Spectrally compatible MIMO radar waveform design for extended target detection

Abstract

Spectrally compatible MIMO radar waveform design is crucial for extended target detection. Existing methods either maximize the worst-case SINR within target aspect angles (TAAs) while ignoring spectral compatibility, or consider spectral compatibility by maximizing the average SINR, but the worst-case SINR performance may not be ensured. Different from above, under constant modulus (CM) and inequality spectral constraints, we maximize the worst-case SINR within the target aspect angles(TAAs) to satisfy the robustness requirement, while the spectral constraints ensure spectral compatibility by limiting the energy spectral density(ESD) below the predefined threshold. This problem is challenging due to the non-smoothness of max–min design and multiple inequality constraints. Noting that exact penalty terms are suitable for solving inequality constraints, and CM constraints satisfying the complex-circle manifold, we propose the Max-Min-Exact Penalized Product Manifold (MM-E${\text{P}}^2$M) method. First, auxiliary variables are used to address the non-smoothness of max–min design, transforming it into a minimization problem. Next, exact penalty terms are constructed to remove inequality constraints, and the problem is then projected onto the Product-Complex-Circle-Euclidean Manifold (P${\text{C}}^2$EM), thus transforming it into an unconstrained problem. Finally, the parallel simplified quasi-Newton (PSQN) method is divided. The dataset obtained by illuminating a T-72 tank is used to validate the performance. Simulation results demonstrate that the proposed method has following advantages: (i) improves SINR by at least 4.49 dB while controlling energy spectral density exactly; (ii) provides SINR performance that meets requirements for each angle within TAAs.