Cumulant-Based DOA Estimation of Noncircular Signals against Unknown Mutual Coupling

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.

A Comprehensive Review of Direction-of-Arrival Estimation and Localization Approaches in Mixed-Field Sources Scenario

“…where M represents the MC matrix (MCM). It is often sufficient to consider the ULA coupling model with finite non-zero coefficients, and a symmetric Toeplitz matrix can be used to model the MC [216,217]. Therefore, the MCM of the array in Fig.…”

Analysis of the fourth-order co-array for a mixture of circular and noncircular signals

“…Moreover, two or all three of the approaches can be combined together to increase the DOFs further. Examples include algorithms combining the noncircular properties and the fourthorder cumulants [15,16,17,18,19], combining the noncircular properties and sparse arrays [20,21,22,23], or combining the fourth-order cumulants and sparse arrays [24,25,26,27,28]. In [29], all the three approaches are employed together.…”

“…2. Whether the additional types of fourth-order cumulants can help extend the virtual co-array aperture further or not has not been studied in literature yet [6,16,17].…”

“…3) The 'noncircular signal' mentioned in these works is mainly focused on the 'strictly noncircular signal', and the possible impact of the nonstrictly noncircular signals on the maximum number of signals to be estimated is often ignored [5,6,16,17,18,21].…”

Sparse Non-Uniform Linear Array-Based Propagator Method for Direction of Arrival Estimation

“…In addition, under the influence of the Gaussian noise, the estimation accuracy declines due to the noise buried in signal covariance matrix, which can not be eliminated. Making the algorithm more noise-resistant, a high-order cumulant [25][26][27][28][29][30] of the received signal becomes a promising countermeasure, which demonstrates outstanding resilience to Gaussian noise, rather than calculating the second-order covariance matrix directly.…”