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A new adaptive carrier recovery algorithm is proposed by using the decision-aided extended Kalman filtering technique. In order to reduce computational complexity of the Kalman recursions, the state model in the new algorithm uses only phase rather than both phase and frequency which are usually used in conventional modeling. The frequency is considered as an input term to the system equation and estimated by a phase error detector. A reduced observation model is also introduced to relieve computing load from multiple matrix to scalar operations in the Kalman recursions. Simulations show that the proposed one-state Kalman algorithm has better performance and lower complexity than the two-state Kalman algorithm for synchronization applications. The new algorithm is applied to the cable modem downstream system to demonstrate its effectiveness with FPGA implementation results.