On the Size and Redundancy of the Fourth-Order Difference Co-Array
Journal
IEEE Signal Processing Letters
Journal Volume
28
Pages
2013-2017
Date Issued
2021
Author(s)
Chen Y.-P
Abstract
In array processing, the fourth-order difference co-Array of sparse arrays with N sensors admits to resolve \mathcal {O}(N4) source directions with proper assumptions. This \mathcal {O}(N4) property is relevant to the size of the central uniform linear array (ULA) segment of the fourth-order difference co-Array. However, among the existing sparse arrays, the fundamental limits for the sizes of the fourth-order difference co-Array remain a topic for further study. This paper characterizes the lower and upper bounds of the size of the fourth-order difference co-Array. It is proved that the ULA and the exponential array achieve the lower and upper bounds, respectively. We also propose the fourth-order redundancy to quantify the efficiency of the ULA segment in the fourth-order difference co-Array. The fourth-order redundancy owns a provable lower bound depending only on N, providing further insights into the size of the central ULA segment of the fourth-order difference co-Array. These bounds are validated through numerical examples. ? 1994-2012 IEEE.
Subjects
exponential arrays
fourth-order difference co-Arrays
fourth-order redundancy
Sparse arrays
Array processing
Direction of arrival
Direction of arrival estimation
Exponential array
Exponentials
Fourth-order
Fourth-order difference coarray
Fourth-order redundancy
Sensors array
Upper Bound
Redundancy
Type
journal article