In this paper, we present a novel approach to compute ambiguities in thinned uniform linear arrays, i.e., sparse non-uniform linear arrays, via a mixed-integer program. Ambiguities arise when there exists a set of distinct directions-of-arrival, for which the corresponding steering matrix is rank-deficient and are associated with nonunique parameter estimation. Our approach uses Young tableaux for which a submatrix of the steering matrix has a vanishing determinant, which can be expressed through vanishing sums of unit roots. Each of these vanishing sums then corresponds to an ambiguous set of directions-of-arrival. We derive a method to enumerate such ambiguous sets using a mixed-integer program and present results on several examples.

翻译：在本文中,我们提出了一个新颖的方法,通过混合整数程序计算稀薄统一线性阵列的模糊性,即稀少的非统一线性阵列。当存在一套不同的抵达方向时,就会出现模糊性。相应的指导矩阵对于这些方向没有等级,而且与非单一参数估计有关。我们的方法使用Young表单,其中方向矩阵的子矩阵有一个消失的决定因素,可以通过单位根根的消失量来表示。这些消失数中的每一数字随后对应一套模糊的抵达方向。我们用混合整数程序得出一种方法来列举这些模棱两可的组合,并展示几个例子的结果。