Antenna array synthesis with clusters of unmanned aerial vehicles

In this paper, we investigate the use of formations of unmanned aerial vehicles (UAVs) as phased antenna arrays. This will help improve communications with clusters of small unmanned aerial vehicles which are currently constrained by on-board power limitations. The problem of maximizing the power output from the array in the direction of the receiver is posed as an optimization problem which happens to be non-convex; a relaxation of this problem is then solved as a computationally tractable (convex) second order conic program (SOCP). The performance obtained by the simplified approach is then tested against rigorous numerical bounds obtained using semidefinite programming (SDP) duality theory; these bounds are of independent interest in antenna theory. In order to maintain the objective value close to the optimal when the vehicles deviate from their positions (due to wind gusts, for example), a linear control law is proposed. Simulation results are given to show the effectiveness of the proposed approaches.