Abstract: In space based constellation network，users are allowed to enter or leave the network arbitrarily.Hence，the number，identities and transmitted data of active users vary with time and have considerable impacts on the receiver’s performance.The so-called problem of multiuser detection means identifying the identity of each active user and detecting the data transmitted by each active user.Traditional methods assume that the number of active users is equal to the maximum number of users that the network can hold.The model of traditional methods is simple and the performance is suboptimal.A maximum posteriori probability（MAP）criterion based multiuser detection method was proposed.The proposed method models the state of users as Markov chain and transforms multiuser detection into searching optimal path in grid map with BCJR algorithm.Simulation results indicate that the proposed method obtains 2.6dB and 1dB E_b/N₀ gains respectively when activity detection error rate and symbol error rate reach 10^-3，comparing with reference methods.

Key words: space based constellation networks, multiuser detection, maximum posteriori probability criterion, BCJR algorithm, Markov chain, grid map