The ambiguity function is fundamental to radar waveform design, characterizing range and Doppler resolution capabilities. However, its traditional formulation involves non-differentiable operations, preventing integration with gradient-based optimization methods and modern machine learning frameworks. This paper presents the first complete mathematical framework and computational implementation for differentiable radar ambiguity functions. Our approach addresses the fundamental technical challenges that have prevented the radar community from leveraging automatic differentiation: proper handling of complex-valued gradients using Wirtinger calculus, efficient computation through parallelized FFT operations, numerical stability throughout cascaded operations, and composability with arbitrary differentiable operations. We term this approach GRAF (Gradient-based Radar Ambiguity Functions), which reformulates the ambiguity function computation to maintain mathematical equivalence while enabling gradient flow through the entire pipeline. The resulting implementation provides a general-purpose differentiable ambiguity function compatible with modern automatic differentiation frameworks, enabling new research directions including neural network-based waveform generation with ambiguity constraints, end-to-end optimization of radar systems, and integration of classical radar theory with modern deep learning. We provide complete implementation details and demonstrate computational efficiency suitable for practical applications. This work establishes the mathematical and computational foundation for applying modern machine learning techniques to radar waveform design, bridging classical radar signal processing with automatic differentiation frameworks.

We propose a novel, learning-based method for adaptively generating low probability of detection (LPD) radar waveforms that blend into their operating environment. Our waveforms are designed to follow a distribution that is indistinguishable from the ambient radio frequency (RF) background -- while still being effective at ranging and sensing. To do so, we use an unsupervised, adversarial learning framework; our generator network produces waveforms designed to confuse a critic network, which is optimized to differentiate generated waveforms from the background. To ensure our generated waveforms are still effective for sensing, we introduce and minimize an ambiguity function-based loss on the generated waveforms. We evaluate the performance of our method by comparing the single-pulse detectability of our generated waveforms with traditional LPD waveforms using a separately trained detection neural network. We find that our method can generate LPD waveforms that reduce detectability by up to 90% while simultaneously offering improved ambiguity function (sensing) characteristics. Our framework also provides a mechanism to trade-off detectability and sensing performance.

A key component of cognitive radar is the ability to generalize, or achieve consistent performance across a range of sensing environments, since aspects of the physical scene may vary over time. This presents a challenge for learning-based waveform selection approaches, since transmission policies which are effective in one scene may be highly suboptimal in another. We address this problem by strategically biasing a learning algorithm by exploiting high-level structure across tracking instances, referred to as meta-learning. In this work, we develop an online meta-learning approach for waveform-agile tracking. This approach uses information gained from previous target tracks to speed up and enhance learning in new tracking instances. This results in sample-efficient learning across a class of finite state target channels by exploiting inherent similarity across tracking scenes, attributed to common physical elements such as target type or clutter statistics. We formulate the online waveform selection problem within the framework of Bayesian learning, and provide prior-dependent performance bounds for the meta-learning problem using Probability Approximately Correct (PAC)-Bayes theory. We present a computationally feasible meta-posterior sampling algorithm and study the performance in a simulation study consisting of diverse scenes. Finally, we examine the potential performance benefits and practical challenges associated with online meta-learning for waveform-agile tracking.

In radar systems, unimodular (or constant-modulus) waveform design plays an important role in achieving better clutter/interference rejection, as well as a more accurate estimation of the target parameters. The design of such sequences has been studied widely in the last few decades, with most design algorithms requiring sophisticated a priori knowledge of environmental parameters which may be difficult to obtain in real-time scenarios. In this paper, we propose a novel hybrid model-driven and data-driven architecture that adapts to the ever changing environment and allows for adaptive unimodular waveform design. In particular, the approach lays the groundwork for developing extremely low-cost waveform design and processing frameworks for radar systems deployed in autonomous vehicles. The proposed model-based deep architecture imitates a well-known unimodular signal design algorithm in its structure, and can quickly infer statistical information from the environment using the observed data. Our numerical experiments portray the advantages of using the proposed method for efficient radar waveform design in time-varying environments.