Abstract: In the practical application of Tomographic Synthetic Aperture Radar (TomoSAR), the number of acquisitions is usually restricted due to their expensive cost. A coprime TomoSAR technique was proposed to reduce the required number of acquisitions by sparsely distributing acquisitions and elongating baseline aperture. To guarantee a reliable tomogram, this study aims to determine the minimum number of acquisitions for the coprime TomoSAR when adopting a subspace method for performing the tomographic reconstruction. However, the performance of the subspace method depends on multiple parameters. In light of this, the selection of acquisition times has to comprehensively weigh the effects of all these parameters on the reconstruction performance. To this end, a prerequisite for reliable reconstruction is established by quantifying the relationship between the sample eigenvalues and all related parameters. Compared with conventional estimation approaches for the minimum number of acquisitions, the proposed approach has twofold advantages of containing all related parameters and of having a closed-form expression. Finally, the simulation experiments verify that the number of acquisitions estimated by our approach is close to the minimum and can guarantee reconstruction reliability.