A Highly Robust Sparse Fractal Array

The term fractal refers to the fractional dimensions that have recursive nature and exhibit better array factor properties. In this article, we present a new class of sparse array where the recursive nature of a fractal can be used in designing an antenna array called a sparse fractal array by combining sparsity properties of the various sparse array and the recursive nature of fractal array. The most important property of the proposed array is the hole-free difference coarray which makes it a good choice for DOA estimation as various algorithms like coarray MUSIC etc demand hole-free difference coarray. But the performance of any array depends on the presence of essential and nonessential sensors in it which governs whether the difference coarray will get affected upon sensor failure or not. Hence, in this paper, a rigorous analysis is done for various combinations of sparse fractal arrays to test their robustness in presence of a faulty sensor environment.