Related papers: Differentiable Radar Ambiguity Functions: Mathemat…
The ability of a radar to discriminate in both range and Doppler velocity is completely characterized by the ambiguity function (AF) of its transmit waveform. Mathematically, it is obtained by correlating the waveform with its…
In order to improve the ability of cognitive radar (CR) to adapt to the environment, the required ambiguity function (AF) can be synthesized by designing the waveform. The key to this problem is how to minimize the interference power.…
We present a systematic analysis of automatic differentiation (AD) applications in astrophysics, identifying domains where gradient-based optimization could provide significant computational advantages. Building on our previous work with…
Frequency-modulated continuous wave (FMCW) radar with inter-chirp coding produces high side-lobes in the Doppler and range dimensions of the radar's ambiguity function. The high side-lobes may cause miss-detection due to masking between…
Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep…
The ambiguity function (AF) is a critical tool in radar waveform design, representing the two-dimensional correlation between a transmitted signal and its time-delayed, frequency-shifted version. Obtaining a radar signal to match a…
This paper addresses a critical preliminary step in radar signal processing: detecting the presence of a radar signal and robustly estimating its bandwidth. Existing methods which are largely statistical feature-based approaches face…
Millimeter-wave radar offers unique advantages in adverse weather but suffers from low spatial fidelity, severe azimuth ambiguity, and clutter-induced spurious returns. Existing methods mainly focus on improving spatial perception…
We investigate the theory of affine groups in the context of designing radar waveforms that obey the desired wideband ambiguity function (WAF). The WAF is obtained by correlating the signal with its time-dilated, Doppler-shifted, and…
This paper presents a novel algorithm to incorporate orbital parameters into radar ambiguity function expressions by extending the standard ambiguity function to match Keplerian two-body orbits. A coherent orbital matched-filter will…
Radar is a key component of the suite of perception sensors used for safe and reliable navigation of autonomous vehicles. Its unique capabilities include high-resolution velocity imaging, detection of agents in occlusion and over long…
Vector-valued discrete Fourier transforms (DFTs) and ambiguity functions are defined. The motivation for the definitions is to provide realistic modeling of multi-sensor environments in which a useful time-frequency analysis is essential.…
Affine frequency division multiplexing (AFDM) is a recently proposed communication waveform for time-varying channel scenarios. As a chirp-based multicarrier modulation technique it can not only satisfy the needs of multiple scenarios in…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…
General requirements for radar digital signal processing are ionospheric distortion and Doppler dispersion correction, which has historically required radar-specific hardware to implement in real time. Although analog solutions are…
Blending representation learning approaches with simultaneous localization and mapping (SLAM) systems is an open question, because of their highly modular and complex nature. Functionally, SLAM is an operation that transforms raw sensor…
There is rising interest in differentiable rendering, which allows explicitly modeling geometric priors and constraints in optimization pipelines using first-order methods such as backpropagation. Incorporating such domain knowledge can…
While camera and LiDAR processing have been revolutionized since the introduction of deep learning, radar processing still relies on classical tools. In this paper, we introduce a deep learning approach for radar processing, working…
Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computing the differentiation in many machine learning and…