Model-Aware Compressive Sensing with Applications to Channel Estimation in mmWave Systems

压缩感知(CS)方法是解决非线性参数估计问题的有力框架。通过将参数空间离散化，可以将原始的估计问题写成一个具有稀疏约束的高维的线性问题。在这个研究方案中，我们的第一个目标是开发和分析现有的连续估计的最优集成，例如最大似然方法，到基于CS的算法中。具体地说，基于CS的离散化参数估计器知道由估计器的连续部分使用的连续模型。我们将这种方法称为模型感知CS(MA-CS)。我们的第二个目标是将MA-CS应用于5G无线基础设施系统的新兴技术毫米波(MmWave)通信系统中的信道估计。由于毫米波信道的特殊性，信道估计成为一项非常具有挑战性的任务。在MA-CS中，可以形成由用于延迟参数的CS部分和用于无线信道的角度参数的连续部分组成的联合估计器。

The compressive sensing (CS) method represents are very powerful framework to solve nonlinear parameter estimation problems. By discretizing the parameter space, it is possible to write the original estimation problem as a high-dimensional, linear problem with sparsity constraints.  In this research proposal, our first goal is to develop and analyze the optimal integration of available continuous estimators, e.g., maximum likelihood methods, into CS based algorithms. Specifically, the CS based estimator for the discretized parameter is made aware of the continuous model, which is used by the continuous part of the estimator. We call this method Model-Aware CS (MA-CS). Our second goal is to apply MA-CS to channel estimation in millimeter wave (mmWave) communication systems, an emerging technology for 5G wireless infrastructure systems. The channel estimation becomes an extraordinary challenging task due to the particularities of the mmWave channel. Within MA-CS, it is possible to formulate a joint estimator that is comprised of a CS part for the delay parameter and a continuous part for the angular parameters of the wireless channel.