In this paper, a new type of coprime-array-based structure, named AtCADiS, is proposed to achieve increased degrees of freedom (DoFs) and reduced mutual coupling. The closed-form expressions for the sensor positions and the number of uniform DoFs (uDoFs) of AtCADiS are provided. Specifically, AtCADiS is constructed via two steps. First, we shift the leftmost sensor of tCADiS to the right by N. Second, we increase the number of sensors of tCADiS by [\lfloor(M/2)\rfloor] that are appropriately placed to connect the positive and negative lags of difference coarray of tCADiS and further improved its uDoFs remarkably. Finally, simulations show that AtCADiS can achieve higher number of uDoFs than the existing coprime array-based structures by using the same number of physical sensors, which leads to stronger resolution capability and higher direction of arrival (DoA) estimation accuracy. In the presence of mutual coupling, AtCADiS can achieve comparable mutual coupling leakage with respect to the existing array structures.