The Multi-Level Dilated Nested Array for Direction of Arrival Estimation

Abstract

In this paper, a more generalized dilated nested array (DNA) named multi-level dilated nested array (multi-level DNA), which further extends the original DNA to the general situation and improves the direction of arrival (DOA) estimation performance, is proposed. The original DNA, which consists of a nested array and a time-shifted array, possesses the capabilities of handling more sources and achieving improved estimation accuracy compared with the nested array. However, only one time-shifted array is employed in DNA and the performance improvement is quite limited. Here, a new multi-level DNA, which utilizes multiple time-shifted nested arrays, is proposed. The multi-level DNA can provide more degrees of freedom (DoFs), meanwhile its difference co-array is still hole-free. The closed form expression of uniform DoFs in multi-level DNA is derived. The corresponding DOA Cramér-Rao bound, which gives the low bound on the variance of estimated DOA, is deduced in detail and some properties related to it are concluded. In total, for the DOA estimation, multi-level DNA can detect more sources and achieve more accurate estimation performance compared with the original DNA. Numerical simulations are performed to verify the superiority of the proposed multi-level DNA.INDEX TERMS Direction of arrival (DOA), co-array, nested array (NA), dilated nested array (DNA).

DOA Estimation With Nonuniform Moving Sampling Scheme Based on a Moving Platform

“…We first compare the number of uDOFs for arrays with different moving sampling schemes. Multi-level dilated nested array (ML-DNA) [27] and dilated nested array (DNA) [23] are nested arrays with uniform linear MSS for M ≥ 2 and M = 1, respectively. The maximum number of consecutive difference co-arrays of NA, DNA, ML-DNA, 2LNA-2LN-MSS exploiting the second-order statistics (q = 1) and 4LNA, 4LNA-4LN-MSS based on the fourth-order statistics (q = 2) are listed in Table I, where optimal array structures offering the highest uDOFs among potential configurations are employed [10], referred to as (N 1 , N 2 ) for q = 1 and (N 1 , N 2 , N 3 , N 4 ) for q = 2 as indicated in Table I.…”

“…In [26], a novel approach to construct virtual array exploiting array motion is proposed, tripling the number of DOFs without changing inter-element spacings. Then, in [27], multi-level dilated nested array (ML-DNA) is proposed, where multiple array motions are considered instead of only one fixed motion, leading to increased number of DOFs. However, uniformly shifted arrays after motions are synthesized, and only the second-order difference co-arrays are considered.…”

Sparse Linear Antenna Arrays: A Review

“…In recent years, moving array platforms or array motion are being exploited to obtain higher DOFs in sparse arrays. The synthetic coprime array [70], dilated nested array [71] and the multi-level dilated nested array [72] are few examples of sparse array designs that leverage platform motion to fill the holes in the DCAs. This topic is pretty new and is widely being explored.…”

2D DOA Estimation Exploiting Vertical Synthetic Planar Arrays

“…Furthermore, the authors analyze the DOA estimation performance of other moving SLAs, such as CAs, NAs, MRAs, MHAs and sparse ULAs (SULAs), with the same short translation assumption [21]. Recently, based on the fact that longer synthetic dis-tance can be realized when the signal environment changes sufficiently slowly [22], the multi-level DNA is proposed to futher increase the array DOF by moving the array K times [23]. Besides, [24] provides the maximum moving time at a slow moving speed to hold the signal environment stationary.…”