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A new technique for blind tracking of fast-fading channels in long-code code division multiple access (CDMA) is proposed by exploiting multipath diversity. Based on a linear interpolation channel model, the proposed method blindly identifies a time-varying channel at arbitrary estimating points within a block up to a scale factor and increases bandwidth efficiency allowing only one pilot symbol within a block, which is much larger than channel coherence time. The proposed method can be implemented using an efficient state-space inversion technique for multiuser cases. The mean square error (MSE) performance of the proposed estimator is compared with the Cramer-Rao bound (CRB) for interpolated channel. Modeling error and bit error rate (BER) are also evaluated using Monte-Carlo simulations and compared with the block fading model and a decision-directed tracking technique.