A Generalized Array Factor for Time-Modulated Hexagonal Based Antenna Array Geometry with Novel Trapezoidal Switching

The concept of the time-modulated array has been emerging as an alternative to the complex phase shifters, which lowers the cost of the array feeding network due to the utilization of radio frequency (RF) switches. The various forms of hexagonal antenna array geometries can be used for applications like surveillance tracking in phased array radar and wireless communication systems. This work proposes the generalized array factor (AF) for the hexagonal antenna array geometry based on time modulation. The time modulation in generalized hexagonal geometry can maintain the fixed static amplitude excitation, giving more flexibility over time. Furthermore, a novel trapezoidal switching function is also proposed and applied to the generalized array factor to enable future researchers to use this array factor in the field of advancement to observe how switching schemes like trapezoidal and rectangular affect the array pattern's side lobe level (SLL). The generalized equation can be utilized for the analysis and synthesis of radiation characteristics of the time-modulated hexagonal array (TMHA), time-modulated concentric hexagonal array (TMCHA), time-modulated hexagonal cylindrical array (TMHCA), and time-modulated hexagonal concentric cylindrical array (TMHCCA). The numerical result illustrates the generation of AF of time-modulated hexagonal structures and also shows that the trapezoidal switching sequence outperforms the rectangular switch using the cat swarm optimization (CSO) approach.