Impaired Fractal Based Sub-Array Diagnosis

Sparse array has attracted a lot of attentions because of its higher DOF $O(N^{2})$ with only few physical elements ($N$). It has this property by imposing the difference co-array, which is defined as the difference between elements locations. However, empirically, the co-array of sparse arrays structure is vulnerable to impaired elements and reliability of sparse arrays is an open topic for investigation. In this context the present work examines fractal based sub-array DOA estimator. Broadly speaking, robustness is analyzed by exploiting element essentiality, fragility and normalized DCA size. Furthermore, the paper compares the robustness and size of difference co-array configurations of fractal based sub array with different existing sparse arrays. From the numerical examples, it is investigated that for the fixed $N$ elements, increase of difference co-array size typically cause in less robustness to element failure.