-The conventional receiver for DS-CDMA communications is the RAKE receiver. The RAKE receiver is a matched filter, matched to the operations of spreading, pulse shape filtering and channel filtering. Such a matched filter maximizes the Signal-to-Interference-plus-Noise Ratio (SINR) at its output if the interference plus noise is white. This may be approximately the case if user-dependent scrambling (aperiodic spreading) is used. This is one option for the uplink in 3rd generation systems. However, this is not the case in the synchronous downlink with cell-dependent scrambling, orthogonal codes and a common channel. In this paper we propose a restricted class of linear receivers for the downlink, exhibiting a limited or no complexity increase with respect to the RAKE receiver. The linear receivers in this class have the same structure as a RAKE receiver, but the channel matched filter gets replaced by an equalizer filter that is designed to maximize the SINR at the output of the receiver. The complexity of the equalizer filter is variable and can possibly be taken to be as low as in the RAKE receiver (same structure as the channel matched filter), while its adaptation guarantees improved performance with respect to (w.r.t.) the RAKE receiver. Various adaptation strategies are considered and compared in simulations.