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In linear time invariant channel model, the systems that are designed based on CDMA are suffering from multiple access interference (MAI) and noise problems. In time varying channel model, the CDMA systems suffer from complex time varying channel's gains plus MAI and noise. A lot of CDMA detectors are designed to overcome the MAI problem. But these detectors have complex structures and their performances are affected by the presence of time varying channel's gains. This paper gives proposal for new linear CDMA detector that has the same MAI cancellation capability as CDMA decorrelator detector but with simpler structure. The operation of the new detector is based on the symmetry property of the cross-correlation matrix of CDMA signatures' codes. The structure complexity of this new detector is as simple as matched filter detector structure. The performance of this new detector is evaluated in the presence of Nakagami time varying channel's complex gains. Closed forms of probability of error for the proposed detector and decorrelator detector are represented for flat and multipath Nakagami fading models. Channel phase estimation error effect is included in the probability of error formulas. Different channel estimators are used with the proposed detector to overcome the fading phenomenon.