We proposed recently a new technique for multiuser detection in CDMA networks, denoted by interference subspace rejection (ISR), and evaluated its performance on the uplink. This paper extends its application to the downlink (DL). On the DL, the information about the interference is sparse, for example, spreading factor (SF) and modulation of interferers may not be known, which makes the task much more challenging. We present three new ISR variants which require no prior knowledge of interfering users. The new solutions are applicable to MIMO systems and can accommodate any modulation, coding, SF, and connection type. We propose a new code allocation scheme denoted by DACCA which significantly reduces the complexity of our solution at the receiving mobile. We present estimates of user capacities and data rates attainable under practically reasonable conditions regarding interferences identified and suppressed in a multicellular interference-limited system. We show that the system capacity increases linearly with the number of antennas despite the existence of interference. Our new DL multiuser receiver consistently provides an Erlang capacity gain of at least 3  db over the single-user detector.