Radar is utilized as an active sensing device across many fields. Its waveform optimization is responsible for target signature extraction, profoundly influencing the overall performance. First, the principle of pulse radar waveform design is explored. Waveform design strategies vary based on target models, whether point-like or extended ones, and are often formulated as high-dimensional, non-convex optimization problems with multiple constraints, such as energy, constant modulus, and sidelobe ratios. Second, to address them, techniques like alternating direction method of multipliers (ADMM), semidefinite relaxation (SDR), and minimization-maximization (MM) algorithms are widely employed. Finally, challenges in multimodal sensing collaborative detection, joint multi-tasking, sparse signal recovery, and intelligent perception highlight the need for innovative solutions to meet future demands.

To enhance the signature of an extended target in a SAR image, a robust waveform design method is presented for spectrally dense environments. First, the problem is formulated by maximizing the worst-case signal-to-clutter ratio (SCR) over the uncertainty set of statistics for both target and background scattering characteristics, subject to energy, similarity, and spectrum constraints. Second, the closed-form solutions for the uncertain statistics are derived. The problem of maximizing worst-case SCR is boiled down to a nonconvex fractional quadratically constrained quadratic problem (QCQP). Resorting to the Dinkelbach’s algorithm and Lagrange duality, the QCQP is split into a series of solvable semidefinite programming problems. A convergence analysis is conducted, where a sufficient condition for global convergence is derived. Finally, numerical examples are presented to demonstrate the performance of the proposed scheme.