An (M, N)-coprime array comprises two well-organized subarrays: an M-element and an N-element. This sparse array configuration is capable of resolving a number of remote sources up to O(MN) solely with the use of an M + N - 1 sensors, which allows the identification of more targets with fewer transceivers while maintaining high resolution. In this way, the coprime array theory can significantly help to simplify the configuration of traditional transceiver systems. However, to date, the coprime array approaches reported in the literature rely strongly on far-field approximation, which is associated with significant error when dealing with the problem of short-range radar detection because the probed objects are nearby the sensors. To solve this problem, we extend the theory of the standard coprime array to short-range detection, whereby the probed object is located NOT far away from the sensors (either the transmitter or receiver). We demonstrate that the (M, N)-coprime array configuration can retrieve the object spectrum over [-2k0, 2k0] with a resolution of 4k0/MN, where k0 denotes the free space wavenumber and  is a scenario-dependent factor. As a consequence, the (M, N)-coprime array allows for the resolution of O(MN) objects nearby sensors, with a spatial resolution of /4. We also examined the performance of the coprime array with respect to the through-wall-imaging problem. Finally, we verified the usefulness of the coprime array for short-range radar detection with a selected number of numerical experiments.