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arXiv 2005.10882cs.ITmath.IT
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多输入单输出线性系统的盲二维的超分辨

Blind Two-Dimensional Super Resolution in Multiple Input Single Output Linear Systems

Shahedeh Sayyari, Sajad Daei, Farzan Haddadi

摘要:

在本文中,我们考虑了一个多输入单输出(MISO)线性时变系统,其输出是一个叠加的缩放和时频移版本的输入。本文的目标是从单个输出信号确定系统特性和输入信号。更准确地说,我们希望从仅一个输出向量恢复连续时频移位对、对应的(复值)幅度和输入信号。这个问题出现在各种应用中,如雷达成像,显微镜,信道估计和定位问题。虽然这个问题自然是不适定的,但通过将未知输入波形约束在单独的已知低维子空间中,它变得易于处理。更明确地说,我们提出了一个半定的计划,准确地恢复时频移对和输入信号。我们证明了该方案的解的唯一性和最优性。此外,我们提供了一个基于网格的方法,可以显着降低计算复杂性,以换取增加一个小的网格误差。数值结果证实了我们所提出的方法能够准确地恢复未知数。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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