论文标题
多个输入单输出线性系统中的盲二维超级分辨率
Blind Two-Dimensional Super Resolution in Multiple Input Single Output Linear Systems
论文作者
论文摘要
在本文中，我们考虑了一个多输入单输出（MISO）线性时间变化系统，其输出是缩放和时频移动版本的输入版本的叠加。本文的目的是确定单个输出信号的系统特性和输入信号。更确切地说，我们希望恢复连续的时频移位对，相应的（复杂值）振幅以及仅从一个输出向量的输入信号。这个问题出现在各种应用中，例如雷达成像，显微镜，通道估计和定位问题。尽管此问题自然不足，但通过将未知的输入波形限制为位于单独的已知低维子空间中，它变得可拖延。更明确地，我们提出了一个半决赛程序，该程序准确地恢复了时频移位对和输入信号。我们证明了该程序解决方案的独特性和最佳性。此外，我们提供了一种基于网格的方法，可以显着降低计算复杂性，以换取添加小的网格错误。数值结果证实了我们提出的方法精确恢复未知数的能力。
In this paper, we consider a multiple-input single-output (MISO) linear time-varying system whose output is a superposition of scaled and time-frequency shifted versions of inputs. The goal of this paper is to determine system characteristics and input signals from the single output signal. More precisely, we want to recover the continuous time-frequency shift pairs, the corresponding (complex-valued) amplitudes and the input signals from only one output vector. This problem arises in a variety of applications such as radar imaging, microscopy, channel estimation and localization problems. While this problem is naturally ill-posed, by constraining the unknown input waveforms to lie in separate known low-dimensional subspaces, it becomes tractable. More explicitly, we propose a semidefinite program which exactly recovers time-frequency shift pairs and input signals. We prove uniqueness and optimality of the solution to this program. Moreover, we provide a grid-based approach which can significantly reduce computational complexity in exchange for adding a small gridding error. Numerical results confirm the ability of our proposed method to exactly recover the unknowns.
