Flexible extended nested arrays for DOA estimation: Degrees of freedom perspective

Abstract

Recently, the design of sparse arrays for direction-of-arrival (DOA) estimation has gained considerable attention due to their ability to yield a sizeable virtual aperture, enhanced degrees-of-freedom (DOF), and high-resolution DOA estimation. This paper presents a flexible extended nested array with multiple subarrays (f-ENAMS), whereby the sensors from the dense uniform subarray of a nested array (NA) are further distributed, and the NA’s DOF is thus improved. Essentially, the dense subarray of NA is split into four sections and distributed equally on either side of NA’s sparse subarray to array aperture while maintaining a hole-free difference co-array (DCA). In this regard, this paper proposes a new extended nested array structure named f-ENAMS, which achieves the same higher DOF capacity as the two-sided extended nested array (TS-ENA). Moreover, an improved f-ENAMS is proposed by relocating further sensors from the dense subarrays of f-ENAMS. As a result, the improved f-ENAMS possess more DOF than other existing extended NAs. For simplicity, the former is called f-ENAMS-I, and the latter is f-ENAMS-II. Both f-ENAMS arrays have closed-form expressions for sensor positions and a hole-free DCA. Numerical examples verify the superiority of the f-ENAMS arrays in terms of achievable DOF, weight functions, and DOA estimation performance.