论文标题
有效估计稀疏延迟多普勒通道
Efficiently Estimating a Sparse Delay-Doppler Channel
论文作者
论文摘要
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传输和接收的信号之间的“通道”或关系。在这项工作中，我们专注于某个称为延迟多普勒通道的通道模型。该模型在高频载体设置中开始很有用，这在毫米波技术的发展中越来越普遍。此外，即使使用较大的带宽信号，延迟多普勒模型也会继续适用，这是实现高分辨率通道估计的标准方法。但是，当需要高分辨率时，这种标准方法会导致对效率的渴望的张力，因为特别是，根据Shannon-NyquistSampling Theorem，它立即暗示着播放中的信号现场直播$ n $ $ n $（例如，在某些应用中〜$ 10^6 $）。 为了解决这一难度，我们提出了一种新颖的随机估计方案，称为稀疏通道估计，或简称SCE，用于$ k $ -sparse设置中的通道估计（例如，在雷达检测中，$ k $对象）。该方案涉及一个估算过程，并在$ k（logn）^3 $的订单上进行采样和空间复杂性，以及$ k（log n）^3 + k^2 $的算术复杂性，$ n $，$ n $足够大。 据我们所知，稀疏的渠道估计（SCE）是同时实现这些复杂性的第一个此类估计 - 似乎非常有效！为了额外的优势，它是三种成分的简单组合，其中两种是众所周知且广泛使用的，即数字CHIRP信号和离散的高斯滤波器功能，第三个是稀疏快速傅立叶变换算法的最新发展。
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.
