MIMO Radar Spectrally Compatible Waveform Design via Inequality Constrained Manifold Optimization

This paper tackles the challenge of designing nonconvex unimodular waveforms under spectral constraints to minimize the spatial Integrated Sidelobe Level Ratio (ISLR) in Multiple Input Multiple Output (MIMO) radar systems. While existing methods primarily rely on the Semidefinite Programming (SDP) framework with prohibitive computational cost or the Alternating Directions Method of Multipliers (ADMM) by relaxing the unimodular constraint or objective function, leading to non-strict unimodular waveforms or performance degradation. We observe that the complex circle manifold (CCM) inherently satisfies the unimodular constraint, and using a non-negative smooth function better adheres to the shape of spectral inequality constraints. Leveraging these insights, we propose the Adaptive Smooth Penalty-Inequality Constrained Manifold Optimization (ASP-ICMO) framework. ASP-ICMO directly addresses the problem without relaxing the objective function, while adaptively adjusting the penalty factor. Our approach combines direct problem solving on manifold space with adaptive penalty factor updates, facilitating quicker convergence compared to the ADMM method, which sequentially solves multiple subproblems with a fixed penalty factor. Furthermore, ASP-ICMO ensures that the Karush-Kuhn-Tucker (KKT) conditions for the converged solution are satisfied. Simulation results demonstrate that the proposed method achieves superior comprehensive system performance with reduced computational cost compared to existing methods.