A Tree Structure One-Dimensional Based Algorithm for Estimating the Two-Dimensional Direction of Arrivals and Its Performance Analysis

Abstract

A tree structure algorithm using one-dimensional (1-D) multiple signal classification (MUSIC) algorithm is proposed to estimate the two-dimensional direction of arrivals (2-D DOAs) of coherent signals impinging on a uniform rectangular array. The basic idea of the proposed algorithm is to successively apply several times of the 1-D spatial smoothing MUSIC algorithm, in tree structure, to estimate the azimuth and the elevation angles independently. To optimally separate the receive signal, constrained spatial beamformers with adjustable null width are exploited in conjunction with the 1-D spatial smoothing MUSIC algorithm to decompose the received signal into several signals each lead by its own 2-D DOA. Performance analysis is provided to investigate the estimation bias caused by the residue signal propagating in the tree structure.Index Terms-Direction of arrival (DOA) estimation, rectangular antenna array, spatial smoothing.

Computationally Efficient 2D DOA Estimation with Uniform Rectangular Array in Low-Grazing Angle

“…The polynomial roots can be obtained by the Linsey–Fox root finding algorithm, which is less than the MATLAB function roots. However, the 2D FBSS-MUSIC method in [15,16], the 2D FBSS based DOA matrix (FBSS-DOAM) method in [23], the conventional spatial differencing (CSD) method in [18,19], and the tree structure one-dimensional (1D) based (TSOD) algorithm in [22] all involve the EVD to obtain the signal subspace or noise subspace. Furthermore, as shown in Table 1, FBSS-MUSIC and CSD both need 2D spectrum peak searching.…”

“…However, the TSOD method can only use the auto-correlations of different subarrays and CSD performs the difference on the whole subarrays. Thus, SDMS can achieve performance improvement over the methods in [18,19,22]. …”

“…To reduce the computational complexity, a partial spectral search based method (PSS) is proposed for limiting the searching region into a small sector [21]. Then, a tree structure one-dimensional (1D) algorithm [22] was developed based on a repeated use of the 1D MUSIC algorithm. However, it requires a large number of eigenvalue decompositions (EVDs) and does not perform well under a low signal-to-noise ratio (SNR).…”

“…The advantages of the proposed method can be given as follows: The methods in [3,4,15,16,17,21] involve the 2D EVD or 2D peak search, while the proposed method can estimate the parameters with 1D subspace-based estimation techniques.The method in [22] can only use the auto-correlations of different subarrays, while the proposed method can use more information including auto-correlations and cross-correlations.The spatial differencing techniques in [18,19] perform a difference operation on the whole subarrays, while the proposed method is only for the auto-correlations and the cross-correlations are kept completely. Thus, the SDMS method has little data loss.…”

“…The method in [22] can only use the auto-correlations of different subarrays, while the proposed method can use more information including auto-correlations and cross-correlations.…”