Guaranteed Deep Learning for Reliable Radar Signal Processing

Recently, there has been a significant level of attention paid to the application of deep learning in radar signal processing. Despite its flexibility, deep learning imposes new challenges in guaranteeing the performance of signal processing systems and in establishing trust with regard to their outcome. This represents a critical bottleneck in the application of deep learning in radar signal processing, where having trust in radar inferences is crucial. In this work, we present a novel implicit deep learning model for learning fast and highly-scalable solvers for a general family of optimization problems commonly encountered in the radar signal processing area, encompassing applications in waveform design and target parameter estimation. Specifically, the proposed methodology is based on generalizing the feed-forward neural networks by introducing implicit layers derived from the dynamics of a fixed-point geometric series. Unlike its black-box data-driven counterparts, the implicit and model-based nature of the proposed neural solver significantly reduces the parameters of the network and implementation cost, and most importantly, makes the network amenable to robustness analysis, as well as deriving performance guarantees/bounds on the output of the model. This presents considerable potential for the adoption of our proposed models in radar applications, be it in the classical settings or emerging applications in autonomous vehicles and automotive radar where a large number of reliable radars are projected to be on the road in the near future.