The unified theoretical frame of a joint transmitter-receiver reduced dimensional Space-Time Adaptive Processing (STAP) method is studied for an airborne Multiple-Input Multiple-Output (MIMO) radar. First, based on the transmitted waveform diverse characteristics of the transmitted waveform of the airborne MIMO radar, a uniform theoretical frame structure for the reduced dimensional joint adaptive STAP is constructed. Based on it, three reduced dimensional STAP fixed structures are established. Finally, three reduced rank STAP algorithms, which are suitable for a MIMO system, are presented corresponding to the three reduced dimensional STAP fixed structures. The simulations indicate that the joint adaptive algorithms have preferable clutter suppression and anti-interference performance.