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.
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.
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
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.
A novel methodology for time-domain characterization of a full anechoic chamb...IJECEIAES
In this paper we present a novel methodology for time-domain characterization of a full anechoic chamber using the finite integral method. This approach is considered fast, accurate and not intensive for computer resources. The validation of this approach is carried out on CST-microwave studio for a full anechoic chamber intended for antennas measurement applications and electromagnetic exposure evaluation for cellular network. Low, medium and high gain sources are used in this study. The simulations are realized on a personal computer of medium performances (i7 CPU and 16 GB of RAM). The stability and the convergence of our approach are obtained thanks to local mesh and auto-regressive linear filtering techniques. The minimization of the simulation time is based on use of the Huygens sources in the place of the antennas. The maximum error of the chamber as well as the wave depolarization into the chamber are at one with the previous work and the catalogs of the principles chambers manufacturers for the proposed tests in this paper. The Full simulations time is about 15 hours in average.
Reduction of Azimuth Uncertainties in SAR Images Using Selective RestorationIJTET Journal
Abstract— A framework is proposed for reduction of azimuth uncertainty space borne strip map synthetic aperture radar (SAR) images. In this paper, the azimuth uncertainty in SAR images is identified by using a local average SAR image, system parameter, and a distinct metric derived from azimuth antenna pattern. The distinct metric helps isolate targets lying at locations of uncertainty. The method for restoration of uncertainty regions is selected on the basis of the size of uncertainty regions. A compressive imaging technique is engaged to bring back isolated ambiguity regions (smaller regions of interrelated pixels), clustered regions (relatively bigger regions of interrelated pixels) are filled by using exemplar-based in-painting. The recreation results on a real Terra SAR-X data set established that the proposed method can effectively remove azimuth uncertainties and enhance SAR image quality.
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.
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.
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
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.
A novel methodology for time-domain characterization of a full anechoic chamb...IJECEIAES
In this paper we present a novel methodology for time-domain characterization of a full anechoic chamber using the finite integral method. This approach is considered fast, accurate and not intensive for computer resources. The validation of this approach is carried out on CST-microwave studio for a full anechoic chamber intended for antennas measurement applications and electromagnetic exposure evaluation for cellular network. Low, medium and high gain sources are used in this study. The simulations are realized on a personal computer of medium performances (i7 CPU and 16 GB of RAM). The stability and the convergence of our approach are obtained thanks to local mesh and auto-regressive linear filtering techniques. The minimization of the simulation time is based on use of the Huygens sources in the place of the antennas. The maximum error of the chamber as well as the wave depolarization into the chamber are at one with the previous work and the catalogs of the principles chambers manufacturers for the proposed tests in this paper. The Full simulations time is about 15 hours in average.
Reduction of Azimuth Uncertainties in SAR Images Using Selective RestorationIJTET Journal
Abstract— A framework is proposed for reduction of azimuth uncertainty space borne strip map synthetic aperture radar (SAR) images. In this paper, the azimuth uncertainty in SAR images is identified by using a local average SAR image, system parameter, and a distinct metric derived from azimuth antenna pattern. The distinct metric helps isolate targets lying at locations of uncertainty. The method for restoration of uncertainty regions is selected on the basis of the size of uncertainty regions. A compressive imaging technique is engaged to bring back isolated ambiguity regions (smaller regions of interrelated pixels), clustered regions (relatively bigger regions of interrelated pixels) are filled by using exemplar-based in-painting. The recreation results on a real Terra SAR-X data set established that the proposed method can effectively remove azimuth uncertainties and enhance SAR image quality.
Space-time adaptive processing (STAP) is a signal
processing technique most commonly used in radar systems where
interference is a problem. The radar signal processor is used to
remove the unintentional cluttering effects caused by ground
reflections and echoes due to sea, desert, forest, etc. and intentional
jamming and make the received signal useful. In this paper a new
approach to STAP based on subspace projection has been described
in detail. According to linear algebra and three dimensional
geometry, if we project a range space on to a subspace spanned by
linearly independent vectors, we can suppress data which is
perpendicular to that subspace. In subspace based technique, the
received data is projected on to a subspace which is orthogonal to
clutter subspace to remove the clutter. The probability of target
detection can be find out in order to analyse the performance of the
proposed algorithm. Two existing algorithms, SMI and DPCA are
chosen to do the comparison. while plotting the detection Probability
against SINR , the results obtained are better for subspace technique
than DPCA and SMI. We got the SINR improved for subspace based
technique for same detection probability. The effect of subspace rank
on SINR was also analysed for understanding the computational load
caused by the technique. We also analysed the convergence of the
algorithm by taking plots of SINR against range snapshots.
Segmentation Based Multilevel Wide Band Compression for SAR Images Using Coif...CSCJournals
Synthetic aperture radar (SAR) data represents a significant resource of information for a large variety of researchers. Thus, there is a strong interest in developing data encoding and decoding algorithms which can obtain higher compression ratios while keeping image quality to an acceptable level. In this work, results of different wavelet-based image compression and segmentation based wavelet image compression are assessed through controlled experiments on synthetic SAR images. The effects of dissimilar wavelet functions, number of decompositions are examined in order to find optimal family for SAR images. The choice of optimal wavelets in segmentation based wavelet image compression is coiflet for low frequency and high frequency component. The results presented here is a good reference for SAR application developers to choose the wavelet families and also it concludes that wavelets transform is rapid, robust and reliable tool for SAR image compression. Numerical results confirm the potency of this approach.
Papr reduction for ofdm oqam signals via alternative signal methodeSAT Journals
Abstract
We deemed the PAPR reduction problem for OFDM/OQAM system. The PAPR reduction is the serious problem for
implementations of both OFDM and OFDM/OQAM systems due to their high PAPR. The OFDM/OQAM signal is generated by
summing over M time-shifted OFDM/OQAM symbols, where the successive symbols are interdependent with each other. The AS
(Alternative-Signal) method directly leads to the independent AS (AS-I) and joint AS (AS-J) algorithms. The AS-I algorithm
reduces the PAPR symbol by symbol with low complexity and AS-J applies optimal joint PAPR reduction among M
OFDM/OQAM symbols with much higher complexity. A sequential optimization procedure denoted AS-S have been proposed to
balance the computation complexity and system performance in this paper. AS-S algorithm, which adopts a sequential
optimization procedure over time with computational complexity linearly increasing with M. The Simulation results have been
provided for performance comparison of AS-I, AS-J, and AS-S algorithms.
Keywords—Peak-to-Average power ratio (PAPR), orthogonal frequency division multiplexing with offset quadrature
amplitude modulation (OFDM/OQAM), Alternative-signal(AS),cyclic prefix(CP).
Investigation of repeated blasts at Aitik mine using waveform cross correlationIvan Kitov
We present results of signal detection from repeated events at the Aitik and Kiruna mines in Sweden as based on waveform cross correlation. Several advanced methods based on tensor Singular Value Decomposition is applied to waveforms measured at seismic array ARCES, which consists of three-component sensors.
Blind separation of complex-valued satellite-AIS data for marine surveillance...IJECEIAES
In this paper, the problem of the blind separation of complex-valued Satellite-AIS data for marine surveillance is addressed. Due to the specific properties of the sources under consideration: they are cyclo-stationary signals with two close cyclic frequencies, we opt for spatial quadratic time-frequency domain methods. The use of an additional diversity, the time delay, is aimed at making it possible to undo the mixing of signals at the multi-sensor receiver. The suggested method involves three main stages. First, the spatial generalized mean Ambiguity function of the observations across the array is constructed. Second, in the Ambiguity plane, Delay-Doppler regions of high magnitude are determined and Delay-Doppler points of peaky values are selected. Third, the mixing matrix is estimated from these Delay-Doppler regions using our proposed non-unitary joint zero-(block) diagonalization algorithms as to perform separation.
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.
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.
Rabid Euclidean direction search algorithm for various adaptive array geometriesjournalBEEI
One of the exciting technologies used to meet the increasing demand for wireless communication services is a smart antenna. A smart antenna is basically confirmed by an array of antennas and a digital beamformer unit through which cellular base station can direct the beam toward the desired user and set nulls toward interfering users. In this paper, different array configurations (linear, circular, and planer) with the REDS algorithm are implemented in the digital beam-forming unit. The wireless system performance is investigated to check the smart antenna potentials assuming Rayleigh fading channel environment beside the AWGN channel. Results show how the REDS algorithm offers a significant improvement through antenna radiation pattern optimization, sidelobe level, and interference reduction, and also the RDES algorithm proves fast convergence with minimum MSE and better sidelobe level reduction comparing with other algorithms.
Space-time adaptive processing (STAP) is a signal
processing technique most commonly used in radar systems where
interference is a problem. The radar signal processor is used to
remove the unintentional cluttering effects caused by ground
reflections and echoes due to sea, desert, forest, etc. and intentional
jamming and make the received signal useful. In this paper a new
approach to STAP based on subspace projection has been described
in detail. According to linear algebra and three dimensional
geometry, if we project a range space on to a subspace spanned by
linearly independent vectors, we can suppress data which is
perpendicular to that subspace. In subspace based technique, the
received data is projected on to a subspace which is orthogonal to
clutter subspace to remove the clutter. The probability of target
detection can be find out in order to analyse the performance of the
proposed algorithm. Two existing algorithms, SMI and DPCA are
chosen to do the comparison. while plotting the detection Probability
against SINR , the results obtained are better for subspace technique
than DPCA and SMI. We got the SINR improved for subspace based
technique for same detection probability. The effect of subspace rank
on SINR was also analysed for understanding the computational load
caused by the technique. We also analysed the convergence of the
algorithm by taking plots of SINR against range snapshots.
Segmentation Based Multilevel Wide Band Compression for SAR Images Using Coif...CSCJournals
Synthetic aperture radar (SAR) data represents a significant resource of information for a large variety of researchers. Thus, there is a strong interest in developing data encoding and decoding algorithms which can obtain higher compression ratios while keeping image quality to an acceptable level. In this work, results of different wavelet-based image compression and segmentation based wavelet image compression are assessed through controlled experiments on synthetic SAR images. The effects of dissimilar wavelet functions, number of decompositions are examined in order to find optimal family for SAR images. The choice of optimal wavelets in segmentation based wavelet image compression is coiflet for low frequency and high frequency component. The results presented here is a good reference for SAR application developers to choose the wavelet families and also it concludes that wavelets transform is rapid, robust and reliable tool for SAR image compression. Numerical results confirm the potency of this approach.
Papr reduction for ofdm oqam signals via alternative signal methodeSAT Journals
Abstract
We deemed the PAPR reduction problem for OFDM/OQAM system. The PAPR reduction is the serious problem for
implementations of both OFDM and OFDM/OQAM systems due to their high PAPR. The OFDM/OQAM signal is generated by
summing over M time-shifted OFDM/OQAM symbols, where the successive symbols are interdependent with each other. The AS
(Alternative-Signal) method directly leads to the independent AS (AS-I) and joint AS (AS-J) algorithms. The AS-I algorithm
reduces the PAPR symbol by symbol with low complexity and AS-J applies optimal joint PAPR reduction among M
OFDM/OQAM symbols with much higher complexity. A sequential optimization procedure denoted AS-S have been proposed to
balance the computation complexity and system performance in this paper. AS-S algorithm, which adopts a sequential
optimization procedure over time with computational complexity linearly increasing with M. The Simulation results have been
provided for performance comparison of AS-I, AS-J, and AS-S algorithms.
Keywords—Peak-to-Average power ratio (PAPR), orthogonal frequency division multiplexing with offset quadrature
amplitude modulation (OFDM/OQAM), Alternative-signal(AS),cyclic prefix(CP).
Investigation of repeated blasts at Aitik mine using waveform cross correlationIvan Kitov
We present results of signal detection from repeated events at the Aitik and Kiruna mines in Sweden as based on waveform cross correlation. Several advanced methods based on tensor Singular Value Decomposition is applied to waveforms measured at seismic array ARCES, which consists of three-component sensors.
Blind separation of complex-valued satellite-AIS data for marine surveillance...IJECEIAES
In this paper, the problem of the blind separation of complex-valued Satellite-AIS data for marine surveillance is addressed. Due to the specific properties of the sources under consideration: they are cyclo-stationary signals with two close cyclic frequencies, we opt for spatial quadratic time-frequency domain methods. The use of an additional diversity, the time delay, is aimed at making it possible to undo the mixing of signals at the multi-sensor receiver. The suggested method involves three main stages. First, the spatial generalized mean Ambiguity function of the observations across the array is constructed. Second, in the Ambiguity plane, Delay-Doppler regions of high magnitude are determined and Delay-Doppler points of peaky values are selected. Third, the mixing matrix is estimated from these Delay-Doppler regions using our proposed non-unitary joint zero-(block) diagonalization algorithms as to perform separation.
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.
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.
Rabid Euclidean direction search algorithm for various adaptive array geometriesjournalBEEI
One of the exciting technologies used to meet the increasing demand for wireless communication services is a smart antenna. A smart antenna is basically confirmed by an array of antennas and a digital beamformer unit through which cellular base station can direct the beam toward the desired user and set nulls toward interfering users. In this paper, different array configurations (linear, circular, and planer) with the REDS algorithm are implemented in the digital beam-forming unit. The wireless system performance is investigated to check the smart antenna potentials assuming Rayleigh fading channel environment beside the AWGN channel. Results show how the REDS algorithm offers a significant improvement through antenna radiation pattern optimization, sidelobe level, and interference reduction, and also the RDES algorithm proves fast convergence with minimum MSE and better sidelobe level reduction comparing with other algorithms.
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.
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.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Diagnosis of Faulty Elements in Array Antenna using Nature Inspired Cuckoo Se...IJECEIAES
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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 Tx 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 4FF a F a F a F a F (5)
where,
2
1 [ (0,0) (0,0)]pso originalF AF AF
2
2 _ _[ ]FSL pso FSL originalF AF AF
2
3 _ _[ ]FN pso FN origF AF AF
90
2
4
90
[ ( , ) ( , )]pso originalF 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
7. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
7
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
9
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.
10. International Journal of Antennas (JANT) Vol.2, No.3, July 2016
10
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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