For the uplink grant-free Multi-User Shared Access（MUSA） scheme

the user has the characteristics of access system randomly

and the user signal has sparseness

which can use the relevant algorithm of compression perception for multi-user detection. In view of the unknown number of active users

a multi-user detection algorithm based on Validation Error Orthogonal Matching Pursuit（VE-OMP） is proposed. The proposed algorithm can estimate the sparsity by using the error to reach the minimum value when the number of iterations is equal to the user’s sparsity. It is also noted that the idea of verifying the error has strong portability

which can be used for block sparse compression sensing. Considering that the base station is equipped with multiple antennas

the transmission signal is transformed into a block sparse model. A Validation Error Block Sparse Orthogonal Matching Pursuit（VE-BOMP） algorithm is also proposed to detect active user data. The simulation results show that the VE-OMP algorithm can jointly detect the activity and data of the users under the condition of unknown sparsity. The VE-BOMP algorithm can also be used in multi antenna receiving system

and its detection performance increases with the increase of the number of antennas.