Stochastic Framework for Evaluating the Effect of Displaced Antenna Elements on DOA Estimation

Abstract

Abstract-We establish a statistical framework for investigating the influence of correlated random displacements of antenna elements in a uniform circular antenna array (UCA) on the distribution of direction-of-arrival (DOA) estimates. More specifically, we apply a stochastic collocation method for modeling the sparse UCA root-MUSIC-DOA estimates as polynomial expansions of the random displacements. Compared to Monte-Carlo simulations, this approach yields a speedup of about 40 for the case of a displacement of two antenna elements.

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

“…Consider a nine-element uniform circular array (UCA) deployed in the azimuth plane. As the effects of the displacement of individual antenna elements on root-MUSIC have already been studied in earlier research—for example, in [ 18 , 19 ]—to showcase the proposed method, we assume that the array deforms in the shape of an ellipse with constant circumference and constant distance between the elements along the elliptical arc. This deformation is characterized by a single (random) variable: an “extended” eccentricity e defined by with being the width of the array (along ) and the height (along ).…”

“…With the appropriate approach, gPC can even compete with MC when a high number of random variables are used [ 12 , 13 , 14 , 15 , 16 , 17 ]. In the context of localization, gPC has also been used—for example, in [ 18 , 19 ], where the effects of element displacements on DOA estimation were investigated; in [ 20 ], where the effects of random element gain and phase variations were studied, and in [ 21 ], where the uncertainty in multiple angle-of-arrival measurements was translated into an uncertainty in position estimation.…”

“…Therefore, this algorithm and array topology are the ideal candidates to study the effects of random deformations on DOA estimation techniques. To be concise and keep the focus on the presence of singularities, we do not include white noise, in contrast to [ 18 , 19 , 20 ].…”

Stochastic Collocation Applications in Computational Electromagnetics

“…The combination of the nonintrusive, sampling based nature of Monte Carlo simulations with the polynomial approximation of output value, which is the characteristic of gPCE methods, made stochastic collocation one of the most researched and applied stochastic approaches [7][8][9]. The 2 Mathematical Problems in Engineering examples of successful coupling of SCM and its variations with different deterministic codes have been reported in stochastic dosimetry [10,11], in the analysis of complex power distribution networks (PDN) [12], in the design of integrated circuits (ICs), microelectromechanical systems, (MEMSs), and photonic circuits [13,14], in the simulation of EMcircuit systems [15,16], and in the area of antenna modeling [17][18][19] and electromagnetic compatibility (EMC) of space applications [20]. This paper reviews the previous work of the authors pertaining to the use of SC techniques in areas of CEM such as ground penetrating radar (GPR), EM-thermal dosimetry of the eye and brain, and buried lines and grounding systems [21].…”