Multiple-Fold Redundancy Arrays With Robust Difference Coarrays: Fundamental and Analytical Design Method

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

“…According to (32) in Corollary 1, O(N 2q ) uDOFs (consecutive 2qth-order difference co-array lags) can be provided by the proposed 2qth-O-Fractal, which is significantly larger than O(N 2 ) provided by the original fractal array or other structures exploiting the second-order difference co-array. Furthermore, for an example with INA [12] as the generator, we can prove that the associated 2qth-O-Fractal provides more uDOFs than existing structures (SE-2qL-NA [9] and 2qL-NA [8]) based on the 2qth-order difference co-array, as shown in the following proposition.…”

“…Most of these techniques keep the number of DOFs provided unchanged or even improved [23], [24], [26]. On the other hand, considering the possibility of physical sensor damage, the robustness of sparse arrays and stability of coarrays have been discussed recently [27]- [29], while structures with improved robustness are presented in [30]- [32].…”

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

“…Sensor failures could occur randomly and may cause significant performance loss [32]- [35]. Considering the possibility of physical sensor damage, the robustness to sensor failures and stability of co-arrays have been studied recently [18], [27], [28], [36], [37]. In terms of avoiding changes (caused by physical sensor failures) in the difference co-array, the essentialness attribution of each sensor is adopted to evaluate the robustness of the array geometry [18].…”

“…MRA, NA, and Cantor arrays [16] were proven to be maximally economic with all sensors being essential ones, while CPA has relatively superior robustness [27], [38]. Towards the goal of designing more robust array structures, robust MRA (RMRA) [39], composite singer array (CSA) [40], and multiple-fold redundancy array (MFRA) [28], [37] have been presented. Furthermore, a general framework for robustness analysis based on the concept of importance function was proposed in [41], where the importance function characterizes the importance of the subarrays in a structure subject to definable properties related to robustness.…”

“…The extremely large number of virtual sensors leads to difficulties in robustness analysis, and the integrity of the entire 2qth-order difference co-array could be easily damaged when sensor failure occurs. By extending the quasiessentialness in [28], we develop a suitable robustness analysis tool for sparse arrays exploiting the 2qth-order difference coarray. An importance function describing the change of the consecutive 2qth-order difference co-arrays is employed since this consecutive segment can be utilized by various DOA estimation methods, especially subspace-based techniques which are easy to implement.…”