# PERFORMANCE ANALYSIS OF DIFFERENT ARRAY CONFIGURATIONS FOR SMART ANTENNA APPLICATIONS USING FIREFLY ALGORITHM

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2 Figure 1. Circular array of 12 elements are uniformly distributed 2.2 Hexagonal array The Figure-2 shows hexagonal array [4] and can be treated as it consists of two -elements of concentric circular arrays of two distinct radii r1 and r2. There are a total of 2 elements out of which elements are placed at the vertices and the other elements are placed at mid points of the sides of hexagon. The array factor of the hexagonal array is given by AF(, θ) = n [A n e jkr 1 sin θ(cos 1n cos +sin 1n sin ) n=1 + B n e jkr 2 sin θ(cos 1n cos +sin 1n sin ) ] (2) Where A n and B n are relative amplitude excitations of - elements placed at the vertices aid points of the hexagon respectively. r 1 and r 2 given as d r 1 = sin( π ), and r 2 = r 1 cos ( π ) in which d is the inter element spacing along any side of hexagonal array and 1n and 2n respectively are angles between positive x- axis and nth element at vertices and midpoint of the hexagon. Figure-2. Hexagonal array of 12 elements arranged in two concentric circular rings. 2.3 Planar uniform hexagonal array Two concentric hexagonal arrays are arranged as shown in Figure-3. There are 2 elements are arranged in equal number on the two concentric hexagonal arrays [5]. The array factor of planar uniform hexagonal array is given by equation AF(θ, Φ) = M {[A nm e jkr 1m sin θ(cos 1n cos +sin 1n sin ) m=1 n=1 + B nm e jkr 2 sin θ(cos 2n cos +sin 2n sin ) ]} (3) Where 2 is number of elements on each hexagon, M is the number of concentric hexagons and d is spacing between two hexagons. d r 1m = sin( π and r 2m = r 1m cos ( π ) ) For maximizing the out power in the intended signal direction at Φ i and in the interferers direction at Φ j, to minimize the total output power, the following objective function [5] is used. Objective function = i=1 a i G(Φ i ) j=1 b j G( Φ j ) (4) Where a i and b j are the constants that represent weights which control the conferment of each term to the overall objective function, G is the antenna array gain. The constant represents the number of intended users and M is number of interferers. In this analysis, =1, M=2 are considered. M 8724

3 x m = x m + β e ϒr2 m,n (x m x n ) + α (rand 1 2 ) (6) Figure-3. Planar uniform hexagonal array of 12 elements are arranged on two concentric hexagonal rings. 3. FIRE FLY ALGORITHM Firefly algorithm was based on the behavior and flashing patterns of fireflies. It was developed by Xin-She- Yang in 28. Essentially Firefly algorithm follows three idealized rules which were mentioned in [9]. The attractiveness is denoted as β that each firefly has and is described by invariably decreasing function of the distance 'r' between any two fireflies. β(r) = β e ϒrm for m 1 Where β represents the maximum attractiveness at r= and the factor ϒ which controls the decrease of the light intensity is called light absorption coefficient. If the positions of two fireflies m and n are denoted as x m and x n, then the distance between two fireflies m and n is given as d r mn = x m x n = (x m,k x n,k ) 2 k=1 (5) Where x m,k is the kth component of spatial coordinate x m of the mth firefly and d signifies the dimension number. The mth firefly movement can be determined from the following equation in which the first term represents mth firefly current position, second term signifies attractiveness of a firefly and the last term is used for the arbiter movement if there is no brighter firefly. rand is an arbitrary number that is uniformly distributed in the range and 1. For most of the cases α is in the range between and 1 and β =1. The characteristic length is denoted as Г = ϒ 1 m for fixed ϒ and also Г 1 as m. Two important limiting cases when ϒ and ϒ. When ϒ, the attractiveness β becomes β and Г,from which we can say that there is no decrease of light intensity. Thus anywhere in the domain, a glowing firefly can be seen. Thus, a global optimum can be reached easily. When ϒ on the other hand, leads to Г and β(r) δ(r) which is a Dirac delta function means that fireflies are short sighted as attractiveness is almost zero. o other fireflies can be seen and each firefly moves completely in random fashion. This corresponds to random search method completely. It is possible to tune the parameter ϒ and α that it can be better than random search and Particle Swarm Optimization (PSO). FA can find simultaneously both global optima and local optima [1]. 4. SIMULATIO RESULTS Different shapes of array geometries are considered and compared with each other. The first array considered is a UCA with 12 isotropic elements uniformly distributed with a radius of 7.6 λ. Also hexagonal array of 2π inner radius r1 is 3.6 λ and outer ring radius r2 is 4 λ. Both 2π 2π rings consist of 6 elements. The third type of array is PUHA consists of two concentric hexagonal arrays as shown in above figure. In the equation (5), M=2, =6 are considered. Assuming all elements are excited with the same amplitude. For adaptive beam forming, with all array geometries, the desired signal is chosen at while two interferers at 65 and -65. Figure 4 shows the radiation pattern of PUHA using both PSO and Firefly algorithm. Firefly algorithm shows better performance over PSO as it achieves more null depth and also it gives minimum cost function compared to PSO [5] [7] as shown in Figure-5. FA also gives good convergence over PSO as it takes less number of iterations to converge as compared to PSO. 8725

4 -1 PSO Firefly -2 Array factor (AF)in Db theta(in degrees) Figure-4. Radiation pattern of PUHA when SOI is and SOI is 65 and -65 using PSO and Firefly algorithms. 7 6 Best Cost vs Iteration PSO Firefly 5 4 Cost Iteration Figure-5. Convergence plot of Firefly and PSO algorithms for 1 number of iterations. 8726

5 -1 cir Hex PUHA -2 Array factor (AF)in Db theta(in degrees) Figure-6. Radiation pattern of of the three array configurations for SOI is and SOI is 65 And -65 using PSO algorithm. Figures 6 and Figure-7 shows the radiation patterns of circular, hexagonal and planar hexagonal array using PSO and firefly algorithm respectively. A first observation from these plots is that as compared to other two geometries, PUHA achieves the deepest nulls towards the interference direction. Especially with Firefly algorithm, the nulls with PUHA towards the interferers are very deep which a desirable property is. PUHA also gives narrowest main beam widths. UHA gives more null depth than UCA and UCA gives more side lobes as compared with UHA [6]. PUHA achieves highest directivity as the main beam width is narrow. The respective beam widths and null depths are tabulated in Table-1 and Table-2 using PSO and Firefly algorithms. Table-1. Beam width and null depth comparison of circular, hexagonal and PUHA using PSO. Parameter Circular Hexagonal PUHA 1. ull depth (in db) 2. Beam width (in degree)

6 -1-2 circular hex PUHA Array factor (AF)in Db theta(in degrees) Figure-7. Radiation pattern of of three array configurations for SOI is and SOI is 65 and -65 using firefly algorithm. Table-2. Beam width and null depth comparison of circular, hexagonal and PUHA using Firefly algorithm. Parameter Circular Hexagonal PUHA 1. ull depth (in db) Beam width (in degree) COCLUSIOS In this paper, smart adaptive arrays such as UCA, UHA and PUHA are considered and the main issue related to smart antennas, adaptive beam forming was investigated for all arrays with the same number of elements by using Particle Swarm Optimization and Firefly algorithm. The investigation reveals that Hexagonal array geometry gives slightly deeper nulls as compared to circular array with the same beam width also it is smaller overall size. PUHA achieved the deepest nulls towards the angles of interference, especially when firefly algorithm is employed and also it gives narrow beam width so that more directivity as compared to UCA and UHA. REFERECES [1] Ioannides P. and C. A. Balanis. 25. Uniform circular arrays for smart antennas. IEEE Antennas and Propagation Magazine. 47(4): [2] K. Guney. 28. Interference suppression of linear antenna arrays by amplitude only control using a Bacterial Foraging Algorithm. Progress in Electro magnetics Research. 79: [3] Ioannides P. and C. A. Balanis. 25. Uniform circular and rectangular arrays for adaptive beamforming applications. IEEE Antennas and Wireless Propagation Letters. 4: [4] Kretly L. C., A. S. Cerqueira Jr., and A. A. S. Tavora. 22. A hexagonal adaptive antenna array concept for wireless communication applications. The 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications. 1: [5] K. R. Mahmoud, M. El-Adawy and S. M. M. Ibrahem. 27. A Comparison between Circular and Hexagonal array Geometries for Smart antenna systems using Particle Swarm Optimization 8728

7 Algorithm. Progress in Electro magnetics Research. 72: [6] Gozasht F., G. R. Dadashzadeh and S. ikmehr. 27. A comprehensive performance study of circular and hexagonal array geometries in the LMS algorithm for smart antenna applications. Progress in Electromagnetics Research, PIER.68, [7] Chen T. B., Y.B. Chen, Y. C. Jiao and F. S. Zhang. 25. Synthesis of antenna array using particle swarm optimization. Microwave Conference Proceedings, 25. APMC 25. Asia-Pacific Conference Proceedings. [8] Yang X.-S. 21. Firefly algorithm, stochastic test functions and design optimization. International Journal of Bio-inspired Computation. 2(2): [9] Basu B. and G. K. Mahanti Firefly and artificial bees colony algorithm for synthesis of scanned and broadside linear array antenna. Progress in Electro magnetics Research B. 32:

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