This paper studies the joint transmit beamforming optimization in the downlink of a single-cell multiuser distributed antenna system. Due to the distributed nature of transmit antennas, the signals received from different distributed antenna units (DAUs) will experience various transmission delays, and it is difficult to realize accurate symbol-level time synchronization at the user terminal. Thus, we turn to finding a robust joint transmit beamforming algorithm by replacing the received signal-to-interference-plus-noise ratio (SINR) with its lower-bound value. Moreover, the joint transmission incurs huge amount of data sharing among DAUs. Under the per-DAU maximum transmit power constraint, we aim to minimize the system backhaul overhead while satisfying the quality-of-service (QoS) requirement of each user. Since the backhaul overhead minimization requires the transmit beam vectors to have a group sparse structure and is NP-hard, we first make a convex relaxation and then apply the reweighted method to improve the sparsity of the beam vectors. Furthermore, an admission control scheme is applied to guarantee the feasibility of the problem, which iteratively removes the unsatisfied user with the worst quality of experience (QoE) away from the system. Simulation results show that our proposed robust algorithm can achieve a much better performance than the traditional nonrobust algorithm when time asynchronism is less than 30% of the symbol duration and can significantly reduce the system backhaul overhead by designing group sparse transmit beam vectors.