L-Shaped Sparse Array Structure for 2-D DOA Estimation

Abstract

In order to improve the performance of two-dimensional (2-D) direction-of-arrival (DOA) estimation, an L-shaped sparse array structured by two new sparse linear arrays is proposed. Each part of the proposed L-shaped array is used for one-dimensional (1-D) azimuth and elevation estimation, respectively. The new sparse linear array configuration is consisted of two subarrays which have N and M physical sensors, respectively. Owing to the advantages of the proposed sparse linear array configuration, higher degrees-of-freedom (DOF) and larger array aperture can be achieved when the second-order statistics of the received data is used. To match the azimuth and elevation angles automatically, the cross-covariance matrix of the two parts of the proposed L-shaped array is used to estimate the paired DOA angles. Based on the proposed L-shaped array configuration, (M + 1)(N − M/2) signal directions can be estimated with M + N sensors in each part and totally 2M + 2N − 1 sensors. Through the comparative analysis of the parameters with other sparse planar arrays, the proposed L-shaped array can achieve better performance due to its higher DOF and larger array aperture. Finally, numerical simulation results verify the superiority of the 2-D DOA method based on the proposed L-shaped array.

A Review of Sparse Sensor Arrays for Two-Dimensional Direction-of-Arrival Estimation

“…The RMSE can also be calculated based on the electrical angles α k and β k . Note that many variations exist in the literature like dividing by K outside the square root instead of inside [32], dividing by 2HK instead of HK [43,49,52], keeping the averaging over sources outside the square root [45], or defining the RMSE keeping only the averaging over sources inside the square root and then average Monte-Carlo trials [54,63].…”

“…structure like Hua et al [99] and Liang and Liu [66]. However, the focus here is on works utilizing orthogonal sparse linear arrays like [40][41][42][43][44][45][46][47][48][49][50][51]. It can be argued that the L-shaped array is sparse when compared to the URA, but since it is composed of ULAs, they can be treated as non-sparse in this survey.…”

“…Another work utilized sparse LAs along each axis. Each sparse LA is made up of two interleaved ULAs [49], and the largest contiguous ULA in the difference coarray is used for estimation. The estimation of azimuth and elevation are done separately using MUSIC, and cross covariance is used to pair the azimuth and elevation estimates.…”

“…In many cases, the aperture is square and the same expression appear in both columns. However, for the work by Wu et al [49], the expression is made to span both columns to save space.…”

DOA estimation of the quasi‐stationary signal using sparse reconstruction

“…steering vector matrix of the array, and it has a larger array aperture and a higher DOF. According to Theorem 3.2 in [37], A* ⊙A corresponding to the interleaved array contains at least 2MN different virtual array elements. Since 2MN < (M + N ) 2 − M − N + 1, there are many repeated elements in A* ⊙A.…”