Ternary redundant sparse linear array design with high robustness

Sparse linear array is prone to element failure affected by environmental and other factors in practical application, resulting in the decline of degrees of freedom and the attenuation or even failure of direction of arrival (DOA) estimation performance. To address this problem, a ternary redundant sparse array composed of three uniform linear arrays with different spacings at specific distances is designed, and the analytical expression of its degrees of freedom is derived. The configuration rules of the array are concise, and the difference coarrays of the array are hole-free. Mathematically proves that all virtual array elements can be covered with a weight of not less than 3 except the 4 farthest. The array has lower sensors importance and less generalized k-fragility. The array design takes into account the maximum degrees of freedom, redundancy and sparsity. In case of sensors failure, compared with the other sparse linear arrays, the array has more stable difference coarrays and higher uniform degrees of freedom. Compared with multiple-fold redundancy arrays, the array has lower mutual coupling. Simulation results show that the ternary redundant array has superior robustness and higher DOA estimation accuracy under sensors failure.