2D-DOA estimation of noncircular signals for uniform rectangular array via NC-PARAFAC method

Fast Noncircular 2D-DOA Estimation for Rectangular Planar Array

“…We also assume the noise is independent of the sources and $d=\lambda /2$. The output signal of the i th subarray $x_{i}false(tfalse)$ can be denoted as [26]: ${boldnormalx}_i(t)={boldnormalA}_x{bold\Phi }^{i-1}S(t)+{boldnormaln}_i(t),i=1,2,\cdots ,N,$ where $A_x=false[a_{x}false(v_{1}false),a_{x}false(v_{2}false),\cdots ,a_{x}false(v_{K}false)false]$ and $a_{x}false(v_{k}false)={false[1,e^{-j\pi v_k},\cdots ,e^{-jfalse(M-1false)\pi v_k}false]}^T$, $v_k=\cos {\varphi }_k\sin {\theta }_k$, ${\theta }_k$ is the elevation angle and ${\varphi }_k$ is the azimuth angle. $bold\Phi =diagfalse(e^{-j\pi u_1},e^{-j\pi u_2},\cdots ,e^{-j\pi u_K}false)$ and $u_k=\sin {\varphi }_k\sin {\theta }_k$.…”

“…In fact, many noncircular signals such as the amplitude modulated (AM), binary phase shift keying (BPSK), minimum shift keying (MSK), and Gaussian MSK (GMSK) signals are used in wireless communication or satellite systems. In recent years, some scholars use non-circular signal characteristics to improve the performance of direction estimation, which contain the noncircular MUSIC (NC-MUSIC) algorithm [ 24 ], the NC-ESPRIT algorithm [ 25 ], and the noncircular parallel factor (NC-PARAFAC) algorithm [ 26 ]. On the one hand, the angle estimation performance can be achieved by the algorithms [ 24 , 25 , 26 ].…”

Estimation of DOA for Noncircular Signals via Vandermonde Constrained Parallel Factor Analysis

“…PARAFAC Model. Since the noncircular signals are considered, we construct the extended data matrix X ∈ ℂ 2M×N as follows [12,14]: Figure 1: Illustration of the array geometry. 2 International Journal of Antennas and Propagation where J ∈ ℝ M × M is the exchange matrix with ones on its antidiagonal and zeros elsewhere.…”

“…Besides taking the noncircularity of signals into account, the maximum number of sources can potentially exceed the number of array elements. Consequently, solid researches on NC signals for DOA estimation have appeared in many literatures [11][12][13][14]. NC ESPRIT algorithm and NC Unitary ESPRIT algorithm for DOA estimation were presented in [11,12], respectively.…”

“…However, the performance of the NC-RI-PM became worse rapidly in the case of low signal-to-noise ratio (SNR). The authors in [14] utilized the parallel factor (PARAFAC) analysis [15] to acquire the two-dimensional (2D) angle estimation of NC signals for uniform rectangular array (URA). The main drawback in [14] is that it has large computational load and is sensitive to the iterative initial value.…”