Considers an asynchronous direct-sequence code division multiple access (DS-CDMA) communication system over an AWGN channel. The authors are interested in reducing the computational complexity of a receiver by lowering the dimensionality of the received vector. Dimension reduction has previously been done in an ad hoc manner by several researchers. The present authors derive an optimum form of dimension reduction. The optimality criteria is that the Cramer-Rao bound on estimators of propagation delay, received phase and power are invariant to the reduction transform.