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.

中文翻译：

---

有效估计稀疏的延迟多普勒信道

多个无线传感任务，例如，用于驾驶员安全的雷达检测，涉及估计“通道”或发送和接收的信号之间的关系。在这项工作中，我们专注于某种称为延迟多普勒信道的信道模型。该模型开始在高频载波环境中有用，随着毫米波技术的发展，这种模式越来越普遍。此外，即使在使用大带宽信号时，延迟多普勒模型也继续适用，这是实现高分辨率信道估计的标准方法。但是，当需要高分辨率时，此标准方法会导致对效率的需求紧张，因为尤其是它立即意味着正在播放的信号生活在非常高的维度$ N $的空间中（例如，根据Shannon-Nyquist采样定理，在某些应用中约为10 ^ 6 $）。为了解决这个困难，我们提出了一种新颖的随机估计方案，称为稀疏信道估计，简称SCE，用于稀疏$ k $设置中的信道估计（例如，雷达检测中的$ k $个对象）。对于$ N $，此方案涉及一个估计过程，该过程的采样和空间复杂度均为$ k（logN）^ 3 $，而算术复杂度为$ k（log N）^ 3 + k ^ 2 $。足够大。据我们所知，稀疏信道估计（SCE）是同类中第一个同时实现这些复杂性的方法-效率极高！另外一个优点是，它是三种成分的简单组合，其中两种成分众所周知且得到广泛使用，即数字线性调频信号和离散高斯滤波器功能，