Array processing is an area with many civilian and military applications, e.g. sonar, radar, seismology and wireless communications. By means of space and space-time processing it is possible to enhance their features and explore new possibilities. This area has been attracting increasingly more attention and gathering more efforts of the science community, especially now, that phased array antennas are established as a commercial and mature technology. Within this context, we address the problem of reduced rank processing in space and space-time radar signal processing and the new area of dual-function radar-communications (DFRC), which may be summarized as embedding communication messages into radar emissions as a secondary task for the radar. In this thesis, we investigate the application of a new joint interpolation and decimation rank reducing scheme in two different areas: beamforming and space-time radar processing. This rank reducing algorithm was never tested within these contexts before and shows impressive results. We also propose simplifications for decreasing the computational complexity of the algorithm in beamforming. In the topic of DFRC, we propose two original robust radar-embedded sidelobe phase/amplitude modulation methods which have simple closed form equations. The proposed methods are much simpler than the state of the art and have superior performance in terms of robustness and real-time applicability.