Multi-user multiple antenna systems have attracted much attention because of large spectral efficiency. However, receiver and transmitter channel state information (CSI) is generally required, especially for the downlink channel. In this study, the authors investigate the ergodic sum rate and present low complexity adaptive transmission scheme for multiple-input single-output downlink multi-user systems with statistical CSI at the base station (BS). The authors derive an approximation of the ergodic sum rate, and the constraint of each user's statistical CSI under which the approximation of the ergodic sum rate is maximised. Then, statistical beamforming space division multiple access transmission is derived through maximising the approximation of the ergodic sum rate, and new adaptive transmission schemes are proposed. The proposed algorithms are shown to perform well and require the BS only to know the statistical CSI of each user.