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Diversity combining of multiple time varying and correlated fading branches is investigated for direct-sequence spread-spectrum systems. The correlated branches are modeled and estimated jointly as a vector autoregressive (VAR) process. The joint estimation is shown to provide performance gain over separate estimation of the fading branches. The parameter matrices of the VAR model are estimated via the method of expectation maximization (EM) with two algorithms. The first algorithm, using results from Kalman smoothing, provides a closed-form solution to the maximization problem in the iterative EM procedure. However, the iterative EM-Kalman algorithm operates repeatedly on a batch of training data and results in large storage requirements and long processing delays. To overcome these disadvantages, a new algorithm with only forward-time recursions is proposed that approximates the iterative EM solution and efficiently adapts to slowly changing Doppler spreads. As a result, the new algorithm significantly reduces memory and training sequence requirements. Through computer simulations, a near ideal bit-error rate performance is found for both algorithms, and the efficacy of the new adaptive algorithm for channels with changing Doppler spreads is demonstrated.