Directivity Optimization in Omnidirectional Volumetric Antenna Arrays

Directivity pattern is a paramount performance measure in antenna array configurations. Applications such as heterogeneous MIMO wireless cellular communication can greatly benefit in exploring antenna directivity improvement. The problem of directivity optimization, which leads to a highly increasing in directivity gain on a certain desired angle of arrive/departure (AoA/AoD), is considered in this work. A new formulation on the volumetric array directivity problem is proposed using the rectangular coordinates to describe each antenna element, and the desired angle in spherical coordinates (θ
₀
, φ
₀
), with a general element pattern given by sin
^u
θ cos
^v
θ. To solve the associated optimization problem, the omnidirectional (cos θ) configuration was selected; besides, generalized scenarios, i.e ∀u, v ≠ 0, can easily be considered deploying a similar formulation. A well-defined genetic algorithm (GA) was selected to expeditiously solve the resultant non-convex optimization problem. Numerical results comparing achieved directivity for N=6,7 and 8 antenna-elements demonstrate gains of ~ 5 dB compared to the regular beamforming technique, using steering vector for uniform linear arrays (ULA) and uniform circular arrays (UCA).