GA-aided directivity in volumetric and planar massive-antenna array design

Abstract

The problem of directivity enhancement, leading to the increasing in the directivity gain over 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 azimuth and elevation angles with a general element pattern. Such directivity problem is formulated to find the optimal minimum distance between the antenna-elements dmin aiming to achieve as high directivity gains as possible. An expedite implementation method is developed consisting in placing the antenna-elements in a distinctive plane dependent on (θ0; ϕ0). A novel concept on the optimizing directivity for the uniform planar array (OUPA) is introduced to find a quasi-optimal solution for the non-convex optimization problem with low-complexity. This solution is reached deploying the proposed successive evaluation and validation (SEV) method. Moreover, the genetic algorithm (GA) method was deployed to expeditiously find the directivity optimization solution. For a small number of antenna-elements, typically N∈[4,⋯,9], the achievable directivity by GA optimization demonstrates gains of ∼3 dBi compared with the regular beamforming technique, using steering vector for uniform linear arrays (ULA) and uniform circular arrays (UCA), while gains of ∼1.5 dBi is attained when compared with an improved UCA directivity method. For a larger number of antenna-elements, two improved GA procedures, namely GA-marginal and GA-stall, were proposed and compared with OUPA method. OUPA also indicates a promising directivity gains surpassing 30 dBi for massive MIMO scenarios.