Analysis of circular polarization antenna design trade‐offs using low‐cost EM‐driven multiobjective optimization

Circular polarization (CP) antennas are vital components of modern communication systems. Their design involves handling several requirements such as low reflection and axial ratio (AR) within the frequency range of interest. Small size is an important criterion for antenna mobility which is normally achieved as a by‐product of performance‐oriented modifications of the structure topology. In this work, multiobjective optimization is used in order to identify and analyze design trade‐offs for miniaturized CP antenna including the antenna capability for maintaining small size while retaining acceptable levels of other performance figures. We use a population‐based metaheuristic algorithm to obtain a set of designs which represent the best attainable compromise between the imposed requirements. To maintain a low optimization cost, the algorithm is executed on a cheap approximation model and the results are further corrected to bring them to the EM model accuracy level. Here, the analysis is carried out for a planar CP antenna. Achievable size reduction of the considered structure—while maintaining acceptable performance—is around 11%. Antenna performance in terms of in‐band reflection and AR varies from ?14 to ?10 dB and from 1.3 to 3 dB, respectively. The numerical results are validated by measurements of fabricated antenna prototypes.     

Simulation‐based optimization for rigorous assessment of ground plane modifications in compact UWB antenna design

Introducing ground plane modifications is a popular approach in the design of compact UWB antennas. Yet, specific topological alterations are normally reported on case to case basis without thorough investigations concerning their general suitability for antenna miniaturization. In particular, detailed performance comparison of different ground plane modifications is lacking in the literature. In this article, the effect of selected ground plane modifications on achievable miniaturization rate is considered based on a set of four UWB antennas. EM‐driven optimization is carried out to minimize the antenna footprints while maintaining acceptable matching within the UWB frequency range. In each case, all geometry parameters of the respective structures are utilized in the design process. For the sake of fair comparison, all antennas are implemented on the same dielectric substrate. Our results indicate a clear performance pattern, here, an advantage of the elliptical ground plane slit below the feed line over the rectangular one (average size reduction ratio of 26% versus 19% across the benchmark set). Our conjectures are confirmed by physical measurements of the fabricated antenna prototypes.     

Multi‐objective design optimization of antennas for reflection,size, and gain variability using kriging surrogates and generalized domain segmentation

Cost‐efficient multi‐objective design optimization of antennas is presented. The framework exploits auxiliary data‐driven surrogates, a multi‐objective evolutionary algorithm for initial Pareto front identification, response correction techniques for design refinement, as well as generalized domain segmentation. The purpose of this last mechanism is to reduce the volume of the design space region that needs to be sampled in order to construct the surrogate model, and, consequently, limit the number of training data points required. The recently introduced segmentation concept is generalized here to allow for handling an arbitrary number of design objectives. Its operation is illustrated using an ultra‐wideband monopole optimized for best in‐band reflection, minimum gain variability, and minimum size. When compared with conventional surrogate‐based approach, segmentation leads to reduction of the initial Pareto identification cost by over 20%. Numerical results are supported by experimental validation of the selected Pareto‐optimal antenna designs.     

Expedited simulation‐driven design optimization of UWB antennas by means of response features

In this work, a method for fast design optimization of broadband antennas is considered. The approach is based on a feature‐based optimization (FBO) concept where reflection characteristics of the structure at hand are formulated in terms of suitably defined feature points. Redefinition of the design problem allows for reducing the design optimization cost, because the dependence of feature point coordinates on antenna dimensions is less nonlinear than for the original frequency characteristics (here, S‐parameters). This results in faster convergence of the optimization algorithm. The cost of the design process is further reduced using variable‐fidelity electromagnetic (EM) simulation models. In case of UWB antennas, the feature points are defined, among others, as the levels of the reflection characteristic at its local in‐band maxima, as well as location of the frequency point which corresponds to acceptable reflection around the lower corner frequency within the UWB band. Also, the number of characteristic points depends on antenna topology and its dimensions. Performance of FBO‐based design optimization is demonstrated using two examples of planar UWB antennas. Moreover, the computational cost of the approach is compared with conventional optimization driven by a pattern search algorithm. Experimental validation of the numerical results is also provided.     

Precise control of reflection response in bandwidth‐enhanced planar antennas

In this work, the issues of bandwidth enhancement of planar antennas and the relevance of precise and automated response control through numerical optimization have been investigated. Using an example of a planar antenna with parasitic radiator we illustrate possible effects of even minor modifications of the antenna geometry (here, applied to the ground plane) on its reflection performance. In particular, a proper handling of geometry parameters may lead to considerable broadening of the antenna bandwidth. For the sake of computational efficiency, the adjustment of geometry parameters is carried out using surrogate‐based optimization methods exploiting coarse‐discretization EM simulations as the underlying low‐fidelity antenna model. Additionally, suitably defined penalty function allows us to precisely control the maximum in‐band reflection so that sufficient margin to accommodate possible manufacturing tolerances can be achieved. The optimized designs of the two antenna structures considered in this work exhibit over 1.75 GHz (>31%) and 2.15 GHz (>38%) bandwidth, respectively, for the center frequency of 5.6 GHz. Simulation results are validated using measurements of the fabricated prototypes. Comparison with state‐of‐the‐art designs is also provided. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:653–659, 2016.     

Improved trust‐region gradient‐search algorithm for accelerated optimization of wideband antenna input characteristics

Full‐wave electromagnetic (EM) simulation models are ubiquitous in carrying out design closure of antenna structures. Yet, EM‐based design is expensive due to a large number of analyses necessary to yield an optimized design. Computational savings can be achieved using, for example, adjoint sensitivities, surrogate‐assisted procedures, design space dimensionality reduction, or similar sophisticated means. In this article, a simple modification of a rudimentary trust‐region‐embedded gradient search with numerical derivatives is proposed for reduced‐cost optimization of input characteristics of wideband antennas. The approach exploits information and history of relative changes of the design (as compared with the trust region size) during algorithm iterations to control the updates of components of the antenna response Jacobian, specifically, to execute them only if necessary. It is demonstrated that the proposed framework may lead to over 50% savings over the reference algorithm with only minor degradation of the design quality, specifically, up to 0.3 dB (or <3%). Numerical results are supported by experimental validation of the optimized antenna designs. The presented algorithm can be utilized as a stand‐alone optimization routine or as a building block of surrogate‐assisted procedures.     

Surrogate‐assisted EM‐driven miniaturization of wideband microwave couplers by means of co‐simulation low‐fidelity models

This article proposes a methodology for rapid design optimization of miniaturized wideband couplers. More specifically, a class of circuits is considered, in which conventional transmission lines are replaced by their abbreviated counterparts referred to as slow‐wave compact cells. Our focus is on explicit reduction of the structure size as well as on reducing the CPU cost of the design process. For the sake of computational feasibility, a surrogate‐based optimization paradigm involving a co‐simulation low‐fidelity model is used. The latter is a fundamental component of the proposed technique. The low‐fidelity model represents cascaded slow‐wave cells replacing the low‐impedance lines of the original coupler circuit. It is implemented in a circuit simulator (here, ADS) and consists of duplicated compact cell EM simulation data as well as circuit theory‐based feeding line models. Our primary optimization routine is a trust‐region‐embedded gradient search algorithm. To further reduce the design cost, the system response Jacobian is estimated at the level of the low‐fidelity model, which is sufficient due to good correlation between the low‐ and high‐fidelity models. The coupler is explicitly optimized for size reduction, whereas electrical performance parameters are controlled using a penalty function approach. The presented methodology is demonstrated through the design of a 1‐GHz wideband microstrip branch‐line coupler. Numerical results are supported by experimental validation of the fabricated coupler prototype.     

Compact cell topology selection for size‐reduction‐oriented design of microstrip rat‐race couplers

In this work, we address the problem of compact cell topology selection for miniaturization of rat‐race couplers. The principal objective of the design process is to achieve the smallest possible footprint of the coupler, while maintaining the required levels of electrical parameters imposed on its components. Our approach permits identification of the minimum achievable coupler area, provided that the circuit is composed of a given compact cell and folded lines. This allows for the quantitative assessment of a set of considered cells with respect to the miniaturization capabilities they exhibit under certain design specifications. The proposed method is validated using 6 different cells with unified parameterization to identify the smallest rectangular‐like rat‐race coupler described by 2 design specifications. The obtained results attest that circuit topology and electrical parameters of the reference design are critical factors determining the final miniaturization rate. The proof‐of‐concept prototype devices occupy merely 8% of the conventional coupler area, while preserving fractional bandwidths (20% and 13.5%) of their conventional counterparts. The experimental results confirm the claims inferred from the numerical data.     

Rapid design and size reduction of microwave couplers using variable‐fidelity EM‐driven optimization

In this article, fast electromagnetic (EM) simulation‐driven design optimization of compact microwave couplers is addressed. The main focus is on explicit reduction of the circuit footprint. Our methodology relies on the penalty function approach, which allows us to minimize the circuit area while ensuring equal power split between the output ports and providing a sufficient bandwidth with respect to the return loss and isolation around the operating frequency. Computational efficiency of the design process is achieved by exploiting variable‐fidelity EM simulations, local response surface approximation models, as well as suitable response correction techniques for design tuning. The technique described in this work is demonstrated using two examples of compact rat‐race couplers. The size‐reduction‐oriented designs are compared with performance‐oriented ones to illustrate available design trade‐offs. Final design solutions of the former case illustrate ～92% of miniaturization for both coupler examples (with corresponding fractional bandwidths of 16%). Alternative design solutions pertaining to the latter case show a lesser size reduction (～90% for both examples), but present a much wider bandwidths (～25% for both couplers). The overall computational cost of the design procedure corresponds to about 20 and 10 high‐fidelity coupler simulations for the first and second design example, respectively. Numerical results are also validated experimentally. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:27–35, 2016.     

Fast simulation‐driven antenna design using response‐feature surrogates

In this article, a computationally efficient procedure for electromagnetic (EM)‐simulation‐driven design of antennas is presented. Our methodology is based on local approximation models of the antenna response, established using a set of suitably selected characteristic features rather than the entire response (such as reflection versus frequency). The approximation model is utilized to verify the level of satisfying/violating given performance requirements, and to guide the optimization process towards a better design. By exploiting the fact that the dependence of the response features on the designable parameters of the antenna of interest is simple (close to linear or quadratic), the feature‐based optimization converges faster than conventional optimization of frequency‐based EM‐simulated responses. In order to further speed up the design, coarse‐discretization simulations are utilized to estimate the feature gradients with respect to adjustable parameters of the problem at hand. The optimization algorithm is embedded in the trust‐region framework for safeguarding convergence. The proposed technique is demonstrated using two antenna examples. In both the cases, the optimum design is obtained at the computational cost corresponding to a few high‐fidelity EM antenna simulations. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:394–402, 2015.     

Phase‐spacing optimization of linear microstrip antenna arrays using simulation‐based surrogate superposition models

A technique for simulation‐driven optimization of the phase excitation tapers and spacings for linear arrays of microstrip patch antennas is presented. Our technique exploits two models of the array under optimization: an analytical model which is based on the array factor, as well as an electromagnetic (EM) simulation‐based surrogate model of the entire array. The former is used to provide initial designs which meet the design requirements imposed on the radiation response. The latter is used for tuning of the array radiation response while controlling the array reflection response as well as for validation of the final design. Furthermore, the simulation‐based surrogate model allows for subsequent evaluation of the array responses in the beam scanning operation at negligible computational costs. The simulation‐based surrogate model is constructed with a superposition of simulated radiation and reflection responses of the array under design with only one radiator active at a time. Low computational cost of the surrogate model is ensured by the EM‐simulation data computed with coarse meshes. Reliability of the model is achieved by means of suitable correction carried out with respect to the high‐fidelity array model. The correction is performed iteratively in the optimization process. Performance, numerical efficiency, and accuracy of the technique is demonstrated with radiation pattern synthesis of linear arrays comprising 32 microstrip patch antennas by phase‐spacing optimization. Properties of the optimal designs in the beam scanning operation are then studied using the superposition models and compared to suitably selected reference designs. The proposed technique is versatile as it also can be applied for simulation‐based optimization of antenna arrays comprising other types of individually fed elements. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:536–547, 2015.     

A π/4 bi‐orthogonal monopole antenna for operation on and beyond of the UWB band

An ultra‐wideband (UWB) π/4 bi‐orthogonal monopole antenna with a highly omnidirectional radiation pattern in the azimuthal plane with a quasi‐independent on the frequency behavior is presented in this article. Here, it is shown that by combining two orthogonal UWB planar monopole elements rotated 45° with respect to each other in a single structure, it is possible to enhance the performance of the radiation pattern at high frequencies of the operational bandwidth without affecting the radiation pattern at lower frequencies. The measured antenna bandwidth goes from 2.82 to 16.7 GHz for a reflection coefficient lower than ?10 dB. The radiation pattern remains almost omnidirectional, and it is enhanced with respect to a conventional single planar monopole antenna of similar characteristics. The basic element used for both the single and the proposed π/4 bi‐orthogonal UWB planar monopole antenna has a rectangular shape, whose impedance bandwidth ratio is achieved based on the bevelling and height‐width ratio techniques. Although the antenna prototype presented in this article has an operational bandwidth of 13.88 GHz, it is possible to design a UWB monopole antenna with the shape and structure proposed here, but for different bandwidths following a design methodology suggested also in this article. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Computational‐budget‐driven automated microwave design optimization using variable‐fidelity electromagnetic simulations

A robust technique for microwave design optimization is presented. It is based on variable‐fidelity electromagnetic (EM) simulations where the approximate optimum of the “coarser” model becomes an initial design for finding the optimum of the “finer” one. The algorithm automatically switches between the models of different fidelity taking into account the computational budget assumed for the design process. Additional mechanisms enhancing the algorithm include: frequency scaling to reduce the misalignment between the models of different fidelity, as well as the local response surface approximation to reduce the number of EM simulations. The presented technique is particularly suitable for problems where simulation‐driven design is the only option, for example, for wideband antennas and dielectric resonator filters. Our method is demonstrated using two filters and one antenna example. In all cases, the optimal design is obtained at a low computational cost corresponding to a few high‐fidelity simulations of the structure. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.     

Reduced‐cost surrogate modeling of input characteristics and design optimization of dual‐band antennas using response features

In this article, a procedure for low‐cost surrogate modeling of input characteristics of dual‐band antennas has been discussed. The number of training data required for construction of an accurate model has been reduced by representing the antenna reflection response to the level of suitably defined feature points. The points are allocated to capture the critical features of the reflection characteristic, such as the frequencies and the levels of the resonances, and supplemented by the additions (infill) points, which is necessary to provide sufficient data that allows restoring the entire response through interpolation. Because the coordinates of the feature points exhibit less nonlinear behavior (as a function of antenna geometry parameters) compared to S‐parameters as a function of frequency, surrogate model construction can be realized with a smaller number of data points. The presented modeling approach is demonstrated using an example of a planar dipole antenna. Also, the feature‐based method is favorably compared to direct modeling of reflection characteristics using kriging. The relevance of the technique is further verified by its application for design optimization.     

Low‐cost multiband compact branch‐line coupler design using response features and automated EM model fidelity adjustment

Design closure of compact microwave components is a challenging problem because of significant electromagnetic (EM) cross‐couplings in densely arranged layouts. A separate issue is a large number of designable parameters resulting from replacement of conventional transmission line sections by compact microstrip resonant cells. This increases complexity of the design optimization problem and requires employment of expensive high‐fidelity EM analysis for reliable performance evaluation of the structure at hand. Consequently, neither conventional numerical optimization algorithms nor interactive approaches (e.g., experience‐driven parameters sweeps) are capable of identifying optimum designs in reasonable timeframes. Here, we discuss application of feature‐based optimization for fast design optimization of dual‐ and multiband compact couplers. On one hand, design of such components is difficult because of multiple objectives (achieving equal power split and good matching and port isolation for all frequency bands of interest). On the other hand, because of well‐defined shapes of the S‐parameter responses for this class of components, feature‐based optimization seems to be well suited to control multiple figures of interest as demonstrated in this work. Two‐level EM modeling is used for further design cost reduction. More importantly, we develop a procedure for automated determination of the low‐fidelity EM model coarseness that allows us to find the fastest possible model that still ensures sufficient correlation with its high‐fidelity counterpart, which is critical for robustness of the optimization process. Our approach is illustrated using two dual‐band compact couplers. Experimental validation is also provided.     

Response correction techniques for surrogate‐based design optimization of microwave structures

Simulation‐based optimization has become an important design tool in microwave engineering. However, using electromagnetic (EM) solvers in the design process is a challenging task, primarily due to a high‐computational cost of an accurate EM simulation. In this article, we present a review of EM‐based design optimization techniques exploiting response‐corrected physically based low‐fidelity models. The surrogate models created through such a correction can be used to yield a reasonable approximation of the optimal design of the computationally expensive structure under consideration (high‐fidelity model). Several approaches using this idea are reviewed including output space mapping, manifold mapping, adaptive response correction, and shape‐preserving response prediction. A common feature of these methods is that they are easy to implement and computationally efficient. Application examples are provided. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.     

Fast simulation‐driven feature‐based design optimization of compact dual‐band microstrip branch‐line coupler

Design of miniaturized microwave components is a challenging task. On one hand, due to considerable electromagnetic (EM) cross‐couplings in highly compressed layouts full‐wave EM analysis is necessary for accurate evaluation of the structure performance. Conversely, high‐fidelity EM simulation is computationally expensive so that automated determination of the structure dimensions may be prohibitive when using conventional numerical optimization routines. In this article, computationally efficient simulation‐driven design of a miniaturized dual‐band microstrip branch‐line coupler is presented. The optimization methodology relies on suitably extracted features of a highly nonlinear response of the coupler structure under design. The design objectives are formulated in terms of the feature point locations, and the optimization is carried out iteratively with the linear model of the features utilized as a fast predictor. The entire process is embedded in the trust‐region framework as convergence safeguard. Owing to only slightly nonlinear dependence of the features on the geometry parameters of the circuit at hand, the optimized design satisfying prescribed performance requirements is obtained at the low computational cost of only 24 high‐fidelity EM simulations of the structure. Experimental validation of the fabricated coupler prototype is also provided. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:13–20, 2016.     

Rapid design closure of microwave components by means of feature‐based optimization and adjoint sensitivities

In this article, fast design closure of microwave components using feature‐based optimization (FBO) and adjoint sensitivities is discussed. FBO is one of the most recent optimization techniques that exploits a particular structure of the system response to “flatten” the functional landscape handled during the optimization process, which leads to reducing its computational complexity. When combined with gradient‐based search involving adjoint sensitivities, the design cost becomes even lower, allowing us to find the optimum design using just a few electromagnetic (EM) simulations of the structure at hand. Here, operation and performance of the algorithm is demonstrated using a waveguide filter and a miniaturized microstrip rat‐race coupler (RRC). Comparative studies indicate considerable savings that can be achieved even compared with adjoint‐based gradient search. In case of RRC, numerical results are supported by experimental validation.     

Design optimization of a pattern reconfigurable microstrip antenna using differential evolution and 3D EM simulation‐based neural network model

In this work, design optimization of a varicap diode loaded antenna consisting of four identical rectangular microstrips is presented as a pattern reconfigurable antenna at 5.2 GHz. The microstrips are printed on the front of a FR4 substrate with the dimensions of 40 mm × 25 mm and ε _r = 4.6, h = 1.58 mm and probe‐fed via a coupling using a rectangular microstrip line symmetrically placed between them. In first stage, S₁₁ of the antenna are obtained as its real and imaginary parts as continuous functions of geometry of the microstrip components within 3 to 7 GHz using multi‐layer perceptron (MLP) trained and validated by 3D EM simulated data. In order to determine the most suitable (MLP) architecture and training algorithm, 20 different MLP architectures are tested. Then, S₁₁ are optimized with respect to the geometry parameters using differential evolution algorithm and MLP based model. The antenna is prototyped with the optimally selected parameters and measured. From the comparison of simulation and measurement results, it can be observed that the measurement results agree with the simulation results, thus it can be concluded that the proposed antenna is a simple and successful design subject to the design purposes with together its design methodology.     

Performance of a circular crossed‐dipole array for SDMA configuration adopting directivity and polarization control using particle swarm optimization algorithm

In this article, the performance of a circular crossed‐dipole array (CCDA) for space division multiple access (SDMA) configurations adopting directivity and polarization control is presented. The array consists of 12 dual‐polarized elements uniformly distributed in a circular configuration; each dual‐polarized element (crossed‐dipole) consists of two half‐wave dipoles in a ±45° slant configuration. The modified particle swarm optimization and moment of method (MPSO‐MOM) algorithm is used to calculate the complex weightings of the array elements in a mutual coupling environment for beamforming synthesis. In addition, the performance of the adaptive array using discrete feedings (1‐bit amplitude and 4‐bit phase shifters or only 4‐bit phase shifters) is studied. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.