FOGNA: An effective Sum-Difference Co-Array Design Based on Fourth-Order Cumulants

Array structures based on the fourth-order difference co-array (FODCA) provide more degrees of freedom (DOF). However, since the growth of DOF is limited by a single case of fourth-order cumulant in FODCA, this paper aims to design a sparse linear array (SLA) with higher DOF via exploring different cases of fourth-order cumulants. This paper presents a mathematical framework based on fourth-order cumulant to devise a fourth-order extend co-array (FOECA), which is equivalent to FODCA. A novel SLA, namely fourth-order generalized nested array (FOGNA), is proposed based on FOECA to provide closed-form expressions for the sensor locations and enhance DOF to resolve more signal sources in direction of arrival (DOA) estimation. FOGNA is consisted of three subarrays, where the first is a concatenated nested array and the other two subarrays are SLA with big inter-spacing between sensors. When the total physical sensors of FOGNA are given, the number of sensors in each subarray is determined by the designed method, which can obtain the maximum DOF under the proposed array structure and derive closed-form expressions for the sensor locations of FOGNA. The proposed array structure not only achieves higher DOF than those of existing FODCAs but also reduces mutual coupling effects. Numerical simulations are conducted to verify the superiority of FOGNA on DOA estimation performance and enhanced DOF over other existing FODCAs.