Generation of Ultra Side lobe levels in Circular Array Antennas using Evolutionary Algorithms

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1 Generation of Ultra Side lobe levels in Circular Array Antennas using Evolutionary Algorithms D. Prabhakar Associate Professor, Dept of ECE DVR & Dr. HS MIC College of Technology Kanchikacherla, AP, India. Ch. Harsha vardhan Dept of ECE DVR & Dr. HS MIC College of Technology Kanchikacherla, AP, India. S. Ratna Spandana Dept of ECE Andhra Loyola Inst. of Engg & Tech Vijayawada, AP, India. Dr. P. Mallikarjuna Rao Professor, Dept of ECE Andhra University College of Engg Visakhapatnam, AP, India. Abstract The antenna arrays have a wide range of applications such as phase array radar, satellite communications and other domains. In order to reduce interference antenna array should have lower side lobes and pattern symmetry in azimuth angles. The nonlinear least square (NLS) method cannot meet the demand of such complex optimization problems. Particles Swarm Optimization (PSO) and Genetic algorithm are evolutionary algorithms following the principle of natural selection and swarm intelligence. In this paper Side lobe levels for a circular array antenna are reduced using these two algorithms out of which the particle swarm optimization algorithm introduces a new method to find an optimal solution of a complex optimization problem, where every particle in swarm represents a solution to the problem. The particle swarm optimization algorithm can improve the global search ability by adding a constriction factor. Particle Swarm Optimization worked well for several problems. It can be used for optimizing mathematical functions and electromagnetic problems. The optimized antennas were determined to have lower Side lobe levels compared to the results obtained by Genetic algorithm and Circular array with uniform excitation. radiation, it is necessary to modify the geometric configuration or the other parameter of the device. A group of antennas arranged in a geometrical configuration is called as a antenna array. Linear arrays with narrow main beamwidth are used in point to point communications and high angular resolution radars. However, in applications where angular symmetry in direction finding is desired, they are not suitable. To overcome this restriction, efforts were made to design the circular arrays. Circular array antenna is an assembly of similar radiating elements geometrically and electrically in the form of a circle. The radiation pattern of circular array antenna with isotropic elements depends mainly on parameters like the excitation current, phase, and the spacing between the elements. In the array design process excitation currents, excitation phases, and inter element spacing are the parameters that can be controlled to achieve the required objective. The below expression gives the array factor of a circular array antenna. Keywords: Circular Array Antenna, Genetic Algorithm, Particle Swarm Optimization, Side Lobe levels, Array Factor. INTRODUCTION The antenna is the basic part of the wireless communication. It is mainly used to transmit and receive signals. To get better 5682

2 Mutation - A genetic operator which maintains genetic diversity from one generation of chromosomes to the next. It is analogous to biological mutation. Mutation Probability determines how often the parts of a chromosome will be mutated. Types of mutation are bit reversal and polynomial. Fitness function - A fitness function quantifies the optimality of a chromosome so that the particular solution may be ranked against all the other solutions. It gives the closeness of a given solution to the desired result. Most functions are stochastic and designed so that a small proportion of less fit solutions are selected. This helps keep the diversity of the population large, preventing premature convergence on poor solutions. The fitness function for the optimization is given as Fitness=min (max (20*log AF)/AF) Figure 1: Circular array antenna Where In =Excitation current of nth element Φo =Excitation phases K =Wave number N =No. of elements Φ =Angle of incidence Termination Termination of the algorithm will be done if a solution is found that satisfies minimum criteria or fixed number of generations found or allocated budget (computation, time/money) reached or the highest ranking solutions fitness has reached. Flow chart For GA: GENETIC ALGORITHM (GA): Genetic algorithm (GA) is a population based global optimization algorithm which works on the mechanics of natural selection. It can be used to optimize a solution of any problem involving a population. GA is best suited if the objective function is discrete, highly non linear, high dimension, stochastic and has unreliable or undefined derivatives. GA conceptually follows steps inspired by the biological process of evolution. It follows the idea of survival of the fittest which means only the fittest of the generations survive to next generation. Better and better solutions evolve from previous generations until a near optimal result is obtained. Terms related to GA: Gene Gene is a single encoded part of the solution space, i. e. either single bits or short block of adjacent bits that encode an element of the candidate solution. Chromosome A string of genes that represents the solution. Population The number of chromosomes available to test. Selection It is a process of selecting proportion of the existing population to bread a new breed of generation. Parents with better fitness can have better chances to produce offspring. Three types of selection mechanisms are there which popular rank, tournament and roulette wheel. Crossover Crossover is a genetic operation that combines (mates) two individuals (parents) to produce two new individuals (Childs). The idea behind this operation is that the new chromosome may be better than both of the parents if it takes the best features from each of their parents. There are 4 types of crossover single point, two point, uniform and real value. Figure 2: Flow chart for Genetic Algorithm 5683

3 Outline of the Algorithm: The following outline summarizes how the genetic algorithm works: 1. The algorithm starts by generating a random initial population. 2. The algorithm then populates a sequence of new populations. At each step, the algorithm makes use of the individuals in the current generation to create the next generation. To create the new population, the algorithm performs the following steps: a. Ranks each member of the current population by computing its fitness value. b. Scales the raw fitness scores to convert them into a more usable range of values. c. Selects parents, based on their fitness. d. Some of the individuals in the current population that have better fitness are chosen as best off springs. These elite individuals are passed to the next population. e. Produces children from the parents. Children are produced either by making random changes to a single parent mutation or by combining the vector entries of a pair of parents crossover. f. Replaces the current population with the children to form the next generation of individuals. 3. The algorithm terminates when one of the stopping criteria is met. Figure 3 shows the initial state of a four-particle PSO algorithm seeking the global maximum in a one-dimensional search space. Flow chart for PSO: Yes Assign current fitness as new pbest Initialize particles Calculate fitness values for each particle Is current fitness value better than pbest? No Keep previous pbest PARTICLE SWARM OPTIMIZATION (PSO): PSO is a optimizing algorithm based on the principle of evolution which relies on the intelligence and co-operation of flock of birds. It maintains a swarm of particles where every particle represents a potential solution. In PSO algorithm particles are flown into a multidimensional search space, where the position of each particle is adjusted according to its own experience and that of its neighbors. The PSO algorithm works by simultaneously maintaining several candidate solutions in the search space. During each iteration of the algorithm, each candidate solution is evaluated by the objective function being optimized, determining the fitness of that solution. Each candidate solution can be considered as a particle flying through the fitness landscape searching the maximum or minimum of the objective function. Initially, the PSO algorithm chooses candidate solutions randomly within the search space. Assign best particle s pbest value to gbest Calculate velocity for each particle Use each particle s velocity value to update its data values No Yes Target reached? End Figure 4: Flowchart for PSO Figure 3: Particles in a Swarm Outline of PSO Algorithm: For each particle Initialize particle END 5684

4 Do For each particle Calculate fitness value If the fitness value is better than the best personal fitness value in history, set current fitness value as a new best personal fitness value End Choose the particle with the best fitness value of all the particles, and if that fitness value is better than current global best, set as a global best fitness value For each particle Calculate particle velocity according velocity change equation Update particle position according position change equation End While maximum iterations or minimum error criteria is not attained v k s k v k+1 s k+1 v gbest v pbest Figure 5: Concept of modification of searching point by PSO sk: current searching point. sk+1: modified searching point. vk: current velocity. vk+1: modified velocity. vpbest : velocity based on pbest. vgbest : velocity based on gbest The search space contains all the possible solutions along the x-axis; the curve represents the objective function. It should be noted that the PSO algorithm has no knowledge of the underlying objective function, and thus has no chance of knowing if any of the candidate solutions are near to or far away from a global or local maximum. The PSO algorithm simply uses the objective function to evaluate its candidate solutions, and operates upon the resultant fitness values. Each particle maintains its position, composed of the candidate solution, its evaluated fitness and its velocity. In addition to this, it remembers the best fitness value it has achieved so far during the operation of the algorithm, referred to as the personal best fitness, and the candidate solution that achieved this fitness considered as the individual best position or individual best candidate solution. Finally, the PSO algorithm maintains the best fitness values achieved among the particles in the swarm, called the global best fitness gbest, and the candidate solution that achieved this fitness, called the global best position or global best candidate solution. Equations (1) and (2) were used to update the particle s velocity and position, respectively. In these equations, vp(t) and xp(t) are the particle s velocity and position at instant t, pbestp(t) is the best position the particle achieved till instant t, gbestp(t) is the best position that any of p s neighbors has achieved till the instant t, c1 is a coefficient that indicates how much the particle trusts its experience, c2 is a social coefficient that indicates how much the particle trusts its best neighbour, rand1 and rand2 are random numbers. vp(t) = vp(t-1) + c1. rand1. (pbest(t-1) xp(t-1)) + c2. rand2. (gbest(t-1) xp(t-1)) (1) xp(t)=xp(t-1)+vp(t) (2) Synthesis of antenna array using particle swarm optimization: In PSO algorithms, every potential solution of optimization problem is considered as a bird in the solution space, which is called a particle. Every particle has its own value of fitness determined by an objective function. They also possess a directional velocity to control its search paths. The particles follow the optimal solution by searching the solution space. Every particle has initial position and velocity, where the positions and velocities are updated in every iteration. In each iteration, two best position are chased to update the particle. The first solution is the optimal solution found by particle, known as personal best position. The other is the optimal solution in the entire group, which is called as global best position. In PSO, the i-th particle in the solution space is determined by a fitness function s value Particle swarm optimization (PSO) is a population based stochastic optimization technique, inspired by social behavior of bird flocking or fish schooling. If a problem is given, and there is some way to find a solution to it in the form of a fitness function, then this method can be used. A population of individuals defined as random guesses of the problem solution is initialized. These individuals are also known as the particles, hence the name particle swarm. Value of the objective function for these individuals represents their positions. An iterative process to improve these positions is then started. The particles iteratively evaluate the positions and remember the location where they had their best success. The individual's best solution is called the particle best or the local best. Each particle makes this information available to their neighbors. They are also able to see where their neighbors have had success. The best solution among all the neighbors is called global best. 5685

5 SIMULATED RESULTS: Figure 6: Plot for a 20- element array Circular array with GA -12dB -13dB -12dB Circular array with PSO -22dB -19dB -19dB Figure 7: Plot for 40-element array Circular array with GA -13dB -14dB -13dB Circular array with PSO -19dB -22dB -19dB Figure 8: Plot for 30 -element array Circular array with GA -18dB -14dB -15dB Circular array with PSO -22dB -19dB -19dB Figure 9: Plot for 50- element array Circular array with GA -13dB -15dB -13dB Circular array with PSO -20dB -19dB -19dB 5686

6 CONCLUSION: It is evident from the above results that the application of excitation currents obtained by PSO optimizes side lobe levels to a greater extent compared to Genetic algorithm and uniformly excited arrays. Above radiation plots clearly show that results obtained with PSO are comparatively better with a SLL reduction of around dB (for 1st SLL) than that of results obtained by GA for the circular antenna arrays. REFERENCES: [1] W. Y. Wei, D. M. Gong, and B. S. Chen, Antenna Theory, Xi an: The publishing house of Xidian University, [2] Y. B. Chen, Y. B. Chen, Y. C. Jiao, and F. S. Zhang, Synthesis of Antenna Array Using Particle Swarm Optimization, [3] Riccardo Poli, An Analysis of Publications on Particle Swarm Optimization Applications May 2007 [4] Daniel Bratton, James Kennedy, Defining a Standard for Particle Swarm Optimization, [5] James Blondin, Particle Swarm Optimization: A Tutorial September 4, [6] D Nagesh Kumar, Classical and Advanced Techniques for Optimization [7] Dr. T. Ghose. Optimization Techniques and an Introduction to Genetic Algorithms and Simulated Annealing [8] Goldberg, D. E. Genetic Algorithms in search, optimization, and machine learning Addition- Wesley [9] K. Deb, Optimization for Engineering Design PHI, New Delhi. [10] T. Ghose, Dr. S. K. Goswami & Professor S. K. Basu, " Solving Capacitor Placement Problem In Distribution Systems Using Genetic Algorithms "Published in Vol. 27, Number 4, 1999 of international journal of Electric Machines and Power Systems. [11] Ashish Ghosh and S. K. Pal, Biologically Inspired New Operations for Genetic Algorithms Published in preceding of int. workshop on soft computing and Int. Systems, ISI Calcutta, January 12-13,

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