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We propose a new linear multiuser receiver for synchronous code-division multiple-access (CDMA) systems, referred to as the orthogonal multiuser (OMU) receiver. Unlike the linear minimum mean-squared error (MMSE) receiver, the OMU receiver depends only on the signature vectors and does not require knowledge of the received amplitudes or the channel signal-to-noise ratio (SNR). Several equivalent representations of the receiver are developed with different implications in terms of implementation. In the first, the receiver consists of a decorrelator demodulator followed by an optimal whitening transformation on a space formed by the signatures. In the second, the receiver consists of a bank of correlators with correlating vectors that are projections of a set of orthogonal vectors, and are closest in a least squares sense to the decorrelator vectors and also closest in a least squares sense to the signature vectors. In the third, the receiver consists of a single-user matched filter (MF) followed by an optimal whitening transformation on a space formed by the signatures. We derive exact and approximate expressions for the probability of bit error, as well as the asymptotic signal-to-interference+noise ratio (SINR) in the large system limit. The analysis suggests that over a wide range of channel parameters the OMU receiver can outperform both the decorrelator and the single-user MF and perform similarly to the linear MMSE receiver, despite not knowing the channel parameters.