Doppler resilient complementary sequence set design via a model driven deep learning method

Doppler-resilient complementary sequence set (CSS) design is a key technology in radar systems, characterized by its inherently non-convex bivariate nature with multiple complex constraints. Existing methods mainly solve it through relaxation, which inevitably introduces relaxation errors. It is worth noting that the multi-constraint formulation can be transformed into an unconstrained optimization through projection onto a unified constraint space (UCS). Within this UCS, the bivariate problem becomes directly tractable via parallel gradient computation, while the original objective function naturally serves as a loss function for training a deep learning network. Motivated by above points, a relaxation-free parallel gradient projection network (PGPN) method is proposed. The proposed PGPN method begins by constructing a UCS that incorporates all constraints, effectively reframing the problem as an unconstrained optimization. A parallel gradient projection (PGP) algorithm is then derived to compute the bivariate gradients efficiently. This PGP algorithm is subsequently unfolded into network layers, with the objective function repurposed as the network’s loss function and adaptive step size updates enabling parallel optimization. The key innovation of this research is that unifying constrained waveform-filter optimization via a constraint-to-unconstrained transformation, parallel gradient-based joint optimization, and deep learning-embedded adaptive tuning, enabling high-fidelity waveform design in dynamic electromagnetic environments. Simulation results show that the signal-to-interference ratio (SIR) of the proposed method achieves better Doppler resilience compared to L-BFGS [18], MMCSR [21], and GP [27], while also enabling better control of the signal-to-noise ratio loss (SNRL).