Design of a Linear Antenna Array: Variable Number of Dimensions Approach

A linear antenna array design is usually formulated as a binary optimization task. A global optimization algorithm is then used to turn on/off a fixed number of elements positioned on a uniform grid. This paper introduces a new formulation of the problem: the optimizer searches for distances between individual elements and their total amount at the same time. Such a formulation has to be solved using the optimization with a variable number of dimensions that enables to work with decision space vectors having different lengths. Here, the Particle Swarm Optimization algorithm is used to solve different formulations of the linear antenna array design problem. The “uniform grid” formulation is compared with the “variable number of dimensions” formulation on several optimization tasks encompassing the minimization of selected antenna parameters: the Side-Lobe Level, the First Null Beam Width and the number of used (active) elements.