# Optimal Design of Aperiodic Reconfigurable Antenna Array Suitable for Broadcasting Applications
## 1 Introduction
The firefly algorithm and particle swarm optimization (PSO) have been employed in Reference [11] to design a uniplanar printed triple band-rejected ultra-wideband antenna. An improved PSO algorithm has been used in Reference [12] to design an aperiodic antenna array with low SLL, minimum half power beamwidth (HPBW) and nulls in desired directions. Finally, the state-of-the-art parallel surrogate model-assisted evolutionary algorithm has been employed in References [13; 14]. Since References [7; 12] concern aperiodic arrays and are relevant to our paper additional discussion will be made. In Reference [7], one of the optimizations presented, concerns the design of a low \(SLL\) 8-element aperiodic array. Only 4 parameters are optimized, specifically the spacing between the array elements and the optimization has 2 objectives, low \(SLL\) and low null-to-null beamwidth. The radiation pattern is calculated on a theoretical basis by expressing it as the product of the array factor and the element pattern without taking into account the mutual coupling. However, the element spacing values are allowed to take large values (greater than two times the wavelength) in order to mitigate the mutual coupling. The simulated and fabricated antenna show an \(SLL<\)\(-10\) dB but it is only shown for \(\theta=0^{\circ}\) to \(\theta=180^{\circ}\), thus, without information on the backlobes. There is also no information about the \(SWR\). In Reference [12], as mentioned earlier, an improved PSO variant is used to achieve low \(SLL\), minimum HPBW and placement of nulls in desired directions. The optimization parameters consist of the element spacings and the feeding weights (only amplitudes). The radiation pattern is expressed as the array factor, thus, not taking into account the element pattern and the mutual coupling making the results very theoretical. The radiation patterns are shown for \(\theta=0^{\circ}\) to \(\theta=180^{\circ}\), and therefore, it is assumed that the \(SLL\) was only optimized in this sector. Also, there is no information on the \(SWR\). In this paper, the preferred optimizer is an improved (PSO) [15] algorithm that induces mutation to the particles' velocities that did not improve their fitness value in the previous iteration (PSOvm) [16]. The idea behind this method is to help the particles that failed to improve their fitness value in the previous iteration, decouple from their previous velocity which actually did not lead to a fitness improvement. Thus, a perturbation is applied on their previous velocity and by doing so it is expected to help the swarm achieve better exploration and escape when being trapped to a local optimum position. The method has been proved to be very competitive against other well known optimization methods [16] and can handle effectively multi-variable and multi-objective problems as is the case of this paper (the problem consists of 26 optimization parameters and 13 objectives which will be demonstrated in later sections). PSOvm has been implemented in Matlab environment [17]. The AMAA has been fully modelled and simulated in CST Studio Suite (CST from now on) and therefore, the mutual coupling and the element pattern of each array element is considered since full wave analysis is performed. This is really important as it makes the results quite realistic. For each fitness evaluation the antenna array model is updated and a full wave analysis is performed by applying the time domain solver of CST. This solver uses the finite integration technique [18] to solve the electromagnetic problem. Therefore, at each fitness evaluation, the AMAA geometry parameters are updated and the solver simulates the updated model by calling CST built-in visual basic scripts inside the Matlab environment. It is evident that each fitness evaluation is costly in terms of resources and time but the results are highly accurate. In Figure 1 the flowchart of the optimization procedure is depicted.