Maximin Design of Wideband Constant Modulus Waveform for Distributed Precision Jamming

Distributed precision jamming (DPJ) is an efficient way to control the combined power spectrum (CPS) of both target and friendly devices in electronic warfare. However, the existing methods neglect the design of worst-case CPS performance, and a great challenge is posed in determining an appropriate Pareto parameter to protect the friendly devices in practice. To address these issues, this paper investigates the maximin design of wideband constant modulus (CM) waveform for DPJ. Specifically, a novel optimization problem is established by maximizing the minimum CPS of the target equipment, and the maximum CPS of friendly devices is controlled under a given threshold in the constraint. The resultant problem is nonconvex and nonsmooth, together with CM and numerous quadratic constraints. Two algorithms, which can start from an infeasible initial point, are proposed to tackle the problem approximated by the
$l_{p}$
-norm. The first algorithm resorts to the alternating direction method of multipliers (ADMM) framework, and each subproblem is obtained with a closed-form solution. The second algorithm merges the penalty distance (PD) method and manifold optimization. The crux of this approach is to obtain the closed-form Euclidean PD term via the Karush-Kuhn-Tucker conditions and leverage the Riemannian conjugate gradient (RCG) framework, and we name this algorithm PD-RCG. Numerical examples demonstrate the effectiveness of our proposed algorithms. Comparatively speaking, the ADMM-based algorithm has better performance in protecting the friendly devices, while the PD-RCG algorithm performs better on the computational efficiency and the worst-case CPS of the target equipment.