This paper deals with the problem of multisensor-multiuser detection in CDMA systems in the presence of interferences external to the system. The paper presents a new method able to estimate the spatial signature of all active users projected onto the subspace orthogonal to the external interference. With this information a specific beamformer can be designed for each user in order to combat the external and multiple access interference. The method performs in frequency non-selective multipath scenarios as they arise from some CDMA satellite and indoor communications systems. The estimation process does not require any training signal nor any a priori spatial information. It exploits the temporal structure of CDMA signals and extract the required information directly from the received signals. In addition, the method is independent of the nature of the external interference and it can cope with narrow-band and wide-band interfering signals.