Self-Organized Drone Swarm Waveform and Array Design for DOA Estimation

In this paper, we focus on the problem of joint waveform and array design for direction-of-arrival (DOA) estimation using self-organized unmanned aerial vehicle (UAV) swarm. Exploiting the Cramér-Rao lower bound (CRLB) as the performance metric, we formulate two waveform and array design models. The first applies the minimax criterion to minimize the maximal flight distance for battery saving, while the second maximizes the minimal pair-wise separation (MPS) between the UAV flight traces for collision avoidance. To handle the nonconvex and nonlinear fractional CRLB constraints, we derive two special parametric quadratic matrices with one positive eigenvalue and three non-positive eigenvalues, where each of them is represented as the difference of two positive semidefinite matrices, to convert them into equivalent convex forms. The parametric maximum block improvement method is then developed to tackle the high-order polynomial optimization subproblem with inhomogeneous waveform and antenna position variables encountered in the two models. Especially in the MPS formulation, which cannot be explicitly expressed, we analyze the corresponding Karush-Kuhn-Tucker conditions of the MPS Lagrangian from nine cases to transform it as a solvable and closed-form constraint set. Numerical results demonstrate the excellent performance of our solutions.