Waveform design and waveform scheduling are addressed in the context of space time adaptive processing (STAP) for radar. An air-borne radar with an array of sensors is assumed, which interrogates ground based targets. The designed waveform is assumed to be transmitted over one coherent processing interval (CPI). The waveform design and waveform scheduling problems are formulated with a cost function similar to the Minimum Variance Distortionless Response (MVDR) cost function as in classical radar STAP. Least-squared solutions for the designed waveform are obtained. It is shown that both the designed waveform and the scheduled waveforms will depend on the spatial and Doppler responses of the desired target; in particular, its spatial and temporal steering vectors. The focus of this paper will be the performance of the designed and scheduled waveforms for unknown correlation matrices but estimated from the training data, and will be addressed via simulations.