Summary: This paper presents a multiple constrained subspace based multiuser detector for synchronous long-code downlink multirate DS-CDMA systems. The novel receiver adapts its fractionally-spaced equaliser tap-weights based upon two modes, namely training and decision-directed modes. Switching between two modes is achieved by changing the code constraint in the associated subspace algorithm. Moreover, detection of the desired user requires the knowledge of the desired user's spreading code only. Simulation results show that the proposed receiver is capable of multiple access interference (MAI) suppression and multipath mitigation. Besides, the results reveal the improvement in terms of convergence speed and mean square error (MSE) of the proposed receiver over the existing receiver in both static and dynamic environments.