Codesign of Unimodular Waveform and Receive Filter for MIMO Radar Extended Target Detection Under Suppression Jamming

The joint design of unimodular waveforms and receive filters is a pivotal technology in Multiple-Input Multiple-Output (MIMO) radar systems. However, most existing methods primarily focus on point target detection or ignore the impact of active jamming in extended target scenarios. To bridge this gap, this paper proposes an optimization framework for the joint design of unimodular waveforms and receive filters specifically for MIMO radar extended target detection in the presence of suppressive jamming. The problem is formulated to maximize the Signal-to-Interference-plus-Noise Ratio (SINR) while strictly satisfying the unimodular constraint and mitigating suppressive jamming. Due to the non-convexity of the unimodular constraint and the quadratic fractional nature of the SINR objective function, the optimization problem is highly challenging. Unlike conventional methods that rely on convex relaxation—which often leads to performance degradation—we exploit the geometric structure of the constraint set. Specifically, the unimodular constraints are modeled using complex circle manifolds, and the suppressive jamming suppression requirements are integrated into the objective function via a smooth penalty metric. Building on these characteristics, a Product Complex Circle Euclidean Manifold (PCCEM) method is developed. This approach transforms the constrained problem into an unconstrained optimization task on a product manifold, which is then efficiently solved using the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm. Simulation results demonstrate that the proposed PCCEM method outperforms baseline algorithms in terms of computational efficiency, output SINR, and the depth of the formed jamming notches.