Robust wideband waveform design with constant modulus and discrete phase constraints for distributed precision jamming

Distributed precision jamming (DPJ) is a novel blanket jamming concept in electronic warfare, which delivers the jamming resource to the opponent equipment precisely and ensures that friendly devices are not affected. Robust jamming performance and low hardware burden on the jammers are crucial for practical DPJ implementation. To achieve these goals, we study the robust design of wideband constant modulus (CM) discrete phase waveform for DPJ, where the worst-case combined power spectrum (CPS) of both the opponent and friendly devices is considered in the objective function, and the CM discrete phase constraints are used to design the wideband waveform. Specifically, the resultant mathematical model is a large-scale minimax multi-objective optimization problem (MOP) with CM and discrete phase constraints. To tackle the challenging MOP, we transform it into a single-objective minimization problem using the Lp-norm and Pareto framework. For the approximation problem, we propose the Riemannian conjugate gradient for CM discrete phase constraints (RCG-CMDPC) algorithm with low computational complexity, which leverages the complex circle manifold and a projection method to satisfy the CM discrete phase constraints within the RCG framework. Numerical examples demonstrate the superior robust DPJ effectiveness and computational efficiency compared to other competing algorithms.