Side Lobe Reduction of Phased Array Antenna using Genetic Algorithm and Particle Swarm Optimization

211 Side Lobe Reduction of Phased Array Antenna using Genetic Algorithm and Particle Swarm Optimization Pampa Nandi* and Jibendu Sekhar Roy School of Electronics Engineering, KIIT University, Bhubaneswar-751024, Odisha, India E-mail: pampanandi@yahoo.com, drjsroy@rediffmail.com Abstract- Two methods of side lobe reduction for linear phased array antenna are described in this paper. In the first case, side lobe of linear phased array is reduced by optimization using real coded genetic algorithm (RGA) and particle swarm optimization (PSO) with non-linear amplitude weight. In the second case, side lobe is reduced by array thinning technique using binary genetic algorithm (BGA) and binary particle swarm optimization (BPSO). Using RGA, maximum side lobe reduction of about 6dB and using PSO, maximum side lobe reduction of 7dB is achieved compared to uniform linear array (ULA). In array thinning, maximum side lobe reduction of about 4dB is obtained for BGA and BPSO compared to uniform linear array (ULA). Index Terms- Genetic algorithm, particle swarm optimization, phased array, side lobe level I. INTRODUCTION In phased array antenna, the main beam can be tilted in desired direction by changing progressive phase shift between the antenna elements in an array, electronically [1, 2]. Major drawback of phased array is appearance of grating lobe with the tilting of main from broadside direction and also side lobe level (SLL) changes with the direction tilted beam [1-4]. These problems cause serious interference, resulting performance degradation. Hence successful communication requires reduced side lobe level. There are different analytical and statistical methods, used to reduce side lobe level [4, 5]. Such methods have limitations. When the array size increases, it is difficult to reduce side lobes [6]. Several optimization techniques such as genetic algorithm [6-7], particle swarm optimization, ant colony optimization, simulated annealing, etc. are used for synthesizing array. In [6], genetic algorithm (GA) is used to reduce side lobe. A fast array thinning method using GA is reported in [7]. Method of thinning of aperiodic array using GA is described in [8]. The array thinning method, using interference suppression by side lobe rejection, is suggested in [9]. Design of a class of thinning for predictable SLL is reported in [10]. Application of particle swarm optimization for side lobe reduction is used in [11-13]. Real-coded GA (RGA) is used for side lobe reduction in [14]. Other methods, like, ant colony optimization, simulated annealing etc. [15-16] are also used for this purpose. In this paper, binary GA (BGA), PSO, binary PSO (BPSO) and real coded GA (RGA) are used to minimize side lobe level of a linear phased array antenna and appreciable amount of side lobe reduction is achieved. For thinning of phased array antenna BGA and BPSO are used due to discrete nature of the algorithms. The performances of SLL reduction using different types of algorithms are compared. Cost function is described in section II. Reduction of SLL using RGA and particle swarm optimization (PSO) with non-linear amplitude weight is included in section III. In section IV, reduction of side lobe level by array thinning method, using BGA and BPSO is described. Comparisons of results are tabulated in section V. II. PHASED ARRAY ANTENNA Consider a uniform linear array consisting of N isotropic antenna with inter element spacing of d (Fig. 1). Total electric field E T, of a uniform linear array at an angle θ is [1, 4].

212 E T = E 0 1 + e jψ + e j2ψ + e j3ψ + + e j(n 1)ψ = E 0 Sin( Nψ 2 )/Sin(ψ ) (1) 2 selection can be performed by roulette wheel method or by tournament selection. These selected parent chromosomes create offspring by combing weighted portion of both parents. If r is a random number, μ is the cross over operator then weight b is [17] b = (2r) 1/(1+μ) if r>0.5 Fig.1. Linear antenna array Where, Ψ = βdcosθ + α, β = 2π/λ, λ = wavelength, α = progressive phase shift between the antenna elements. It can be seen from equation (1), far field radiation pattern is governed by array factor (AF) and expressed as, AF = Sin( Nψ 2 )/Sin(ψ ) (2) 2 To tilt main beam at any angle ø, the array factor can be written in exponential form as, AF = N jn2πd(cos θ cos ) 1 I n. e (3) Cost function is the normalized maximum side lobe level which is to be minimized and can be derived from equation (3) by excluding the main beam from the array factor equation. Hence the cost function is = [(1/2(1 r)] 1/(1+μ) otherwise (5) The newly generated offspring are, Offspring1 = [(1 +b)parent 1 + (1-b)parent 2]/2 Offspring2 = [(1 -b)parent 1 + (1+b)parent 2]/2 Mutation is performed on some randomly selected chromosome to maintain search in diversified direction according to probability of mutation. If η is mutation operator, then mutation weight p is [17], 1 p = (2r) 1+η 1 if r 0.5 = 1 [2(1 r)] 1/(1+η) otherwise (6) RGA is applied for optimization of 100 element linear array with fixed inter element spacing of 0.3λ and the results for normalized array factor are shown in Fig. 2 and Fig. 3 respectively. SLL max = max AF(θ) max (AF) θ= θ SLM (4) Where, θ SLM = (ø LN) (ø + RN) θ 180. Here, LN and RN are the first left null point and the first right null point to main beam. III. SIDE LOBE LEVEL REDUCTION USING RGA AND PSO Real coded GA (RGA) operates on the real value parameter. Chromosomes are formed by group of random (0 to 1) valued genes and a set of such chromosome creates initial population [14]. After evaluating cost of each chromosome from this population a finite number of elite chromosomes are kept for natural selection process and rest are discarded. Like binary GA (BGA) parent Fig. 2. Normalized array factor for RGA optimized 100 element array and ULA at 30 0 tilt angle PSO is a real coded optimization technique [11, 18] that developed on behaviour of bird swarm. PSO is initialized with random particles or solution, evaluate the fitness of each particle using the cost function and directing towards optimum value by updating its present best position pbest, the best value obtained by a

213 particle so far, and global best position gbest, best value achieved by a particle in the swarm of each particle in every iteration. Minimum side lobe level also determined for 20 element linear phased array, by optimizing the cost function, given by equation (4), using PSO and RGA and plotted for different scanning angle in Fig. 6 and Fig. 7 respectively. Fig. 3. Normalized array factor for RGA optimized 100 element array and ULA at 90 0 tilt angle These best values are obtained by updating the Fig. 6. Normalized array factor using PSO and RGA velocity as for 20 element linear array at 60 0 tilt angle velocity(i+1)= velocity(i) + c1*rand*(pbest present(i)) + c2*rand* (gbest position(i)) position(i+1) = position(i) + v(i+1) Here i is the no. of iterations, rand is a random number between (0, 1). c1, c2 are social and cognitive learning factors [18]. The process will iterate until stopping criteria met. PSO is used for optimization of 100 element array, with d= 0.3λ and the results are shown in Fig. 4 and Fig. 5. Fig. 4. Normalized array factor for PSO optimized 100 element array and ULA at 0 0 angle Fig. 7. Normalized array factor using PSO and RGA for 20 element linear array at 90 0 tilt angle In Fig. 6, Amplitude weight of PSO optimized array is 1.00 0 1.00 1.00 0.82 0.74 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0 1.00 1.00 1.00 and RGA optimized array is 0.47 0.80 0.70 0.94 0.51 1.26 0.78 1.08 0.96 1.05 1.06 1.08 1.44 0.79 1.29 1.03 0.32 0.53 1.04 0.65. In Fig. 7, Amplitude weight of PSO optimized array is 1.00 0.27 1.00 0.51 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0 1.00 0 1.00 and RGA optimized array is 0.385 0.47 0.48 1.03 0.83 0.38 1.12 1.01 1.02 0.57 1.25 0.82 0.87 0.82 0.70 0.54 0.60 0.59 0.63 0.54. IV. SIDE LOBE LEVEL REDUCTION BY THINNING USING BGA AND BPSO Fig. 5. Normalized array factor for PSO optimized 100 element array and ULA at 90 0 tilt angle Array thinning is a technique of strategically switching off some elements to achieve narrowest main beam with minimum side lobe

214 level. An antenna element, when it is excited, the element is in on state. If the element is passively terminated to a matched load, effectively it is considered as the antenna element is switched to off state. There are many methods of array thinning, but most popular method is to use optimization technique. In this section, BGA and BPSO are used for optimization of on and off states of thinned array to achieve lowest side lobe level. Equation (4) is the cost function for array thinning. Binary Genetic Algorithm (BGA) is a random search optimization technique which can cover a large search space, operate on coding of parameters by changing real value parameters to equivalent binary string called gene and assembling all parameters formed chromosome [19, 20]. In case of thinned array each bit represents the condition of each element. Natural selection process such as roulette wheel method or tournament selection method generally used to select two parent chromosomes randomly from the population for crossover. Crossover process inheriting the bit pattern from the initial population, to explore other search area mutation is required, that process selects some of the bits according to mutation rate from the population and toggles their values. After mutations the cost is again evaluated for every chromosome of the new population. This whole process will iterate again until the stopping criteria met. Results for BGA optimization for thinning of 100 elements antenna array with inter element spacing 0.3λ at scanning angle 30 0, and 90 0 are shown in Fig. 8 and Fig. 9 respectively. Fig. 9. Normalized array factor for BGA optimized 100 element thinned array and ULA at 90 0 In Fig. 8, 59 elements are on and 41 elements are off. In Fig. 9, 65 elements are on and 35 elements are off. BPSO algorithm optimizes such problems defined in discrete valued spaces where the domain of the variables is finite [11, 12, 18]. BPSO algorithm converts particle s local best, global best position and velocities into real value and afterwards values are updated like PSO. BPSO is programmed for optimization of cost function (side lobe level) for 100 elements antenna array with inter element spacing of 0.3λ and results at different scanning angle are shown in Fig. 10 and Fig. 11 respectively. Fig.10. Normalized array factor for BPSO optimized 100 element thinned array and ULA at 0 0 In Fig. 10, 58 elements are on and 42 elements are off. In Fig. 11, 62 elements are on and 38 elements are off. Fig. 8. Normalized array factor for BGA optimized 100 element thinned array and ULA at 30 0

215 Fig.11. Normalized array factor for BPSO optimized 100 element thinned array and ULA at 30 0 Results for side lobe reduction for 20 elements linear phased array, using BGA and BPSO are plotted in Fig. 12 and Fig. 13 respectively. Fig. 12. Normalized array factor for BPSO and BGA optimized 20 element thinned array at tilt angle 60 0 In Fig. 12, the on and off positions of BGA optimized Array are 10111111111111011100 and of BPSO optimized Array are 11011111111111111011. In Fig. 13, the on and off positions of BGA optimized Array are 10010110110110110100, and of BPSO optimized Array are 10101011011111110101. Fig.13. Normalized array factor for BPSO and BGA optimized 20 element thinned array at tilt angle 90 0 V. COMPARISON OF PERFORMANCES OF ALGORITHMS Two approaches are considered for side lobe level reduction, one of them is thinned array, dealing with discrete values therefore BGA and BPSO are applied. Another approach is non uniform amplitude weight technique dealing with real value, hence RGA and PSO are applied. Such optimization algorithms are applied in a 20 element and a 100 element linear phased array at different scanning angle with inter-element spacing of 0.3λ and 0.45λ. Performances are compared with respect to maximum side lobe level and respective null-to-null beam width (NNBW) and tabulated for 20 element linear phased array in Table-1. The results for 100 element linear phased array are tabulated in Table-2. Optimization of the cost function requires problem specific value adjustment of different algorithm parameters otherwise cannot score the best result. In this paper MATLAB software is used to program such optimization using Intel i5 processor computer. Table 1: Performance Comparison of 20 and 100 Element Array Synthesis Using BGA, BPSO, RGA, PSO Optimization Algorithm N=20, d=0.3λ Tilted at NNBW SLL max(db) ULA 0 34-13.19 30 46-13.19 60 23-13.20 90 20-13.21 BGA 0 36-16.04 30 49-16.21 60 25-15.87 90 21.5-17.30 BPSO 0 37-15.91 30 49-16.27 60 25-16.46 90 21-17.12 RGA 0 33-16.58 30 48-16.74 45 27-16.58 90 17-19.54 PSO 0 37-18.54 30 49-18.92 45 30-16.74 75 23.5-20.40

216 Algorithm N= 20, d=0.45λ Tilted at NNBW SLL max(db) ULA 0 27-13.21 45 17-13.23 60 15-13.19 90 12-13.21 BGA 0 30-15.92 30 31-15.43 60 20-16.34 75 17-15.53 BPSO 0 30-16.01 45 22-15.88 60 20-16.35 90 16-17.01 RGA 0 31-16.50 30 29-16.09 60 19-16.38 90 12-16.91 PSO 0 31-19.16 45 20-16.76 60 17-18.93 90 14-18.22 Table 2: Performance Comparison of 20 and 100 Element Array Synthesis Using BGA, BPSO, RGA, PSO Optimization Algorithm N=100, d=0.3λ Tilted at NNBW SLL max(db) ULA 0 15-13.21 45 6-13.26 60 4-13.37 90 3.80-14.00 BGA 0 16-16.83 30 9-16.88 60 5.5-16.24 75 4-17.36 BPSO 0 16-15.68 30 9-16.57 60 5-16.02 90 3.9-17.32 RGA 0 16-17.68 45 6-16.35 60 5.5-19.99 90 5-18.91 PSO 0 17-21.50 Algorithm 30 9-19.22 60 5-17.55 90 4-20.88 N=100, d=0.45λ Tilted at NNBW SLL max(db) ULA 0 13-13.72 45 5-13.96 60 4-13.80 90 3.80-14.03 BGA 0 13-15.64 30 6-16.38 60 5-17.02 75 6-17.76 BPSO 0 14-16.85 30 7-16.06 60 6-17.65 90 4-17.32 RGA 0 16-16.42 45 7-20.01 60 7-21.32 90 4-22.57 PSO 0 13-17.78 45 6-20.50 60 5-24.16 90 4-21.96 The chosen value of different algorithm specific parameters for optimization of 20 elements and 100 elements linear phased arrays with interelement spacing of d=0.3λ are given in Table 3. Table 3: Computation specifications of different optimization techniques Algorith m BGA [Popula tion size 100] BPSO [Swarm Size Parameter Crossover = Uniform Mutation rate = 0.15 No. of elements=20 Cognitive & Social parameter C1=1.5, C2=1 Vmax=4 Comp utation Time (sec) 161.13 26.41

217 100] Inertia weight W= 0.5 Normalized function = logsigmoid No. of elements=20 PSO [Swarm Size 100] RGA [Poulati on size 100] BGA [Popula tion size 200] BPSO [Swarm size 200] PSO [Swarm Size 200] RGA [Popula tion size 200] Cognitive & Social parameter C1=1, C2=3 Constriction factor C=1, Iinertia weight W=0 to +1 No. of elements=20 Crossover rate = 0.7 Mutation rate = 0.05 Crossover operator μ=40 Mutation operator η = 10 No. of elements=20 Crossover = Uniform Mutation rate = 0.2 No. of elements=100 Cognitive & Social parameter C1=1, C2= 1 Vmax=4 Inertia weight W= 0.5 Normalized function= logsigmoid No. of elements=100 Cognitive & Social parameter C1=1, C2=3 Constriction factor C=1, Inertia weight W= 0 to +1 No. of elements=100 No. of Iterations=300 Crossover rate = 0.8 Mutation rate =0.1 Crossover operator μ=20 Mutation operator η = 10 No. of elements=100 No. of Iterations=300 135.47 352.35 891.19 72.62 506.44 1188.7 4 Observing the outcome of different optimization it is noticed that more appreciating side lobe level reduction can be achieved by non uniform amplitude weighting technique using real value or inputs. BPSO optimization takes very less time with respect to BGA. PSO is also faster than RGA though PSO produces best result when the program runs for more iterations than number of iterations of RGA. It is also observed that better beamwidth can be achieved by RGA optimized phased array. Side lobe reduction technique presented in [5] using PSO is for linear phased array of 2 to 6 elements. But when the number of antenna elements is large, side lobe reduction becomes difficult. In the present paper, side lobe reduction of large array like 100 element linear antenna array is presented. In [13], side lobe is reduced for non-uniformly spaced linear array. But for non-uniformly spaced array, design of feed network is complex. In the present paper side lobe level is reduced for small and large arrays where antennas are uniformly spaced and feed network design is easier. In [21] different windowing techniques are used where the amplitude and phase of each radiating element are adjusted as per to window profile. This is realized by setting the size and position of the antenna elements. The method is complex for simulation and also for practical implementation compared to the proposed method used in this paper. VI. DISCUSSION AND CONCLUSION GA inherently designed for binary variables whereas PSO inherently designed for real valued variables. In case of BGA first the input variables are changed into binary variables and later crossover and mutation processes modify the algorithm using binary pattern. BPSO convert the input binary variables into analogue values of velocity and position modification like PSO, in addition with the normalization function for binary transform. In BPSO, maximum velocity or velocity clamping and the inertia weight values differ from PSO. In PSO large value of maximum velocity is good for exploration of large area. In BPSO small value of maximum velocity creates good exploration, if, the maximum velocity is zero then the algorithm provides pure random search. In array thinning problem, it is observed that BPSO has higher

218 computational speed than BGA though BGA has more flexibility and easy to implement with respect to BPSO. On the contrary RGA implementation is difficult, here crossover and mutation generally not same as BGA, that gives a scope of experiment with these operators for better performance. PSO is easy to implement, as it requires only modification of velocity and position, therefore, less complexity. PSO can also work with the out of the range variables, but it was noticed in RGA when the initial population is going beyond the range, RGA becomes very sensitive, also this algorithm requires adjustment of different operator or parameter values when the initial population or the number of array elements changes. When all the conditions are satisfied, RGA needs less iteration to reach the optimum value and provide best beam shaping in addition with reduced side lobe. PSO has no evolutionary operator and no complex updating calculation, therefore, it is very fast with respect to RGA and it is less sensitive to out of the range inputs. REFERENCES [1] C. A. Balanis, Antenna Theory Analysis and Design, 2nd Edition, John Willy & Sons, New York, 1997. [2] R. S. Elliott, Antenna Theory and Design, John Wiley, New Jersey, 2003. [3] R. J. Mailloux, Phased array theory and technology, Proceedings of the IEEE, Vol. 70, no. 3, pp. 246-291, March 1982. [4] R. C. Hansen, Phased Arrays Antennas, 2nd Edition, John Willy & Sons, New Jersy,2009. [5] P.J. Bevelacqua and C. A. Balanis, Minimum sidelobe levels for linear arrays, IEEE Transactions on Antennas and Propagation, Vol. 55, no. 12, pp. 3442-3449, December 2007. [6] R. L. Haupt, Thinned arrays using genetic algorithms, IEEE Transactions on Antennas and Propagation, Vol. 42, no. 7, pp. 993 999, July 1994. [7] M. Fernández-Delgado, J. A. Rodríguez-González, R. Iglesias, S. Barro and F. J. Ares-Pena, Fast array thinning using global optimization methods, Journal of Electromagnetic Waves and Applications, Vol. 24, pp. 2259 2271, December 2010. [8] M. G. Bray, D. H. Werner, Daniel W. Boeringer and D. W. Machuga, Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning, IEEE Transactions on Antennas and Propagation, Vol. 50, no. 12, pp. 1732-1782, December 2002. [9] R. L. Haupt, Adaptively thinned arrays, IEEE Transactions on Antennas and Propagation, Vol. 63, no. 4, pp. 1626-1633, April 2015. [10] G. Olivieri, L. Manica and A. Massa, Linear array thinning exploiting almost difference sets, IEEE Transaction on Antennas Propagation, Vol. 57, no. 12, pp. 3800 3812, December 2009. [11] W.B. Wang, Q.Y. Feng and D. Liu, Synthesis of thinned linear and planar antenna arrays using binary PSO Algorithm, Progress In Electromagnetic Research, Vol. 127, pp. 371-387, April 2012. [12] D. Cao, A. Modiri, G. Sureka and K. Kiasaleh, DSP implementation of the particle swarm and genetic algorithms for real-time design of thinned array antennas, IEEE Antennas and Wireless Propagation Letters, Vol. 11, pp. 1170-1173, October 2012. [13] A. Recioui, Sidelobe level reduction in linear array pattern synthesis using particle swarm optimization, Journal of Optimization Theory and Applications, Springer, Vol. 153, no. 2, pp. 497-512, November 2011. [14] G. K. Mahanti, N. Pathak, and P. Mahanti, Synthesis of thinned linear antenna arrays with fixed sidelobe level using real-coded genetic algorithm, Progress in Electromagnetics Research, PIER 75, pp. 319 328, 2007. [15] O. Quevedo-Teruel and E. Rajo-Iglesias, Ant colony optimization in thinned array synthesis with minimum sidelobe level, IEEE Antennas and Wireless Propagation Letters, Vol. 5, no. 1, pp. 349-352, December 2006. [16] A. Zangene, H. R. D. Oskouei and M. Nourhoseini, Reduction of side lobe level in non-uniform circular antenna arrays using the simulated annealing algorithm, Journal of Electrical and Electronics Engineering Research, Vol. 6, no. 2, pp. 6-12, August 2014. [17] K. Deb and A. Kumar, Real-coded genetic algorithm with simulated binary crossover: Studies on multimodal and multiobjective problems, Complex Systems, Vol. 9, pp. 431-454, January 1995. [18] J. Kennedy and R. Eberhart, Particle swarm optimization, Proceedings of the IEEE International Conference on Neural Networks, Vol. IV, pp. 1942 1948, December 1995. [19] D. E. Goldberg, Genetic Algorithms, Addison- Wesley, Boston 1989. [20] R. L. Haupt, An introduction to genetic algorithms for electromagnetics, IEEE Antennas and Propagation Magazine, Vol. 37, pp. 7-15, April 1995. [21] M. R. Sarkar, M. M. Islam, M. T. Alam and M. H. Haider, Side lobe level reduction in antenna array using weighting function, International Conference ICEEICT, IEEE Xplore, pp. 1-5, April 2014.