The Incidence and Cross Methods for Efficient Radar Detection

The designation of the radar system is to detect the position and velocity of targets around us. The radar transmits a waveform, which is reflected back from the targets, and echo waveform is received. In a commonly used model, the echo is a sum of a superposition of several delay-Doppler shifts of the transmitted waveform, and a noise component. The delay and Doppler parameters encode, respectively, the distances, and relative velocities, between the targets and the radar. Using standard digital-to-analog and sampling techniques, the estimation task of the delay-Doppler parameters, which involves waveforms, is reduced to a problem for complex sequences of finite length N. In these notes we introduce the Incidence and Cross methods for radar detection. One of their advantages, is robustness to inhomogeneous radar scene, i.e., for sensing small targets in the vicinity of large objects. The arithmetic complexity of the incidence and cross methods is O(NlogN + r^3) and O(NlogN + r^2), for r targets, respectively. In the case of noisy environment, these are the fastest radar detection techniques. Both methods employ chirp sequences, which are commonly used by radar systems, and hence are attractive for real world applications.Comment: 8 pages. Accepted for publication in Proceedings of Allerton Conference on Communication, Control, and Computing, October, 201

Efficiently Estimating a Sparse Delay-Doppler Channel

Multiple wireless sensing tasks, e.g., radar detection for driver safety, involve estimating the "channel" or relationship between signal transmitted and received. In this work, we focus on a certain channel model known as the delay-doppler channel. This model begins to be useful in the high frequency carrier setting, which is increasingly common with developments in millimeter-wave technology. Moreover, the delay-doppler model then continues to be applicable even when using signals of large bandwidth, which is a standard approach to achieving high resolution channel estimation. However, when high resolution is desirable, this standard approach results in a tension with the desire for efficiency because, in particular, it immediately implies that the signals in play live in a space of very high dimension $N$ (e.g., ~$10^6$ in some applications), as per the Shannon-Nyquist sampling theorem. To address this difficulty, we propose a novel randomized estimation scheme called Sparse Channel Estimation, or SCE for short, for channel estimation in the $k$-sparse setting (e.g., $k$ objects in radar detection). This scheme involves an estimation procedure with sampling and space complexity both on the order of $k(logN)^3$, and arithmetic complexity on the order of $k(log N)^3 + k^2$, for $N$ sufficiently large. To the best of our knowledge, Sparse Channel Estimation (SCE) is the first of its kind to achieve these complexities simultaneously -- it seems to be extremely efficient! As an added advantage, it is a simple combination of three ingredients, two of which are well-known and widely used, namely digital chirp signals and discrete Gaussian filter functions, and the third being recent developments in sparse fast fourier transform algorithms.Comment: PhD thesis, University of Wisconsin -- Madison, May 2020. Thesis advisor: Shamgar Gurevic