CIF: Small: Blind Channel Estimation and Solving Bilinear Equations by Lifting and Factoring

CIF：小：盲通道估计并通过提升和因式分解求解双线性方程

• 批准号: 1422540
• 负责人: Justin Romberg
• 金额: $ 15万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2017-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1422540&HistoricalAwards=false
• 关键词: CIF; Small; Blind; Channel; Estimation; CIF; Small; Blind; Channel; Estimation

The focus of this research is a fundamental problem in the acquisition and transmission of data: blind channel estimation. The goal is to develop novel and widely applicable methods for making communications and imaging robust against the types of perturbations that occur when a wireless signal travels through the air between cell phone and base station, an image passes through a uncalibrated lens, or a voice reverberates off of the walls and floors of a room. One of the most challenging aspects of these problems is that these perturbations cause the observations to be non-linear functions of the unknown variables. This research program will develop a new framework for solving and analyzing the robustness of the solutions to special classes of bilinear inverse problems, and then specialize these results to particular problems in blind channel estimation.Specifically, the investigator will study a new method for blind channel estimation based on recently developed techniques for solving constrained bilinear inverse problems. This methodology, called ?lifting? in the literature, recasts the bilinear problem as a linear matrix recovery problem with a rank constraint. This recasting allows the analytical and computational techniques from the large body of work on low rank matrix recovery to be unleashed, yielding new (very effective and scalable) algorithms for solving these classical problems, and a new mathematical understanding about when they can be tractably solved. The proposed framework will also be extended to the case where there are multiple sources present, which need to be separated as the channels are estimated.

这项研究的重点是数据获取和传输数据的基本问题：盲信估计。 目的是开发新颖且广泛适用的方法，以使无线信号通过手机和基站之间的空气传播时发生的通信和成像可靠，图像通过未校准的镜头或声音从墙壁和房间的地板上散发出来。 这些问题最具挑战性的方面之一是，这些扰动导致观察值是未知变量的非线性函数。 该研究计划将开发一个新的框架，用于解决和分析针对双线性逆问题的特殊类别的解决方案的鲁棒性，然后将这些结果专门针对盲渠道估计中的特定问题。特别是，研究人员将研究一种基于最近开发的盲信估算方法的新方法，用于解决求解双线性逆向问题的最近开发的技术。这种方法称为“举起？在文献中，将双线性问题重新提出为具有等级约束的线性矩阵恢复问题。 这种重铸允许从低级矩阵恢复上的大量工作中释放出分析和计算技术，从而产生用于解决这些经典问题的新（非常有效且可扩展的）算法，以及何时可以解决这些问题的新数学理解。 所提出的框架也将扩展到存在多个来源的情况，而这些来源需要在估计渠道时进行分开。