In this paper, we consider a low-complexity multiuser detection for downlink of high speed packet access (HSPA) system. Instead of attempting to perform the maximum likelihood (ML) detection of all users in multiple cells, which is impractical for battery powered mobile receiver, we utilize interference cancelled chips obtained from iterative linear minimum mean square error (LMMSE) estimation to perform a near ML detection in a reduced dimensional system. As a result, the worst case complexity of the detection process, achieved by the closest lattice point search (CLPS), is bounded to a controllable level irrespective of multipath spans. Further, by exploiting the LMMSE estimate in tightening the hypersphere condition of the CLPS algorithm so called sphere decoding, we achieve significant improvement in search complexity. From the simulations on realistic downlink communication scenario in HSPA systems, we show that the proposed method offers substantial performance gain over conventional receiver algorithms with implementable complexity.