Multi-h CPM has great potential advantages in future space telemetry due to its high bandwidth efficiency and power efficiency, but the high complexity of demodulation technology limits its wide application. In order to simplify the demodulation structure under the premise of less performance loss, after a brief introduction of the characteristics and development status of Multi-h CPM system, the basic structure of the receiver for multi-h CPM signal is emphasized. Carrier synchronization, timing synchronization, modulation index synchronization and sequence are summarized in detail. The origin, development process and theoretical basis of detection technology are analyzed. The advantages and disadvantages of each method are analyzed. Finally, the further research direction of Multi-h CPM system is proposed.