Adaptive phase control using recursive least squares (RLS) phase estimation

This paper considers the realization of high-speed phase synchronization when there exists a frequency error and discusses the application of the recursive least square (RLS) algorithm to the burst signal demodulator. Especially, as a phase control algorithm for the coherent detection where there is an error in the carrier frequency, a method is proposed to represent the phase variation by the frequency error as the state transition function and a detailed algorithm is derived. It is shown that the theoretical convergence and the tracking performance of the algorithm agree with those of the ordinary RLS algorithm. The algorithm is applied to the frequency control circuit of the π/4-QPSK differential detector and the phase control circuit of the 16-QAM quasi-coherent detector. It is demonstrated experimentally that the system has an excellent performance and that the initial convergence is complete in approximately ten symbols when there exists a frequency error.