Generalized Closed-Form Sidebands’ Radiation Expressions for 4-D Antenna Arrays

In this communication, a closed-form formulation for calculating the radiated power at sidebands of four-dimensional (4-D) antenna arrays using a generalized element pattern of type (sin θ)u| cosθ|^u is derived. All the expressions exist when the exponents u, u lie in the region: u > -1 and u > -1/2. Compared with numerical integration, the proposed expression uses less computational resources and time. Examples show the efficiency and accuracy of proposed expression.