This work proposes an augmented variation of conventional space-time adaptive processing (STAP), and explores the application of multi-branch matching pursuit (MBMP) to a multiple-input multiple-output (MIMO) beamformer whose steering vector is created over an array having random, inter-element spacing. By applying compressive sensing (CS), a radar system is able to minimize the undesired effects of an undersampled array while providing adequate clutter suppression and reduced burden on array integration. In this paper, we compare the performance and computational complexity of the MBMP applied to the STAP problem and the STAP beamformer. In addition we propose two methods to reduce the computational complexity of MBMP, a modification to the MBMP algorithm which we refer to as truncated MBMP, and a grid refinement technique. We evaluate our approach and extend this aspect to help in understanding the necessary computations required for practical target detection.