In this paper the application of a linear-quadratic processor is proposed for detection of each user's signal in a direct sequence code division multiple access scheme and, in particular, for W-CDMA systems. In this method, the knowledge of the user of interest, and some statistical knowledge of interfering transmitters' signals are used to detect the desired user's signal without needing exact "a priori" knowledge of the interfering signal parameters such as spreading sequences and signal powers. Parameters of the proposed processor, which are derived so as to maximise the signal-to-interference-plus-noise ratio (SINR), can generally be obtained by solving a system of linear equations for which many effective techniques exist. A model for this detection procedure is developed and shown--through analytical and numerical results--to offer a good compromise between complexity and quality of performance.