Pattern Synthesis Method Research Articles

A Novel Two-Way Pattern Synthesis Method With the Uniform and Thinned Arrays

A Novel Two-Way Pattern Synthesis Method With the Uniform and Thinned Arrays

Fast Low-Sidelobe Pattern Synthesis Using the Symmetry of Array Geometry.

Array pattern synthesis with low sidelobe levels is widely used in practice. An effective way to incorporate sensor patterns in the design procedure is to use numerical optimization methods. However, the dimension of the optimization variables is very high for large-scale arrays, leading to high computational complexity. Fortunately, sensor arrays used in practice usually have symmetric structures that can be utilized to accelerate the optimization algorithms. This paper studies a fast pattern synthesis method by using the symmetry of array geometry. In this method, the problem of amplitude weighting is formulated as a second-order cone programming (SOCP) problem, in which the dynamic range of the weighting coefficients can also be taken into account. Then, by utilizing the symmetric property of array geometry, the dimension of the optimization problem as well as the number of constraints can be reduced significantly. As a consequence, the computational efficiency is greatly improved. Numerical experiments show that, for a uniform rectangular array (URA) with 1024 sensors, the computational efficiency is improved by a factor of 158, while for a uniform hexagonal array (UHA) with 1261 sensors, the improvement factor is 284.

On Difference Pattern Synthesis for Spherical Sensor Arrays.

An innovative method for synthesizing optimum difference patterns of the spherical sensor array is introduced, along with a sidelobe tapering technique. Firstly, we suggest employing the spherical harmonics of degree ±1 to synthesize the spherical array difference pattern; secondly, we study the mapping relationship between the difference pattern of the spherical sensor array and the difference pattern of the uniformly spaced linear array (ULA) with odd-numbered elements; finally, we enhance the Zolotarev difference pattern, which is a counterpart to the Dolph-Chebyshev sum pattern that traditionally allows synthesis only for ULA with even-numbered elements. Our modification extends its applicability to synthesize difference patterns for ULA with odd-numbered elements. Leveraging the optimal difference pattern, a generalized Bayliss difference pattern synthesis method designed for the ULA with odd-numbered elements is further proposed. To illustrate the effectiveness of our approach, we present several design examples through experimental simulation.

Convex Optimization Algorithm for Maximizing Directivity of Conformal Array With DRR Constraint

The inconsistency of conformal array elements poses a huge challenge to pattern synthesis. Based on convex optimization theory, this paper proposes a novel directivity pattern synthesis method. It can maximize the directivity of dual‐polarized conformal arrays with a low dynamic range ratio (DRR). Firstly, the directivity function is presented under a dual‐polarized conformal array. Then the pattern synthesis based on maximizing directivity is summarized as a multiconstraint optimization problem. In addition, the DRR constraint is introduced to control the weight range. By using Taylor expansion, the problem is transformed into a convex optimization problem and solved iteratively. Finally, simulation results demonstrate that the proposed method can effectively achieve a good directivity pattern with low sidelobe level (SLL) and low DRR.

Frequency diverse array beampattern synthesis method with low sidelobes by integrating mayfly algorithm and convex programming

AbstractThe range‐angle coupling characteristics of traditional frequency diverse array (FDA) will deteriorate target localization performance. To address this problem, several decoupling methods for FDA have been developed in the past decade, mainly including deterministic methods and global optimization methods. However, most of these methods are based on frequency offset design and do not fully utilize other design degrees of freedom, such as excitation and element spacing, which limits obtained pattern performance. In this letter, a low‐sidelobe FDA pattern synthesis method is proposed by jointly optimizing frequency offset, array spacing and excitation. The entire optimization process is treated as two sub‐optimization problems, that is, a non‐convex sub‐problem involves frequency offset and array spacing, and a convex sub‐problem involves excitation. By integrating the mayfly algorithm and convex programming techniques, this synthesis problem can be effectively solved. Compared with the current state‐of‐the‐art counterparts, the proposed method takes full advantage of the FDA's design freedom and generates a doted beampattern with lower sidelobes.

Pattern synthesis of distorted phased array antenna with unsteady surface deformation considering dynamic range ratio

Abstract This paper presents an optimization method for pattern synthesis of distorted phased array antenna with unsteady surface deformation considering the dynamic range ratio (DRR). In the synthesis approach, different array deformations under unsteady mechanical loads are considered, and the distorted distribution of array elements is calculated after solving the mechanical deformation model. Then, optimize the excitation coefficients of each array element including amplitude and phase with DRR control so as to recover a high-quality pattern from a deteriorated pattern caused by the unsteady deformations. The optimization objective is to minimize the peak sidelobe level, which is synthesized by using a gradient-based algorithm. The optimized excitations can be used as the initial excitation, and the corresponding phase excitations can be derived according to the different deformations.

Simple Matrix Equation (SME) Method for Pattern Synthesis of Conformal Antenna Array with Arbitrary Architecture

A novel noniterative method for pattern synthesis of conformal antenna array is put forward. First, a new pattern function formula for general conformal antenna array is derived. Then, according to the new pattern function formula, a new block matrix equation (BME) and a simple matrix equation (SME) are obtained. SME has the same form as the equation of linear array pattern synthesis. The new method can be applied to pattern synthesis of any conformal array. Moreover, due to SME having the same form as the matrix equation of linear array pattern synthesis, the new simple matrix equation can be dealt with by the approaches for linear array pattern synthesis, which significantly expands the existing approaches for conformal antenna array pattern synthesis. Two different conformal array configurations are taken as the examples to demonstrate the advantages of the new method. Results of the simulations show that the new method can flexibly and effectively be applied to synthesize patterns for various conformal array architectures.

A Wide-Beam Antenna Array With Spatially Variable-Orthogonal-Polarizations (SVOP) Achieved by Polarization-Mixing

This paper introduces a novel polarization-mixing strategy to significantly widen the beamwidth of dual-linear-polarized antenna arrays without changing the array topology. Instead of using the two polarizations separately as usual, it blends the orthogonal linearly-polarized radiations to achieve wider beamwidth. The proposed method is implemented on a typical ±45°-polarized base station antenna array with its thought process and working mechanism elaborated. Much wider beamwidth is achieved compared to the traditional pattern synthesis methods based on amplitude and phase weighting or sparse arrays. The beamwidth can be controlled by simply tuning one phase shifter. Importantly, this method allows all the elements to be fully excited with the same amplitude, thus avoiding using additional amplifiers or attenuators. In the meantime, the polarization-mixing method leads to spatially-variable polarizations (SVP). To obtain polarization diversity required in cellular communication systems, two SVP arrays with the same pattern shapes are designed to have their polarizations orthogonal to each other in all directions of interest. The conditions of achieving orthogonal patterns using this method are theoretically derived and thoroughly validated in theory and in simulation. It is shown that the obtained spatially-variable-orthogonal-polarization (SVOP) arrays have a much broader beam pattern and better polarization orthogonality (PO) than that of the dual-polarized antenna element.

A convex optimization based multistage wideband pattern accurate synthesis method for overlapping subarrays

Due to frequency variation and overlapping architecture, some overlapping subarrays may exhibit significant grating lobe problems in their wideband patterns. Furthermore, accurate synthesis methods for wideband patterns with subarray architecture are lacking in traditional approaches, as they cannot control sidelobe level (SLL) accurately while maintaining a narrow half-power beam width (HPBW). To address these challenges, this paper proposes a multistage control approach for achieving precise wideband pattern synthesis of subarray structures. Firstly, we propose a subarray pattern synthesis method based on multi-frequency null control (MNC) to address the grating lobe issue under specific overlapping architectures. Secondly, building on the MNC method, we introduce an improved approach called single-frequency null control (SNC) to enhance the array degrees of freedom utilization. Thirdly, we propose an array factor synthesis method based on multi-frequency minimum mainlobe width (M3W) to accurately control SLL and minimize HPBW. This method leverages the subarray pattern synthesis outcome and enforces the multi-frequency SLL constraint to minimize the mainlobe width. Finally, we validate our proposed methods by comparing wideband array patterns, integration array patterns, and traditional methods. The simulation results demonstrate that our methods offer superior GLL suppression, accurate SLL control, and HPBW minimization. Furthermore, the proposed techniques can be applied to arbitrary overlapping subarray systems without being affected by grating lobes, thus overcoming a limitation of traditional methods.

Design of Leaky-Wave Antenna With Wide-Angle Backfire-to-Forward Beam Scanning Based on Generalized Pattern Synthesis

Frequency-scanning antenna has been extensively explored in radar and vehicle communication systems, but it is a challenge to provide methodological guidance to achieve a wide scanning angle. Here, a generalized pattern synthesis method is proposed and a leaky-wave antenna with wide scanning range is designed to verify the technique. First, a generalized antenna element (GAE) is presented, whose main beam can steer continuously with frequency. Meanwhile, the phase constant of the leaky wave determines the beam direction of the array factor. Then, a leaky-wave antenna can steer with a large beam scanning angle and stable gain as patterns of the array factor and the GAE are manipulated simultaneously. To verify, a prototype SIW LWA with double-layer transverse slots is fabricated and measured. Experimental results show this antenna achieves continuous dual-beam scanning from backfire (-90∘) to forward (±20∘) from 12.4 GHz to 19.9 GHz with a total coverage range of 220∘ and the realized gain varying from 8.3 dBi to 12.8 dBi.

Hierarchical Codebook-Based Beam Training for RIS-Assisted mmWave Communication Systems

Reconfigurable intelligent surface (RIS) has emerged as a competitive solution to the blocking problem in millimeter wave (mmWave) communications. However, due to the passive nature of the RIS, obtaining channel state information (CSI) for RIS-assisted mmWave communication systems is rather difficult. Considering that the currently available RIS hardware cannot arbitrarily switch between the active (reflection with configurable phase response) and deactivate (absorption) modes, we suggest a new beam training method for RIS-assisted mmWave communication systems in this study. First, a predefined hierarchical codebook is created using the pattern synthesis method. Then, we provide a novel hierarchical beam training method using two multi-mainlobe codewords in each layer of the hierarchical codebook for beam sweeping. Combining the results of the beam identification in all the layers will yield the ultimate ideal beam direction. Theoretical analyses demonstrate that the suggested approach can effectively reduce training overhead while ensuring successful beam alignment. Simulation results show that the practical codebook can be created successfully, and the suggested method can achieve accurate beam alignment with reduced training overhead.

Circularly Polarized Dual-Frequency MIMO Antenna With Cosecant-Squared Radiation Pattern for Ku-Band Applications

In this paper, the realization of a circularly polarized multiple-input, multiple-output (MIMO) array antenna with a cosecant squared pattern, is presented. The proposed antenna structure consists of microstrip patches with rectangular slots etched from the top. The desired radiation pattern is generated using amplitude tapering obtained by modifying patch widths and slot lengths, based upon the amplitude coefficients of the Woodward-Lawson method for pattern synthesis. A MIMO arrangement with circular polarization is formed by connecting two such arrays excited by two ports. A <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -shaped slot is used to minimize the mutual coupling. Using two shorting pins, the isolation is enhanced and kept above 30 dB. This arrangement offers a small size (52 mm ×24 mm × 0.8 mm), wide bandwidth, and high gain antenna operating at 13.2 and 16.6 GHz. The antenna operates in a wide bandwidth, from 12.6 GHz to 14.25 GHz, and from 16 to 17.61 GHz, with admirable directional characteristics. The achieved gain is 16.9 dB and 16.6 dB with a cosecant pattern and low side lobe level. The analysis of the, VSWR, gain, axial ratio, group delay, efficiency, and MIMO performance metrics are also investigated, both in simulation and in experiment.

COSECANT-SQUARED BEAM PATTERN SYNTHESIS OF CONCENTRIC CIRCULAR ANTENNA ARRAY IN A RANGE OF AZIMUTH PLANE USING EVOLUTIONARY ALGORITHM

This paper presents, a pattern synthesis method based on Differential Evolutionary Algorithm. A cosec2 beam pattern has been generated from different concentric circular ring arrays of isotropic elements by finding the optimum set of elements amplitude and phase using the Differential Evolution algorithm. The shaped beam pattern (cosec2) is generated in three predefined azimuth planes (φ=0°, 5° and 10°) from a Concentric Circular Antenna Array (CCAA) having two rings, three rings, and four rings. The total number or isotropic elements are equal for array geometries. The optimum excitation for array geometries is also verified for a range of arbitrarily chosen azimuth planes. The obtained main beam is similar to the desired pattern with some minor variations in peak Side Lobe Level (peak SLL) and ripple. Dynamic range ratio (DRR) is improved by using 4-bit discrete Amplitudes and 5-bit discrete Phases. These discrete excitations also simplify the design complexity of the feed networks.

Robust Low Sidelobe Synthesis for Arbitrary Arrays Based on Gradient Ascent With Min-Oracle

This article studies the robust pattern synthesis of a narrow main beam and low sidelobes of arbitrary arrays, which represents a classical but challenging problem for array antennas. In addition, pattern synthesis for a given sidelobe envelope is discussed. The synthesis problem is formulated as a nonconvex–nonconcave minimax problem with nonconvex constraints, which avoids the design of the optimal desired pattern and ensures the robustness of pattern synthesis for arbitrary arrays by nonconvex constraints. An algorithm named gradient ascent with min-oracle (GAmin) is proposed to address the considered minimax problem. Furthermore, the majorization–minimization algorithmic framework is used to reduce computational complexity. It is shown that for arbitrary linear and planar arrays, the proposed GAmin-based pattern synthesis method can perform well for pattern synthesis both without and with a given sidelobe envelope. A variety of numerical examples are provided to demonstrate the superior performance of the proposed method.

Synthesis of Continuous Source Current for Gain Enhancement and Sidelobe Suppression of High-Order Mode Dipoles

A synthesis method of continuous source current on a high-order mode dipole is proposed to enhance gain and suppress sidelobe levels (SLLs) based on compression coefficients. First, a high-order mode dipole with the current distribution determined by designed compression coefficients is proposed to generate a typical continuous source. Then, a pattern synthesis method of continuous source current is presented to enhance gain with desired SLLs by calculating the compression coefficients. Finally, the fifth-order mode dipole is designed to verify the proposed synthesis method. Both measurement and theoretical prediction show the gain of 6.6 dBi and an SLL of −13.3 dB by the single dipole of the length of 1.5 wavelengths at 3.25 GHz. Compared with an array composed of three convention half-wave dipoles, the proposed fifth-order mode dipole of a similar length achieves a gain increase up to 1.13 dBi, or an effective length increases up to 30% while the SLL keeps unchanged.

Development of the adaptive pattern synthesis method for accurate structured illumination

Structured illumination, which projects a predefined spatially varying intensity pattern, has been widely used in a variety of applications, including 3D shape estimation, optical property estimation, and super-resolution imaging. The precision of the structured illumination method is determined by the accuracy of the illumination pattern captured by the detector; however, acquiring images of the precise pattern is difficult due to distortion and nonlinear response in the imaging system. We proposed an adaptive pattern synthesis method that could overcome projecting system distortion and the system's nonlinear response. The proposed method consists of four steps: estimation of the geometric transformation matrix between the structured illumination unit and detector, estimation of the detector's intensity lookup table, and synthesis of the corrected patterns. Furthermore, by measuring the 3D printed target and tissue-mimicking phantom, the proposed method demonstrated its ability to improve the accuracy of phase shift profilometry and spatial frequency domain imaging. It does not require fine alignment or optical system details because all procedure is performed by projecting digital patterns and its measurement without calibration targets. The proposed method could be applied to any optical technique that uses structured illumination to improve accuracy and performance, making it useful in both academic and industrial applications.

High‐efficient optimisation method of antenna array radiation pattern synthesis based on multi‐layer perceptron network

With the increasing complexity of the application environment of antenna arrays and the increasing requirements for antenna array radiation patterns, efficient optimisation methods of antenna array radiation pattern synthesis have always been the challenges of the research. This paper proposes a method of utilising a multi-layer perceptron network to optimise the radiation patterns of antenna array. The optimisation requirements of the antenna array radiation pattern are described by defining the objective mask function, which is designed to shape the target radiation pattern by desired features. Simulation experiments have been designed with a variety of antenna array layouts, of which the radiation patterns with different requirements were successfully synthesised and optimised. The results show that the proposed method has high efficiency and satisfactory optimisation effect in dealing with the problem of complex radiation pattern requirements.

Pattern Synthesis With Closed-Form Array Response Control Algorithms

In this letter, the problem of array pattern synthesis is considered by developing two array response control algorithms. The devised two algorithms build on the basis of the accurate array response control approach, and both of them have closed-form solutions and low computational complexities. More specifically, the first proposed algorithm realizes multipoint array response control from an any given weight vector, and the second algorithm modifies the first one by avoiding the possible beam axis shift. The proposed two algorithms are able to control array responses accurately under the conditions of independence on steering vectors. By applying the first and the second array response control algorithm, two effective pattern synthesis methods for focused patterns and shaped patterns are devised, respectively. Representative examples are presented to demonstrate the performance of the proposed algorithms in array response control and pattern synthesis.

Radiation Pattern Synthesis Method of Antenna Arrays with an Arbitrary Arrangement of Radiating Elements

As a result of the analysis of methods for synthesizing radiation patterns, in order to find the required amplitude-phase distribution in antenna arrays with an arbitrary arrangement of radiating elements, a technique based on the method of partial radiation patterns is proposed. The results of implementing the technique for a lowprofile combined ring concentric antenna array, a five-element antenna array based on asymmetric wave channel antennas, and a conformal antenna array consisting of arbitrarily located PIFA antennas are presented. The calculated amplitude-phase distributions and radiation patterns are given. The technique makes it possible to evaluate the potential capabilities of antennas, with adaptation taking into account the mutual coupling.

An optimal far field radiation pattern synthesis of mutually coupled antenna arrays

This article presents a precise approach for far-field radiation pattern (FFRP) correction of mutually coupled discrete dipole element (DDE) array of monopole antennas and concentric circular antenna array (CCAA) of dipole elements by employing the parametric assimilation technique (PAT). The effect of mutual coupling is a crucial part of any practical antenna array design issue. Various techniques have been suggested to calculate, compensate and reduce the mutual coupling effect during the last few decades. This article shows an exact method for mutual coupling inclusive corrected radiation pattern synthesis using PAT. The parameters of mutual impedance are calculated and assimilated with the values of the desired radiation pattern. The employed technique is cost-effective, less complex and easy to implement while achieving better performance for mutually coupled DDE array and CCAA synthesis. Grey wolf optimisation (GWO) is a state-of-the-art stochastic algorithm applied here to find the optimal values of the current amplitude excitation weights and the inter-element spacing between each element of the array in the DDE array and three-rings structure CCAA for the desired, uncorrected and corrected FFRP synthesis. Some well-established evolutionary optimisation techniques like particle swarm optimisation (PSO), differential evolution (DE) and social spider algorithm (SSA) are also employed in this article for the sake of comparison with the results achieved by using the GWO algorithm. Finally, the supremacy of GWO algorithm based design is demonstrated and validated by employing the 16-elements DDE array of monopole antennas and the three-ring CCAA of dipole elements.