Compressed Sensing Multi-User Detection is a recently developed physical layer method to decrease signaling in massive Machine communications by using means from the field of Compressed Sensing and sparse signal processing. Within this work we use the advances of recent research and present a non-coherent CS-MUD system concept basing on a combination of multi-carrier modulation and CDMA. This so called Multi- Carrier Compressed Sensing Multi-User Detection (MCSM) concept aims at multiplexing machine-to-machine traffic in narrow band transmissions over the radio resources. Using non-coherent modulation schemes further decreases the needs for pilot symbols and increases robustness with respect to carrier frequency offsets.