Robust Wideband Constant Modulus Waveform Design for Distributed Precision Jamming Under Imperfectly Calibrated UAVs

The distributed precision jamming (DPJ) system consists of multiple distributed Unmanned Aerial Vehicles (UAVs) and exhibits efficient blanket jamming performance in electronic warfare. However, the existing waveform design methods only consider the imprecise prior knowledge of the target but neglect the imperfect calibration of UAVs, which leads to a sharp decrease in the DPJ performance in practice. This paper designs a robust wideband constant modulus waveform against both the imprecise prior knowledge of targets and the imperfect calibrations of UAVs, and the spectral constraints are also attached for the protection of friendly devices. Specifically, we take the localization errors of UAVs as examples and characterize them as uncertain steering vectors, which can be extended to account for other nonidealities in the distributed platforms. Then, we maximize the worst combined power spectrum of opponent equipment over all the spatial-frequency points and the uncertain steering vector sets. For the challenging max-min-min problem, we utilize the Karush-Kuhn-Tucker conditions to tackle the second inner minimization and obtain the closed-form solution of the worst uncertain steering vector. The original problem is transformed equivalently into a maximin problem with a piece-wise but differential objective function. The resultant maximin problem is tackled efficiently by merging the alternating direction method of multipliers and the Riemannian conjugate gradient algorithm. Numerical examples demonstrate that our design outperforms the existing methods in the robustness against the localization errors of UAVs.