Compressive sensing (CS) has been widely used in multiple-input-multiple-output (MIMO) radar in recent years. Unlike traditional MIMO radar, detection/estimation of targets in a CS-based MIMO radar is accomplished via sparse recovery. In this article, for a CS-based colocated MIMO radar with linear arrays, we attempt to improve the target detection performance by reducing the coherence of the associated sensing matrix. Our tool in reducing the coherence is the placement of the antennas across the array aperture. In particular, we choose antenna positions within a given grid. Initially, we formalize the position selection problem as finding binary weights for each of the locations. This problem is highly nonconvex and combinatorial in nature. Instead, we find continuous weight values for each location and interpret them as the probability of including an antenna at the given location. Next, we select antenna locations randomly according to the obtained probability distribution. We formulate the problem for the general case of a MIMO radar with independent transmit and receive arrays for which we propose an iterative algorithm. For the special case of a transceiver array, the solution is obtained through a convex optimization approach. Our experiments show that the proposed method achieves a superior detection performance compared to a uniform random placement of the antennas within the array aperture.