Co-design of Constant Modulus Waveform and Receive Filters for Polarimetric Radar

The joint design of waveforms and filters has key applications in polarimetric radar target detection. This paper studies the joint design of waveforms and filters to maximize the signal-to-interference-to-noise ratio (SINR) of polarimetric radar, which is a non-convex and NP-hard problem. Most existing works solve it based on matrix inversion and problem relaxation, which inevitably introduce high complexity and relaxation errors. We notice that a unified manifold space naturally satisfies the constant modulus constraint (CMC) and the norm constraint. Based on this characteristic, we proposed a parallel manifold joint optimization (PMJO) method to solve it without relaxing the objective function. Specifically, the unified product manifold is constructed to satisfy both waveform and filter constraints. Subsequently, the problem is transformed into an unconstrained one by projecting it onto the product manifold space. Finally, a parallel conjugate gradient method is proposed to simultaneously optimize waveforms and filters, which can adaptively adjust the step size and fully explore the product manifold space. Simulation results show that our method can obtain a 2dB performance advantage compared to existing methods, while having a half order of magnitude advantage in time complexity.