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Multi-rate coprime sampling for frequency estimation with increased degrees of freedom

机译：多速率共质数采样，用于提高自由度的频率估计

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摘要

For frequency estimation, the recently proposed coprime sampling scheme receives increasing interest as it reduces sampling rate and exhibits high degrees of freedom. However, the virtual coarray generated by coprime configuration is a linear virtual array structure with some missing elements. This leads to information loss if only the contiguous part of the virtual coarray is used. In this paper, we propose a new approach to fix this problem. A multi-rate coprime sampling mechanism is designed to fill all the holes in the classical coprime virtual coarray. This is achieved by constructing new virtual coarrays containing the hole elements which can be selected to fill all the holes in the original virtual coarray. Furthermore, by properly setting the multi-rate coefficients to positive integers, our approach allows to reuse some samples obtained with the classical coprime sampling configuration. The closed-form expression of the positions of the holes is also given, which can be used to choose the appropriate multi-rate coefficients. Simulation results show that the proposed approach can increase the degrees of freedom without requiring additional samples. The estimation accuracy is also improved because our proposed approach fully exploits the information from the available samples. (C) 2019 Elsevier B.V. All rights reserved.
机译：对于频率估计，最近提出的互质采样方案受到越来越多的关注，因为它降低了采样率并表现出很高的自由度。但是，通过互素配置生成的虚拟协同数组是具有某些缺失元素的线性虚拟数组结构。如果仅使用虚拟协同阵列的连续部分，则会导致信息丢失。在本文中，我们提出了一种解决此问题的新方法。设计了一种多速率互质采样机制，以填补经典互质虚拟协数组中的所有漏洞。这是通过构造包含空穴元素的新虚拟协同阵列来实现的，可以选择这些空穴阵列来填充原始虚拟协同阵列中的所有空穴。此外，通过将多速率系数正确设置为正整数，我们的方法允许重用一些通过经典互质采样配置获得的样本。还给出了孔位置的闭合形式的表达式，该表达式可用于选择适当的多速率系数。仿真结果表明，所提出的方法可以增加自由度，而无需额外的样本。由于我们提出的方法充分利用了可用样本中的信息，因此估计准确性也得到了提高。 （C）2019 Elsevier B.V.保留所有权利。

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