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In the uplink of a long-code CDMA system, the base station knows the spreading codes of all serviced users. Given propagation delays, code-decorrelation can be performed to separate users' inputs in each symbol interval even in a multipath environment. To detect information symbols, we first apply the subspace technique to estimate multipath parameters for the user of interest based on the correlation matrix of whitened data. Then we construct different linear receivers. The statistics of the estimated channel vectors are analyzed and verified by our numerical examples. Performance of the receivers is also studied in simulations.