# Optimal Design of Aperiodic Reconfigurable Antenna Array Suitable for Broadcasting Applications
## 1 Introduction  
Microstrip antenna arrays are very popular as they are low cost and easily fabricated antennas, and therefore can be used as base station antennas for broadcasting. Base station antennas must satisfy multiple requirements, which are essential in broadcasting applications [1; 2; 3; 4; 5; 6]. Such requirements are: (i) high forward gain (\(FG\)) in order to enhance reception at long distances, (ii) main lobe tilting, as the base station is usually located at places of higher altitude than the service area, (iii) null filling inside an angular sector under the main lobe, as the directional gain must stay above a specific value for proper reception, (iv) low sidelobe level (\(SLL\)) so power is not wasted outside the service area, and finally (v) low standing wave ratio (\(SWR\)) so power is not wasted inside the feeding network. In this paper, an eight-element aperiodic microstrip antenna array (AMAA) has been designed to satisfy all the above requirements at 698 MHz (center frequency of DVB-T channel 49) and more specifically to exhibit the following characteristics:1. maximum possible \(FG\) at \(\theta=93^{\circ}\) (\(\theta\) is the elevation angle),
2. null level \(\geq\)\(-20\) dB with respect to the main lobe peak inside the service area defined from \(\theta=93^{\circ}\) to \(\theta=143^{\circ}\) (a \(50^{\circ}\) service area),
3. \(SL\leq\)\(-20\) dB with respect to the main lobe peak outside the service area,
4. \(SWR\leq\)1.2 (S-parameters \(\leq\)\(-21\) dB) at the inputs of all the array elements. The first three requirements imply a significant degradation in the directional gain when passing from the service area to the area where no service is provided. Due to this rapid gain degradation, a transition area is necessary between the previous two areas. Therefore, two transition areas, from \(\theta=80^{\circ}\) to \(\theta=93^{\circ}\) and from \(\theta=143^{\circ}\) to \(\theta=150^{\circ}\), are defined where the gain will transition from high to low values. Consequently the 3 rd requirement must be defined in two angular sectors, the first one ranging from \(\theta=0^{\circ}\) to \(\theta=80^{\circ}\) (sector above the main lobe) and the second one from \(\theta=150^{\circ}\) to \(\theta=360^{\circ}\). The fourth requirement also helps at enhancing the bandwidth of the antenna by requesting a very low \(SWR\) value at the channel center frequency. To satisfy all the above requirements, an AMAA with proper geometry dimensions must be found together with eight appropriate feeding weights (amplitudes and phases). The main lobe tilting is achieved by calculating the proper feeding weights and not mechanically. This is important as the array has big height, since the design frequency is 698 MHz, and it alleviates the mechanical pressure that stresses the whole structure. It is evident that this is a complex multi-variable and multi-objective problem, and such problems can be efficiently solved by using evolutionary optimization algorithms. Furthermore, the antenna studied in this paper can be turned to a reconfigurable one by implementing on-off switches with pin diodes in the feeding network in order to create different feeding weight sets and thus produce different shapes of radiation patterns that provide the desired values of gain, main lobe tilting, null filling and \(SLL\). Many papers can be found in the literature where different optimization algorithms have been successfully employed to optimize antenna arrays. In Reference [7] three different PSO variants, real-number PSO, binary PSO and multi-objective PSO, are applied to different designs to obtain an optimal solution. The genetic algorithm has been employed in Reference [8] to optimize a quadrifilar helical-spiral antenna for GPS application. In Reference [9] quasi-Newton optimization has been used to design optimal implantable antennas for medical telemetry. Evolutionary techniques combined with machine learning can be found in Reference [10].