Aiming at the problem of delays of multiple users arriving at the base station in the uplink sparse code multiple access (SCMA) macro-cell system asynchronous detection algorithms were proposed with users grouped according to different delays and the same information between symbols was utilized and iterated, forming a message passing algorithm based on serial propagation (SP-MPA). Besides, aiming at the problem of worse bit error rate caused by partial marginalization algorithm used in MIMO-SCMA system, dynamic threshold partial marginalization algorithm (DTPM-MPA) was proposed. The simulation results show that the high bit error rate caused by symbol interference of asynchronous transmission is effectively reduced with SP-MPA and a flexible balance between computing complexity and bit error rate is formed with DTPM-MPA.