Abstract

To effectively find the direction of non-circular signals received by a uniform linear array (ULA) in the presence of non-negligible perturbations between array elements, i.e., mutual coupling, in colored noise, a direction of arrival (DOA) estimation approach in the context of high order statistics is proposed in this correspondence. Exploiting the non-circularity hidden behind a certain class of wireless communication signals to build up an augmented cumulant matrix, and carrying out a reformulation of the distorted steering vector to extract the angular information from the unknown mutual coupling, by exploiting the characteristic of mutual coupling, i.e., a limited operating range and an inverse relation of coupling effects to interspace, we develop a MUSIC-like estimator based on the rank-reduction (RARE) technique to directly determine directions of incident signals without mutual coupling compensation. Besides, we provide a solution to the problem of coherency between signals and mutual coupling between sensors co-existing, by selecting a middle sub-array to mitigate the undesirable effects and exploiting the rotation-invariant property to blindly separate the coherent signals into different groups to enhance the degrees of freedom. Compared with the existing robust DOA methods to the unknown mutual coupling under the framework of fourth-order cumulants (FOC), our work takes advantage of the larger virtual array and is able to resolve more signals due to greater degrees of freedom. Additionally, as the effective aperture is virtually extended, the developed estimator can achieve better performance under scenarios with high degree of mutual coupling between two sensors. Simulation results demonstrate the validity and efficiency of the proposed method.

Highlights

  • Direction of arrival (DOA) estimation, an important research area of sensor array signal processing, has attracted a large amount of attention because of its wide applications to electromagnetic, acoustic, seismic sensing, etc [1,2,3,4,5,6]

  • Weiss and Friedlander [7] first discuss the structure of the mutual coupling matrix (MCM) in uniform linear and circular arrays and estimated the DOAs and mutual coupling coefficients in an iterative way

  • Making use of the characteristic of mutual coupling, such as a limited operating range and an inverse relation of coupling effects to interspace, to parameterize the steering vector, as well as the non-circularity of the observations to form a virtual array, we develop a MUSIC-like estimator by means of the rank-reduction (RARE) property to resolve the DOA estimates without any calibration process

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Summary

Introduction

Direction of arrival (DOA) estimation, an important research area of sensor array signal processing, has attracted a large amount of attention because of its wide applications to electromagnetic, acoustic, seismic sensing, etc [1,2,3,4,5,6]. We introduce a solution to the problem of coherent signal estimation in the presence of mutual coupling between sensors, mitigating the detrimental effects via a middle sub-array and enhancing the DOFs through blind separation of the coherent signals into different groups. The symbol Z( a : b, c : d) refers to a constructed sub-matrix by the entries from a to b-th row and c to d-th column of Z, and the symbol Z( a, b) denotes the entry in the a-th row and b-th column of Z

Strictly Second-Order Non-Circular Signals
Array Model for Non-Circular Signals
Proposed Non-Circular FOC-Based Estimator
Performance Analysis
Identifiability of DOA Estimation
Computational Complexity
Solution to the Case of Coherent Signals
Simulation Results and Discussion
Conclusions
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