Chen Y.-PCHUN-LIN LIU2022-04-252022-04-25202110709908https://www.scopus.com/inward/record.uri?eid=2-s2.0-85116913398&doi=10.1109%2fLSP.2021.3116522&partnerID=40&md5=bcdbdc9115294b6ed2465873d666ee1dhttps://scholars.lib.ntu.edu.tw/handle/123456789/607053In 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.exponential arraysfourth-order difference co-Arraysfourth-order redundancySparse arraysArray processingDirection of arrivalDirection of arrival estimationExponential arrayExponentialsFourth-orderFourth-order difference coarrayFourth-order redundancySensors arrayUpper BoundRedundancyjournal article10.1109/LSP.2021.31165222-s2.0-85116913398