband generalized sidelobe canceler (Broadband-GSC) application for near-field beamforming is proposed. This approach is implemented in the wavelet domain. Broadband-GSC provides a set of complex, adapted apodization weights for each wavelet subband. The proposed method constrains interference and noise signal to improve the lateral resolution with only one single emission. Performance of the proposed beamforming is tested on simulated data obtained with Field II. Experiments have proved that the new beamforming can significantly increase the image quality compared with delay-and-sum (DAS) and synthetic aperture (SA). Imaging of scattering points show that Broadband-GSC improves the lateral resolution by 43.2% and 58.0% compared with SA and DAS, respectively. Meanwhile，Broadband-GSC reduces the peak sidelobe level by 11.6 dB and 26.4 dB compared with SA and DAS, respectively. Plane wave emission experiment indicates that Broadband-GSC can improve the lateral resolution by 44.2% compared with DAS. Furthermore, the new beamforming introduces the possibility for higher frame-rate and higher investigation depth with increased lateral resolution.

Transmit beamformer design with a PAPR constraint to trade-off between beampattern shape and power efficiency

This study examines the effect of peak-to-average power ratio (PAPR) constraint on the transmit beamformer design problem with the goal of establishing a trade-off between the power efficiency (maximizing the average transmitted power) and other metrics such as the power level fluctuation in mainlobe, peak-sidelobe level (PSL), etc. Typically, unimodular weights are utilized in transmit beamforming to maximize the average transmitted power. Yet, unimodular weights maximize the power efficiency at the expense of other performance metrics. It is shown that even a slight relaxation of the design problem from the unimodular condition (PAPR=1), say setting PAPR⩽1.1, results in a significant improvement in other performance metrics at a negligible loss of power efficiency. To achieve the trade-off between the metrics, an alternating direction method of multipliers (ADMM) based solution to the transmit beamformer design is given. The suggested solution is applicable to both narrowband and wideband beamformers and also to some other related problems such as the unimodular radar waveform design (code design) problem.