Abstract
In array signal processing systems, the direction of arrival (DOA) and polarization of signals based on uniform linear or rectangular sensor arrays are generally obtained by rotational invariance techniques (ESPRIT). However, since the ESPRIT algorithm relies on the rotational invariant structure of the received data, it cannot be applied to electromagnetic vector sensor arrays (EVSAs) featuring uniform circular patterns. To overcome this limitation, a fourth-order cumulant-based ESPRIT algorithm is proposed in this paper, for joint estimation of DOA and polarization based on a uniform circular EVSA. The proposed algorithm utilizes the fourth-order cumulant to obtain a virtual extended array of a uniform circular EVSA, from which the pairs of rotation invariant sub-arrays are obtained. The ESPRIT algorithm and parameter pair matching are then utilized to estimate the DOA and polarization of the incident signals. The closed-form parameter estimation algorithm can effectively reduce the computational complexity of the joint estimation, which has been demonstrated by numerical simulations.
Highlights
In the past few decades, the direction of arrival (DOA) estimation of incident signals has been demonstrated to play a significant role in array signal processing [1,2,3,4]
In order to demonstrate the remarkable performance of the proposed algorithm, we compare the performance of the proposed algorithm with that of the LV-MUSIC algorithm and the Cramer-Rao bound (CRB) with different values of SNR.As shown in Figure 6 above, the computational complexity of LV-MUSIC algorithm is huge when DOA and polarization parameters
In order to demonstrate the remarkable performance of the proposed algorithm, we compare the performance of the proposed algorithm with that of the LV-MUSIC algorithm and the Cramer-Rao bound (CRB) with different values of SNR.As shown in Figure 6 above, the computational complexity of LV-MUSIC algorithm is huge when DOA and polarization parameters are estimated within acceptable searching steps
Summary
In the past few decades, the direction of arrival (DOA) estimation of incident signals has been demonstrated to play a significant role in array signal processing [1,2,3,4]. ESPRIT-based algorithms require the data to possess certain “invariant” structures, inapplicable to the uniform circular EVSAs. In recent years, characteristics of vector sensors within hypercomplex frameworks, such as quaternions [27], biquaternions [28], and quad-quaternions [29], etc., have been studied extensively. The proposed algorithm utilizes the fourth-order cumulant to construct the rotation invariance structure and combine the ESPRIT algorithm to estimate the DOA and polarization information of the incident signals based on uniform circular EVSAs. The proposed algorithm utilizes only part of the fourth-order cumulant matrix which contains non-redundant information to reduce the computational cost, other than the whole matrix. Regarding the notations used in this paper, the operator ⊗ denotes the Kronecker product; angle(·) denotes the phase of a complex number; E{·} denotes the expected value; diag(·) denotes a diagonal matrix composed of the columns or row vectors; cum(·) denotes the fourth-order cumulants; (·)∗ , (·)T , (·)H and (·)+ represent the complex conjugate, transpose, conjugate transpose and matrix inverse, respectively
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