The problem of direction finding has primal importance in modern life. Today, smart direction finding systems are used in various technical fields such as RADAR, SONAR, interference reduction, multi-user or multi-channel data transmission, environmental sounding, medical purposes and in many other areas of human life. Recent achievements in the field of signal processing provide a new paradigm known as Compressed Sensing (CS), where the advantages of sparse signal representation are utilized. The DOA model can be also formulated as sparse, i.e. with reduced measurement effort of the antenna....