Spectrum Anti-Jamming Waveform Design with Good Correlation

To design a spectrum anti-jamming waveform with good correlation, this paper directly minimizes the spectral power within the jamming band and auto-correlation function (ACF) sidelobe level, rather than imposing additional user-defined constraints on spectral notch depth or ACF sidelobe level. Several weighting factors are introduced to balance the trade-off between spectrum anti-jamming and correlation. The problem is formulated as a quartic optimization problem with nonconvex, nonlinear unimodular constraint, and is solved using a majorization-minimization (MM) framework. This approach relaxes the original quartic formulation into the simplified linear expression. An acceleration scheme is also integrated into the proposed algorithm to improve convergence speed. Furthermore, for scenarios involving multiple jamming bands, individual weight factors are employed to flexibly adjust the relative suppression levels across different notches. Simulation results demonstrate that the proposed algorithm achieves both effective spectrum anti-jamming (deep notches in jamming bands) and favorable correlation performance (low ACF sidelobe levels).