PATTERN SYNTHESIS OF NON-UNIFORM AMPLITUDE EQUALLY SPACED MICROSTRIP ARRAY ANTENNA USING GA, PSO AND DE ALGORITHMS

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1 International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 7, Issue 2, March-April 2016, pp , Article ID: IJARET_07_02_013 Available online at Journal Impact Factor (2016): (Calculated by GISI) ISSN Print: and ISSN Online: IAEME Publication PATTERN SYNTHESIS OF NON-UNIFORM AMPLITUDE EQUALLY SPACED MICROSTRIP ARRAY ANTENNA USING GA, PSO AND DE ALGORITHMS K. Karuna Kumari Department of ECE, GITAM University, Visakhapatnam, A.P., India Prof. P. V. Sridevi Department of ECE, Andhra University, Visakhapatnam, A.P., India ABSTACT In the recent years the development in communication systems requires the development of low cost, minimal weight, low profile antennas that are capable of maintaining high performance over a wide spectrum of frequencies. This technological trend has focused much effort into the design of a micro strip patch antennas. Nowadays Evolutionary Computation has its growth to extent. Generally electromagnetic optimization problems generally involve a large number of parameters. Synthesis of non-uniform linear antenna arrays is one of the most important electromagnetic optimization problems of the current interest. This paper is mainly focus on the reduction in side lobe level of Microstrip linear arrays by using evolutionary programming-real valued genetic algorithm (EP-GA), particle swarm optimization algorithm(pso) and Differential Evolution Algorithm(DE). The simulation results of non uniform linear arrays in terms of SLL is calculated. The Best-Weights for 20 elements array are listed.the Radiation patterns are presented for different number of elements. All the simulated results are obtained by using MATLAB software. Key words: Microstrip antenna Linear array, Real valued-genetic Algorithm (GA), Particle Swarm Optimization (PSO) algorithm, Differential Evolution (DE) algorithm, Side-lobe Level. Cite this Article: K. Karuna Kumari and Prof. P. V. Sridevi. Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using GA, PSO and DE Algorithms. International Journal of Advanced Research in Engineering and Technology, 7(2), 2016, pp editor@iaeme.com

2 Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using GA, PSO and DE Algorithms 1. INTRODUCTION Low side lobe antennas are becoming an increasingly important component of high performance electronic systems, particularly those operating in heavy clutter and jamming environments. Practically, the radiation pattern of antenna array has not only having the main beam but also side lobes.most of the power is confined in main beam which provides the coverage in desired portion. Some of the power is also remained in sidelobe levels that are nothing but wastage of transmitting power [16]. If the sidelobe levels are very high, large amount of transmitting power is wastage. For efficient use of transmitting power and desired radiation characteristics can be achieved by using this five following control methods: 1) The geometrical configuration of the overall array 2) The relative displacement between the elements 3) The excitation amplitude of the individual elements 4) The excitation phase of individual elements 5) The relative pattern of the individual elements.various analytical and numerical methods have been used to optimize the side lobe levels relative to the main beam by using above controls. Several new optimization techniques have been emerged in the past two decades, that mimic biological evolution, or the way biological entities communicate in nature. Some of these algorithms have been used successively in many electromagnetic and antenna problems include Genetic Algorithms (GA) [1], Particle Swarm Optimization (PSO) [2], and the method of Differential Evolution (DE) Algorithm [3]. In the electromagnetism research area, mainly the antenna synthesis, the use of these optimizers is widely and clearly appreciated. To date, different GA, PSO and DE algorithms have been successfully applied to different problems including antenna design and the array synthesis. Many efforts have also been devoted to compare these algorithms to each other. Typically, such comparisons have been based on artificial numerical benchmark problems. The goal of many studies was to verify that one algorithm outperformed another on a given set of problems. In general, it has been possible to improve a given standard method within a restricted set of benchmark problems by making minor modifications to it.recently, Genetic Algorithms (GA),particle swarm optimization (PSO) and differential evolution (DE) have been introduced and particularly PSO has received increased interest from the EC community. These techniques have shown great promise in several real-world applications [4]-[7]. In this paper, we investigated the performance of GA, DE, PSO for the optimization of SLL. In the following part of the paper, the theory and formulation of the optimization problem will be explained. After words, the details of the proposed ensemble based Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms will be given. Finally, the application of algorithms in the optimization of SLL will be demonstrated for 20 element antenna array. The corresponding results of three algorithms will be compared. 2. MICRO STRIP PATCH ANTENNA Microstrip antennas are used not only as single element but are very popular in arrays. Arrays are very versatile and are used to synthesize a required pattern that cannot be achieved with a single element. Arrays increase the directivity, and perform various other functions which would be difficult with any one single element. For the microstrip antenna, the x-y plane (π/2, 0 π /2, 3 π /2 2 π) is the principal E-plane. For this plane, the expression for the radiated fields is[8-9] editor@iaeme.com

3 K. Karuna Kumari and Prof. P. V. Sridevi E k0h sin cos 2 k0l sin cos k0h 2 cos 2 2. DESIGN OF LINEAR ARRAY ANTENNAS Consider a Linear array of 2N symmetric array elements uniformly spaced of distance d between the elements in x-z plane. The array factor for the linear antenna array is shown below [10]. Where k is the wave number, k=2ᴨ/λ, θ is the angle measured from the axis of the array, θo is the steering angle, [, ] is the excitation of the current for the element on either side of the array midpoint to be controlled and d is the spacing between elements. By the array factor, the fitness function is obtained. Here, the fitness function is used to obtain the optimum weights and to achieve maximum SLL. Assuming the linear array is symmetric about its center of the array. Mathematically, the array factor of a 2N element linear array is given by [10] N Jn AF 2 I e cos k( n 0.5) d cos( cos 0) n 1 N k 2 Where k is the wave number d Fig 1: Geometry of Linear Antenna Array θ is the angle measured from the axis of the array, θ o is the steering angle,[, ] is the excitation of the current for the element on either side of the array midpoint to be controlled and d is the spacing between elements. The fitness function associated with this array is the maximum SLL of its associated far-field pattern to be minimized. The general form of the fitness function is given by Fitness Max( 20log 10 AF( ) ) Max AF( ) Where AF(θ) = AF(θ o ) 0, θ editor@iaeme.com

4 Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using GA, PSO and DE Algorithms 3. THE GENETIC ALGORITHM (GA) The Genetic Algorithm (GA) is an optimization and global search technique based on the mechanics of natural selection and natural genetics. A Genetic Algorithm allows a population composed of many individuals to involve under specified selection rules to a state that minimizes the cost function. This optimization algorithm is more powerful for problems with more number of variables and local minima. GA is very efficient in exploring the entire search space or the solution space, which is large and complex. The Genetic algorithm is implemented using computer simulation [9]. Genetic Algorithm may be represented as shown in Fig.3. In computer algorithm, a chromosome is an array of genes, a number of chromosomes make up one population. The chromosomes are generated randomly in the selected space. Each chromosome has an associated fitness function, assigning a relative merit to that chromosome. The algorithm begins with a large list of random chromosomes. Create initial population Evaluate SLL for each chromosome yes SLL SLL_Max No Chromosomes having best SLL as parent Cross over and mutation to generate new chromosome as child New Chromosomes= parents+ new offspring Select best SLL No SLL SLL_ Max yes Stop Figure 2 Genetic Algorithm for optimization of side lobe level editor@iaeme.com

5 K. Karuna Kumari and Prof. P. V. Sridevi Fitness functions are evaluated for each chromosome. The chromosomes are ranked from the best-fit to the least-fit, according to their respective fitness functions. Unacceptable chromosomes are discarded, leaving a superior species-subset of an original list, which is the process of selection. Genes that survive become parents, by crossing over some of their genetic material to produce two new offspring. The parents reproduce enough to offset the discarded chromosomes. Thus, the total number of chromosomes remains constant after every iteration. Mutations cause small random changes in a chromosome. Fitness functions are evaluated for the offspring and mutated chromosome, and the process is repeated. The algorithm stops after a set number of iterations, or when an acceptable solution is obtained. In the genetic algorithm, initial chromosomes are combination of random chromosome and amplitude excitations of linear array instead of all random chromosomes. The halves of the chromosome are discarded and new half of chromosomes are generated from parents chromosome which are best fits to fitness function. The cost function is the maximum side lobe level for the antenna pattern. 4. PRACTICAL SWARM OPTIMIZATION ALGORITHM Practical swarm optimization (PSO) is a population-based self-adaptive search optimization technique first introduced by Kennedy and Eberhart [11]. The PSO method is becoming very popular due to its simplicity of implementation and ability to quickly converge to a reasonably good solution. In the practical swarm algorithm, the trajectory of each individual in the search space is adjusted by dynamically altering the velocity of each particle, according to its own flying particles in the D- dimensional search space can be represented as and respectively editor@iaeme.com

6 Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using GA, PSO and DE Algorithms Start sss Ss ss St ar t Initialize particles with random position& Velocity Vectors Calculate fitness values for each particle Is current fitness value better than pbest YES Assign current fitness as new pbest Keep previous pbest NO Assign best particle s p Best value to g Best Calculate velocity for each particle Use each particle s velocity value to update its data values NO Target or maximum epochs reached YES Fig 3.PSO Algorithm for optimization of side lobe level END DE ALGORITHM To update the velocity matrix at each iteration K, every particle should now its personal best and global best position vectors in addition to the neighbor best position. The personal best position vector defines the position at which each particle attained its best fitness value up to the present iteration. The personal best position of the particle is represented as the global best position vector defines the position in the solution space at which the best fitness value was achieved by all particles, and is defined by [12] editor@iaeme.com

7 K. Karuna Kumari and Prof. P. V. Sridevi The particles are manipulated according to the following equations: (2) (3) In 1995, Price and Storn commenced the Differential Evolution (DE) algorithm [10] which is based upon differential mutation operator. Practically there are many problems with different types of objective functions such as non-linear, noisy, flat, non-differentiable, non-continuous, and multi-dimensional or have many local minima which are difficult to solve analytically. DE is a robust statistical method for cost function minimization which does not make use of a single nominal parameter vector but instead it uses a population of equally important vectors and is very advantageous to find the most approximate solution to any type of problems. Differential evolution is a simple, efficient and robust evolutionary algorithm, and is usually mark as DE/x/y/z, where x denotes how the differential mutation base is chosen, y denotes the number of vectors differences added to the base vector and z indicates the crossover method. It has been successfully applied to the array synthesis problems, electromagnetic inverse problems and many other scientific and engineering problems. Although it has been reported that differential evolution performs better than many other algorithms, it is still a dream for differential evolution users to have a strategy perfectly balancing exploration and exploitation, or equivalently, reliability and efficiency. It has been well known that the critical idea behind the success of Differential Evolution is the creative invention of differential mutation [13-15]. Different differential mutation strategies balance exploration and exploitation differently. For example, DE/Best/*/* generally converges faster due to the guidance by the best individual but may be locally trapped because of loss of directivity, while DE/Rand/*/* gains directivity at the cost of efficiency. In order to simultaneously, provide both diversity and guidance so that exploration and exploitation can be more efficiently balanced. Synthesis capability, reliability and efficiency of DE/Rand/*/* are tested. The simulation results show that DE/Rand/*/* is able to achieve lower peak side lobe levels and converge reliably and efficiently. In DE algorithm the objective function is sampled by a set of initial points which are chosen randomly from the entire search space. Then in the next step the algorithm adds the weighted difference between the two randomly selected population vectors to the third random population vector to generate a new parameter vector. This process of generating the new parameter vector is called mutation. Now this parameter vector is further mixed with the predefined parameters to produce the trial vector and this process is called crossover. Then in the last step, called selection in which trial vector is replaced by the target vector if the trial vector reduces the values of the cost function then that obtained due to the target vector. To realize the algorithm let the problem is function of D number of independent parameters. In this work for N element array, the number of independent parameters is 2N in which the first N parameters are the normalized amplitude coefficient of the N array elements and remaining N parameters are to represent the static phase of each element. Hence, if NP be the population size then the parameter vectors are represented as editor@iaeme.com

8 Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using GA, PSO and DE Algorithms The target vector compared with the trial vector and the minimum value is admitted to the next generation. The above steps are continued until the predefined number of generations reached or the desired value of the cost function is obtained. The entire process of DE for solving problem is shown in flowchart in Fig 4. Start Set G=0 and randomly initiate Compute i=1 G Yes M U No Save the result and stop T A +F( ) T I O i=i+1 N C R O S S O V E R S E L E f( Yes No C G=G+1 T I O f ( N Yes i=np No Fig4: DE Algorithm for optimization of SLL editor@iaeme.com

9 cost function Normalized Amplitude(dB) K. Karuna Kumari and Prof. P. V. Sridevi 6. RESUITS AND DISCUSSIONS In this paper, the Non-Uniform linear antenna array is synthesized using global optimizing techniques called GA, PSO and DE algorithms. The Non-Uniform array is symmetric array of 2N elements towards the center of the array. The array having progressive phase and uniform spacing between the elements is 0.5λ.The radiation pattern of linear antenna array with N=20 elements at scan angles and deg are given for GA, PSO and DE. In this paper, the array factor is the objective function for optimizing the fitness /cost function called SLL. By using this evaluation techniques the est weights are obtained for linear antenna arrays to reduce the SLL. 0 Optimized Radiation pattern of microstrip array using GA Theta in (Radians) Figure 5 Radiation pattern of 20 element microstrip array antenna using GA No.of generation Figure 6 Cost function graph for 500 iterations editor@iaeme.com

10 Cost function Normalized Amplitude(dB) Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using GA, PSO and DE Algorithms 0 Optimized Radiation pattern of microstrip array using PSO Theta in (Radians) Figure 7 Radiation pattern of 20 element microstrip array antenna using GA No.generation Figure 8 Cost function graph for 500 iterations editor@iaeme.com

11 cost function Normalized Amplitude(dB) K. Karuna Kumari and Prof. P. V. Sridevi 0 Optimized Radiation pattern of microstrip array using DE Theta in (Radians) Figure 9 Radiation pattern of 20 element microstrip array antenna using GA No.of generations Figure 10 Cost function graph for 500 iterations editor@iaeme.com

12 Normalized Amplitude(dB) Normalized Amplitude(dB) Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using GA, PSO and DE Algorithms Optimized Radiation pattern of microstrip array using GA,PSO,DE GA PSO DE Theta in (Radians) Figure 11 Radiation Pattern of Linear antenna array of 20 elements using GA, PSO and DE at θ= (deg) Optimized Radiation pattern of microstrip array using GA,PSO,DE GA PSO DE Theta in Radians Figure 13 Radiation Pattern of Linear antenna array of 20 elements using GA, PSO and DE at θ= (deg) editor@iaeme.com

13 K. Karuna Kumari and Prof. P. V. Sridevi S.No Table 1 Best weights for GA, PSO and DE Algorithms with 200 iterations Optimized weights using GA(N=20) Optimized weights using PSO (N=20) Table 2 SLL for GA, PSO and DE Algorithms with 200 iterations Optimized weights using DE (N=20) No.of element s GENETIC ALGORITHM Side lobe level(db) Converging time (sec) PARTICLE SWARM ALGORITHM Side lobe level(db) Converging time (sec) DIFFERENTIAL EVOLUTION ALGORITHM Side lobe level(db) Converging time (sec) editor@iaeme.com

14 Elapse Time(seconds) Normalised Amplitude(dB) Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using GA, PSO and DE Algorithms No.of elements verse Normalised Amplitude(dB) GA PSO DE No.of Elements(N) Figure 14 Maximum Side lobe level with the number of elements No.of elements verse Elapse Time(seconds) GA PSO DE No.of Elements(N) Figure 15 No. of elements verse Elapse time editor@iaeme.com

15 K. Karuna Kumari and Prof. P. V. Sridevi In three algorithms N=20 elements are used. The radiation pattern of Linear antenna array of 20 elements using GA, PSO algorithm and DE algorithm at θ= (deg) and at θ= (deg) are represented. The radiation pattern of Linear antenna array of 20 elements using GA, PSO and DE algorithms at θ= (deg),the SLL is db,.45db and db obtained respectively. The cost functions of GA,PSO and DE algorithms of 200 iterations are represented. All the three algorithms produced best results than normal linear antenna array having -13.6dB and comparatively DE Algorithm produces maximum SLL than PSO and GA. All the simulation results are obtained using MATLAB software 7. CONCLUSION In this paper the optimization of 20 elements linear arrays in terms of side level using genetic algorithm,particle swarm optimization algorithm,differential Evaluations are given. The side level for GA is db, PSO is -.45 db and for DE is for 20 element arrays. All three optimization techniques gives the good results for given problem, however the elapsed time or converging time for genetic algorithm is more when compared with PSO algorithm and DE algorithm. The number of generations /iterations required to get best fitness value for DE is more compared with GA and PSO. REFERENCES [1] Rahmat-Samii, Y., and Michielssen, E.: Electromagnetic Optimization by Genetic Algorithms. (New York: Wiley-Interscience, 1999) [2] Robinson, J., and Rahmat-Samii, Y.: Particle swarm optimization in electromagnetics. IEEE Transactions on Antennas and Propagation, 2004, 52, pp [3] Storn, R. and K. Price, Differential evolution A simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11(4), pp , [4] M. M. Khodier and C. G. Christodoulou, Linear array geometry synthesis with minimum side lobe level and null control using particle swarm optimization, IEEE Transactions on Antennas and Propagation, 53(8), August [5] S. Yang, Y. B. Gan, and A. Qing, Sideband suppression in time modulated linear arrays by the differential evolution algorithm, IEEE Antennas Wireless Propagat. Lett., 1, pp , [6] D. Gies and Y. Rahmat-Samii, Particle swarm optimization for reconfigurable phased-differentiated array design, Microw. Opt. Tech. Lett., 38(3), pp , Aug [7] Kurup, D., Himdi, M., and Rydberg, A.: Synthesis of uniform amplitude unequally spaced antenna arrays using the differential algorithm, IEEE Trans. Antennas Propagation, 2003, 51, pp [8] K. Karuna Kumari, Dr.P.V.Sridevi Performance Evaluation of Circular Microstrip Patch Array with Difference Dielectric Substrate Materials, International Journal of Electronics and communication Engineering & Technology 4(1) 2013,pp [9] K.Karuna Kumari, Dr.P.V.Sridevi, Side lobe level optimization of circular Microstrip array antenna using Genetic Algorithm, IJECIERD 4(1) January- Feb14pp editor@iaeme.com

16 Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using GA, PSO and DE Algorithms [10] F. Soltankarimi1, J. Nourinia and Ch. Ghobadi, Side Lobe Level Optimization in Phased Array Antennas Using Genetic Algorithm, ISSST A2004, Sydney, Australia, 30 Aug, 2 Sep [11] J. Kennedy, R. Eberhart, Particle Swarm Optimization, IEEE Int. Conf. Neural Networks (Perth, Australia), 4, 1995, pp [12] J.Robinson, Y.Rahmat-Samii, ParticleSwarm Optimization (PSO) in Electromagnetics, IEEE Trans. Antennas Propagation, 52(2), February 2004, pp [13] S. Das, P. N. Suganthan, Differential Evolution: A survey of the State of- the- Art, IEEE Transactions on Evolutionary Computation, 15(1), pp. 4 31, 2011 [14] Y. Wang, Z. Cai, and Q. Zhang, Differential evolution with composite trial vector generation strategies and control parameters, IEEE Transactions on Evolutionary Computation, 15(1), pp , [15] J.Robinson, Y.Rahmat-Samii, ParticleSwarm Optimization (PSO) in Electromagnetics, IEEE Trans. Antennas Propagation, 52(2), February 2004, pp [16] Balanis, C.: Antenna Theory-Analysis and Design. (2nd Edition New York: Wiley, 1997) [17] Dr. Nagraj Kulkarni and Dr. S. N. Mulgi. A Novel Design and Development of Superimposed Square Slot Two Element Rectangular Microstrip Array Antenna for Wide Bandwidth and Intensified Gain. International Journal of Advanced Research in Engineering and Technology, 5(1), 2014, pp [18] Gangadhar P Maddani, Sameena N Mahagavin, Shivasharanappa N Mulgi. Design and Development of Microstrip Array Antenna for Wide Dual Band Operation. International Journal of Electronics and communication Engineering & Technology, 1(1), 2010, pp [19] Gangadhar P Maddani, Sameena N Mahagavin, Shivasharanappa N Mulgi, Rectangular Microstrip Array Antennas For Wide Triple Band Operation. International Journal of Electronics and communication Engineering & Technology, 1(1), 2010, pp [20] James Blondin, Particle Swarm Optimization: A Tutorial September4, editor@iaeme.com