Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
A RRAY F ACTOR O PTIMIZATION OF AN A CTIVE P LANAR P HASED A RRAY USING...jantjournal
Evolutionary algorithms (EAs) have the potential to
handle complex, multi-dimensional optimization
problems in the field of phased array. Out of diffe
rent EAs, particle swarm optimization (PSO) is a po
pular
choice. In a phased array, antenna element failure
is a common phenomenon and this leads to degradatio
n
of the array factor (AF) pattern, primarily in term
s of increased side lobe levels (SLLs), displacemen
t of
nulls and reduction in the null depths. The recover
y of a degraded pattern using a cost and time-effec
tive
approach is on demand. In this context, an attempt
made to obtain an optimized AF pattern after fault
in a
49 elements quasi-circular aperture equilateral tri
angular grid active planar phased array using PSO.
In
the paper, multiple cases on recovery are discussed
having a maximum 20% element failure. Each recover
y
is also further evaluated by different statistical
analyses. A dedicated software tool was developed t
o carry
out the work presented in this paper.
The document describes the design and testing of a circular microstrip patch array antenna for C-band altimeter systems. It discusses using an array of four circular microstrip elements with equal size and spacing to achieve a gain of 12 dB. The antenna was simulated using HFSS and Microwave Office software. Comparison of simulated and measured results showed good agreement, achieving the design goals.
Elements Space and Amplitude Perturbation Using Genetic Algorithm for Antenna...CSCJournals
A simple and fast genetic algorithm (GA) developed to reduce the sidelobes in non-uniformly spaced linear antenna arrays. The proposed GA algorithm optimizes two vectors of variables to increase the Main lobe to Sidelobe power ratio (M/S) of array’s radiation pattern. The algorithm, in the first phase calculates the positions of the array elements and in the second phase, it manipulates the amplitude of excitation signals for each element. The simulations performed for 16 and 24 elements array structure. The results indicated that M/S improved in first phase from 13.2 to over 22.2dB meanwhile the half power beamwidth (HPBW) left almost unchanged. After element replacement, in the second phase, by using amplitude tapering further improvement up to 32dB was achieved. Also, the simulations shown that after element space perturbation, some antenna elements can be merged together without any performance degradation in radiation pattern in terms of gain and sidelobes level.
Spherical array of annular ring microstrip antennaswailGodaymi1
The paper discusses the analytical study of spherical arrays of annular ring microstrip antenna (ARMSA) elements excited by electric dipole. A new empirical relation for calculating the nonunifrom current amplitude distributions of these elements has been obtained. The relation contains the information about the current amplitude factor ()Δ of the antenna elements of the spherical array. The narrow beamwidth and low side lobe levels can be obtain by choosing appropriate the current amplitude factor. It is found that for current amplitude factor ()5.0=Δ the radiation pattern have narrow beamwidth and low side lobe levels compared with uniform current distribution array. Circular polarization is realized by this study depends on the spherical array geometry. By using appropriate phase of each antenna elements in spherical arrays, radiation pattern is steered without change of gain and beamwidth.
Ill-posedness formulation of the emission source localization in the radio- d...Ahmed Ammar Rebai PhD
To contact the authors : tarek.salhi@gmail.com and ahmed.rebai2@gmail.com
In the field of radio detection in astroparticle physics, many studies have shown the strong dependence of the solution of the radio-transient sources localization problem (the radio-shower time of arrival on antennas) such solutions are purely numerical artifacts. Based on a detailed analysis of some already published results of radio-detection experiments like : CODALEMA 3 in France, AERA in Argentina and TREND in China, we demonstrate the ill-posed character of this problem in the sens of Hadamard. Two approaches have been used as the existence of solutions degeneration and the bad conditioning of the mathematical formulation problem. A comparison between experimental results and simulations have been made, to highlight the mathematical studies. Many properties of the non-linear least square function are discussed such as the configuration of the set of solutions and the bias.
Particle Swarm Optimization with Constriction Factor and Inertia Weight Appro...IDES Editor
In this paper, an evolutionary optimization
technique, Particle Swarm Optimization with Constriction
Factor and Inertia Weight Approach (PSOCFIWA) is adopted
for the complex synthesis of three-ring Concentric Circular
Antenna Arrays (CCAA) with non-isotropic elements and
without and with central element feeding. It is shown that by
selection of a fitness function which controls more than one
parameter of the array pattern, and also by proper setting of
weight factors in fitness function, one can achieve very good
results. For each optimal design, optimal current excitation
weights and optimal radii are determined having the objective
of maximum Sidelobe Level (SLL) reduction. The extensive
computational results show that the CCAA designs having
central element feeding with non-isotropic elements yield
much more reduction in SLL as compared to the same not
having central element feeding. Moreover, the particular
CCAA containing 4, 6 and 8 number of elements in three
successive rings along with central element feeding yields
grand minimum SLL (-46.4 dB). Standard Particle Swarm
Optimization (PSO) is adopted to compare the results of the
PSOCFIWA algorithm.
Comparative and comprehensive study of linear antenna arrays’ synthesisIJECEIAES
In this paper, a comparative and comprehensive study of synthesizing linear antenna array (LAA) designs, is presented. Different desired objectives are considered in this paper; reducing the maximum sidelobe radiation pattern (i.e., pencil-beam pattern), controlling the first null beamwidth (FNBW), and imposing nulls at specific angles in some designs, which are accomplished by optimizing different array parameters (feed current amplitudes, feed current phase, and array elements positions). Three different optimization algorithms are proposed in order to achieve the wanted goals; grasshopper optimization algorithms (GOA), ant lion optimization (ALO), and a new hybrid optimization algorithm based on GOA and ALO. The obtained results show the effectiveness and robustness of the proposed algorithms to achieve the wanted targets. In most experiments, the proposed algorithms outperform other well-known optimization methods, such as; Biogeography based optimization (BBO), particle swarm optimization (PSO), firefly algorithm (FA), cuckoo search (CS) algorithm, genetic algorithm (GA), Taguchi method, self-adaptive differential evolution (SADE), modified spider monkey optimization (MSMO), symbiotic organisms search (SOS), enhanced firefly algorithm (EFA), bat flower pollination (BFP) and tabu search (TS) algorithm.
This document summarizes research on using particle swarm optimization (PSO) to enhance the radiation pattern of a phase array antenna. It begins by introducing the problem of high sidelobes in phase array antenna patterns. It then provides background on phased array antennas and array pattern modeling. A 24-element linear array modeled in MATLAB is used as a case study. Standard PSO and a modified PSO algorithm are applied to optimize the current excitations and minimize the sidelobe levels. Simulation results show that both PSO approaches reduce sidelobes compared to uniform excitation, with the modified PSO performing better. Overall, the document presents research on using computational optimization methods to improve phase array antenna radiation patterns by controlling sidelobe levels
A RRAY F ACTOR O PTIMIZATION OF AN A CTIVE P LANAR P HASED A RRAY USING...jantjournal
Evolutionary algorithms (EAs) have the potential to
handle complex, multi-dimensional optimization
problems in the field of phased array. Out of diffe
rent EAs, particle swarm optimization (PSO) is a po
pular
choice. In a phased array, antenna element failure
is a common phenomenon and this leads to degradatio
n
of the array factor (AF) pattern, primarily in term
s of increased side lobe levels (SLLs), displacemen
t of
nulls and reduction in the null depths. The recover
y of a degraded pattern using a cost and time-effec
tive
approach is on demand. In this context, an attempt
made to obtain an optimized AF pattern after fault
in a
49 elements quasi-circular aperture equilateral tri
angular grid active planar phased array using PSO.
In
the paper, multiple cases on recovery are discussed
having a maximum 20% element failure. Each recover
y
is also further evaluated by different statistical
analyses. A dedicated software tool was developed t
o carry
out the work presented in this paper.
The document describes the design and testing of a circular microstrip patch array antenna for C-band altimeter systems. It discusses using an array of four circular microstrip elements with equal size and spacing to achieve a gain of 12 dB. The antenna was simulated using HFSS and Microwave Office software. Comparison of simulated and measured results showed good agreement, achieving the design goals.
Elements Space and Amplitude Perturbation Using Genetic Algorithm for Antenna...CSCJournals
A simple and fast genetic algorithm (GA) developed to reduce the sidelobes in non-uniformly spaced linear antenna arrays. The proposed GA algorithm optimizes two vectors of variables to increase the Main lobe to Sidelobe power ratio (M/S) of array’s radiation pattern. The algorithm, in the first phase calculates the positions of the array elements and in the second phase, it manipulates the amplitude of excitation signals for each element. The simulations performed for 16 and 24 elements array structure. The results indicated that M/S improved in first phase from 13.2 to over 22.2dB meanwhile the half power beamwidth (HPBW) left almost unchanged. After element replacement, in the second phase, by using amplitude tapering further improvement up to 32dB was achieved. Also, the simulations shown that after element space perturbation, some antenna elements can be merged together without any performance degradation in radiation pattern in terms of gain and sidelobes level.
Spherical array of annular ring microstrip antennaswailGodaymi1
The paper discusses the analytical study of spherical arrays of annular ring microstrip antenna (ARMSA) elements excited by electric dipole. A new empirical relation for calculating the nonunifrom current amplitude distributions of these elements has been obtained. The relation contains the information about the current amplitude factor ()Δ of the antenna elements of the spherical array. The narrow beamwidth and low side lobe levels can be obtain by choosing appropriate the current amplitude factor. It is found that for current amplitude factor ()5.0=Δ the radiation pattern have narrow beamwidth and low side lobe levels compared with uniform current distribution array. Circular polarization is realized by this study depends on the spherical array geometry. By using appropriate phase of each antenna elements in spherical arrays, radiation pattern is steered without change of gain and beamwidth.
Ill-posedness formulation of the emission source localization in the radio- d...Ahmed Ammar Rebai PhD
To contact the authors : tarek.salhi@gmail.com and ahmed.rebai2@gmail.com
In the field of radio detection in astroparticle physics, many studies have shown the strong dependence of the solution of the radio-transient sources localization problem (the radio-shower time of arrival on antennas) such solutions are purely numerical artifacts. Based on a detailed analysis of some already published results of radio-detection experiments like : CODALEMA 3 in France, AERA in Argentina and TREND in China, we demonstrate the ill-posed character of this problem in the sens of Hadamard. Two approaches have been used as the existence of solutions degeneration and the bad conditioning of the mathematical formulation problem. A comparison between experimental results and simulations have been made, to highlight the mathematical studies. Many properties of the non-linear least square function are discussed such as the configuration of the set of solutions and the bias.
Particle Swarm Optimization with Constriction Factor and Inertia Weight Appro...IDES Editor
In this paper, an evolutionary optimization
technique, Particle Swarm Optimization with Constriction
Factor and Inertia Weight Approach (PSOCFIWA) is adopted
for the complex synthesis of three-ring Concentric Circular
Antenna Arrays (CCAA) with non-isotropic elements and
without and with central element feeding. It is shown that by
selection of a fitness function which controls more than one
parameter of the array pattern, and also by proper setting of
weight factors in fitness function, one can achieve very good
results. For each optimal design, optimal current excitation
weights and optimal radii are determined having the objective
of maximum Sidelobe Level (SLL) reduction. The extensive
computational results show that the CCAA designs having
central element feeding with non-isotropic elements yield
much more reduction in SLL as compared to the same not
having central element feeding. Moreover, the particular
CCAA containing 4, 6 and 8 number of elements in three
successive rings along with central element feeding yields
grand minimum SLL (-46.4 dB). Standard Particle Swarm
Optimization (PSO) is adopted to compare the results of the
PSOCFIWA algorithm.
Comparative and comprehensive study of linear antenna arrays’ synthesisIJECEIAES
In this paper, a comparative and comprehensive study of synthesizing linear antenna array (LAA) designs, is presented. Different desired objectives are considered in this paper; reducing the maximum sidelobe radiation pattern (i.e., pencil-beam pattern), controlling the first null beamwidth (FNBW), and imposing nulls at specific angles in some designs, which are accomplished by optimizing different array parameters (feed current amplitudes, feed current phase, and array elements positions). Three different optimization algorithms are proposed in order to achieve the wanted goals; grasshopper optimization algorithms (GOA), ant lion optimization (ALO), and a new hybrid optimization algorithm based on GOA and ALO. The obtained results show the effectiveness and robustness of the proposed algorithms to achieve the wanted targets. In most experiments, the proposed algorithms outperform other well-known optimization methods, such as; Biogeography based optimization (BBO), particle swarm optimization (PSO), firefly algorithm (FA), cuckoo search (CS) algorithm, genetic algorithm (GA), Taguchi method, self-adaptive differential evolution (SADE), modified spider monkey optimization (MSMO), symbiotic organisms search (SOS), enhanced firefly algorithm (EFA), bat flower pollination (BFP) and tabu search (TS) algorithm.
This document summarizes research on using particle swarm optimization (PSO) to enhance the radiation pattern of a phase array antenna. It begins by introducing the problem of high sidelobes in phase array antenna patterns. It then provides background on phased array antennas and array pattern modeling. A 24-element linear array modeled in MATLAB is used as a case study. Standard PSO and a modified PSO algorithm are applied to optimize the current excitations and minimize the sidelobe levels. Simulation results show that both PSO approaches reduce sidelobes compared to uniform excitation, with the modified PSO performing better. Overall, the document presents research on using computational optimization methods to improve phase array antenna radiation patterns by controlling sidelobe levels
Enhancing the Radiation Pattern of Phase Array Antenna Using Particle Swarm O...IOSR Journals
The document describes a study that uses particle swarm optimization to enhance the radiation pattern of a phase array antenna by minimizing sidelobe levels. It first provides background on issues with high sidelobes in phase array antennas, such as power losses and interference. It then summarizes previous research using techniques like genetic algorithms for antenna array optimization. The study models the radiation pattern of linear arrays with different element numbers and calculates gain, finding that gain increases with more elements. However, sidelobe levels also increase relatively. Therefore, the study proposes using particle swarm optimization to optimize current excitation and control sidelobe levels while maintaining a narrow beamwidth.
Implementation of Digital Beamforming Technique for Linear Antenna Arraysijsrd.com
A digital Beamforming technique used for increased channel capacity and also increased signal to noise and interference ratio. In smart antenna, different type of radiation pattern of an antenna can be changed either by selecting appropriate weights or by changing the array geometry. This paper presented based on auxiliary phase algorithm by using this algorithm in linear antenna array determine the array pattern approximating the auxiliary function in both amplitude and phase. Cost function involving auxiliary function and array pattern is minimized by modifying the pattern.
Designing a pencil beam pattern with low sidelobesPiyush Kashyap
In this paper, a system has been designed for an operational frequency of 1.27 GHz consisting of an 8 element array of parasitic dipoles illuminated by a 4 element center fed array of active dipoles with Dolph-Chebyshev excitation coefficients. The array is designed to achieve a fairly pencil beam pattern suitable for direction of arrival estimation purposes. Array geometry and configuration is optimized for both active and parasitic elements using the PSO tool in FEKO. A directive radiation pattern is obtained with a gain of 14.5 dBi in the broadside direction along with a beamwidth of 30.29o. VSWR of 1.58 is achieved. Further, an iterative least square valued error estimation approach using phase control to achieve a desired array factor pattern for an n-element linear array, has been shown to be effective for larger number of iterations. The array excitation coefficients achieved were consistent with the Dolph-Chebyshev coefficients used in our antenna array design. With the ability to introduce nulls and steering the main beam in desired directions along with a pencil beam radiation pattern, beamsteering has been illustrated and the MUSIC algorithm for direction of arrival estimation has been implemented
The document summarizes research on thinning semi-elliptical and quarter-elliptical antenna arrays using genetic algorithm optimization to reduce side-lobe levels. Key points:
1) Genetic algorithms were used to optimize thinning of semi-elliptical and quarter-elliptical arrays with uniform excitation and spacing to produce narrow beams without degrading performance.
2) Simulation results showed thinning using genetic algorithms reduced side-lobe levels of the arrays compared to fully populated arrays.
3) Maximum side-lobe levels, beamwidths, and other metrics were tabulated for various array sizes and geometries, indicating thinning effectively lowered side-lobes.
Rabid Euclidean direction search algorithm for various adaptive array geometriesjournalBEEI
This document summarizes the Rabid Euclidean direction search (REDS) algorithm for adaptive beamforming in different antenna array geometries. The REDS algorithm is analyzed for linear, circular, and planar array configurations. Simulation results show that the REDS algorithm provides significant improvements over other algorithms, including faster convergence, lower mean square error, better interference reduction, and lower sidelobe levels. Specifically, the REDS algorithm cyclically searches and updates weights along individual Euclidean directions to minimize error, offering computational advantages over algorithms like least mean square and recursive least squares.
Diagnosis of Faulty Sensors in Antenna Array using Hybrid Differential Evolut...IJECEIAES
In this work, differential evolution based compressive sensing technique for detection of faulty sensors in linear arrays has been presented. This algorithm starts from taking the linear measurements of the power pattern generated by the array under test. The difference between the collected compressive measurements and measured healthy array field pattern is minimized using a hybrid differential evolution (DE). In the proposed method, the slow convergence of DE based compressed sensing technique is accelerated with the help of parallel coordinate decent algorithm (PCD). The combination of DE with PCD makes the minimization faster and precise. Simulation results validate the performance to detect faulty sensors from a small number of measurements.
This document summarizes a research paper about designing beampatterns for MIMO radar systems using a covariance-based method while accounting for the locations of transmitter antennas. It discusses how changing antenna locations is equivalent to changing carrier frequency. The paper proposes optimizing two cost functions: 1) Pushing sidelobes away from the main lobe to minimize interference, and 2) Maximizing power around target locations without extra sidelobes to improve target detection. It formulates these cost functions and outlines an algorithm to optimize them using the cross-correlation matrix and antenna locations as design variables.
Optimal Synthesis of Array Pattern for Concentric Circular Antenna Array Usin...IDES Editor
In this paper one optimization heuristic search
technique, Hybrid Evolutionary Programming (HEP) is
applied to the process of synthesizing three-ring Concentric
Circular Antenna Array (CCAA) focused on maximum
sidelobe-level reduction. This paper assumes non-uniform
excitations and uniform spacing of excitation elements in each
three-ring CCAA design. Experimental results reveal that the
design of non-uniformly excited CCAAs with optimal current
excitations using the method of HEP provides a considerable
sidelobe level reduction with respect to the uniform current
excitation with d=λ/2 element-to-element spacing. Among the
various CCAA designs, the design containing central element
and 4, 6 and 8 elements in three successive concentric rings
proves to be such global optimal design with global minimum
SLL (-40.22 dB) as determined by HEP.
Reduction of Azimuth Uncertainties in SAR Images Using Selective RestorationIJTET Journal
The document proposes a framework to reduce azimuth uncertainties in synthetic aperture radar (SAR) images. It identifies azimuth uncertainty using a local average SAR image, system parameters, and a metric from the azimuth antenna pattern. Uncertainties are classified as isolated or clustered based on size. Isolated ambiguities consisting of smaller interconnected pixel regions are restored using compressive imaging. Clustered ambiguities consisting of larger interconnected pixel regions are restored using exemplar-based image inpainting. The proposed method was tested on real TerraSAR-X data and was able to effectively remove azimuth uncertainties and enhance image quality.
Sparsity based Joint Direction-of-Arrival and Offset Frequency EstimatorJason Fernandes
- The document proposes a method to jointly estimate direction-of-arrival (DoA) and offset frequency of signals impinging on an antenna array using sparse representation.
- It builds on previous work by extending the estimation to include both spatial (DoA) and temporal (offset frequency) dimensions. This is done by constructing a joint dictionary as the Kronecker product of discrete spatial and temporal steering vector grids.
- Sparse recovery algorithms can then be applied to estimate the sparse coefficients and jointly infer the DoAs and offset frequencies of impinging signals from compressed measurements of the antenna array output over multiple time snapshots.
International Journal of Engineering Research and DevelopmentIJERD Editor
This document presents a technique for estimating parameters of a deployable mesh reflector antenna using 3D coordinate data and least squares fitting. It involves determining the unknown coefficients of the general quadratic surface equation that best fits the 3D points. The shape of the surface is then estimated as an elliptic paraboloid based on its invariants. Key parameters of the elliptic paraboloid like the focal length are then determined by reconstructing the surface in its standard form based on the estimated coefficients and orientations. Estimating these parameters at different stages of deployment testing can help validate the stability of the antenna surface and placement of its feed.
Design of switched beam planer arrays using the method of genetic alograthim marwaeng
The document describes the use of genetic algorithms to design switched beam planar antenna arrays. Specifically, genetic algorithms are used to determine the element positions, radii, and excitation amplitudes and phases to produce radiation patterns with main beams pointing in specific directions. Both arbitrary element positioning and circular arrays are considered. The genetic algorithm is able to design arrays with 4 to 8 radiation patterns covering the x-y plane or a portion of it.
This document presents a low-cost method for electromagnetic signal spectral analysis and direction finding using a two-element time-modulated antenna array and multiple signal classification (MUSIC) algorithms. It describes a prototype array constructed using quarter-wave monopoles as antenna elements switched using PIN diodes. Measurements show the array output is phase modulated depending on signal arrival angle, producing a directional pattern at the carrier frequency and null at the first harmonic. MUSIC algorithms are applied to estimate signal directions from the received signals. The method provides a low-cost alternative to conventional direction finding techniques with potential applications in wireless communications and homeland security.
International Journal of Computer Vision 71(2), 127–141, 2007.docxvrickens
This document proposes a kernel spectral matched filter for target detection in hyperspectral imagery. It begins with an overview of linear matched filtering and introduces the concept of implementing algorithms in kernel feature spaces. It then defines a nonlinear matched filter model in a kernel feature space, which is equivalent to a nonlinear matched filter in the original input space. Finally, it derives an expression for the kernel spectral matched filter by rewriting the matched filter defined in the kernel feature space in terms of kernel functions using the kernel trick. Simulation results on hyperspectral imagery show the kernel spectral matched filter outperforms the conventional linear matched filter.
International Refereed Journal of Engineering and Science (IRJES) is a peer reviewed online journal for professionals and researchers in the field of computer science. The main aim is to resolve emerging and outstanding problems revealed by recent social and technological change. IJRES provides the platform for the researchers to present and evaluate their work from both theoretical and technical aspects and to share their views.
www.irjes.com
Diagnosis of Faulty Elements in Array Antenna using Nature Inspired Cuckoo Se...IJECEIAES
Detection and correction of faulty elements in a linear array have great importance in radar, sonar, mobile communications and satellite. Due to single element failure, the whole radiation pattern damage in terms of side lobes level and nulls. Once we have detect the position of defective element, then correction method is applied to achieve the desired pattern. In this work, we introduce a nature inspired meta-heuristic cuckoo search algorithm to diagnose the position of defective elements in a linear array. The nature inspired cuckoo search algorithm is new to the optimization family and is used first time for fault detection in an array antenna. Cuckoo search algorithm is a global search optimization technique. The cost function is used as a fitness function which defines an error between the degraded far field power pattern and the estimated one. The proposed technique is used effectively for the diagnosis of complete, as well as, for partial faulty elements position. Different simulation results are evaluated for 40 elements Taylor pattern to validate and check the performance of the proposed technique.
This document discusses using a genetic algorithm to optimize the resonant frequency of a coaxially fed rectangular microstrip antenna. The genetic algorithm optimizes patch length, width, and feed position at frequencies of 3GHz, 5GHz, and 10GHz. Results showed the optimized antennas had return losses of -18.7dB, -22.03dB, and -41.75dB respectively at the desired frequencies, indicating good impedance matching. Radiation patterns were also verified to show forward radiation and no backward radiation, validating the design accuracy. The use of genetic algorithms for antenna design optimization encourages accurate resonant frequency evaluation.
Application of genetic algorithm to the optimization of resonant frequency of...IOSR Journals
Abstract : Microstrip antenna is gathering a lot of interest in communication systems. Genetic algorithm is a popular optimization technique and has been introduced for design optimization of microstrip patch antenna. In this paper, genetic algorithm has been used for optimization of resonant frequency of coaxially fed rectangular microstrip antenna. The investigation is made at 3 different frequencies 3GHz, 5GHz and 10GHz respectively. Patch length, patch width & feed position are taken as optimization parameters. Return loss and radiation pattern for the optimized antenna are verified using IE3D software. Accuracy of the results encourages the use of genetic algorithm. Keywords - Rectangular microstrip antenna, genetic algorithm, resonant frequency, IE3D
Application of genetic algorithm to the optimization of resonant frequency of...IOSR Journals
Microstrip antenna is gathering a lot of interest in communication systems. Genetic algorithm is a
popular optimization technique and has been introduced for design optimization of microstrip patch antenna. In
this paper, genetic algorithm has been used for optimization of resonant frequency of coaxially fed rectangular
microstrip antenna. The investigation is made at 3 different frequencies 3GHz, 5GHz and 10GHz respectively.
Patch length, patch width & feed position are taken as optimization parameters. Return loss and radiation
pattern for the optimized antenna are verified using IE3D software. Accuracy of the results encourages the use
of genetic algorithm.
AN ANALYSIS OF THE KALMAN, EXTENDED KALMAN, UNCENTED KALMAN AND PARTICLE FILT...sipij
Tracking the Direction of Arrival (DOA) Estimation of a multiple moving sources is a significant task
which has to be performed in the field of navigation, RADAR, SONAR, Wireless Sensor Networks (WSNs)
etc. DOA of the moving source is estimated first, later the estimated DOA using Estimation of Signal
Parameters via Rotational Invariance Technique (ESPRIT) is used as an initial value and will be provided
to any of the Kalman filter (KF), Extended Kalman filter (EKF), Uncented Kalman filter (UKF) and
Particle filter (PF) algorithms to track the moving source based on the motion model governing the motion
of the source. ESPRIT algorithm used for the estimation of the DOA is accurate but computationally
complex. The present comparative study deals with analysis of tracking the DOA Estimation Of Noncoherent,
Narrowband moving sources under different scenarios. The KF (Kalman Filter) is used when the
linear motion model corrupted by Gaussian noise, The Extended Kalman Filter (EKF), an approximated
and non-linear version of the KF is used whenever the motion model is slightly non-linear but corrupted by
Gaussian noise. The process of linearization involves the explicit computation of Jacobian and
approximation using Taylor’s series is computationally complex and expensive. The computationally
complex and expensive procedures of EKF viz explicit computation of Jacobian and approximation using
Taylor series are disadvantageous. In order to minimize the disadvantages of EKF are overcomed by the
usage of UKF, which uses a transform technique viz Unscented Transform to linearize the non-linear
model corrupted by Gaussian noise and Particle Filter (PF) Algorithms are used when the resultant model
is highly non-linear and is corrupted by non-Gaussian noise. Further the literature is concluded with
appropriate findings based on the results of the studies of different algorithms in different scenarios carried
out.
Home security is of paramount importance in today's world, where we rely more on technology, home
security is crucial. Using technology to make homes safer and easier to control from anywhere is
important. Home security is important for the occupant’s safety. In this paper, we came up with a low cost,
AI based model home security system. The system has a user-friendly interface, allowing users to start
model training and face detection with simple keyboard commands. Our goal is to introduce an innovative
home security system using facial recognition technology. Unlike traditional systems, this system trains
and saves images of friends and family members. The system scans this folder to recognize familiar faces
and provides real-time monitoring. If an unfamiliar face is detected, it promptly sends an email alert,
ensuring a proactive response to potential security threats.
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Enhancing the Radiation Pattern of Phase Array Antenna Using Particle Swarm O...IOSR Journals
The document describes a study that uses particle swarm optimization to enhance the radiation pattern of a phase array antenna by minimizing sidelobe levels. It first provides background on issues with high sidelobes in phase array antennas, such as power losses and interference. It then summarizes previous research using techniques like genetic algorithms for antenna array optimization. The study models the radiation pattern of linear arrays with different element numbers and calculates gain, finding that gain increases with more elements. However, sidelobe levels also increase relatively. Therefore, the study proposes using particle swarm optimization to optimize current excitation and control sidelobe levels while maintaining a narrow beamwidth.
Implementation of Digital Beamforming Technique for Linear Antenna Arraysijsrd.com
A digital Beamforming technique used for increased channel capacity and also increased signal to noise and interference ratio. In smart antenna, different type of radiation pattern of an antenna can be changed either by selecting appropriate weights or by changing the array geometry. This paper presented based on auxiliary phase algorithm by using this algorithm in linear antenna array determine the array pattern approximating the auxiliary function in both amplitude and phase. Cost function involving auxiliary function and array pattern is minimized by modifying the pattern.
Designing a pencil beam pattern with low sidelobesPiyush Kashyap
In this paper, a system has been designed for an operational frequency of 1.27 GHz consisting of an 8 element array of parasitic dipoles illuminated by a 4 element center fed array of active dipoles with Dolph-Chebyshev excitation coefficients. The array is designed to achieve a fairly pencil beam pattern suitable for direction of arrival estimation purposes. Array geometry and configuration is optimized for both active and parasitic elements using the PSO tool in FEKO. A directive radiation pattern is obtained with a gain of 14.5 dBi in the broadside direction along with a beamwidth of 30.29o. VSWR of 1.58 is achieved. Further, an iterative least square valued error estimation approach using phase control to achieve a desired array factor pattern for an n-element linear array, has been shown to be effective for larger number of iterations. The array excitation coefficients achieved were consistent with the Dolph-Chebyshev coefficients used in our antenna array design. With the ability to introduce nulls and steering the main beam in desired directions along with a pencil beam radiation pattern, beamsteering has been illustrated and the MUSIC algorithm for direction of arrival estimation has been implemented
The document summarizes research on thinning semi-elliptical and quarter-elliptical antenna arrays using genetic algorithm optimization to reduce side-lobe levels. Key points:
1) Genetic algorithms were used to optimize thinning of semi-elliptical and quarter-elliptical arrays with uniform excitation and spacing to produce narrow beams without degrading performance.
2) Simulation results showed thinning using genetic algorithms reduced side-lobe levels of the arrays compared to fully populated arrays.
3) Maximum side-lobe levels, beamwidths, and other metrics were tabulated for various array sizes and geometries, indicating thinning effectively lowered side-lobes.
Rabid Euclidean direction search algorithm for various adaptive array geometriesjournalBEEI
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ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY ALGORITHM
1. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
DOI: 10.5121/jant.2016.2301 1
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE
PLANAR PHASED ARRAY USING EVOLUTIONARY
ALGORITHM
Samaresh Bhattacharjee, Ashish Kumar, Manish Naja
Aryabhatta Research Institute of observational sciencES (ARIES),
Nainital-263001, Uttarakhand, India
ABSTRACT
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization
problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular
choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation
of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of
nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective
approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a
49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In
the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery
is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry
out the work presented in this paper.
KEYWORDS
Active planar phased array, array factor (AF), particle swarm optimization (PSO), radar, transmit receive
module (TRM)
1. INTRODUCTION
With rapid development and advancement in the technologies, the trend of incorporating an
„active‟ phased array configuration in majority of wireless, mobile, space and radar
communication system is increasing day by day [1, 2]. Studies revealed that an active phased
array configuration offers the collective advantages of high reliability, improved efficiency, low
loss and higher sensitivity over a passive configuration [3]. An active phased array system
contains several antenna elements assembled with individual solid state transmit receive module
(TRM) to meet the required power aperture product. The system uses the abilities of active array
to electronically steer the array beam instantaneously in any direction by controlling in-build
phase shifters of TRMs [4].
Failure of single or multiple TRMs in such systems is a common occurrence which makes an
antenna element become non-radiative. In the event of the failure, the far field array factor (AF)
pattern of the system degrades seriously in terms of increased side lobe levels (SLLs),
displacement of nulls and reduction in the null depths. To get rid of such degradations, repair/
replacement of the faulty modules could be best choice, as it always gives the best recovery of the
original AF pattern. However, such repair/ replacement in a space based or ground based systems
commissioned with hundreds of TRMs will be expensive in terms of time and budget. Under such
circumstances, without undergoing any repair/ replacement, evolutionary algorithms (EAs) could
2. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
2
be used as an alternative to recover the optimized pattern closest to the original by perturbing the
input amplitudes and/ or phases of input excitations of remaining functional TRMs.
EAs are inspired by the biological models of evolution and natural selection [5, 6]. To solve a
particular problem using EAs, a situation is created in which potential solutions can evolve. The
situation is outlined by the parameters of the problem that pushes the algorithm towards optimal
solutions. Most commonly used EAs are genetic algorithm (GA) [7], particle swarm optimization
(PSO) [8, 9], cuckoo search (CS) [10], and artificial bee colony (ABC) [11]. Several studies have
been reported on optimization of AF pattern by amplitude and/ or phase perturbation using EAs
for linear array [12 – 15]. The present work deals with recovery of the AF pattern of an active
planar phased array by recalculating a new set of amplitudes of input excitations of working
elements using PSO. Being a stochastic technique and based on the movement and intelligence
of swarms, PSO has gained an immense popularity in the field of electromagnetics [16]. The
reason behind selecting PSO is that PSO algorithm has the advantages of its simplicity and less
computational complexity over the other EAs. The computational time taken by PSO to arrive at
the desired solution is also less as compared to other EAs [17 – 19].
This paper presents multiple cases on the recovery of the AF pattern of a 49 elements active
planar phased array operating in very high frequency (VHF) band. Active array in VHF band has
wide application in the areas of wind profiling and weather radar [20]. In the presented cases, the
number of non-working elements is increased to a maximum 20% of the total elements. The
recovered pattern in each case is evaluated numerically by comparing the levels of first side lobes
(FSLs) and the depth of the first nulls (FNs) with the corresponding values in the original AF
pattern.
2. ARRAY CONCEPT
The AF pattern of an active planar phased array consisting of M x N identical elements placed on
XY plane (Fig. 1) scanning to a direction (θo, φo) may be expressed as [4]:
1 1
[ ( ) ( )]
0 0
( , )
M N
j m T T n T T
x xs y ys
mn
m n
AF A e
(1)
where, dx and dy = inter-element spacing along X and Y direction respectively; Tx = (2π/λ) dx
cos(αx); Ty = (2π/λ) dy cos(αy); Txs = (2π/λ) dx cos(αxs ) ; Tys = (2π/λ) dy cos(αys); cos(αx) =
sin(θ)cos(φ); cos(αy) = sin(θ) sin(φ); cos(αxs) = sin(θo)cos(φo); cos(αys) = sin(θo) sin(φo); and Amn =
Amplitude of input excitation of the mnth
element.
Fig. 1. A planar phased array
3. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
3
The phasing of mnth
element, ψmn for beam steering is calculated as mTxs + nTys and the far field
radiation pattern of the array is:
ff(θ,φ) = AF(θ,φ) x EP(θ,φ) (2)
where, EP(θ,φ) is the Element Pattern (EP) of an antenna element at (θ,φ) plane.
3. PSO
EAs are stochastic optimization techniques popularly being used for real life problem solving
tasks in wide and diverse range of application areas like science, engineering, medical and
economics [5, 6] and [21]. Among all EAs inspired from biological process, the PSO technique is
simple, effective and capable of handling tricky multidimensional nonlinear optimization
problems across the fields [16 – 19]. The PSO was originally introduced in 1995 by Russell
Eberhart, an electrical engineer, and James Kennedy, a social psychologist [8, 9]. Here it is
necessary to mention that the present work is not intended to carry an extensive review on PSO,
and therefore only the main steps of the algorithm are discussed.
The PSO is a population based search strategy which is applied in an N dimensional search space
containing set of points, referred as particles. These set of particles moves in the search space
with velocities that are dynamically adjusted according to their historical performance as well as
the experience and knowledge of its neighbours. During movement, at each iteration, the particles
update their velocities according to the best positions already found by themselves as personnel
best (Pbest) and global best (Gbest) [16].
1 1 2 2
, ,
1
( ) ( )
. . .
best n n best n n
n n
inertia
cognitive personal component social neighbourhood component
P X G X
v wv c rand c rand
t t
(3)
where, vn+1 and vn are the velocity vectors of the particle in the present and previous iterations
respectively; Xn is the current position of the particle; w is the inertial weight which varies as the
algorithm progresses and determines the weight by which the particles current velocity depends
on its previous velocity; c1 is the cognitive coefficient controlling the pull to the Pbest position; c2
is the social rate coefficient controlling the pull to the Gbest position; rand1 and rand2 are the
random numbers uniformly distributed in (0, 1); Δt is the time difference between the two
successive positions of the particles and is most often taken as unity. The next position, Xn+1 of
particle in the search space is calculated as:
1 1
.
n n n
X X v t
(4)
The choice of different parameters and the constants in above two equations can be decided
according to the work described in [22– 25]. During the process of algorithm, the Pbest and Gbest
are decided according to the criteria set by a fitness function (FF) [16]. A FF plays a vital role in
controlling the performance of the algorithm. The selection of FF depends on the type and
complexities present in the identified problem.
4. METHODOLOGY OF THE WORK
4. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
4
In the present work, a planar phased array having a quasi-circular aperture is considered as the
test array. The diagram of the array shown in Fig. 2 is populated with 49 elements, each
represented by a square box labeled with a fixed numerical number for easy identification of
element location. Elements of the array are arranged as equilateral triangular grid in 9 rows and
15 columns. During the design of the array geometry, it is attempted to make the periphery of the
aperture close to circular to maintain angular symmetry in the AF pattern. A configuration of a
planar array having circular or near to circular aperture with triangular grid gives a grating lobe
free AF pattern at maximum possible off-zenith angle with comparatively low FSLs without any
amplitude tapering. Triangular grid also helps to reduce the number of elements demanded to fill
a certain aperture [26]. These inherent advantages make the configuration a popular choice in
applications like wireless, space borne synthetic aperture radar (SAR), weather radar, wind
profilers [20], [27-29].
Fig. 2. The test array
EP of the array elements is considered as isotropic and initial amplitude of input excitations are
taken as unity. The inter-element spacing is kept 0.7 λ which places the rows and columns at 0.88
m and 1.02 m apart, respectively. Regardless of aperture or grid structure, the AF equation
described in equation (1) takes individual element location as inputs. The same equation is used
for calculating the AF of the test array. Effect of mutual coupling among elements is not
considered during the analysis and discussion.
After finalizing the structure of the test array, a suitable FF is developed and expressed as
equation (5). There could be many possibilities of the FF depending on the factors decided to
achieve the optimization. The present FF is developed after a number of trials to bring the
solution close to the optima by minimizing it till last iteration. The weights (a1, a2, a3 and a4) in
the FF equation are taken as unity.
1 1 2 2 3 3 4 4
FF a F a F a F a F
(5)
where,
2
1 [ (0,0) (0,0)]
pso original
F AF AF
2
2 _ _
[ ]
FSL pso FSL original
F AF AF
2
3 _ _
[ ]
FN pso FN orig
F AF AF
90
2
4
90
[ ( , ) ( , )]
pso original
F AF 0 AF 0
Balanis says that the characteristic of an AF pattern can be broadly determined by the three
levels: main beam, FSLs and FNs [30]. F1, F2 and F3 of FF uses these three levels of optimized
and original patterns for deciding movement of particles in problem space. To test the
5. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
5
effectiveness of the PSO algorithm for the present problem with the FF, a software tool is
developed. The coding of the tool is done based on the array concepts and the PSO algorithm.
The tool takes the values of all the PSO parameters and the location of non-working element as
user inputs. Research revealed that PSO can achieve faster convergence towards optima with less
oscillation by careful selection of its parameters [22 – 25]. After a detailed study, following
values of the PSO parameters are fed into the developed tool and kept fixed in all the presented
cases.
No of particles = 200, No of iterations =100,
Cognitive component (c1) = 2, and Social component (c2) =1
Different schemes on variation of „w‟ of equation (3) are tested, and finally for faster convergence
„w‟ is linearly decreased over 100 iterations from 0.9 to 0.4. The same tool can be used for
optimization of any configurations of planar phased array by modifying the elements co-
ordinates.
In the code, Amn of equation (1) is written as (1+ μmn), where, μmn is introduced to represent the
perturbation required in initial amplitude of the input excitations of working elements for
recovery. Each iteration produces a new set of μmn which is algebraically added with unity to
generate a new set of amplitudes for calculating the AF in present iteration required by all four
entities of FF. The perturbations are restricted within a window of ±0.3, so the final amplitude
factor, Amn is restricted within a boundary between 0.7 and 1.3, which is equal to ± 30%
perturbation of initial amplitude. The window in amplitude factor can be linked with the tuning of
power amplifier modules in TRMs. In practical application, depending on the type and quality of
a power amplifier module, the set window may vary. Based on the methodologies, the results
obtained after single run for each case are presented and discussed in the next section.
5. RESULTS AND DISCUSSION
The original AF pattern of the test array in normalized form without any element failure at zenith
(θo, = 0, φo = 0) is depicted in Fig. 3. From the figure, it is noted that the levels of FSLs are -
19.08 dB down whereas the depths of FNs are -38.84 dB down from the peak level of the main
beam which is at 0 dB after normalization. Throughout the work, the recovery of the pattern at
zenith is only presented. No beam steering to other elevation (θo) or azimuth (φo) plane is
introduced during the pattern optimization. After recovery in each case, the original AF, AF with
fault and PSO optimized AF patterns are presented in a single figure for visual comparison and
performance evaluation.
Fig. 3. Original AF pattern of the test array
6. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
6
In the next couple of paragraphs detailed evaluations on the AF pattern recovery in four different
cases using the developed methodologies are discussed. Work starts with the recovery of the
original pattern when a single element is made non-working. Thereafter, number of non-working
elements are increased in subsequent cases to three, five and ten, respectively. The locations of
the non-working elements are picked up randomly.
Case-1: In the first case the center element at location 1 is made non-working. The presence of a
non-working element at the said location increases the levels of both FSLs and FNs by 1.64 dB
and 7.16 dB, respectively. After creation of the fault, now the tool runs with set PSO parameters
to recover the original pattern. At the end of 100th
iteration with 200 particles, the tool produces
an optimized AF pattern close to the original one shown in Fig. 4. The tool has recovered the
pattern by generating a new set of amplitudes of input excitations of 48 working elements and
brings down the levels of FSLs and FNs to -19.09 dB and -38.87 dB, respectively resulting very
close matching with the corresponding values in the original pattern.
Fig. 4. AF patterns for case-1
Case-2: Work advances with three elements failure at locations 5, 2 and 28 selected randomly as
user inputs. With these three non-working elements, the levels of FSLs increase to -16.52 dB. But
in opposite of the case-1, the depths of FNs increase to -49.67 dB with one degree shift towards
the main beam. Again the tool runs to recover the original pattern by amplitude perturbation of
remaining 46 working elements. Both fault and PSO optimized patterns with original one are
depicted in Fig. 5.
Fig. 5. AF pattern for case-2
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The figure illustrates that the optimized pattern nicely follows the original pattern at every
location of θ with hardly any variation in the levels. The shifting of FNs after faults is also
rectified by placing them exactly at their original locations.
Case-3: Till now the tool has shown satisfactory performances in recovering the optimized
pattern closest to the original after the occurrence of faults. But to imitate a more complex
situation in an active phased array having hundreds of TRM, the tool is tested further with 10%
non-working elements i.e. 5 of 49 elements. The location numbers of non-working elements are
randomly taken as 37, 12, 30, 1 and 18. Remaining 44 working elements with a void at said
locations produces a pattern with phenomena entirely opposite to the occurrences in the last two
cases. FSLs of the fault pattern remain at very close to its original levels with one degree shift
towards the main beam, whereas the second side lobes (SSLs) increase from -20.87 dB to -15.9
dB. These increased SSLs may pick up a strong interference signal from any external source and
may raise the probability of occurrence of ambiguous detection [4] and [30]. Fig. 6 plots the AF
pattern with faults at the said locations. The plot also depicts that the optimized pattern achieved
after the final iteration is made highly resemble the original pattern. After optimization, the
maximum levels of SLLs are brought down to -20.84 dB close to the original value -20.87 dB. In
optimized pattern, the shifts in FSLs are rectified and original levels are also maintained.
Fig. 6. AF pattern for case-3
Case-4: To add much more complexity, the number of non-working elements is increased further
to ten which is equal to 20 % of the total elements. The position numbers of the fault elements are
again randomly selected as 49, 42, 13, 5, 10, 32, 31, 19, 26 and 17. Fig. 7 presents the AF pattern
before and after faults. The fault pattern is deformed to a typical formation. The lobes after
second nulls are merged together and pop up to maximum -15.98 dB at ±30o
. This merging
eliminates the third and fourth nulls in both sides of the main beam. In opposite, on occurrence of
merging, FSLs shift downward by approximately 10 dB. This downward shifting of FSLs could
be better at the cost of the deformation, but the popping up of second and third side lobes could
damage the entire application by inviting strong interferences into the system.
8. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
8
Fig. 7. AF pattern for case-4
Once again the tool runs in the quest of searching a new set of amplitudes for the remaining 39
working elements for correcting the failed pattern. The optimized pattern after recovery is
presented in Fig. 7. The pattern illustrates that the process of recovery is successfully handled by
the tool to a great extent. FSLs are pulled up to the values of the original pattern. The region after
FSL in both sides of the main lobe is restructured at every point and brought near to the original
values.
The convergence profiles of 200 particles obtained by minimizing the FF are presented in Fig. 8.
The figure illustrates that the profiles of convergence are nicely damped and reached closest to
optima at around 70th
iteration. Out of 200 particles, the 81th
particle emerges as the global best to
produce the best optimized AF pattern.
Fig. 8. Convergence profiles of the FF for case-4
The final amplitudes of input excitations of 39 working elements of case-4 are displayed in Fig.
9. The values of excitations are represented by a grey scale whose values vary between 0.6 and
1.3. The figure depicts the final excitations searched by the tool within the set window. In the
figure, the non-working elements are represented by only number without any shaded box.
9. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
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Fig. 9. Final amplitude distribution for case-4
A comparative summary on the values of the critical parameters of AF patterns in original, fault
and recovered conditions discussed in above four cases is presented in Table-1.
Table-1. Comparative results
Cases Parameters Original After fault
After
recovery
Case-1 FSLs -19.08 dB -17.44 dB -19.09 dB
FNs -38.84 dB -31.68 dB -38.87 dB
FNBW 28o
26 o
28 o
Case-2 FSLs -19.08 dB -16.52 dB -19.08 dB
FNs -38.84 dB -49.67 dB -38.85 dB
FNBW 28o
26 o
28 o
Case-3 FSLs
FNs
FNBW
-19.08 dB
-38.84 dB
28o
-18.28 dB
-39.48 dB
26 o
-19.15 dB
-38.16 dB
28 o
Case-4 FSLs -19.08 dB -27.73 dB -19.18 dB
FNs -38.84 dB -32.65 dB -36.87 dB
FNBW 28o
30 o
28 o
The degree of recovery of each case is further examined and compared using linear correlation
coefficient (LCC), median absolute deviation correlation coefficient (MADCC), linear least
square regression (LLSR) and root mean square error (RMSE) statistical methods [31]. The
results after examination are tabulated in Table-2.
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Table-2. Statistical comparison
Cases
LCC MADCC LLSR RMSE (%)
O-F O-P O-F O-P O-F O-P O-F O-P
Case-1 0.9965 0.9999 0.8564 0.9991 0.9931 0.9999 1.9029 0.0395
Case-2 0.9966 0.9999 0.8838 0.9990 0.9933 0.9999 1.8526 0.0272
Case-3 0.9821 0.9997 -0.0683 0.9679 0.9646 0.9995 4.2718 0.4674
Case-4 0.9883 0.9992 0.7615 0.9643 0.9768 0.9985 4.1567 1.0870
The first two methods estimate the correlation coefficients, LLSR calculates the linear regression
and RMSE gives the errors before and after recovery. In the table, O-F represents estimation
between original and fault patterns, whereas O-P signifies the relation between original and PSO
optimized patterns. The values in Table-1 and Table-2 illustrate that the recovery process after
faults works satisfactorily.
6. CONCLUSION
The recovery of the AF pattern in case of element failure by perturbing the amplitudes of input
excitations is discussed. The FF with set PSO parameters was able to produce close optimization
even when 20 % fault elements were present in the array. The numerical results and the statistical
data presented for all the cases shows that the developed methodology worked well in obtaining
the optimized AF pattern with acceptable values of SLLs, FNs and its depths. In present era when
any solid state based active array system is equipped with embedded technology where the
algorithm can be stored and processed, the developed methodology can easily be adopted for
recovering AF pattern of any large and complex planar phased array. However, the present work
shows that the performance of the recovery degrades with the number of fault elements present in
an array. Therefore for large number of faults, the replacement of TRMs could be the right
choice. In future, AF optimization using phase or combination of phase and amplitude
perturbation will be attempted as the extension of the present work.
ACKNOWLEDGEMENTS
The authors are thankful to Dr. D. V. Phanikumar for going through the manuscript critically and
suggesting improvements.
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