Amplitude-Only Null Positioning in Circular Arrays Using Genetic Algorithm V.V.S.S.Sameer Chakravarthy Dept of ECE, Raghu Institute of Technology Visakhapatnam, AP, India sameersree@gmail.com P.Mallikarjuna Rao Dept of ECE, AUCE(A), Andhra University Visakhapatnam, AP, India Abstract—Null positioning and beam steering are the basic building blocks of Beamforming. Nulls in the radiation pattern of a radiating element are characterized by minimum radiation in the direction of its position. They suppress any radiation received in its direction. Some traditional numerical and computational intelligent heuristic techniques are proposed to position and steer nulls. In this paper simple Genetic Algorithm is used to position the nulls in the desired locations in the radiation pattern of a circular array. Nulls with predefined null depths are obtained with and without side lobe level (SLL) constraint. The convergence plots have shown the impact of the SLL constraint on the convergence. Keywords— Null positioning, circular array, genetic algorithm, side lobe level, computational intelligence I. INTRODUCTION Beamforming involves in accepting desired signal and rejected any undesired signal. In order to accept the desired signal the main beam of the antenna array is steered towards the direction of the angle of arrival (AOA) of the desired signal. The undesired signals are rejected by placing nulls in the AOA of interference signals. Numerical techniques like schelkunoff [1] are employed to design antenna array with desired nulls. Later computational intelligent techniques like evolutionary and heuristic approaches [2] are adopted in array synthesis as the traditional numerical techniques have the most possibility of getting trapped in the local minima. In addition to this they show their inability in handling multimodal problems. Amplitude, Phase and Spacing between the elements are the three steering parameters for an antenna array. Evolutionary optimization methods are used to generate radiation pattern with predefined nulls by controlling complex weights in linear arrays [3,4]. Similarly amplitude only [5,6], phase only [7,8] and spacing only [9-11] array synthesis using evolutionary and heuristic algorithms have also reported good results in obtaining desired nulls and optimised SLL. In this paper circular array is considered as they have become more popular since they have used in mobile communications. Determining suitable weights for the amplitudes of the current distribution for each element in the circular array that produces desired pattern with desired nulls is the aim of this paper. In this regard the entire work is divided into two objectives. Achieving nulls in the desired position is the first objective where as the other objective is to maintain the predefined SLL while observing nulls in the desired direction. The two objectives are further classified into 4 cases. In case 1&2, both the objectives are observed under the condition that the main beam is positioned at 0 0 . Where as in case 3&4 the main beam is steered towards an angle of 25 0 . For the all the cases the corresponding radiation pattern plots and their convergence plots are given. The genetic algorithm incorporated here is simple GA [2] with standard population size varying between 40 to 60 and with a mutation rate is 0.15. The rest of the paper is organised into 5 sections. Section II describes the simple Real coded GA and its implementation to the current synthesis problem. The formulation of the circular array and fitness function are described in Section III & Section IV. Results pertaining to the work are presented in Section V in which a case wise splitting of the problem and the description are given. II. GENETIC ALGORITHM A simple GA is characterized by initial population, selection, cross over, mutation, survival and fitness evaluation. A. Initial population Initial population is the set of chromosomes generated randomly, where each chromosome represents an individual or an array with specific radiation pattern. The type of GA considered here is real coded GA (RCGA) where the genes are real valued number unlike conventional binary GA (BGA). The construction of the chromosome and the gene are given below [12]. Chrom= [C 1 C 2 C 3 …………. C n ] C= [G 1 G 2 G 3 … …..G N ] where, 'n' is number of chromosomes constituting population 'N' is number of genes in a chromosome B. Cross over and Mutation The type of crossover considered here is different from that adopted usually in BGA. If P1 and P2 are two parents