An efficient method for equalization of downlink CDMA channels is presented. By describing the observed signal in terms of a state-space model, the method employs the Kalman filter (KF) to achieve an unbiased signal estimate satisfying the linear minimum mean-squared error (LMMSE) criterion. The state-space model is realized at the symbol and chip levels. With the symbol-level model, the KF is used to estimate the transmitted chips that correspond to each symbol interval; whereas at the chip level, the transmitted chips are estimated individually. The symbol-level KF has a built-in tracking capability that takes advantage of the a priori known scrambling sequence, which renders the transmitted signal nonstationary. The chip-level KF reduces the complexity of the symbol-level KF significantly by ignoring the nonstationarity introduced by scrambling. A simple method for further reducing the KF complexity is also presented. The computational complexity of the proposed technique is analyzed and compared with that of several linear approaches based on finite-impulse response (FIR) filtering. Simulations under realistic channel conditions are carried out which indicate that the KF-based approach is superior to FIR equalizers by 1 - 2   dBs in error-rate performance.