In this paper, we propose a blind multiuser detection scheme in a direct sequence CDMA downlink scenario by means of a chiplevel equaliser, which can be updated even if not all possible users are active, i.e. the system is partially loaded. The active synchronous users are separated by re-establishing orthogonality of their spreading sequences in a common chip-level equaliser. The adaptation algorithm is mainly based on a constant modulus (CM) criterion applied to the active users. The inactive codes in the system must be considered, for which we proposed and compare three different methods: (i) a mean square error criterion for absent users, and a CM approach with (ii) zero modulus or (iii) the transmission of arbitrary signals with small code amplitude. For all three cases, stochastic gradient descent algorithms are derived. The proposed algorithms are analysed and compared through various simulations, which demonstrate the algorithms' convergence and BER performance.