High-Order Cumulants Based Sparse Array Design Via Fractal Geometries—Part II: Robustness and Mutual Coupling

Abstract

This is a repository copy of High-order cumulants based sparse array design via fractal geometries-part II: robustness and mutual coupling.

High-Order Cumulants Based Sparse Array Design Via Fractal Geometries—Part I: Structures and DOFs

“…Typically, the mutual coupling effect [21]- [23] and the influence of element loss [27], [28] are analyzed in DOA estimation. These practical factors prompt us to consider Criterion 4 (Robustness and economy) and Criterion 5 (Low mutual coupling), which will be introduced, discussed, and analyzed in the companion Part II [60].…”

“…In the following, the fractal idea for sparse array design is introduced based on higher-order statistics, and the popular properties of the proposed structure (including the number of uDOFs, potential hole-free difference co-array, robustness, and mutual coupling effect) are analyzed, showing property inheritance with the generator array and flexibility in joint multi-criterion design. The new structure and discussions on the number of uDOFs and hole-free property are presented in this part, while the companion Part II focuses on the analysis of array robustness and the mutual coupling effect [60].…”

“…We have shown that for the special case of q = 2, Criteria 1-3 can be satisfied. Other generalized properties in Criteria 4-5 will be discussed in the companion paper of Part II [60].…”

“…Properties of robustness and mutual coupling of the proposed framework are analyzed in the companion Part II [60]. In future work, it is interesting to further investigate the theoretical performance analysis of estimation methods based on high-order difference co-arrays, especially for the underdetermined case.…”

Wideband DOA Estimation With Frequency Decomposition via a Unified GS-WSpSF Framework

“…In the narrowband case, it is necessary to employ sparse array structures for underdetermined DOA estimation, and accordingly nested arrays [6], co-prime arrays [7], [8] and their extensions [9]- [16] have been proposed. In order to exploit the increased degrees of freedom (DOFs) provided by sparse arrays, many effective methods including spatial smoothing (SS) based subspace methods [6], compressive sensing (CS) based methods [17], [18], and maximum likelihood (ML) methods [19], have been employed to resolve more sources than the number of physical sensors.…”