Space-time Adaptive Processing (STAP) is a two-dimensional filtering technique for antenna array with multiple spatial channels. The name "space-time" describes the coupling of these spatial channels with pulse-Doppler waveforms. Applications for STAP includes ground moving target indicator (GMTI) for airborne radar systems. Today, there are strong interests to develop STAP algorithms for operations in “sample starved” environments, where intense environmental interference can reduce STAP capacity to detect and track ground targets. Careful applications of STAP can effectively overcome these conditions by suppressing these interferences and maximize the signal to interference plus noise ratio (SINR). The Multi-stage Wiener filter (MWF) and principal component signal dependent (PC-SD) algorithm are two such methods that can suppress these interference through truncation of the signal subspace. This thesis makes contribution in several ways. First it details the importance of rank compression and sample compression for effective STAP operations in “sample starved” environments. Second, it shows how MWF and PC-SD could operate in this type of environment. Third it details how a “soft stop” technique like diagonal loading (DL) could improve STAP performance in target detection for MWF and PC-SD. Fourth, this thesis contrasts the performance of several existing “hard stop” techniques in rank compression and introduces a new one using a-priori knowledge.